%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE180+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:58:30 PM UTC 2026
% Result : Satisfiable 1.45s 1.84s
% Output : Saturation 0.75s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] : multiplication(A,omega(A)) = omega(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C] :
( leq(A,addition(multiplication(B,A),C))
=> leq(A,addition(omega(B),multiplication(star(B),C))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X0,X1,X2] :
( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2))
=> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f51,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f52,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f53,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [A,B,C] :
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f55,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0] : multiplication(X0,omega(X0)) = omega(X0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f57,plain,
! [A,B,C] :
( leq(A,addition(omega(B),multiplication(star(B),C)))
| ~ leq(A,addition(multiplication(B,A),C)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f58,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f65,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f68,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f69,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f71,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f72,plain,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(X2)) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f75,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(X2)) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f80,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f37,f35]) ).
fof(f97,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f36]) ).
fof(f99,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f38,f36]) ).
fof(f103,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f35,f36]) ).
fof(f105,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f38,f36]) ).
fof(f119,plain,
antidomain(one) = zero,
inference(paramodulation,[status(thm)],[f40,f59]) ).
fof(f126,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f59,f39]) ).
fof(f136,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f126]) ).
fof(f141,plain,
! [X0] : domain(antidomain(X0)) = antidomain(domain(X0)),
inference(paramodulation,[status(thm)],[f62,f62]) ).
fof(f142,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f119,f62]) ).
fof(f143,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f62,f59]) ).
fof(f144,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f39,f63]) ).
fof(f146,plain,
coantidomain(one) = zero,
inference(paramodulation,[status(thm)],[f41,f63]) ).
fof(f150,plain,
! [X0,X1] : multiplication(X0,multiplication(coantidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f63,f39]) ).
fof(f151,plain,
! [X0,X1] : multiplication(X0,multiplication(coantidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f150]) ).
fof(f153,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f42]) ).
fof(f157,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f59,f42]) ).
fof(f160,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f42]) ).
fof(f162,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f40,f42]) ).
fof(f164,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f59,f42]) ).
fof(f167,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f63,f42]) ).
fof(f169,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f40,f42]) ).
fof(f170,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f42,f36]) ).
fof(f177,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f157]) ).
fof(f181,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f160]) ).
fof(f186,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f164]) ).
fof(f190,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f167]) ).
fof(f192,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f169]) ).
fof(f193,plain,
! [X0] : codomain(coantidomain(X0)) = coantidomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f66,f66]) ).
fof(f194,plain,
codomain(one) = coantidomain(zero),
inference(paramodulation,[status(thm)],[f146,f66]) ).
fof(f195,plain,
! [X0] : multiplication(coantidomain(X0),codomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f66,f63]) ).
fof(f196,plain,
! [X0] : domain(domain(X0)) = antidomain(c(X0)),
inference(paramodulation,[status(thm)],[f67,f62]) ).
fof(f197,plain,
! [X0] : multiplication(c(X0),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f67,f59]) ).
fof(f198,plain,
c(one) = antidomain(antidomain(zero)),
inference(paramodulation,[status(thm)],[f142,f67]) ).
fof(f199,plain,
c(one) = domain(zero),
inference(forward_demodulation,[status(thm)],[f62,f198]) ).
fof(f201,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f35,f43]) ).
fof(f204,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f39,f43]) ).
fof(f205,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f59,f43]) ).
fof(f207,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f41,f43]) ).
fof(f208,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(zero,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f63,f43]) ).
fof(f211,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f39,f43]) ).
fof(f212,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f59,f43]) ).
fof(f214,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f41,f43]) ).
fof(f215,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),zero),
inference(paramodulation,[status(thm)],[f63,f43]) ).
fof(f219,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f43,f36]) ).
fof(f224,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f80,f205]) ).
fof(f226,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f80,f208]) ).
fof(f230,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f212]) ).
fof(f232,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f214]) ).
fof(f233,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f215]) ).
fof(f239,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f49,f38]) ).
fof(f240,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f49,f80]) ).
fof(f241,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f43,f49]) ).
fof(f242,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f42,f49]) ).
fof(f243,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f36,f49]) ).
fof(f245,plain,
! [X0] :
( X0 != zero
| leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f37,f49]) ).
fof(f246,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f35,f49]) ).
fof(f251,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f50,f48]) ).
fof(f252,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f39,f50]) ).
fof(f253,plain,
leq(addition(one,zero),star(zero)),
inference(paramodulation,[status(thm)],[f45,f50]) ).
fof(f254,plain,
leq(addition(one,star(one)),star(one)),
inference(paramodulation,[status(thm)],[f41,f50]) ).
fof(f255,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f36,f251]) ).
fof(f256,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f35,f255]) ).
fof(f257,plain,
leq(one,star(zero)),
inference(forward_demodulation,[status(thm)],[f37,f253]) ).
fof(f260,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f51,f48]) ).
fof(f263,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f36,f260]) ).
fof(f264,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f35,f263]) ).
fof(f289,plain,
addition(one,star(zero)) = star(zero),
inference(resolution,[status(thm)],[f257,f48]) ).
fof(f290,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f43,f53]) ).
fof(f291,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f42,f53]) ).
fof(f293,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f35,f53]) ).
fof(f295,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f38,f53]) ).
fof(f296,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f39,f53]) ).
fof(f297,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f59,f53]) ).
fof(f298,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f45,f53]) ).
fof(f299,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f41,f53]) ).
fof(f300,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),coantidomain(X1))
| ~ leq(addition(zero,X0),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f63,f53]) ).
fof(f301,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f44,f53]) ).
fof(f302,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f40,f53]) ).
fof(f304,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f297]) ).
fof(f305,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f298]) ).
fof(f306,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f300]) ).
fof(f307,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f301]) ).
fof(f308,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))) = omega(multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f56]) ).
fof(f309,plain,
zero = omega(zero),
inference(paramodulation,[status(thm)],[f45,f56]) ).
fof(f314,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),omega(X0))
| ~ leq(addition(omega(X0),X1),omega(X0)) ),
inference(paramodulation,[status(thm)],[f56,f53]) ).
fof(f315,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = addition(multiplication(X0,omega(X1)),omega(X1)),
inference(paramodulation,[status(thm)],[f56,f43]) ).
fof(f316,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = addition(omega(X0),multiplication(X1,omega(X0))),
inference(paramodulation,[status(thm)],[f56,f43]) ).
fof(f317,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(X0))) = addition(multiplication(X0,X1),omega(X0)),
inference(paramodulation,[status(thm)],[f56,f42]) ).
fof(f318,plain,
! [X0,X1] : multiplication(X0,addition(omega(X0),X1)) = addition(omega(X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f56,f42]) ).
fof(f319,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(X0),X1)) = multiplication(omega(X0),X1),
inference(paramodulation,[status(thm)],[f56,f39]) ).
fof(f320,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = addition(omega(X1),multiplication(X0,omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f315]) ).
fof(f321,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(X0))) = addition(omega(X0),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f317]) ).
fof(f326,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X1,X2),star(X2)),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f43,f55]) ).
fof(f327,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f42,f55]) ).
fof(f329,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f35,f55]) ).
fof(f331,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f38,f55]) ).
fof(f332,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f39,f55]) ).
fof(f333,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f59,f55]) ).
fof(f334,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f45,f55]) ).
fof(f335,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f41,f55]) ).
fof(f336,plain,
! [X0,X1] :
( leq(multiplication(X1,star(omega(X0))),X0)
| ~ leq(addition(omega(X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f56,f55]) ).
fof(f337,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f63,f55]) ).
fof(f339,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f40,f55]) ).
fof(f340,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f326]) ).
fof(f341,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f327]) ).
fof(f343,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f331]) ).
fof(f344,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f333]) ).
fof(f345,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f334]) ).
fof(f346,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f337]) ).
fof(f351,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f43,f246]) ).
fof(f352,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f42,f246]) ).
fof(f353,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f36,f246]) ).
fof(f361,plain,
! [X0] : domain(antidomain(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f67,f141]) ).
fof(f362,plain,
! [X0] : domain(c(X0)) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f67,f361]) ).
fof(f363,plain,
! [X0] : domain(domain(X0)) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f62,f361]) ).
fof(f369,plain,
! [X0] : multiplication(domain(domain(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f67,f143]) ).
fof(f372,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),domain(X1))
| ~ leq(addition(zero,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f143,f55]) ).
fof(f373,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f143,f53]) ).
fof(f374,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = addition(multiplication(X0,antidomain(X1)),zero),
inference(paramodulation,[status(thm)],[f143,f43]) ).
fof(f375,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = addition(zero,multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f143,f43]) ).
fof(f376,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = addition(multiplication(domain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f143,f42]) ).
fof(f377,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = addition(zero,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f143,f42]) ).
fof(f378,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f143,f39]) ).
fof(f383,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f372]) ).
fof(f384,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f373]) ).
fof(f385,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = multiplication(X0,antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f374]) ).
fof(f386,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f80,f375]) ).
fof(f387,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f376]) ).
fof(f388,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f377]) ).
fof(f389,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f378]) ).
fof(f391,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X2,X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f43,f58]) ).
fof(f392,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X2))))
| ~ leq(X0,multiplication(X1,addition(X0,X2))) ),
inference(paramodulation,[status(thm)],[f42,f58]) ).
fof(f393,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),zero)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f37,f58]) ).
fof(f394,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f35,f58]) ).
fof(f396,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f38,f58]) ).
fof(f397,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),X1)))
| ~ leq(antidomain(X0),addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f143,f58]) ).
fof(f398,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),X3)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f39,f58]) ).
fof(f399,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f59,f58]) ).
fof(f403,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(coantidomain(X0),addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f63,f58]) ).
fof(f405,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f40,f58]) ).
fof(f406,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),zero))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f44,f393]) ).
fof(f407,plain,
! [X0,X1] :
( leq(X0,omega(X1))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f406]) ).
fof(f408,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),X1)))
| ~ leq(antidomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f397]) ).
fof(f409,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f399]) ).
fof(f413,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(coantidomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f403]) ).
fof(f424,plain,
! [X0,X1] :
( leq(codomain(X0),addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),X1)))
| ~ leq(codomain(X0),addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f195,f58]) ).
fof(f425,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),coantidomain(X1))
| ~ leq(addition(zero,X0),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f195,f55]) ).
fof(f426,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(addition(zero,X0),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f195,f53]) ).
fof(f427,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = addition(multiplication(X0,codomain(X1)),zero),
inference(paramodulation,[status(thm)],[f195,f43]) ).
fof(f428,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = addition(zero,multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f195,f43]) ).
fof(f429,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f195,f42]) ).
fof(f430,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = addition(zero,multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f195,f42]) ).
fof(f431,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f195,f39]) ).
fof(f436,plain,
! [X0,X1] :
( leq(codomain(X0),addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),X1)))
| ~ leq(codomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f424]) ).
fof(f437,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f425]) ).
fof(f438,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f426]) ).
fof(f439,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f427]) ).
fof(f440,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f80,f428]) ).
fof(f441,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f429]) ).
fof(f442,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f430]) ).
fof(f443,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f431]) ).
fof(f444,plain,
! [X0] : domain(antidomain(c(X0))) = antidomain(c(domain(X0))),
inference(paramodulation,[status(thm)],[f196,f196]) ).
fof(f445,plain,
! [X0] : domain(c(X0)) = antidomain(c(antidomain(X0))),
inference(paramodulation,[status(thm)],[f361,f196]) ).
fof(f449,plain,
! [X0] : c(c(X0)) = antidomain(c(domain(X0))),
inference(forward_demodulation,[status(thm)],[f361,f444]) ).
fof(f456,plain,
! [X0] : multiplication(c(domain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f196,f197]) ).
fof(f457,plain,
! [X0] : multiplication(c(antidomain(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f361,f197]) ).
fof(f459,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(domain(X0),addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f197,f58]) ).
fof(f460,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(addition(zero,X0),c(X1)) ),
inference(paramodulation,[status(thm)],[f197,f55]) ).
fof(f461,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),domain(X1))
| ~ leq(addition(zero,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f197,f53]) ).
fof(f462,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = addition(multiplication(X0,domain(X1)),zero),
inference(paramodulation,[status(thm)],[f197,f43]) ).
fof(f463,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = addition(zero,multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f197,f43]) ).
fof(f464,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f197,f42]) ).
fof(f465,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f197,f42]) ).
fof(f466,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f197,f39]) ).
fof(f470,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(domain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f459]) ).
fof(f471,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f460]) ).
fof(f472,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f461]) ).
fof(f473,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f462]) ).
fof(f474,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f80,f463]) ).
fof(f475,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f464]) ).
fof(f476,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f465]) ).
fof(f477,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f466]) ).
fof(f478,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f62,f60]) ).
fof(f479,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f62,f478]) ).
fof(f480,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(resolution,[status(thm)],[f479,f49]) ).
fof(f481,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),domain(domain(X0))))) = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f197,f479]) ).
fof(f482,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))) = antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f195,f479]) ).
fof(f483,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(domain(X0),domain(antidomain(X0))))) = antidomain(multiplication(domain(X0),domain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f143,f479]) ).
fof(f484,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(multiplication(X0,X1),domain(X2)))) = antidomain(multiplication(multiplication(X0,X1),domain(X2))),
inference(paramodulation,[status(thm)],[f39,f479]) ).
fof(f485,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(X0)))) = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f59,f479]) ).
fof(f487,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(one,domain(X0)))) = antidomain(multiplication(one,domain(X0))),
inference(paramodulation,[status(thm)],[f41,f479]) ).
fof(f488,plain,
! [X0] : addition(antidomain(omega(X0)),antidomain(multiplication(X0,domain(omega(X0))))) = antidomain(multiplication(X0,domain(omega(X0)))),
inference(paramodulation,[status(thm)],[f56,f479]) ).
fof(f489,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(X0,domain(coantidomain(X0))))) = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f63,f479]) ).
fof(f492,plain,
! [X0] : addition(antidomain(multiplication(c(X0),X0)),antidomain(zero)) = antidomain(multiplication(c(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f197,f479]) ).
fof(f497,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,antidomain(c(X1))))) = antidomain(multiplication(X0,domain(domain(X1)))),
inference(paramodulation,[status(thm)],[f196,f479]) ).
fof(f498,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))) = antidomain(multiplication(X0,domain(antidomain(X1)))),
inference(paramodulation,[status(thm)],[f361,f479]) ).
fof(f499,plain,
! [X0] : addition(antidomain(multiplication(X0,one)),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,domain(one))),
inference(paramodulation,[status(thm)],[f142,f479]) ).
fof(f500,plain,
! [X0,X1] :
( antidomain(multiplication(X0,domain(X1))) != antidomain(multiplication(X0,X1))
| leq(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f479,f246]) ).
fof(f502,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)) = addition(antidomain(multiplication(X0,domain(X1))),X2),
inference(paramodulation,[status(thm)],[f479,f36]) ).
fof(f503,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),antidomain(c(X0))))) = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f481]) ).
fof(f504,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),antidomain(c(X0))))) = antidomain(multiplication(c(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f503]) ).
fof(f505,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(domain(X0),c(X0)))) = antidomain(multiplication(domain(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f361,f483]) ).
fof(f506,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(domain(X0),c(X0)))) = antidomain(multiplication(domain(X0),c(X0))),
inference(forward_demodulation,[status(thm)],[f361,f505]) ).
fof(f507,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))) = antidomain(multiplication(multiplication(X0,X1),domain(X2))),
inference(forward_demodulation,[status(thm)],[f39,f484]) ).
fof(f508,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f39,f507]) ).
fof(f511,plain,
! [X0] : addition(antidomain(X0),antidomain(domain(X0))) = antidomain(multiplication(one,domain(X0))),
inference(forward_demodulation,[status(thm)],[f41,f487]) ).
fof(f512,plain,
! [X0] : addition(antidomain(X0),c(X0)) = antidomain(multiplication(one,domain(X0))),
inference(forward_demodulation,[status(thm)],[f67,f511]) ).
fof(f513,plain,
! [X0] : addition(antidomain(X0),c(X0)) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f41,f512]) ).
fof(f514,plain,
! [X0] : addition(antidomain(X0),c(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f67,f513]) ).
fof(f517,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),X0))) = antidomain(multiplication(c(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f492]) ).
fof(f518,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),X0))) = antidomain(zero),
inference(forward_demodulation,[status(thm)],[f197,f517]) ).
fof(f533,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,antidomain(c(X1))))) = antidomain(multiplication(X0,antidomain(c(X1)))),
inference(forward_demodulation,[status(thm)],[f196,f497]) ).
fof(f534,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))) = antidomain(multiplication(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f361,f498]) ).
fof(f535,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,domain(one))),
inference(forward_demodulation,[status(thm)],[f40,f499]) ).
fof(f536,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,antidomain(zero))),
inference(forward_demodulation,[status(thm)],[f142,f535]) ).
fof(f538,plain,
! [X0] : domain(c(domain(X0))) = c(antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f196,f362]) ).
fof(f539,plain,
! [X0] : domain(c(antidomain(X0))) = c(c(X0)),
inference(paramodulation,[status(thm)],[f361,f362]) ).
fof(f540,plain,
domain(c(one)) = c(antidomain(zero)),
inference(paramodulation,[status(thm)],[f142,f362]) ).
fof(f542,plain,
! [X0] : domain(domain(c(X0))) = c(antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f362,f538]) ).
fof(f543,plain,
! [X0] : antidomain(c(c(X0))) = c(antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f196,f542]) ).
fof(f544,plain,
domain(domain(zero)) = c(antidomain(zero)),
inference(forward_demodulation,[status(thm)],[f199,f540]) ).
fof(f545,plain,
antidomain(c(zero)) = c(antidomain(zero)),
inference(forward_demodulation,[status(thm)],[f196,f544]) ).
fof(f547,plain,
! [X0] : antidomain(c(X0)) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f196,f363]) ).
fof(f557,plain,
! [X0] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f35,f61]) ).
fof(f558,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f62,f557]) ).
fof(f560,plain,
! [X0] : addition(domain(X0),domain(antidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f62,f558]) ).
fof(f561,plain,
addition(zero,domain(one)) = one,
inference(paramodulation,[status(thm)],[f119,f558]) ).
fof(f562,plain,
! [X0] : addition(antidomain(domain(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f196,f558]) ).
fof(f564,plain,
addition(antidomain(one),antidomain(zero)) = one,
inference(paramodulation,[status(thm)],[f142,f558]) ).
fof(f565,plain,
! [X0] :
( one != antidomain(X0)
| leq(domain(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f558,f246]) ).
fof(f566,plain,
! [X0] :
( one != domain(X0)
| leq(antidomain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f558,f49]) ).
fof(f567,plain,
! [X0,X1] : addition(antidomain(X0),addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f558,f36]) ).
fof(f569,plain,
! [X0] : addition(domain(X0),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f361,f560]) ).
fof(f570,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f80,f561]) ).
fof(f571,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f67,f562]) ).
fof(f575,plain,
addition(antidomain(zero),antidomain(one)) = one,
inference(forward_demodulation,[status(thm)],[f35,f564]) ).
fof(f576,plain,
addition(antidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f119,f575]) ).
fof(f577,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f37,f576]) ).
fof(f582,plain,
multiplication(c(one),one) = zero,
inference(paramodulation,[status(thm)],[f570,f197]) ).
fof(f583,plain,
domain(one) = antidomain(c(one)),
inference(paramodulation,[status(thm)],[f570,f196]) ).
fof(f594,plain,
c(one) = zero,
inference(forward_demodulation,[status(thm)],[f40,f582]) ).
fof(f595,plain,
one = antidomain(c(one)),
inference(forward_demodulation,[status(thm)],[f570,f583]) ).
fof(f596,plain,
one = antidomain(domain(zero)),
inference(forward_demodulation,[status(thm)],[f199,f595]) ).
fof(f597,plain,
one = c(zero),
inference(forward_demodulation,[status(thm)],[f67,f596]) ).
fof(f602,plain,
multiplication(domain(zero),one) = zero,
inference(paramodulation,[status(thm)],[f577,f143]) ).
fof(f607,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f40,f602]) ).
fof(f614,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(forward_demodulation,[status(thm)],[f66,f64]) ).
fof(f615,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(codomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f66,f614]) ).
fof(f616,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(resolution,[status(thm)],[f615,f49]) ).
fof(f617,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(c(X0)),domain(X0)))) = coantidomain(multiplication(codomain(c(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f197,f615]) ).
fof(f618,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0)))) = coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0))),
inference(paramodulation,[status(thm)],[f195,f615]) ).
fof(f619,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(domain(X0)),antidomain(X0)))) = coantidomain(multiplication(codomain(domain(X0)),antidomain(X0))),
inference(paramodulation,[status(thm)],[f143,f615]) ).
fof(f620,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(X0,multiplication(X1,X2))),coantidomain(multiplication(codomain(multiplication(X0,X1)),X2))) = coantidomain(multiplication(codomain(multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f39,f615]) ).
fof(f621,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),X0))) = coantidomain(multiplication(codomain(antidomain(X0)),X0)),
inference(paramodulation,[status(thm)],[f59,f615]) ).
fof(f622,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(zero),X0))) = coantidomain(multiplication(codomain(zero),X0)),
inference(paramodulation,[status(thm)],[f45,f615]) ).
fof(f623,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(one),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(paramodulation,[status(thm)],[f41,f615]) ).
fof(f624,plain,
! [X0] : addition(coantidomain(omega(X0)),coantidomain(multiplication(codomain(X0),omega(X0)))) = coantidomain(multiplication(codomain(X0),omega(X0))),
inference(paramodulation,[status(thm)],[f56,f615]) ).
fof(f625,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),coantidomain(X0)))) = coantidomain(multiplication(codomain(X0),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f63,f615]) ).
fof(f627,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(X0),one))) = coantidomain(multiplication(codomain(X0),one)),
inference(paramodulation,[status(thm)],[f40,f615]) ).
fof(f628,plain,
! [X0] : addition(coantidomain(multiplication(X0,omega(codomain(X0)))),coantidomain(omega(codomain(X0)))) = coantidomain(multiplication(codomain(X0),omega(codomain(X0)))),
inference(paramodulation,[status(thm)],[f56,f615]) ).
fof(f629,plain,
! [X0] : addition(coantidomain(multiplication(X0,coantidomain(codomain(X0)))),coantidomain(zero)) = coantidomain(multiplication(codomain(X0),coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f63,f615]) ).
fof(f631,plain,
! [X0] : addition(coantidomain(multiplication(X0,one)),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(paramodulation,[status(thm)],[f40,f615]) ).
fof(f632,plain,
! [X0,X1] : addition(coantidomain(multiplication(coantidomain(X0),X1)),coantidomain(multiplication(coantidomain(codomain(X0)),X1))) = coantidomain(multiplication(codomain(coantidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f193,f615]) ).
fof(f633,plain,
! [X0] : addition(coantidomain(multiplication(one,X0)),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(paramodulation,[status(thm)],[f194,f615]) ).
fof(f634,plain,
! [X0,X1] :
( coantidomain(multiplication(codomain(X0),X1)) != coantidomain(multiplication(X0,X1))
| leq(coantidomain(multiplication(codomain(X0),X1)),coantidomain(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f615,f246]) ).
fof(f635,plain,
! [X0,X1] :
( coantidomain(multiplication(codomain(X0),X1)) != coantidomain(multiplication(codomain(X0),X1))
| leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))) ),
inference(paramodulation,[status(thm)],[f615,f49]) ).
fof(f636,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(X0,X1)),addition(coantidomain(multiplication(codomain(X0),X1)),X2)) = addition(coantidomain(multiplication(codomain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f615,f36]) ).
fof(f637,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0)))) = coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0))),
inference(forward_demodulation,[status(thm)],[f193,f618]) ).
fof(f638,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0)))) = coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0))),
inference(forward_demodulation,[status(thm)],[f193,f637]) ).
fof(f639,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(forward_demodulation,[status(thm)],[f194,f623]) ).
fof(f640,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(coantidomain(zero),X0)),
inference(forward_demodulation,[status(thm)],[f194,f639]) ).
fof(f643,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f40,f627]) ).
fof(f644,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f643]) ).
fof(f645,plain,
! [X0] : addition(coantidomain(omega(codomain(X0))),coantidomain(multiplication(X0,omega(codomain(X0))))) = coantidomain(multiplication(codomain(X0),omega(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f628]) ).
fof(f646,plain,
! [X0] : addition(coantidomain(omega(codomain(X0))),coantidomain(multiplication(X0,omega(codomain(X0))))) = coantidomain(omega(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f56,f645]) ).
fof(f647,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(X0,coantidomain(codomain(X0))))) = coantidomain(multiplication(codomain(X0),coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f629]) ).
fof(f648,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(X0,coantidomain(codomain(X0))))) = coantidomain(zero),
inference(forward_demodulation,[status(thm)],[f63,f647]) ).
fof(f652,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,one))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f35,f631]) ).
fof(f653,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(X0)) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f40,f652]) ).
fof(f654,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f35,f653]) ).
fof(f655,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f654]) ).
fof(f656,plain,
! [X0,X1] : addition(coantidomain(multiplication(coantidomain(X0),X1)),coantidomain(multiplication(coantidomain(codomain(X0)),X1))) = coantidomain(multiplication(coantidomain(codomain(X0)),X1)),
inference(forward_demodulation,[status(thm)],[f193,f632]) ).
fof(f657,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(forward_demodulation,[status(thm)],[f41,f633]) ).
fof(f658,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(coantidomain(zero),X0)),
inference(forward_demodulation,[status(thm)],[f194,f657]) ).
fof(f659,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(trivial_equality_resolution,[status(thm)],[f635]) ).
fof(f682,plain,
! [X0] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f35,f65]) ).
fof(f683,plain,
! [X0] : addition(coantidomain(X0),codomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f66,f682]) ).
fof(f684,plain,
! [X0] : addition(codomain(X0),codomain(coantidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f66,f683]) ).
fof(f685,plain,
addition(zero,codomain(one)) = one,
inference(paramodulation,[status(thm)],[f146,f683]) ).
fof(f686,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(codomain(X0))) = one,
inference(paramodulation,[status(thm)],[f193,f683]) ).
fof(f687,plain,
addition(coantidomain(one),coantidomain(zero)) = one,
inference(paramodulation,[status(thm)],[f194,f683]) ).
fof(f688,plain,
! [X0] :
( one != coantidomain(X0)
| leq(codomain(X0),coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f683,f246]) ).
fof(f689,plain,
! [X0] :
( one != codomain(X0)
| leq(coantidomain(X0),codomain(X0)) ),
inference(paramodulation,[status(thm)],[f683,f49]) ).
fof(f690,plain,
! [X0,X1] : addition(coantidomain(X0),addition(codomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f683,f36]) ).
fof(f691,plain,
! [X0] : addition(codomain(X0),coantidomain(codomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f193,f684]) ).
fof(f692,plain,
codomain(one) = one,
inference(forward_demodulation,[status(thm)],[f80,f685]) ).
fof(f693,plain,
! [X0] : addition(codomain(X0),coantidomain(codomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f66,f686]) ).
fof(f694,plain,
addition(coantidomain(zero),coantidomain(one)) = one,
inference(forward_demodulation,[status(thm)],[f35,f687]) ).
fof(f695,plain,
addition(coantidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f146,f694]) ).
fof(f696,plain,
coantidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f37,f695]) ).
fof(f707,plain,
! [X0] : domain_difference(X0,X0) = zero,
inference(backward_demodulation,[status(thm)],[f68,f143]) ).
fof(f708,plain,
! [X0] : domain_difference(zero,X0) = multiplication(zero,antidomain(X0)),
inference(paramodulation,[status(thm)],[f607,f68]) ).
fof(f709,plain,
! [X0,X1] : domain_difference(domain(X0),X1) = multiplication(antidomain(c(X0)),antidomain(X1)),
inference(paramodulation,[status(thm)],[f196,f68]) ).
fof(f710,plain,
! [X0,X1] : domain_difference(antidomain(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f361,f68]) ).
fof(f711,plain,
! [X0] : domain_difference(one,X0) = multiplication(one,antidomain(X0)),
inference(paramodulation,[status(thm)],[f570,f68]) ).
fof(f712,plain,
! [X0] : domain_difference(X0,zero) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f577,f68]) ).
fof(f713,plain,
! [X0,X1] : domain_difference(X0,domain(X1)) = multiplication(domain(X0),c(X1)),
inference(paramodulation,[status(thm)],[f67,f68]) ).
fof(f714,plain,
! [X0,X1] : domain_difference(X0,antidomain(X1)) = multiplication(domain(X0),domain(X1)),
inference(paramodulation,[status(thm)],[f62,f68]) ).
fof(f715,plain,
! [X0] : domain_difference(X0,one) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f119,f68]) ).
fof(f716,plain,
! [X0,X1] : addition(coantidomain(domain_difference(X0,X1)),coantidomain(multiplication(codomain(domain(X0)),antidomain(X1)))) = coantidomain(multiplication(codomain(domain(X0)),antidomain(X1))),
inference(paramodulation,[status(thm)],[f68,f615]) ).
fof(f717,plain,
! [X0,X1] : addition(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),domain(antidomain(X1))))) = antidomain(multiplication(domain(X0),domain(antidomain(X1)))),
inference(paramodulation,[status(thm)],[f68,f479]) ).
fof(f718,plain,
! [X0,X1,X2] :
( leq(antidomain(X0),addition(omega(domain(X1)),multiplication(star(domain(X1)),X2)))
| ~ leq(antidomain(X0),addition(domain_difference(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f68,f58]) ).
fof(f719,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(antidomain(X1))),domain(X0))
| ~ leq(addition(domain_difference(X0,X1),X2),domain(X0)) ),
inference(paramodulation,[status(thm)],[f68,f55]) ).
fof(f720,plain,
! [X0,X1,X2] :
( leq(multiplication(star(domain(X0)),X2),antidomain(X1))
| ~ leq(addition(domain_difference(X0,X1),X2),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f68,f53]) ).
fof(f721,plain,
! [X0,X1,X2] : multiplication(addition(X0,domain(X1)),antidomain(X2)) = addition(multiplication(X0,antidomain(X2)),domain_difference(X1,X2)),
inference(paramodulation,[status(thm)],[f68,f43]) ).
fof(f722,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),X1),antidomain(X2)) = addition(domain_difference(X0,X2),multiplication(X1,antidomain(X2))),
inference(paramodulation,[status(thm)],[f68,f43]) ).
fof(f723,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(X1,antidomain(X2))) = addition(multiplication(domain(X0),X1),domain_difference(X0,X2)),
inference(paramodulation,[status(thm)],[f68,f42]) ).
fof(f724,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(antidomain(X1),X2)) = addition(domain_difference(X0,X1),multiplication(domain(X0),X2)),
inference(paramodulation,[status(thm)],[f68,f42]) ).
fof(f725,plain,
! [X0,X1,X2] : multiplication(domain(X0),multiplication(antidomain(X1),X2)) = multiplication(domain_difference(X0,X1),X2),
inference(paramodulation,[status(thm)],[f68,f39]) ).
fof(f726,plain,
! [X0] : domain_difference(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f45,f708]) ).
fof(f727,plain,
! [X0] : domain_difference(one,X0) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f41,f711]) ).
fof(f728,plain,
! [X0] : domain_difference(X0,zero) = domain(X0),
inference(forward_demodulation,[status(thm)],[f40,f712]) ).
fof(f729,plain,
! [X0] : domain_difference(X0,one) = zero,
inference(forward_demodulation,[status(thm)],[f44,f715]) ).
fof(f730,plain,
! [X0,X1] : addition(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),c(X1)))) = antidomain(multiplication(domain(X0),domain(antidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f361,f717]) ).
fof(f731,plain,
! [X0,X1] : addition(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),c(X1)))) = antidomain(multiplication(domain(X0),c(X1))),
inference(forward_demodulation,[status(thm)],[f361,f730]) ).
fof(f733,plain,
multiplication(one,codomain(zero)) = zero,
inference(paramodulation,[status(thm)],[f696,f195]) ).
fof(f737,plain,
codomain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f41,f733]) ).
fof(f753,plain,
! [X0] : forward_diamond(c(X0),X0) = domain(zero),
inference(paramodulation,[status(thm)],[f197,f69]) ).
fof(f754,plain,
! [X0,X1,X2] : forward_diamond(multiplication(X0,X1),X2) = domain(multiplication(X0,multiplication(X1,domain(X2)))),
inference(paramodulation,[status(thm)],[f39,f69]) ).
fof(f756,plain,
! [X0] : forward_diamond(zero,X0) = domain(zero),
inference(paramodulation,[status(thm)],[f45,f69]) ).
fof(f757,plain,
! [X0] : forward_diamond(one,X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f41,f69]) ).
fof(f758,plain,
! [X0,X1,X2] : forward_diamond(X0,multiplication(X1,domain(X2))) = domain(multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f69,f69]) ).
fof(f759,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f607,f69]) ).
fof(f760,plain,
! [X0,X1] : forward_diamond(X0,domain(X1)) = domain(multiplication(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f196,f69]) ).
fof(f761,plain,
! [X0,X1] : forward_diamond(X0,antidomain(X1)) = domain(multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f361,f69]) ).
fof(f762,plain,
! [X0] : forward_diamond(X0,one) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f570,f69]) ).
fof(f763,plain,
! [X0,X1,X2] : domain_difference(multiplication(X0,domain(X1)),X2) = multiplication(forward_diamond(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f69,f68]) ).
fof(f764,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f69,f558]) ).
fof(f765,plain,
! [X0,X1] : domain(c(multiplication(X0,domain(X1)))) = c(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f69,f362]) ).
fof(f766,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,forward_diamond(X1,X2)))) = antidomain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
inference(paramodulation,[status(thm)],[f69,f479]) ).
fof(f767,plain,
! [X0,X1] : multiplication(c(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f69,f197]) ).
fof(f768,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = antidomain(c(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f69,f196]) ).
fof(f769,plain,
! [X0,X1] : c(multiplication(X0,domain(X1))) = antidomain(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f69,f67]) ).
fof(f770,plain,
! [X0] : forward_diamond(c(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f607,f753]) ).
fof(f773,plain,
! [X0] : forward_diamond(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f607,f756]) ).
fof(f774,plain,
! [X0] : forward_diamond(one,X0) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f196,f757]) ).
fof(f775,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f44,f759]) ).
fof(f776,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f607,f775]) ).
fof(f777,plain,
! [X0] : forward_diamond(X0,one) = domain(X0),
inference(forward_demodulation,[status(thm)],[f40,f762]) ).
fof(f778,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f35,f764]) ).
fof(f779,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,forward_diamond(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))) = antidomain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
inference(forward_demodulation,[status(thm)],[f35,f766]) ).
fof(f780,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,forward_diamond(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))) = antidomain(multiplication(X0,forward_diamond(X1,X2))),
inference(forward_demodulation,[status(thm)],[f69,f779]) ).
fof(f792,plain,
divergence(zero) = zero,
inference(paramodulation,[status(thm)],[f73,f773]) ).
fof(f795,plain,
! [X0] : backward_diamond(omega(codomain(X0)),X0) = codomain(omega(codomain(X0))),
inference(paramodulation,[status(thm)],[f56,f70]) ).
fof(f796,plain,
! [X0] : backward_diamond(coantidomain(codomain(X0)),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f63,f70]) ).
fof(f797,plain,
! [X0] : backward_diamond(zero,X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f44,f70]) ).
fof(f798,plain,
! [X0] : backward_diamond(one,X0) = codomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f40,f70]) ).
fof(f799,plain,
! [X0,X1,X2] : backward_diamond(X0,multiplication(codomain(X1),X2)) = codomain(multiplication(backward_diamond(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f70,f70]) ).
fof(f800,plain,
! [X0] : backward_diamond(X0,zero) = codomain(multiplication(zero,X0)),
inference(paramodulation,[status(thm)],[f737,f70]) ).
fof(f801,plain,
! [X0,X1] : backward_diamond(X0,coantidomain(X1)) = codomain(multiplication(coantidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f193,f70]) ).
fof(f802,plain,
! [X0] : backward_diamond(X0,one) = codomain(multiplication(one,X0)),
inference(paramodulation,[status(thm)],[f692,f70]) ).
fof(f803,plain,
! [X0,X1] : addition(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = one,
inference(paramodulation,[status(thm)],[f70,f683]) ).
fof(f804,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(multiplication(codomain(X0),X1),X2)),coantidomain(multiplication(backward_diamond(X1,X0),X2))) = coantidomain(multiplication(codomain(multiplication(codomain(X0),X1)),X2)),
inference(paramodulation,[status(thm)],[f70,f615]) ).
fof(f805,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f70,f195]) ).
fof(f806,plain,
! [X0] : backward_diamond(coantidomain(codomain(X0)),X0) = zero,
inference(forward_demodulation,[status(thm)],[f737,f796]) ).
fof(f807,plain,
! [X0] : backward_diamond(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f737,f797]) ).
fof(f808,plain,
! [X0] : backward_diamond(X0,zero) = codomain(zero),
inference(forward_demodulation,[status(thm)],[f45,f800]) ).
fof(f809,plain,
! [X0] : backward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f737,f808]) ).
fof(f810,plain,
! [X0] : backward_diamond(X0,one) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f41,f802]) ).
fof(f811,plain,
! [X0,X1] : addition(backward_diamond(X0,X1),coantidomain(multiplication(codomain(X1),X0))) = one,
inference(forward_demodulation,[status(thm)],[f35,f803]) ).
fof(f812,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(backward_diamond(X0,X1),X2)),coantidomain(multiplication(multiplication(codomain(X1),X0),X2))) = coantidomain(multiplication(codomain(multiplication(codomain(X1),X0)),X2)),
inference(forward_demodulation,[status(thm)],[f35,f804]) ).
fof(f813,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(backward_diamond(X0,X1),X2)),coantidomain(multiplication(codomain(X1),multiplication(X0,X2)))) = coantidomain(multiplication(codomain(multiplication(codomain(X1),X0)),X2)),
inference(forward_demodulation,[status(thm)],[f39,f812]) ).
fof(f814,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(backward_diamond(X0,X1),X2)),coantidomain(multiplication(codomain(X1),multiplication(X0,X2)))) = coantidomain(multiplication(backward_diamond(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f70,f813]) ).
fof(f825,plain,
! [X0] : forward_box(zero,X0) = c(zero),
inference(paramodulation,[status(thm)],[f773,f71]) ).
fof(f826,plain,
! [X0,X1,X2] : forward_box(X0,forward_diamond(X1,c(X2))) = c(forward_diamond(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f71,f71]) ).
fof(f827,plain,
! [X0] : forward_box(X0,zero) = c(forward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f597,f71]) ).
fof(f828,plain,
! [X0,X1] : forward_box(X0,antidomain(X1)) = c(forward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f547,f71]) ).
fof(f829,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = c(forward_diamond(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f362,f71]) ).
fof(f830,plain,
! [X0] : forward_box(X0,one) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f594,f71]) ).
fof(f831,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f71,f197]) ).
fof(f832,plain,
! [X0] : forward_box(zero,X0) = one,
inference(forward_demodulation,[status(thm)],[f597,f825]) ).
fof(f833,plain,
! [X0] : forward_box(X0,one) = c(zero),
inference(forward_demodulation,[status(thm)],[f776,f830]) ).
fof(f834,plain,
! [X0] : forward_box(X0,one) = one,
inference(forward_demodulation,[status(thm)],[f597,f833]) ).
fof(f845,plain,
! [X0] : backward_box(zero,X0) = c(zero),
inference(paramodulation,[status(thm)],[f807,f72]) ).
fof(f846,plain,
! [X0,X1,X2] : backward_box(X0,backward_diamond(X1,c(X2))) = c(backward_diamond(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f72,f72]) ).
fof(f847,plain,
! [X0,X1,X2] : backward_box(X0,forward_diamond(X1,c(X2))) = c(backward_diamond(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f71,f72]) ).
fof(f848,plain,
! [X0] : backward_box(X0,zero) = c(backward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f597,f72]) ).
fof(f849,plain,
! [X0,X1] : backward_box(X0,antidomain(X1)) = c(backward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f547,f72]) ).
fof(f850,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = c(backward_diamond(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f362,f72]) ).
fof(f851,plain,
! [X0] : backward_box(X0,one) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f594,f72]) ).
fof(f852,plain,
! [X0,X1,X2] : forward_box(X0,backward_diamond(X1,c(X2))) = c(forward_diamond(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f72,f71]) ).
fof(f853,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f72,f197]) ).
fof(f854,plain,
! [X0] : backward_box(zero,X0) = one,
inference(forward_demodulation,[status(thm)],[f597,f845]) ).
fof(f855,plain,
! [X0] : backward_box(X0,one) = c(zero),
inference(forward_demodulation,[status(thm)],[f809,f851]) ).
fof(f856,plain,
! [X0] : backward_box(X0,one) = one,
inference(forward_demodulation,[status(thm)],[f597,f855]) ).
fof(f868,plain,
! [X0,X1,X2,X3] :
( addition(domain(multiplication(X0,domain(X1))),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,domain(multiplication(X0,domain(X1)))),domain(X3))) != addition(forward_diamond(X2,domain(multiplication(X0,domain(X1)))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f69,f75]) ).
fof(f870,plain,
! [X0,X1,X2] :
( addition(domain(domain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(c(X0)),addition(forward_diamond(X1,domain(domain(X0))),domain(X2))) != addition(forward_diamond(X1,domain(domain(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f196,f75]) ).
fof(f871,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2))) != addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f361,f75]) ).
fof(f872,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,domain(one)),domain(X1))) != addition(forward_diamond(X0,domain(one)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f570,f75]) ).
fof(f873,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X2),forward_diamond(star(X2),domain(X1)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X1)))
| addition(domain(X0),addition(domain(X1),forward_diamond(X2,domain(X0)))) != addition(forward_diamond(X2,domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f35,f75]) ).
fof(f874,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X2),forward_diamond(star(X2),domain(X1)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X1)))
| addition(domain(X0),addition(domain(X1),forward_diamond(X2,domain(X0)))) != addition(forward_diamond(X2,domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f35,f75]) ).
fof(f875,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(zero),forward_diamond(star(zero),domain(X1)))) = addition(divergence(zero),forward_diamond(star(zero),domain(X1)))
| addition(domain(X0),addition(zero,domain(X1))) != addition(forward_diamond(zero,domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f773,f75]) ).
fof(f876,plain,
! [X0,X1,X2,X3] :
( addition(domain(multiplication(X0,domain(X1))),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(domain(multiplication(X0,domain(X1))),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(multiplication(X0,domain(X1)))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f69,f75]) ).
fof(f878,plain,
! [X0,X1,X2] :
( addition(domain(domain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(domain(X0)),addition(forward_diamond(X1,antidomain(c(X0))),domain(X2))) != addition(forward_diamond(X1,domain(domain(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f196,f75]) ).
fof(f879,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(antidomain(X0)),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f361,f75]) ).
fof(f880,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(domain(one),addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(one)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f570,f75]) ).
fof(f881,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(multiplication(X2,domain(X3)))))) = addition(divergence(X1),forward_diamond(star(X1),domain(multiplication(X2,domain(X3)))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3))) != addition(forward_diamond(X1,domain(X0)),domain(multiplication(X2,domain(X3)))) ),
inference(paramodulation,[status(thm)],[f69,f75]) ).
fof(f882,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(zero)))) = addition(divergence(X1),forward_diamond(star(X1),domain(zero)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),zero)) != addition(forward_diamond(X1,domain(X0)),domain(zero)) ),
inference(paramodulation,[status(thm)],[f607,f75]) ).
fof(f883,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(domain(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(domain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),antidomain(c(X2)))) != addition(forward_diamond(X1,domain(X0)),domain(domain(X2))) ),
inference(paramodulation,[status(thm)],[f196,f75]) ).
fof(f884,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),c(X2))) != addition(forward_diamond(X1,domain(X0)),domain(antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f361,f75]) ).
fof(f885,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(one)))) = addition(divergence(X1),forward_diamond(star(X1),domain(one)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),one)) != addition(forward_diamond(X1,domain(X0)),domain(one)) ),
inference(paramodulation,[status(thm)],[f570,f75]) ).
fof(f886,plain,
! [X0,X1,X2,X3] :
( addition(domain(multiplication(X0,domain(X1))),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(multiplication(X0,domain(X1)))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f868]) ).
fof(f887,plain,
! [X0,X1,X2,X3] :
( addition(domain(multiplication(X0,domain(X1))),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f886]) ).
fof(f888,plain,
! [X0,X1,X2,X3] :
( addition(forward_diamond(X0,X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f887]) ).
fof(f897,plain,
! [X0,X1,X2] :
( addition(domain(domain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(c(X0)),addition(forward_diamond(X1,antidomain(c(X0))),domain(X2))) != addition(forward_diamond(X1,domain(domain(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f196,f870]) ).
fof(f898,plain,
! [X0,X1,X2] :
( addition(domain(domain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(c(X0)),addition(forward_diamond(X1,antidomain(c(X0))),domain(X2))) != addition(forward_diamond(X1,antidomain(c(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f196,f897]) ).
fof(f899,plain,
! [X0,X1,X2] :
( addition(antidomain(c(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(c(X0)),addition(forward_diamond(X1,antidomain(c(X0))),domain(X2))) != addition(forward_diamond(X1,antidomain(c(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f196,f898]) ).
fof(f900,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f871]) ).
fof(f901,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,c(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f900]) ).
fof(f902,plain,
! [X0,X1,X2] :
( addition(c(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,c(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f901]) ).
fof(f903,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(one)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f872]) ).
fof(f904,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f903]) ).
fof(f905,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f904]) ).
fof(f906,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(zero),forward_diamond(star(zero),domain(X1)))) = addition(divergence(zero),forward_diamond(star(zero),domain(X1)))
| addition(domain(X0),domain(X1)) != addition(forward_diamond(zero,domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f875]) ).
fof(f907,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(zero),forward_diamond(star(zero),domain(X1)))) = addition(divergence(zero),forward_diamond(star(zero),domain(X1)))
| addition(domain(X0),domain(X1)) != addition(zero,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f773,f906]) ).
fof(f908,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(zero),forward_diamond(star(zero),domain(X1)))) = addition(divergence(zero),forward_diamond(star(zero),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f80,f907]) ).
fof(f909,plain,
! [X0,X1] :
( addition(domain(X0),addition(zero,forward_diamond(star(zero),domain(X1)))) = addition(divergence(zero),forward_diamond(star(zero),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f792,f908]) ).
fof(f910,plain,
! [X0,X1] :
( addition(domain(X0),forward_diamond(star(zero),domain(X1))) = addition(divergence(zero),forward_diamond(star(zero),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f80,f909]) ).
fof(f911,plain,
! [X0,X1] :
( addition(domain(X0),forward_diamond(star(zero),domain(X1))) = addition(zero,forward_diamond(star(zero),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f792,f910]) ).
fof(f912,plain,
! [X0,X1] :
( addition(domain(X0),forward_diamond(star(zero),domain(X1))) = forward_diamond(star(zero),domain(X1))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f80,f911]) ).
fof(f913,plain,
! [X0,X1,X2,X3] :
( addition(domain(multiplication(X0,domain(X1))),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(multiplication(X0,domain(X1)))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f876]) ).
fof(f914,plain,
! [X0,X1,X2,X3] :
( addition(domain(multiplication(X0,domain(X1))),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f913]) ).
fof(f915,plain,
! [X0,X1,X2,X3] :
( addition(forward_diamond(X0,X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f914]) ).
fof(f924,plain,
! [X0,X1,X2] :
( addition(domain(domain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(c(X0)),addition(forward_diamond(X1,antidomain(c(X0))),domain(X2))) != addition(forward_diamond(X1,domain(domain(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f196,f878]) ).
fof(f925,plain,
! [X0,X1,X2] :
( addition(domain(domain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(c(X0)),addition(forward_diamond(X1,antidomain(c(X0))),domain(X2))) != addition(forward_diamond(X1,antidomain(c(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f196,f924]) ).
fof(f926,plain,
! [X0,X1,X2] :
( addition(antidomain(c(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(c(X0)),addition(forward_diamond(X1,antidomain(c(X0))),domain(X2))) != addition(forward_diamond(X1,antidomain(c(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f196,f925]) ).
fof(f927,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f879]) ).
fof(f928,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,c(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f927]) ).
fof(f929,plain,
! [X0,X1,X2] :
( addition(c(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,c(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f928]) ).
fof(f930,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(one)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f880]) ).
fof(f931,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f930]) ).
fof(f932,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f931]) ).
fof(f933,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(multiplication(X2,domain(X3)))))) = addition(divergence(X1),forward_diamond(star(X1),domain(multiplication(X2,domain(X3)))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f881]) ).
fof(f934,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),domain(multiplication(X2,domain(X3)))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f933]) ).
fof(f935,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f934]) ).
fof(f936,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(zero)))) = addition(divergence(X1),forward_diamond(star(X1),domain(zero)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != addition(forward_diamond(X1,domain(X0)),domain(zero)) ),
inference(forward_demodulation,[status(thm)],[f37,f882]) ).
fof(f937,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(zero)))) = addition(divergence(X1),forward_diamond(star(X1),domain(zero)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != addition(domain(zero),forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f936]) ).
fof(f938,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(zero)))) = addition(divergence(X1),forward_diamond(star(X1),domain(zero)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != addition(zero,forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f607,f937]) ).
fof(f939,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(zero)))) = addition(divergence(X1),forward_diamond(star(X1),domain(zero)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != forward_diamond(X1,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f938]) ).
fof(f940,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),zero))) = addition(divergence(X1),forward_diamond(star(X1),domain(zero)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != forward_diamond(X1,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f607,f939]) ).
fof(f941,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),zero)) = addition(divergence(X1),forward_diamond(star(X1),domain(zero)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != forward_diamond(X1,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f776,f940]) ).
fof(f942,plain,
! [X0,X1] :
( addition(domain(X0),divergence(X1)) = addition(divergence(X1),forward_diamond(star(X1),domain(zero)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != forward_diamond(X1,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f941]) ).
fof(f943,plain,
! [X0,X1] :
( addition(domain(X0),divergence(X1)) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != forward_diamond(X1,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f607,f942]) ).
fof(f944,plain,
! [X0,X1] :
( addition(domain(X0),divergence(X1)) = addition(divergence(X1),zero)
| addition(domain(X0),forward_diamond(X1,domain(X0))) != forward_diamond(X1,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f776,f943]) ).
fof(f945,plain,
! [X0,X1] :
( addition(domain(X0),divergence(X1)) = divergence(X1)
| addition(domain(X0),forward_diamond(X1,domain(X0))) != forward_diamond(X1,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f944]) ).
fof(f946,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(domain(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(domain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),antidomain(c(X2)))) != addition(forward_diamond(X1,domain(X0)),antidomain(c(X2))) ),
inference(forward_demodulation,[status(thm)],[f196,f883]) ).
fof(f947,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),antidomain(c(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(domain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),antidomain(c(X2)))) != addition(forward_diamond(X1,domain(X0)),antidomain(c(X2))) ),
inference(forward_demodulation,[status(thm)],[f196,f946]) ).
fof(f948,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),antidomain(c(X2))))) = addition(divergence(X1),forward_diamond(star(X1),antidomain(c(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),antidomain(c(X2)))) != addition(forward_diamond(X1,domain(X0)),antidomain(c(X2))) ),
inference(forward_demodulation,[status(thm)],[f196,f947]) ).
fof(f949,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),c(X2))) != addition(forward_diamond(X1,domain(X0)),c(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f884]) ).
fof(f950,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),c(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),c(X2))) != addition(forward_diamond(X1,domain(X0)),c(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f949]) ).
fof(f951,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),c(X2)))) = addition(divergence(X1),forward_diamond(star(X1),c(X2)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),c(X2))) != addition(forward_diamond(X1,domain(X0)),c(X2)) ),
inference(forward_demodulation,[status(thm)],[f361,f950]) ).
fof(f952,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(one)))) = addition(divergence(X1),forward_diamond(star(X1),domain(one)))
| addition(domain(X0),addition(one,forward_diamond(X1,domain(X0)))) != addition(forward_diamond(X1,domain(X0)),domain(one)) ),
inference(forward_demodulation,[status(thm)],[f35,f885]) ).
fof(f953,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(one)))) = addition(divergence(X1),forward_diamond(star(X1),domain(one)))
| addition(domain(X0),addition(one,forward_diamond(X1,domain(X0)))) != addition(domain(one),forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f952]) ).
fof(f954,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(one)))) = addition(divergence(X1),forward_diamond(star(X1),domain(one)))
| addition(domain(X0),addition(one,forward_diamond(X1,domain(X0)))) != addition(one,forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f570,f953]) ).
fof(f955,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),domain(one)))
| addition(domain(X0),addition(one,forward_diamond(X1,domain(X0)))) != addition(one,forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f570,f954]) ).
fof(f956,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(domain(X0),addition(one,forward_diamond(X1,domain(X0)))) != addition(one,forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f570,f955]) ).
fof(f959,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f72,f770]) ).
fof(f960,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f71,f770]) ).
fof(f962,plain,
! [X0] : forward_diamond(antidomain(c(X0)),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f547,f770]) ).
fof(f963,plain,
! [X0] : forward_diamond(domain(c(X0)),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f362,f770]) ).
fof(f965,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))) = addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))
| addition(domain(X0),addition(zero,domain(X1))) != addition(forward_diamond(c(domain(X0)),domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f770,f75]) ).
fof(f966,plain,
! [X0] : forward_box(c(c(X0)),X0) = c(zero),
inference(paramodulation,[status(thm)],[f770,f71]) ).
fof(f969,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))) = addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))
| addition(domain(X0),domain(X1)) != addition(forward_diamond(c(domain(X0)),domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f965]) ).
fof(f970,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))) = addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))
| addition(domain(X0),domain(X1)) != addition(zero,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f770,f969]) ).
fof(f971,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))) = addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f80,f970]) ).
fof(f972,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(domain(c(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))) = addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f362,f971]) ).
fof(f973,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(domain(c(X0))),forward_diamond(star(domain(c(X0))),domain(X1)))) = addition(divergence(c(domain(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f362,f972]) ).
fof(f974,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(domain(c(X0))),forward_diamond(star(domain(c(X0))),domain(X1)))) = addition(divergence(domain(c(X0))),forward_diamond(star(c(domain(X0))),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f362,f973]) ).
fof(f975,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(domain(c(X0))),forward_diamond(star(domain(c(X0))),domain(X1)))) = addition(divergence(domain(c(X0))),forward_diamond(star(domain(c(X0))),domain(X1)))
| addition(domain(X0),domain(X1)) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f362,f974]) ).
fof(f976,plain,
! [X0] : forward_box(c(c(X0)),X0) = one,
inference(forward_demodulation,[status(thm)],[f597,f966]) ).
fof(f985,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f36,f97]) ).
fof(f989,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f35,f97]) ).
fof(f990,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f35,f97]) ).
fof(f991,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(addition(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f38,f97]) ).
fof(f992,plain,
! [X0,X1,X2] : addition(X0,coantidomain(multiplication(codomain(X1),X2))) = addition(coantidomain(multiplication(codomain(X1),X2)),addition(X0,coantidomain(multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f615,f97]) ).
fof(f993,plain,
! [X0,X1] : addition(X0,one) = addition(codomain(X1),addition(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f683,f97]) ).
fof(f994,plain,
! [X0,X1,X2] : addition(X0,antidomain(multiplication(X1,domain(X2)))) = addition(antidomain(multiplication(X1,domain(X2))),addition(X0,antidomain(multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f479,f97]) ).
fof(f995,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f558,f97]) ).
fof(f996,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(X2,X3),addition(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f43,f97]) ).
fof(f997,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,X3),addition(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f42,f97]) ).
fof(f998,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f97]) ).
fof(f1000,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X2),addition(X0,X3)),
inference(paramodulation,[status(thm)],[f97,f97]) ).
fof(f1001,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X3,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f97,f97]) ).
fof(f1003,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f35,f97]) ).
fof(f1004,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f35,f97]) ).
fof(f1005,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f38,f97]) ).
fof(f1006,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f97]) ).
fof(f1012,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f38,f97]) ).
fof(f1013,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(X0,X1)),addition(coantidomain(multiplication(codomain(X0),X1)),X2)) = addition(X2,coantidomain(multiplication(codomain(X0),X1))),
inference(paramodulation,[status(thm)],[f615,f97]) ).
fof(f1014,plain,
! [X0,X1] : addition(coantidomain(X0),addition(codomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f683,f97]) ).
fof(f1015,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)) = addition(X2,antidomain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f479,f97]) ).
fof(f1016,plain,
! [X0,X1] : addition(antidomain(X0),addition(domain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f558,f97]) ).
fof(f1017,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(X3,multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f43,f97]) ).
fof(f1018,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(X3,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f42,f97]) ).
fof(f1019,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(X3,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f97]) ).
fof(f1021,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f97,f97]) ).
fof(f1022,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f97,f97]) ).
fof(f1024,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f35,f97]) ).
fof(f1025,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f35,f97]) ).
fof(f1026,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f38,f97]) ).
fof(f1027,plain,
! [X0,X1,X2] :
( addition(domain(X1),addition(divergence(X2),forward_diamond(star(X2),domain(X0)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X0)))
| addition(domain(X0),addition(domain(X1),forward_diamond(X2,domain(X1)))) != addition(forward_diamond(X2,domain(X1)),domain(X0)) ),
inference(paramodulation,[status(thm)],[f97,f75]) ).
fof(f1028,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X2),multiplication(star(X2),addition(X3,X1))))
| ~ leq(X0,addition(X1,addition(multiplication(X2,X0),X3))) ),
inference(paramodulation,[status(thm)],[f97,f58]) ).
fof(f1029,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X3,X0),star(X2)),X1)
| ~ leq(addition(X0,addition(multiplication(X1,X2),X3)),X1) ),
inference(paramodulation,[status(thm)],[f97,f55]) ).
fof(f1030,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X1),addition(X3,X0)),X2)
| ~ leq(addition(X0,addition(multiplication(X1,X2),X3)),X2) ),
inference(paramodulation,[status(thm)],[f97,f53]) ).
fof(f1031,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f97,f36]) ).
fof(f1033,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f97,f246]) ).
fof(f1034,plain,
! [X0,X1,X2] :
( addition(X2,addition(X0,X1)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f97,f49]) ).
fof(f1035,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X2,addition(X0,X1)),X3),
inference(paramodulation,[status(thm)],[f97,f36]) ).
fof(f1036,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f97,f35]) ).
fof(f1037,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f97,f35]) ).
fof(f1038,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f97,f38]) ).
fof(f1039,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X3),multiplication(star(X3),addition(X1,X2))))
| ~ leq(X0,addition(X1,addition(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f97,f58]) ).
fof(f1040,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X0,X1),star(X3)),X2)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X3))),X2) ),
inference(paramodulation,[status(thm)],[f97,f55]) ).
fof(f1041,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X2),addition(X0,X1)),X3)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f97,f53]) ).
fof(f1042,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f97,f36]) ).
fof(f1044,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f97,f246]) ).
fof(f1045,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f97,f49]) ).
fof(f1046,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X1,addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f97,f36]) ).
fof(f1049,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f97,f38]) ).
fof(f1050,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f36,f985]) ).
fof(f1052,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,addition(X1,X0))),
inference(forward_demodulation,[status(thm)],[f36,f991]) ).
fof(f1053,plain,
! [X0,X1,X2] : addition(X0,coantidomain(multiplication(codomain(X1),X2))) = addition(coantidomain(multiplication(X1,X2)),addition(coantidomain(multiplication(codomain(X1),X2)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f992]) ).
fof(f1054,plain,
! [X0,X1] : addition(X0,one) = addition(coantidomain(X1),addition(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f993]) ).
fof(f1055,plain,
! [X0,X1,X2] : addition(X0,antidomain(multiplication(X1,domain(X2)))) = addition(antidomain(multiplication(X1,X2)),addition(antidomain(multiplication(X1,domain(X2))),X0)),
inference(forward_demodulation,[status(thm)],[f97,f994]) ).
fof(f1056,plain,
! [X0,X1] : addition(X0,one) = addition(antidomain(X1),addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f995]) ).
fof(f1058,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f36,f1000]) ).
fof(f1059,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f36,f1001]) ).
fof(f1060,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f36,f1019]) ).
fof(f1062,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f36,f1021]) ).
fof(f1063,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f36,f1022]) ).
fof(f1065,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f36,f1031]) ).
fof(f1067,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,addition(X0,X1)),X3),
inference(forward_demodulation,[status(thm)],[f36,f1035]) ).
fof(f1068,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(addition(X0,X1),X3)),
inference(forward_demodulation,[status(thm)],[f36,f1067]) ).
fof(f1069,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f36,f1068]) ).
fof(f1070,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f36,f1038]) ).
fof(f1071,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f36,f1046]) ).
fof(f1072,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(addition(X2,X0),X3)),
inference(forward_demodulation,[status(thm)],[f36,f1071]) ).
fof(f1073,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f36,f1072]) ).
fof(f1074,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),c(multiplication(X0,domain(X1)))) = one,
inference(paramodulation,[status(thm)],[f69,f569]) ).
fof(f1077,plain,
! [X0] : addition(c(X0),c(antidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f361,f569]) ).
fof(f1079,plain,
! [X0,X1] : addition(domain(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f72,f569]) ).
fof(f1080,plain,
! [X0,X1] : addition(domain(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f71,f569]) ).
fof(f1082,plain,
! [X0] : addition(domain(antidomain(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f547,f569]) ).
fof(f1085,plain,
! [X0,X1] : addition(domain(X0),addition(c(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f569,f97]) ).
fof(f1086,plain,
! [X0,X1] : addition(X0,one) = addition(c(X1),addition(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f569,f97]) ).
fof(f1087,plain,
! [X0] :
( one != domain(X0)
| leq(c(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f569,f246]) ).
fof(f1088,plain,
! [X0] :
( one != c(X0)
| leq(domain(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f569,f49]) ).
fof(f1089,plain,
! [X0,X1] : addition(domain(X0),addition(c(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f569,f36]) ).
fof(f1092,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f547,f1077]) ).
fof(f1094,plain,
! [X0,X1] : addition(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f35,f1079]) ).
fof(f1095,plain,
! [X0,X1] : addition(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f35,f1080]) ).
fof(f1098,plain,
! [X0] : addition(antidomain(c(X0)),domain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f35,f1082]) ).
fof(f1099,plain,
! [X0] : addition(antidomain(c(X0)),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f361,f1098]) ).
fof(f1100,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f35,f1099]) ).
fof(f1103,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f1086]) ).
fof(f1110,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X0,X1),X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f36,f99]) ).
fof(f1112,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f97,f99]) ).
fof(f1113,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f36,f99]) ).
fof(f1116,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f97,f99]) ).
fof(f1124,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X2,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f36,f99]) ).
fof(f1127,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X2),addition(X1,addition(X2,X0)))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f97,f99]) ).
fof(f1128,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X2),addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f97,f99]) ).
fof(f1130,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f35,f99]) ).
fof(f1131,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f35,f99]) ).
fof(f1133,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),addition(X2,addition(multiplication(X1,X0),X2)))))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f99,f58]) ).
fof(f1134,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X2,addition(multiplication(X0,X1),X2)),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f99,f55]) ).
fof(f1135,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(X2,addition(multiplication(X0,X1),X2))),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f99,f53]) ).
fof(f1136,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X0,X1),X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f99,f36]) ).
fof(f1138,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f99,f97]) ).
fof(f1139,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,addition(X0,X1)),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f99,f97]) ).
fof(f1140,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,addition(X1,X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f99,f97]) ).
fof(f1141,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,addition(X1,X0)),X1) ),
inference(paramodulation,[status(thm)],[f99,f246]) ).
fof(f1142,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X1,addition(X0,X1))
| leq(X0,addition(X1,addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f99,f49]) ).
fof(f1143,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,addition(X0,X1)),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f99,f36]) ).
fof(f1144,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f36,f1110]) ).
fof(f1145,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f36,f1144]) ).
fof(f1148,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f36,f1112]) ).
fof(f1167,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f36,f1124]) ).
fof(f1168,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f36,f1167]) ).
fof(f1173,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,addition(X2,X0))))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f36,f1127]) ).
fof(f1174,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X2,addition(X0,X1))))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f36,f1128]) ).
fof(f1177,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f36,f1136]) ).
fof(f1178,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f36,f1177]) ).
fof(f1181,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f36,f1138]) ).
fof(f1182,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f36,f1139]) ).
fof(f1183,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f36,f1182]) ).
fof(f1184,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(addition(X1,X2),addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f36,f1140]) ).
fof(f1185,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,addition(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f36,f1184]) ).
fof(f1186,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f36,f1143]) ).
fof(f1187,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f36,f1186]) ).
fof(f1188,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f36,f1187]) ).
fof(f1191,plain,
divergence(one) = antidomain(c(divergence(one))),
inference(paramodulation,[status(thm)],[f73,f774]) ).
fof(f1193,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(antidomain(c(domain(X0))),domain(X1))) != addition(forward_diamond(one,domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f774,f75]) ).
fof(f1194,plain,
! [X0] : forward_box(one,X0) = c(antidomain(c(c(X0)))),
inference(paramodulation,[status(thm)],[f774,f71]) ).
fof(f1196,plain,
antidomain(c(divergence(one))) = divergence(one),
inference(paramodulation,[status(thm)],[f774,f73]) ).
fof(f1202,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(antidomain(domain(c(X0))),domain(X1))) != addition(forward_diamond(one,domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f362,f1193]) ).
fof(f1203,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(c(c(X0)),domain(X1))) != addition(forward_diamond(one,domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f67,f1202]) ).
fof(f1204,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(c(c(X0)),domain(X1))) != addition(antidomain(c(domain(X0))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f774,f1203]) ).
fof(f1205,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(c(c(X0)),domain(X1))) != addition(antidomain(domain(c(X0))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f362,f1204]) ).
fof(f1206,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(c(c(X0)),domain(X1))) != addition(c(c(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f67,f1205]) ).
fof(f1207,plain,
! [X0] : forward_box(one,X0) = antidomain(c(c(c(X0)))),
inference(forward_demodulation,[status(thm)],[f547,f1194]) ).
fof(f1212,plain,
! [X0,X1] : backward_diamond(coantidomain(backward_diamond(X0,X1)),multiplication(codomain(X1),X0)) = zero,
inference(paramodulation,[status(thm)],[f70,f806]) ).
fof(f1214,plain,
! [X0] : backward_diamond(coantidomain(coantidomain(codomain(X0))),coantidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f193,f806]) ).
fof(f1217,plain,
! [X0] : backward_box(coantidomain(codomain(c(X0))),X0) = c(zero),
inference(paramodulation,[status(thm)],[f806,f72]) ).
fof(f1223,plain,
! [X0] : backward_diamond(codomain(codomain(X0)),coantidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f66,f1214]) ).
fof(f1230,plain,
! [X0] : backward_box(coantidomain(codomain(c(X0))),X0) = one,
inference(forward_demodulation,[status(thm)],[f597,f1217]) ).
fof(f1234,plain,
! [X0] : backward_box(one,X0) = c(codomain(codomain(c(X0)))),
inference(paramodulation,[status(thm)],[f798,f72]) ).
fof(f1241,plain,
! [X0,X1] : forward_box(c(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f72,f976]) ).
fof(f1242,plain,
! [X0,X1] : forward_box(c(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f71,f976]) ).
fof(f1244,plain,
! [X0] : forward_box(c(antidomain(c(X0))),antidomain(X0)) = one,
inference(paramodulation,[status(thm)],[f547,f976]) ).
fof(f1245,plain,
! [X0] : forward_box(c(domain(c(X0))),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f362,f976]) ).
fof(f1249,plain,
! [X0] : forward_box(antidomain(c(c(X0))),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f547,f1244]) ).
fof(f1250,plain,
! [X0] : forward_box(domain(c(c(X0))),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f362,f1245]) ).
fof(f1251,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f36,f103]) ).
fof(f1252,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X1,X0),X2)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f99,f103]) ).
fof(f1253,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f97,f103]) ).
fof(f1254,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f97,f103]) ).
fof(f1256,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f35,f103]) ).
fof(f1257,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f35,f103]) ).
fof(f1258,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f38,f103]) ).
fof(f1259,plain,
! [X0,X1] : addition(c(X0),addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f569,f103]) ).
fof(f1260,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(codomain(X0),X1)),addition(coantidomain(multiplication(X0,X1)),X2)) = addition(coantidomain(multiplication(codomain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f615,f103]) ).
fof(f1261,plain,
! [X0,X1] : addition(codomain(X0),addition(coantidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f683,f103]) ).
fof(f1262,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(antidomain(multiplication(X0,X1)),X2)) = addition(antidomain(multiplication(X0,domain(X1))),X2),
inference(paramodulation,[status(thm)],[f479,f103]) ).
fof(f1263,plain,
! [X0,X1] : addition(domain(X0),addition(antidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f558,f103]) ).
fof(f1264,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X2,X0),X1),X3),
inference(paramodulation,[status(thm)],[f43,f103]) ).
fof(f1265,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X2,X1)),X3),
inference(paramodulation,[status(thm)],[f42,f103]) ).
fof(f1266,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X2,addition(X1,X0)),X3),
inference(paramodulation,[status(thm)],[f103,f103]) ).
fof(f1269,plain,
! [X0,X1,X2] : addition(addition(X0,addition(X1,X0)),addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f99,f103]) ).
fof(f1270,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f97,f103]) ).
fof(f1271,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X1,addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f97,f103]) ).
fof(f1276,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f103,f36]) ).
fof(f1277,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X1,X0),X2)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f103,f99]) ).
fof(f1278,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X2,X1))))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f103,f99]) ).
fof(f1279,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f103,f97]) ).
fof(f1280,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f103,f97]) ).
fof(f1282,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X2,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f103,f99]) ).
fof(f1283,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(X3,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f103,f97]) ).
fof(f1284,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f103,f97]) ).
fof(f1285,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f103,f246]) ).
fof(f1286,plain,
! [X0,X1,X2] :
( addition(X1,addition(X0,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f103,f49]) ).
fof(f1287,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X1,addition(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f103,f36]) ).
fof(f1288,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f103,f35]) ).
fof(f1289,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f103,f35]) ).
fof(f1290,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f103,f38]) ).
fof(f1291,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f1252]) ).
fof(f1292,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1291]) ).
fof(f1293,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f103,f1254]) ).
fof(f1295,plain,
! [X0,X1] : addition(domain(X0),addition(X1,c(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f97,f1259]) ).
fof(f1296,plain,
! [X0,X1,X2] : addition(coantidomain(multiplication(X0,X1)),addition(X2,coantidomain(multiplication(codomain(X0),X1)))) = addition(coantidomain(multiplication(codomain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f1260]) ).
fof(f1297,plain,
! [X0,X1] : addition(coantidomain(X0),addition(X1,codomain(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f97,f1261]) ).
fof(f1298,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f97,f1262]) ).
fof(f1299,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,domain(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f97,f1263]) ).
fof(f1300,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f103,f1266]) ).
fof(f1301,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,X0),addition(X1,X3)),
inference(forward_demodulation,[status(thm)],[f103,f1300]) ).
fof(f1302,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X0,addition(X2,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f103,f1301]) ).
fof(f1305,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f103,f1269]) ).
fof(f1306,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f1305]) ).
fof(f1307,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1306]) ).
fof(f1308,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f1270]) ).
fof(f1309,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,X2),addition(X1,X3)),
inference(forward_demodulation,[status(thm)],[f103,f1308]) ).
fof(f1310,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f103,f1309]) ).
fof(f1311,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f103,f1271]) ).
fof(f1312,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,X1),addition(X0,X3)),
inference(forward_demodulation,[status(thm)],[f103,f1311]) ).
fof(f1313,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f103,f1312]) ).
fof(f1314,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f1277]) ).
fof(f1315,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1314]) ).
fof(f1316,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f103,f1280]) ).
fof(f1318,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f1282]) ).
fof(f1319,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1318]) ).
fof(f1320,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f103,f1283]) ).
fof(f1321,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f1287]) ).
fof(f1322,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X2),addition(X0,X3)),
inference(forward_demodulation,[status(thm)],[f103,f1321]) ).
fof(f1323,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X1,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f103,f1322]) ).
fof(f1324,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f105,f49]) ).
fof(f1325,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f103,f105]) ).
fof(f1326,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f36,f105]) ).
fof(f1329,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f97,f105]) ).
fof(f1331,plain,
! [X0] : addition(domain(X0),one) = addition(domain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f569,f105]) ).
fof(f1333,plain,
! [X0] : addition(coantidomain(X0),one) = addition(coantidomain(X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f683,f105]) ).
fof(f1335,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f558,f105]) ).
fof(f1338,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f103,f105]) ).
fof(f1339,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f36,f105]) ).
fof(f1343,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f97,f105]) ).
fof(f1344,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f97,f105]) ).
fof(f1349,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),addition(multiplication(X1,X0),X2))))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f105,f58]) ).
fof(f1350,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f105,f55]) ).
fof(f1351,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(multiplication(X0,X1),X2)),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f105,f53]) ).
fof(f1352,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f105,f103]) ).
fof(f1353,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f105,f36]) ).
fof(f1361,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f105,f97]) ).
fof(f1362,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f105,f97]) ).
fof(f1363,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f105,f246]) ).
fof(f1365,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f105,f36]) ).
fof(f1366,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f1325]) ).
fof(f1367,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1366]) ).
fof(f1368,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f103,f1326]) ).
fof(f1369,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f105,f1368]) ).
fof(f1370,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1369]) ).
fof(f1374,plain,
! [X0] : addition(one,domain(X0)) = addition(domain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f35,f1331]) ).
fof(f1375,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f569,f1374]) ).
fof(f1376,plain,
! [X0] : addition(one,coantidomain(X0)) = addition(coantidomain(X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f1333]) ).
fof(f1377,plain,
! [X0] : addition(one,coantidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f683,f1376]) ).
fof(f1378,plain,
! [X0] : addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f1335]) ).
fof(f1379,plain,
! [X0] : addition(one,antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f558,f1378]) ).
fof(f1384,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f1338]) ).
fof(f1385,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1384]) ).
fof(f1386,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f1339]) ).
fof(f1387,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f105,f1386]) ).
fof(f1388,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1387]) ).
fof(f1391,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f1352]) ).
fof(f1392,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1391]) ).
fof(f1393,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f103,f1353]) ).
fof(f1394,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f105,f1393]) ).
fof(f1395,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1394]) ).
fof(f1402,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f1361]) ).
fof(f1403,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f1362]) ).
fof(f1405,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f103,f1365]) ).
fof(f1406,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f1405]) ).
fof(f1408,plain,
! [X0] : leq(domain(X0),one),
inference(paramodulation,[status(thm)],[f569,f1324]) ).
fof(f1409,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(paramodulation,[status(thm)],[f615,f1324]) ).
fof(f1410,plain,
! [X0] : leq(coantidomain(X0),one),
inference(paramodulation,[status(thm)],[f683,f1324]) ).
fof(f1411,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f479,f1324]) ).
fof(f1412,plain,
! [X0] : leq(antidomain(X0),one),
inference(paramodulation,[status(thm)],[f558,f1324]) ).
fof(f1413,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f43,f1324]) ).
fof(f1414,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f42,f1324]) ).
fof(f1415,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f103,f1324]) ).
fof(f1416,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f1324]) ).
fof(f1420,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f97,f1324]) ).
fof(f1421,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f97,f1324]) ).
fof(f1423,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f35,f1324]) ).
fof(f1427,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),one),
inference(paramodulation,[status(thm)],[f69,f1408]) ).
fof(f1430,plain,
! [X0] : leq(c(X0),one),
inference(paramodulation,[status(thm)],[f361,f1408]) ).
fof(f1435,plain,
! [X0] : leq(codomain(X0),one),
inference(paramodulation,[status(thm)],[f66,f1410]) ).
fof(f1444,plain,
! [X0,X1] : leq(X0,addition(omega(X1),multiplication(star(X1),X0))),
inference(resolution,[status(thm)],[f1423,f58]) ).
fof(f1451,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f43,f1423]) ).
fof(f1452,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f42,f1423]) ).
fof(f1456,plain,
! [X0,X1] : leq(addition(X0,addition(X1,X0)),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f99,f1423]) ).
fof(f1458,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f97,f1423]) ).
fof(f1459,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f97,f1423]) ).
fof(f1464,plain,
! [X0] : addition(c(X0),one) = one,
inference(resolution,[status(thm)],[f1430,f48]) ).
fof(f1465,plain,
! [X0,X1] : leq(backward_box(X0,X1),one),
inference(paramodulation,[status(thm)],[f72,f1430]) ).
fof(f1466,plain,
! [X0,X1] : leq(forward_box(X0,X1),one),
inference(paramodulation,[status(thm)],[f71,f1430]) ).
fof(f1471,plain,
! [X0] : addition(one,c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f35,f1464]) ).
fof(f1472,plain,
! [X0] : addition(codomain(X0),one) = one,
inference(resolution,[status(thm)],[f1435,f48]) ).
fof(f1473,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),one),
inference(paramodulation,[status(thm)],[f70,f1435]) ).
fof(f1477,plain,
! [X0] : addition(one,codomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f35,f1472]) ).
fof(f1478,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1427,f48]) ).
fof(f1484,plain,
! [X0] : leq(divergence(X0),one),
inference(paramodulation,[status(thm)],[f73,f1427]) ).
fof(f1485,plain,
! [X0,X1] : addition(one,forward_diamond(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f35,f1478]) ).
fof(f1486,plain,
! [X0] : addition(divergence(X0),one) = one,
inference(resolution,[status(thm)],[f1484,f48]) ).
fof(f1488,plain,
! [X0] : addition(one,divergence(X0)) = one,
inference(forward_demodulation,[status(thm)],[f35,f1486]) ).
fof(f1489,plain,
! [X0,X1] : addition(backward_box(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1465,f48]) ).
fof(f1492,plain,
! [X0,X1] : addition(one,backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f35,f1489]) ).
fof(f1493,plain,
! [X0,X1] : addition(forward_box(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1466,f48]) ).
fof(f1497,plain,
! [X0,X1] : addition(one,forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f35,f1493]) ).
fof(f1498,plain,
! [X0,X1] : addition(backward_diamond(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1473,f48]) ).
fof(f1504,plain,
! [X0,X1] : addition(one,backward_diamond(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f35,f1498]) ).
fof(f1514,plain,
! [X0,X1] : addition(domain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1375,f103]) ).
fof(f1516,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1375,f97]) ).
fof(f1517,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1375,f97]) ).
fof(f1518,plain,
! [X0] :
( one != one
| leq(domain(X0),one) ),
inference(paramodulation,[status(thm)],[f1375,f246]) ).
fof(f1519,plain,
! [X0] :
( one != domain(X0)
| leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f1375,f49]) ).
fof(f1520,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1375,f36]) ).
fof(f1522,plain,
! [X0,X1] : addition(one,addition(X0,domain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f1514]) ).
fof(f1524,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f1517]) ).
fof(f1525,definition,
! [X0] :
( sQ0_spl
<=> leq(domain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1528,definition,
( sQ1_spl
<=> one = one ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1530,plain,
( sQ1_spl
| one != one ),
inference(component_clause,[status(thm)],[f1528]) ).
fof(f1531,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1518,f1525,f1528]) ).
fof(f1539,plain,
! [X0,X1] : addition(coantidomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1377,f103]) ).
fof(f1541,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1377,f97]) ).
fof(f1542,plain,
! [X0,X1] : addition(X0,one) = addition(coantidomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1377,f97]) ).
fof(f1543,plain,
! [X0] :
( one != one
| leq(coantidomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1377,f246]) ).
fof(f1544,plain,
! [X0] :
( one != coantidomain(X0)
| leq(one,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f1377,f49]) ).
fof(f1545,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1377,f36]) ).
fof(f1547,plain,
! [X0,X1] : addition(one,addition(X0,coantidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f1539]) ).
fof(f1549,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f1542]) ).
fof(f1550,definition,
! [X0] :
( sQ2_spl
<=> leq(coantidomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1553,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1543,f1550,f1528]) ).
fof(f1554,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1530]) ).
fof(f1555,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1554]) ).
fof(f1558,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f67,f136]) ).
fof(f1559,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f62,f136]) ).
fof(f1563,plain,
! [X0,X1] : multiplication(antidomain(domain(X0)),domain_difference(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f68,f136]) ).
fof(f1564,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))) = zero,
inference(paramodulation,[status(thm)],[f39,f136]) ).
fof(f1569,plain,
! [X0] : multiplication(antidomain(X0),omega(X0)) = zero,
inference(paramodulation,[status(thm)],[f56,f136]) ).
fof(f1573,plain,
! [X0,X1] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),multiplication(X0,X1)))) = coantidomain(multiplication(codomain(antidomain(X0)),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f136,f615]) ).
fof(f1574,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1))))) = antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f136,f479]) ).
fof(f1575,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X2)))
| ~ leq(multiplication(X0,X1),addition(zero,X2)) ),
inference(paramodulation,[status(thm)],[f136,f58]) ).
fof(f1576,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X1,X2))),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f136,f55]) ).
fof(f1577,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f136,f53]) ).
fof(f1578,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f136,f43]) ).
fof(f1579,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = addition(zero,multiplication(X1,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f136,f43]) ).
fof(f1580,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f136,f42]) ).
fof(f1581,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = addition(zero,multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f136,f42]) ).
fof(f1585,plain,
! [X0,X1] : multiplication(c(X0),domain_difference(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f67,f1563]) ).
fof(f1587,plain,
! [X0,X1] : addition(one,coantidomain(multiplication(codomain(antidomain(X0)),multiplication(X0,X1)))) = coantidomain(multiplication(codomain(antidomain(X0)),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f696,f1573]) ).
fof(f1588,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(antidomain(X0)),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1377,f1587]) ).
fof(f1589,plain,
! [X0,X1] : addition(one,antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1))))) = antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f577,f1574]) ).
fof(f1590,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X2)))
| ~ leq(multiplication(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f1575]) ).
fof(f1591,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X1,X2))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f1576]) ).
fof(f1592,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f1577]) ).
fof(f1593,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f1578]) ).
fof(f1594,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f80,f1579]) ).
fof(f1595,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f1580]) ).
fof(f1596,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = multiplication(antidomain(X0),X2),
inference(forward_demodulation,[status(thm)],[f80,f1581]) ).
fof(f1607,plain,
! [X0,X1] : addition(antidomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1379,f103]) ).
fof(f1609,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1379,f97]) ).
fof(f1610,plain,
! [X0,X1] : addition(X0,one) = addition(antidomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1379,f97]) ).
fof(f1611,plain,
! [X0] :
( one != one
| leq(antidomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1379,f246]) ).
fof(f1612,plain,
! [X0] :
( one != antidomain(X0)
| leq(one,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f1379,f49]) ).
fof(f1613,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1379,f36]) ).
fof(f1615,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f1607]) ).
fof(f1617,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f1610]) ).
fof(f1618,definition,
! [X0] :
( sQ3_spl
<=> leq(antidomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1621,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f1611,f1618,f1528]) ).
fof(f1623,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(multiplication(X0,X1),X2))))) = zero,
inference(paramodulation,[status(thm)],[f39,f144]) ).
fof(f1627,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(paramodulation,[status(thm)],[f39,f144]) ).
fof(f1632,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),coantidomain(domain_difference(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f68,f144]) ).
fof(f1633,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2))))) = zero,
inference(paramodulation,[status(thm)],[f39,f144]) ).
fof(f1643,plain,
! [X0,X1] : backward_diamond(multiplication(X0,coantidomain(multiplication(codomain(X1),X0))),X1) = codomain(zero),
inference(paramodulation,[status(thm)],[f144,f70]) ).
fof(f1645,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(multiplication(X0,X1),X2))))) = zero,
inference(paramodulation,[status(thm)],[f144,f39]) ).
fof(f1650,plain,
! [X0,X1] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1)))))) = coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f144,f615]) ).
fof(f1651,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1))))))) = antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f144,f479]) ).
fof(f1652,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(zero,X2)) ),
inference(paramodulation,[status(thm)],[f144,f58]) ).
fof(f1653,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,coantidomain(multiplication(X1,X2))))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f144,f55]) ).
fof(f1654,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X2),X0),multiplication(X1,coantidomain(multiplication(X2,X1))))
| ~ leq(addition(zero,X0),multiplication(X1,coantidomain(multiplication(X2,X1)))) ),
inference(paramodulation,[status(thm)],[f144,f53]) ).
fof(f1655,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = addition(multiplication(X0,multiplication(X2,coantidomain(multiplication(X1,X2)))),zero),
inference(paramodulation,[status(thm)],[f144,f43]) ).
fof(f1656,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X0,X2)))) = addition(zero,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))),
inference(paramodulation,[status(thm)],[f144,f43]) ).
fof(f1657,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f144,f42]) ).
fof(f1658,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = addition(zero,multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f144,f42]) ).
fof(f1659,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(zero,X2),
inference(paramodulation,[status(thm)],[f144,f39]) ).
fof(f1661,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f39,f1623]) ).
fof(f1668,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f39,f1633]) ).
fof(f1679,plain,
! [X0,X1] : backward_diamond(multiplication(X0,coantidomain(multiplication(codomain(X1),X0))),X1) = zero,
inference(forward_demodulation,[status(thm)],[f737,f1643]) ).
fof(f1684,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f39,f1645]) ).
fof(f1686,plain,
! [X0,X1] : addition(one,coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1)))))) = coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f696,f1650]) ).
fof(f1687,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f1377,f1686]) ).
fof(f1688,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1))))))) = antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f577,f1651]) ).
fof(f1689,plain,
! [X0,X1] : one = antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f1379,f1688]) ).
fof(f1690,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f1652]) ).
fof(f1691,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,coantidomain(multiplication(X1,X2))))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f1653]) ).
fof(f1692,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X2),X0),multiplication(X1,coantidomain(multiplication(X2,X1))))
| ~ leq(X0,multiplication(X1,coantidomain(multiplication(X2,X1)))) ),
inference(forward_demodulation,[status(thm)],[f80,f1654]) ).
fof(f1693,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(X0,multiplication(X2,coantidomain(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f37,f1655]) ).
fof(f1694,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X0,X2)))) = multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f80,f1656]) ).
fof(f1695,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f1657]) ).
fof(f1696,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f80,f1658]) ).
fof(f1697,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = multiplication(zero,X2),
inference(forward_demodulation,[status(thm)],[f39,f1659]) ).
fof(f1698,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(forward_demodulation,[status(thm)],[f45,f1697]) ).
fof(f1709,plain,
! [X0,X1] : addition(c(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1471,f103]) ).
fof(f1711,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1471,f97]) ).
fof(f1712,plain,
! [X0,X1] : addition(X0,one) = addition(c(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1471,f97]) ).
fof(f1713,plain,
! [X0] :
( one != one
| leq(c(X0),one) ),
inference(paramodulation,[status(thm)],[f1471,f246]) ).
fof(f1714,plain,
! [X0] :
( one != c(X0)
| leq(one,c(X0)) ),
inference(paramodulation,[status(thm)],[f1471,f49]) ).
fof(f1715,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1471,f36]) ).
fof(f1717,plain,
! [X0,X1] : addition(one,addition(X0,c(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f1709]) ).
fof(f1719,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f1712]) ).
fof(f1720,definition,
! [X0] :
( sQ4_spl
<=> leq(c(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1723,plain,
( ~ sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1713,f1720,f1528]) ).
fof(f1732,plain,
! [X0,X1] : addition(codomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1477,f103]) ).
fof(f1734,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1477,f97]) ).
fof(f1735,plain,
! [X0,X1] : addition(X0,one) = addition(codomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1477,f97]) ).
fof(f1736,plain,
! [X0] :
( one != one
| leq(codomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1477,f246]) ).
fof(f1737,plain,
! [X0] :
( one != codomain(X0)
| leq(one,codomain(X0)) ),
inference(paramodulation,[status(thm)],[f1477,f49]) ).
fof(f1738,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1477,f36]) ).
fof(f1740,plain,
! [X0,X1] : addition(one,addition(X0,codomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f1732]) ).
fof(f1742,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f1735]) ).
fof(f1743,definition,
! [X0] :
( sQ5_spl
<=> leq(codomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1746,plain,
( ~ sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1736,f1743,f1528]) ).
fof(f1752,plain,
! [X0,X1] : addition(divergence(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1488,f103]) ).
fof(f1754,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1488,f97]) ).
fof(f1755,plain,
! [X0,X1] : addition(X0,one) = addition(divergence(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1488,f97]) ).
fof(f1756,plain,
! [X0] :
( one != one
| leq(divergence(X0),one) ),
inference(paramodulation,[status(thm)],[f1488,f246]) ).
fof(f1757,plain,
! [X0] :
( one != divergence(X0)
| leq(one,divergence(X0)) ),
inference(paramodulation,[status(thm)],[f1488,f49]) ).
fof(f1758,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1488,f36]) ).
fof(f1760,plain,
! [X0,X1] : addition(one,addition(X0,divergence(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f1752]) ).
fof(f1762,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f1755]) ).
fof(f1763,definition,
! [X0] :
( sQ6_spl
<=> leq(divergence(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1766,plain,
( ~ sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1756,f1763,f1528]) ).
fof(f1767,plain,
! [X0,X1,X2] : leq(X0,addition(omega(X1),multiplication(star(X1),addition(X2,X0)))),
inference(resolution,[status(thm)],[f1420,f58]) ).
fof(f1768,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f1420,f48]) ).
fof(f1769,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f103,f1420]) ).
fof(f1770,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f36,f1420]) ).
fof(f1779,plain,
! [X0,X1] : leq(divergence(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1488,f1420]) ).
fof(f1780,plain,
! [X0,X1] : leq(codomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1477,f1420]) ).
fof(f1781,plain,
! [X0,X1] : leq(c(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1471,f1420]) ).
fof(f1782,plain,
! [X0,X1] : leq(antidomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1379,f1420]) ).
fof(f1783,plain,
! [X0,X1] : leq(coantidomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1377,f1420]) ).
fof(f1784,plain,
! [X0,X1] : leq(domain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1375,f1420]) ).
fof(f1790,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f43,f1420]) ).
fof(f1791,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f42,f1420]) ).
fof(f1792,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f103,f1420]) ).
fof(f1793,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f36,f1420]) ).
fof(f1795,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X0)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f99,f1420]) ).
fof(f1797,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f97,f1420]) ).
fof(f1798,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X1,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f97,f1420]) ).
fof(f1806,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(paramodulation,[status(thm)],[f39,f151]) ).
fof(f1813,plain,
! [X0] : multiplication(X0,omega(coantidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f56,f151]) ).
fof(f1818,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f66,f151]) ).
fof(f1820,plain,
! [X0,X1] : backward_diamond(multiplication(coantidomain(codomain(X0)),X1),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f151,f70]) ).
fof(f1822,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(paramodulation,[status(thm)],[f151,f39]) ).
fof(f1828,plain,
! [X0,X1] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),multiplication(coantidomain(X0),X1)))) = coantidomain(multiplication(codomain(X0),multiplication(coantidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f151,f615]) ).
fof(f1829,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1))))) = antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f151,f479]) ).
fof(f1830,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(multiplication(coantidomain(X0),X1),addition(zero,X2)) ),
inference(paramodulation,[status(thm)],[f151,f58]) ).
fof(f1831,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(coantidomain(X1),X2))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f151,f55]) ).
fof(f1832,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),multiplication(coantidomain(X1),X2))
| ~ leq(addition(zero,X0),multiplication(coantidomain(X1),X2)) ),
inference(paramodulation,[status(thm)],[f151,f53]) ).
fof(f1833,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = addition(multiplication(X0,multiplication(coantidomain(X1),X2)),zero),
inference(paramodulation,[status(thm)],[f151,f43]) ).
fof(f1834,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = addition(zero,multiplication(X1,multiplication(coantidomain(X0),X2))),
inference(paramodulation,[status(thm)],[f151,f43]) ).
fof(f1835,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f151,f42]) ).
fof(f1836,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = addition(zero,multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f151,f42]) ).
fof(f1841,plain,
! [X0,X1] : backward_diamond(multiplication(coantidomain(codomain(X0)),X1),X0) = zero,
inference(forward_demodulation,[status(thm)],[f737,f1820]) ).
fof(f1848,plain,
! [X0,X1] : addition(one,coantidomain(multiplication(codomain(X0),multiplication(coantidomain(X0),X1)))) = coantidomain(multiplication(codomain(X0),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f696,f1828]) ).
fof(f1849,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(X0),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f1377,f1848]) ).
fof(f1850,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1))))) = antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f577,f1829]) ).
fof(f1851,plain,
! [X0,X1] : one = antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f1379,f1850]) ).
fof(f1852,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(multiplication(coantidomain(X0),X1),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f1830]) ).
fof(f1853,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(coantidomain(X1),X2))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f1831]) ).
fof(f1854,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),multiplication(coantidomain(X1),X2))
| ~ leq(X0,multiplication(coantidomain(X1),X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f1832]) ).
fof(f1855,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f37,f1833]) ).
fof(f1856,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f80,f1834]) ).
fof(f1857,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f1835]) ).
fof(f1858,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f80,f1836]) ).
fof(f1861,plain,
! [X0,X1,X2] : leq(X0,addition(omega(X1),multiplication(star(X1),addition(X0,X2)))),
inference(resolution,[status(thm)],[f1421,f58]) ).
fof(f1862,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f1421,f48]) ).
fof(f1863,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f103,f1421]) ).
fof(f1864,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f36,f1421]) ).
fof(f1880,plain,
! [X0,X1,X2] : leq(coantidomain(multiplication(X0,X1)),addition(X2,coantidomain(multiplication(codomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f615,f1421]) ).
fof(f1882,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f479,f1421]) ).
fof(f1884,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f43,f1421]) ).
fof(f1885,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f42,f1421]) ).
fof(f1886,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X1,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f103,f1421]) ).
fof(f1887,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f36,f1421]) ).
fof(f1891,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f97,f1421]) ).
fof(f1892,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f97,f1421]) ).
fof(f1907,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1485,f1420]) ).
fof(f1911,plain,
! [X0,X1,X2] : addition(forward_diamond(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1485,f103]) ).
fof(f1913,plain,
! [X0,X1,X2] : addition(one,addition(forward_diamond(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1485,f97]) ).
fof(f1914,plain,
! [X0,X1,X2] : addition(X0,one) = addition(forward_diamond(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1485,f97]) ).
fof(f1915,plain,
! [X0,X1] :
( one != one
| leq(forward_diamond(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1485,f246]) ).
fof(f1916,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(one,forward_diamond(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1485,f49]) ).
fof(f1917,plain,
! [X0,X1,X2] : addition(one,addition(forward_diamond(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1485,f36]) ).
fof(f1919,plain,
! [X0,X1,X2] : addition(one,addition(X0,forward_diamond(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f1911]) ).
fof(f1921,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f97,f1914]) ).
fof(f1922,definition,
! [X0,X1] :
( sQ7_spl
<=> leq(forward_diamond(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1925,plain,
( ~ sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1915,f1922,f1528]) ).
fof(f1927,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f42,f153]) ).
fof(f1931,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f197,f153]) ).
fof(f1932,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = addition(zero,multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f195,f153]) ).
fof(f1933,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(X1,antidomain(X2))) = addition(domain_difference(X0,X2),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f68,f153]) ).
fof(f1934,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f39,f153]) ).
fof(f1935,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f136,f153]) ).
fof(f1936,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f59,f153]) ).
fof(f1939,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f151,f153]) ).
fof(f1940,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f144,f153]) ).
fof(f1941,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(X0))) = addition(omega(X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f56,f153]) ).
fof(f1942,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f153]) ).
fof(f1944,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f40,f153]) ).
fof(f1945,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f197,f153]) ).
fof(f1946,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f195,f153]) ).
fof(f1947,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(antidomain(X1),X2)) = addition(multiplication(domain(X0),X2),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f68,f153]) ).
fof(f1948,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(multiplication(X0,X1),X3),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f39,f153]) ).
fof(f1949,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = addition(multiplication(antidomain(X0),X2),zero),
inference(paramodulation,[status(thm)],[f136,f153]) ).
fof(f1950,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f59,f153]) ).
fof(f1953,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f151,f153]) ).
fof(f1954,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f144,f153]) ).
fof(f1955,plain,
! [X0,X1] : multiplication(X0,addition(omega(X0),X1)) = addition(multiplication(X0,X1),omega(X0)),
inference(paramodulation,[status(thm)],[f56,f153]) ).
fof(f1956,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f63,f153]) ).
fof(f1958,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f40,f153]) ).
fof(f1960,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f153,f42]) ).
fof(f1961,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X2))))
| ~ leq(X0,multiplication(X1,addition(X2,X0))) ),
inference(paramodulation,[status(thm)],[f153,f58]) ).
fof(f1962,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),star(X2)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f153,f55]) ).
fof(f1963,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f153,f53]) ).
fof(f1964,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f153,f1421]) ).
fof(f1965,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f153,f1420]) ).
fof(f1966,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f153,f1423]) ).
fof(f1967,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f153,f1324]) ).
fof(f1968,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,addition(X2,X1))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f153,f105]) ).
fof(f1969,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f153,f103]) ).
fof(f1971,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f153,f97]) ).
fof(f1972,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,X2),addition(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f153,f97]) ).
fof(f1973,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f153,f246]) ).
fof(f1974,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f153,f49]) ).
fof(f1975,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X2,X1)),X3),
inference(paramodulation,[status(thm)],[f153,f36]) ).
fof(f1980,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f1931]) ).
fof(f1981,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f1932]) ).
fof(f1982,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f1934]) ).
fof(f1983,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f1982]) ).
fof(f1984,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f153,f1983]) ).
fof(f1985,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f153,f1984]) ).
fof(f1986,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f1935]) ).
fof(f1987,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f1936]) ).
fof(f1992,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f1939]) ).
fof(f1993,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f1940]) ).
fof(f1994,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f1942]) ).
fof(f1996,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f1945]) ).
fof(f1997,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f1946]) ).
fof(f1998,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(multiplication(X0,X1),X3),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f1948]) ).
fof(f1999,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f1998]) ).
fof(f2000,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f153,f1999]) ).
fof(f2001,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f153,f2000]) ).
fof(f2002,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = multiplication(antidomain(X0),X2),
inference(forward_demodulation,[status(thm)],[f37,f1949]) ).
fof(f2003,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f1950]) ).
fof(f2008,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f37,f1953]) ).
fof(f2009,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f37,f1954]) ).
fof(f2010,plain,
! [X0,X1] : multiplication(X0,addition(omega(X0),X1)) = addition(omega(X0),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f1955]) ).
fof(f2011,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f1956]) ).
fof(f2013,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f1958]) ).
fof(f2015,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f1962]) ).
fof(f2016,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,X2),X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f153,f1968]) ).
fof(f2017,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,X1))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f2016]) ).
fof(f2018,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,X1))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2017]) ).
fof(f2028,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1492,f1420]) ).
fof(f2032,plain,
! [X0,X1,X2] : addition(backward_box(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1492,f103]) ).
fof(f2034,plain,
! [X0,X1,X2] : addition(one,addition(backward_box(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1492,f97]) ).
fof(f2035,plain,
! [X0,X1,X2] : addition(X0,one) = addition(backward_box(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1492,f97]) ).
fof(f2036,plain,
! [X0,X1] :
( one != one
| leq(backward_box(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1492,f246]) ).
fof(f2037,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(one,backward_box(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1492,f49]) ).
fof(f2038,plain,
! [X0,X1,X2] : addition(one,addition(backward_box(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1492,f36]) ).
fof(f2040,plain,
! [X0,X1,X2] : addition(one,addition(X0,backward_box(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f2032]) ).
fof(f2042,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f97,f2035]) ).
fof(f2043,definition,
! [X0,X1] :
( sQ8_spl
<=> leq(backward_box(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f2046,plain,
( ~ sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f2036,f2043,f1528]) ).
fof(f2052,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1497,f1420]) ).
fof(f2056,plain,
! [X0,X1,X2] : addition(forward_box(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1497,f103]) ).
fof(f2058,plain,
! [X0,X1,X2] : addition(one,addition(forward_box(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1497,f97]) ).
fof(f2059,plain,
! [X0,X1,X2] : addition(X0,one) = addition(forward_box(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1497,f97]) ).
fof(f2060,plain,
! [X0,X1] :
( one != one
| leq(forward_box(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1497,f246]) ).
fof(f2061,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(one,forward_box(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1497,f49]) ).
fof(f2062,plain,
! [X0,X1,X2] : addition(one,addition(forward_box(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1497,f36]) ).
fof(f2064,plain,
! [X0,X1,X2] : addition(one,addition(X0,forward_box(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f2056]) ).
fof(f2066,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f97,f2059]) ).
fof(f2067,definition,
! [X0,X1] :
( sQ9_spl
<=> leq(forward_box(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f2070,plain,
( ~ sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f2060,f2067,f1528]) ).
fof(f2078,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1504,f1420]) ).
fof(f2082,plain,
! [X0,X1,X2] : addition(backward_diamond(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1504,f103]) ).
fof(f2084,plain,
! [X0,X1,X2] : addition(one,addition(backward_diamond(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1504,f97]) ).
fof(f2085,plain,
! [X0,X1,X2] : addition(X0,one) = addition(backward_diamond(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1504,f97]) ).
fof(f2086,plain,
! [X0,X1] :
( one != one
| leq(backward_diamond(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1504,f246]) ).
fof(f2087,plain,
! [X0,X1] :
( one != backward_diamond(X0,X1)
| leq(one,backward_diamond(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1504,f49]) ).
fof(f2088,plain,
! [X0,X1,X2] : addition(one,addition(backward_diamond(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1504,f36]) ).
fof(f2090,plain,
! [X0,X1,X2] : addition(one,addition(X0,backward_diamond(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f2082]) ).
fof(f2092,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f97,f2085]) ).
fof(f2093,definition,
! [X0,X1] :
( sQ10_spl
<=> leq(backward_diamond(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f2096,plain,
( ~ sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f2086,f2093,f1528]) ).
fof(f2099,plain,
! [X0] : multiplication(c(X0),omega(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f67,f1569]) ).
fof(f2100,plain,
! [X0] : multiplication(domain(X0),omega(antidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f62,f1569]) ).
fof(f2103,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(omega(X0),X1)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f1569,f153]) ).
fof(f2104,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,omega(X0))) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f1569,f153]) ).
fof(f2107,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),omega(X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),omega(X0))),
inference(paramodulation,[status(thm)],[f1569,f615]) ).
fof(f2108,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(omega(X0))))) = antidomain(multiplication(antidomain(X0),domain(omega(X0)))),
inference(paramodulation,[status(thm)],[f1569,f479]) ).
fof(f2109,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(omega(X0),addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f1569,f58]) ).
fof(f2110,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(X1))),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f1569,f55]) ).
fof(f2111,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),omega(X1))
| ~ leq(addition(zero,X0),omega(X1)) ),
inference(paramodulation,[status(thm)],[f1569,f53]) ).
fof(f2112,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),omega(X1)) = addition(multiplication(X0,omega(X1)),zero),
inference(paramodulation,[status(thm)],[f1569,f43]) ).
fof(f2113,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),omega(X0)) = addition(zero,multiplication(X1,omega(X0))),
inference(paramodulation,[status(thm)],[f1569,f43]) ).
fof(f2114,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,omega(X0))) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f1569,f42]) ).
fof(f2115,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(omega(X0),X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f1569,f42]) ).
fof(f2116,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(omega(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f1569,f39]) ).
fof(f2119,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(omega(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f2103]) ).
fof(f2120,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,omega(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f2104]) ).
fof(f2123,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(antidomain(X0)),omega(X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),omega(X0))),
inference(forward_demodulation,[status(thm)],[f696,f2107]) ).
fof(f2124,plain,
! [X0] : one = coantidomain(multiplication(codomain(antidomain(X0)),omega(X0))),
inference(forward_demodulation,[status(thm)],[f1377,f2123]) ).
fof(f2125,plain,
! [X0] : addition(one,antidomain(multiplication(antidomain(X0),domain(omega(X0))))) = antidomain(multiplication(antidomain(X0),domain(omega(X0)))),
inference(forward_demodulation,[status(thm)],[f577,f2108]) ).
fof(f2126,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),domain(omega(X0)))),
inference(forward_demodulation,[status(thm)],[f1379,f2125]) ).
fof(f2127,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(omega(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f2109]) ).
fof(f2128,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f2110]) ).
fof(f2129,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),omega(X1))
| ~ leq(X0,omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f2111]) ).
fof(f2130,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),omega(X1)) = multiplication(X0,omega(X1)),
inference(forward_demodulation,[status(thm)],[f37,f2112]) ).
fof(f2131,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),omega(X0)) = multiplication(X1,omega(X0)),
inference(forward_demodulation,[status(thm)],[f80,f2113]) ).
fof(f2132,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,omega(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f2114]) ).
fof(f2133,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(omega(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f2115]) ).
fof(f2134,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(omega(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f2116]) ).
fof(f2136,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(antidomain(domain(X0)),X1),
inference(paramodulation,[status(thm)],[f67,f177]) ).
fof(f2137,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(antidomain(antidomain(X0)),X1),
inference(paramodulation,[status(thm)],[f62,f177]) ).
fof(f2149,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f569,f177]) ).
fof(f2151,plain,
! [X0] : multiplication(antidomain(coantidomain(X0)),one) = multiplication(antidomain(coantidomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f683,f177]) ).
fof(f2153,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),one) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f558,f177]) ).
fof(f2154,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(X2,X1))) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f153,f177]) ).
fof(f2155,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(X0,X2),X1)) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f43,f177]) ).
fof(f2156,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(X1,X2))) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f42,f177]) ).
fof(f2157,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X1,addition(X0,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f103,f177]) ).
fof(f2158,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,addition(X1,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f36,f177]) ).
fof(f2160,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),addition(X1,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f99,f177]) ).
fof(f2162,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(paramodulation,[status(thm)],[f97,f177]) ).
fof(f2163,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f97,f177]) ).
fof(f2165,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(paramodulation,[status(thm)],[f35,f177]) ).
fof(f2166,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(paramodulation,[status(thm)],[f35,f177]) ).
fof(f2168,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(addition(X0,X1),X2)) = addition(multiplication(antidomain(X0),X2),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f177,f153]) ).
fof(f2169,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = addition(multiplication(antidomain(X0),X2),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f177,f153]) ).
fof(f2170,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X0,X1),coantidomain(multiplication(antidomain(X0),X1)))) = zero,
inference(paramodulation,[status(thm)],[f177,f144]) ).
fof(f2172,plain,
! [X0,X1] : addition(coantidomain(multiplication(antidomain(X0),X1)),coantidomain(multiplication(codomain(antidomain(X0)),addition(X0,X1)))) = coantidomain(multiplication(codomain(antidomain(X0)),addition(X0,X1))),
inference(paramodulation,[status(thm)],[f177,f615]) ).
fof(f2173,plain,
! [X0,X1] : addition(antidomain(multiplication(antidomain(X0),X1)),antidomain(multiplication(antidomain(X0),domain(addition(X0,X1))))) = antidomain(multiplication(antidomain(X0),domain(addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f177,f479]) ).
fof(f2174,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X2)))
| ~ leq(addition(X0,X1),addition(multiplication(antidomain(X0),X1),X2)) ),
inference(paramodulation,[status(thm)],[f177,f58]) ).
fof(f2175,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X0,X1))),antidomain(X0))
| ~ leq(addition(multiplication(antidomain(X0),X1),X2),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f177,f55]) ).
fof(f2176,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X0)),X2),addition(X0,X1))
| ~ leq(addition(multiplication(antidomain(X0),X1),X2),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f177,f53]) ).
fof(f2177,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X1,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(antidomain(X1),X2)),
inference(paramodulation,[status(thm)],[f177,f43]) ).
fof(f2178,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X0,X2)) = addition(multiplication(antidomain(X0),X2),multiplication(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f177,f43]) ).
fof(f2179,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f177,f42]) ).
fof(f2180,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(addition(X0,X1),X2)) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f177,f42]) ).
fof(f2181,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X0,X1),X2)) = multiplication(multiplication(antidomain(X0),X1),X2),
inference(paramodulation,[status(thm)],[f177,f39]) ).
fof(f2185,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f67,f2136]) ).
fof(f2186,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f2137]) ).
fof(f2209,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f40,f2149]) ).
fof(f2210,plain,
! [X0] : c(X0) = multiplication(antidomain(domain(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f67,f2209]) ).
fof(f2211,plain,
! [X0] : c(X0) = multiplication(c(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f67,f2210]) ).
fof(f2212,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(antidomain(coantidomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f2151]) ).
fof(f2213,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f2153]) ).
fof(f2214,plain,
! [X0] : domain(X0) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f2213]) ).
fof(f2215,plain,
! [X0] : domain(X0) = multiplication(domain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f2214]) ).
fof(f2216,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f177,f2160]) ).
fof(f2218,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = addition(multiplication(antidomain(X0),X2),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f103,f2168]) ).
fof(f2219,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f153,f2218]) ).
fof(f2220,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f153,f2169]) ).
fof(f2221,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X1,X2)) = addition(multiplication(antidomain(X1),X2),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f2177]) ).
fof(f2222,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2179]) ).
fof(f2223,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f103,f2180]) ).
fof(f2224,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2223]) ).
fof(f2225,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X0,X1),X2)) = multiplication(antidomain(X0),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f2181]) ).
fof(f2226,plain,
! [X0,X1] : leq(divergence(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f1779,f58]) ).
fof(f2227,plain,
! [X0,X1] : addition(divergence(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1779,f48]) ).
fof(f2229,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f103,f1779]) ).
fof(f2230,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f36,f1779]) ).
fof(f2232,plain,
! [X0,X1] : leq(divergence(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f35,f1779]) ).
fof(f2235,plain,
! [X0,X1] : leq(divergence(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2226]) ).
fof(f2236,plain,
! [X0,X1] : leq(divergence(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f2235]) ).
fof(f2237,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f97,f2227]) ).
fof(f2238,plain,
! [X0,X1] : leq(codomain(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f1780,f58]) ).
fof(f2239,plain,
! [X0,X1] : addition(codomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1780,f48]) ).
fof(f2242,plain,
! [X0,X1] : leq(coantidomain(codomain(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f193,f1780]) ).
fof(f2244,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f103,f1780]) ).
fof(f2245,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f36,f1780]) ).
fof(f2247,plain,
! [X0,X1] : leq(codomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f35,f1780]) ).
fof(f2250,plain,
! [X0,X1] : leq(codomain(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2238]) ).
fof(f2251,plain,
! [X0,X1] : leq(codomain(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f2250]) ).
fof(f2252,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f97,f2239]) ).
fof(f2253,plain,
! [X0,X1] : leq(c(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f1781,f58]) ).
fof(f2254,plain,
! [X0,X1] : addition(c(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1781,f48]) ).
fof(f2258,plain,
! [X0,X1] : leq(antidomain(c(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f547,f1781]) ).
fof(f2259,plain,
! [X0,X1] : leq(domain(c(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f362,f1781]) ).
fof(f2261,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f103,f1781]) ).
fof(f2262,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f36,f1781]) ).
fof(f2264,plain,
! [X0,X1] : leq(c(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f35,f1781]) ).
fof(f2267,plain,
! [X0,X1] : leq(c(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2253]) ).
fof(f2268,plain,
! [X0,X1] : leq(c(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f2267]) ).
fof(f2269,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f97,f2254]) ).
fof(f2270,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f39,f181]) ).
fof(f2274,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,codomain(X0)),
inference(paramodulation,[status(thm)],[f683,f181]) ).
fof(f2275,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,addition(X1,addition(coantidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f99,f181]) ).
fof(f2277,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f97,f181]) ).
fof(f2278,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f97,f181]) ).
fof(f2280,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f35,f181]) ).
fof(f2281,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f35,f181]) ).
fof(f2284,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(paramodulation,[status(thm)],[f66,f181]) ).
fof(f2286,plain,
! [X0,X1] : backward_diamond(addition(coantidomain(codomain(X0)),X1),X0) = codomain(multiplication(codomain(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f70]) ).
fof(f2287,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,addition(coantidomain(codomain(X0)),X1))),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(codomain(X0),addition(coantidomain(codomain(X0)),X1))),
inference(paramodulation,[status(thm)],[f181,f615]) ).
fof(f2289,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f181,f39]) ).
fof(f2292,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f181,f153]) ).
fof(f2293,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f181,f153]) ).
fof(f2294,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f181,f144]) ).
fof(f2296,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),addition(coantidomain(X0),X1)))) = coantidomain(multiplication(codomain(X0),addition(coantidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f181,f615]) ).
fof(f2297,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(addition(coantidomain(X0),X1))))) = antidomain(multiplication(X0,domain(addition(coantidomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f181,f479]) ).
fof(f2298,plain,
! [X0,X1,X2] :
( leq(addition(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(addition(coantidomain(X0),X1),addition(multiplication(X0,X1),X2)) ),
inference(paramodulation,[status(thm)],[f181,f58]) ).
fof(f2299,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(coantidomain(X0),X1))),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f181,f55]) ).
fof(f2300,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(coantidomain(X0),X1))
| ~ leq(addition(multiplication(X0,X1),X2),addition(coantidomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f181,f53]) ).
fof(f2301,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X1),X2)) = addition(multiplication(X0,addition(coantidomain(X1),X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f181,f43]) ).
fof(f2302,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X0),X2)) = addition(multiplication(X0,X2),multiplication(X1,addition(coantidomain(X0),X2))),
inference(paramodulation,[status(thm)],[f181,f43]) ).
fof(f2303,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f181,f42]) ).
fof(f2304,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f181,f42]) ).
fof(f2305,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f181,f39]) ).
fof(f2306,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f2270]) ).
fof(f2309,plain,
! [X0] : X0 = multiplication(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f2274]) ).
fof(f2310,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,addition(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f181,f2275]) ).
fof(f2315,plain,
! [X0,X1] : backward_diamond(addition(coantidomain(codomain(X0)),X1),X0) = backward_diamond(X1,X0),
inference(forward_demodulation,[status(thm)],[f70,f2286]) ).
fof(f2316,plain,
! [X0,X1] : addition(coantidomain(multiplication(codomain(X0),X1)),coantidomain(multiplication(X0,addition(coantidomain(codomain(X0)),X1)))) = coantidomain(multiplication(codomain(X0),addition(coantidomain(codomain(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f35,f2287]) ).
fof(f2317,plain,
! [X0,X1] : addition(coantidomain(multiplication(codomain(X0),X1)),coantidomain(multiplication(X0,addition(coantidomain(codomain(X0)),X1)))) = coantidomain(multiplication(codomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f181,f2316]) ).
fof(f2318,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f2289]) ).
fof(f2321,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f2292]) ).
fof(f2322,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f153,f2321]) ).
fof(f2323,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f153,f2293]) ).
fof(f2324,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X1),X2)) = addition(multiplication(X1,X2),multiplication(X0,addition(coantidomain(X1),X2))),
inference(forward_demodulation,[status(thm)],[f35,f2301]) ).
fof(f2325,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2303]) ).
fof(f2326,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f2304]) ).
fof(f2327,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2326]) ).
fof(f2328,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f2305]) ).
fof(f2330,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,multiplication(X1,codomain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f39,f2309]) ).
fof(f2333,plain,
! [X0,X1] : multiplication(codomain(X0),X1) = multiplication(multiplication(codomain(X0),X1),backward_diamond(X1,X0)),
inference(paramodulation,[status(thm)],[f70,f2309]) ).
fof(f2335,plain,
! [X0] : coantidomain(X0) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f193,f2309]) ).
fof(f2337,plain,
! [X0] : backward_diamond(codomain(codomain(X0)),X0) = codomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f2309,f70]) ).
fof(f2338,plain,
! [X0] : addition(coantidomain(multiplication(X0,codomain(codomain(X0)))),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),codomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f2309,f615]) ).
fof(f2340,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,codomain(multiplication(X0,X1)))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f2309,f39]) ).
fof(f2343,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f2309,f153]) ).
fof(f2344,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2309,f153]) ).
fof(f2345,plain,
! [X0] : multiplication(X0,multiplication(codomain(X0),coantidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f2309,f144]) ).
fof(f2347,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(X0),codomain(X0)))) = coantidomain(multiplication(codomain(X0),codomain(X0))),
inference(paramodulation,[status(thm)],[f2309,f615]) ).
fof(f2348,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,domain(codomain(X0))))) = antidomain(multiplication(X0,domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f2309,f479]) ).
fof(f2349,plain,
! [X0,X1] :
( leq(codomain(X0),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(codomain(X0),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2309,f58]) ).
fof(f2350,plain,
! [X0,X1] :
( leq(multiplication(X1,star(codomain(X0))),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2309,f55]) ).
fof(f2351,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),codomain(X0))
| ~ leq(addition(X0,X1),codomain(X0)) ),
inference(paramodulation,[status(thm)],[f2309,f53]) ).
fof(f2352,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(multiplication(X0,codomain(X1)),X1),
inference(paramodulation,[status(thm)],[f2309,f43]) ).
fof(f2353,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(X0,multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f2309,f43]) ).
fof(f2354,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f2309,f42]) ).
fof(f2355,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2309,f42]) ).
fof(f2356,plain,
! [X0,X1] : multiplication(X0,multiplication(codomain(X0),X1)) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f2309,f39]) ).
fof(f2358,plain,
! [X0,X1] : multiplication(codomain(X0),X1) = multiplication(codomain(X0),multiplication(X1,backward_diamond(X1,X0))),
inference(forward_demodulation,[status(thm)],[f39,f2333]) ).
fof(f2359,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,codomain(codomain(X0))))) = coantidomain(multiplication(codomain(X0),codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f2338]) ).
fof(f2360,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,codomain(codomain(X0))))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f2309,f2359]) ).
fof(f2361,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f2343]) ).
fof(f2362,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(X1,multiplication(X0,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f35,f2352]) ).
fof(f2363,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f2354]) ).
fof(f2364,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f1782,f58]) ).
fof(f2365,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1782,f48]) ).
fof(f2370,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f103,f1782]) ).
fof(f2371,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f36,f1782]) ).
fof(f2373,plain,
! [X0,X1] : leq(antidomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f35,f1782]) ).
fof(f2376,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2364]) ).
fof(f2377,plain,
! [X0,X1] : leq(antidomain(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f2376]) ).
fof(f2378,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f97,f2365]) ).
fof(f2379,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f1783,f58]) ).
fof(f2380,plain,
! [X0,X1] : addition(coantidomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1783,f48]) ).
fof(f2384,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f103,f1783]) ).
fof(f2385,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f36,f1783]) ).
fof(f2387,plain,
! [X0,X1] : leq(coantidomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f35,f1783]) ).
fof(f2390,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2379]) ).
fof(f2391,plain,
! [X0,X1] : leq(coantidomain(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f2390]) ).
fof(f2392,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f97,f2380]) ).
fof(f2393,plain,
! [X0,X1] : leq(domain(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f1784,f58]) ).
fof(f2394,plain,
! [X0,X1] : addition(domain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1784,f48]) ).
fof(f2400,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f103,f1784]) ).
fof(f2401,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f36,f1784]) ).
fof(f2403,plain,
! [X0,X1] : leq(domain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f35,f1784]) ).
fof(f2406,plain,
! [X0,X1] : leq(domain(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2393]) ).
fof(f2407,plain,
! [X0,X1] : leq(domain(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f2406]) ).
fof(f2408,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f97,f2394]) ).
fof(f2412,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,backward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f1504,f162]) ).
fof(f2413,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f1497,f162]) ).
fof(f2414,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f1492,f162]) ).
fof(f2415,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f1485,f162]) ).
fof(f2416,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,divergence(X1))),
inference(paramodulation,[status(thm)],[f1488,f162]) ).
fof(f2417,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f1477,f162]) ).
fof(f2418,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f1471,f162]) ).
fof(f2419,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f1379,f162]) ).
fof(f2420,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f1377,f162]) ).
fof(f2421,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f1375,f162]) ).
fof(f2422,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(X1,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f99,f162]) ).
fof(f2423,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f105,f162]) ).
fof(f2424,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f97,f162]) ).
fof(f2425,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f97,f162]) ).
fof(f2427,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f162]) ).
fof(f2428,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f162]) ).
fof(f2430,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(one,X1)) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f43,f162]) ).
fof(f2431,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X1,addition(X0,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f103,f162]) ).
fof(f2432,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f36,f162]) ).
fof(f2436,plain,
! [X0,X1] : multiplication(domain(X0),addition(one,antidomain(X1))) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f68,f162]) ).
fof(f2437,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(one,X2)) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f39,f162]) ).
fof(f2438,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X0,X1))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f177,f162]) ).
fof(f2439,plain,
! [X0] : multiplication(antidomain(X0),addition(one,omega(X0))) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f1569,f162]) ).
fof(f2440,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f136,f162]) ).
fof(f2441,plain,
! [X0] : multiplication(antidomain(X0),addition(one,X0)) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f59,f162]) ).
fof(f2444,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(coantidomain(X0),X1))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f181,f162]) ).
fof(f2445,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f151,f162]) ).
fof(f2446,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f144,f162]) ).
fof(f2447,plain,
! [X0] : multiplication(X0,addition(one,omega(X0))) = addition(X0,omega(X0)),
inference(paramodulation,[status(thm)],[f56,f162]) ).
fof(f2453,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(one,X1),X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f162,f153]) ).
fof(f2454,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(addition(X0,multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f162,f153]) ).
fof(f2455,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(addition(X0,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f162,f144]) ).
fof(f2457,plain,
! [X0,X1] : addition(coantidomain(addition(X0,multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),addition(one,X1)))) = coantidomain(multiplication(codomain(X0),addition(one,X1))),
inference(paramodulation,[status(thm)],[f162,f615]) ).
fof(f2458,plain,
! [X0,X1] : addition(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(one,X1))))) = antidomain(multiplication(X0,domain(addition(one,X1)))),
inference(paramodulation,[status(thm)],[f162,f479]) ).
fof(f2459,plain,
! [X0,X1,X2] :
( leq(addition(one,X0),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(one,X0),addition(addition(X1,multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f162,f58]) ).
fof(f2460,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(one,X1))),X0)
| ~ leq(addition(addition(X0,multiplication(X0,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f162,f55]) ).
fof(f2461,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(one,X1))
| ~ leq(addition(addition(X0,multiplication(X0,X1)),X2),addition(one,X1)) ),
inference(paramodulation,[status(thm)],[f162,f53]) ).
fof(f2462,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(multiplication(X0,addition(one,X2)),addition(X1,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f162,f43]) ).
fof(f2463,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(addition(X0,multiplication(X0,X2)),multiplication(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f162,f43]) ).
fof(f2464,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f162,f42]) ).
fof(f2465,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(one,X1),X2)) = addition(addition(X0,multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f162,f42]) ).
fof(f2466,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(one,X1),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f162,f39]) ).
fof(f2468,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(paramodulation,[status(thm)],[f162,f43]) ).
fof(f2469,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),X2))))
| ~ leq(X0,multiplication(multiplication(X1,X0),addition(one,X2))) ),
inference(paramodulation,[status(thm)],[f162,f58]) ).
fof(f2470,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(multiplication(multiplication(X0,X1),addition(one,X2)),X0) ),
inference(paramodulation,[status(thm)],[f162,f55]) ).
fof(f2471,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X1)
| ~ leq(multiplication(multiplication(X0,X1),addition(one,X2)),X1) ),
inference(paramodulation,[status(thm)],[f162,f53]) ).
fof(f2472,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),X2))) = multiplication(addition(X1,X0),addition(one,X2)),
inference(paramodulation,[status(thm)],[f162,f103]) ).
fof(f2473,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),X2))) = multiplication(addition(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f162,f36]) ).
fof(f2475,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f162,f1421]) ).
fof(f2476,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f162,f1420]) ).
fof(f2477,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f162,f1423]) ).
fof(f2478,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f162,f1324]) ).
fof(f2479,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f162,f105]) ).
fof(f2480,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f162,f103]) ).
fof(f2481,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,X1),multiplication(X0,addition(one,X1)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f162,f99]) ).
fof(f2482,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(X2,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f162,f97]) ).
fof(f2483,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(one,X2))) = addition(multiplication(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f162,f97]) ).
fof(f2484,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != X0
| leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f162,f246]) ).
fof(f2485,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != multiplication(X0,X1)
| leq(X0,multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f162,f49]) ).
fof(f2486,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f162,f36]) ).
fof(f2488,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_diamond(X1,X2))),
inference(forward_demodulation,[status(thm)],[f40,f2412]) ).
fof(f2489,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(forward_demodulation,[status(thm)],[f40,f2413]) ).
fof(f2490,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(forward_demodulation,[status(thm)],[f40,f2414]) ).
fof(f2491,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(forward_demodulation,[status(thm)],[f40,f2415]) ).
fof(f2492,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,divergence(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2416]) ).
fof(f2493,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2417]) ).
fof(f2494,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2418]) ).
fof(f2495,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2419]) ).
fof(f2496,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2420]) ).
fof(f2497,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f40,f2421]) ).
fof(f2502,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f39,f2430]) ).
fof(f2507,plain,
! [X0,X1] : multiplication(domain(X0),one) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1379,f2436]) ).
fof(f2508,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f40,f2507]) ).
fof(f2509,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f2437]) ).
fof(f2510,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = multiplication(X0,addition(multiplication(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f153,f2509]) ).
fof(f2511,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = multiplication(X0,addition(X1,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f2510]) ).
fof(f2512,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X0,X1))) = multiplication(antidomain(X0),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f162,f2438]) ).
fof(f2513,plain,
! [X0] : multiplication(antidomain(X0),addition(one,omega(X0))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f37,f2439]) ).
fof(f2514,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f37,f2440]) ).
fof(f2515,plain,
! [X0] : multiplication(antidomain(X0),addition(one,X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f37,f2441]) ).
fof(f2520,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = X0,
inference(forward_demodulation,[status(thm)],[f37,f2445]) ).
fof(f2521,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f37,f2446]) ).
fof(f2529,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f2453]) ).
fof(f2530,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f2529]) ).
fof(f2531,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f2530]) ).
fof(f2532,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f2454]) ).
fof(f2533,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f2532]) ).
fof(f2534,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f2533]) ).
fof(f2536,plain,
! [X0,X1,X2] :
( leq(addition(one,X0),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(one,X0),addition(multiplication(X1,X0),addition(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f103,f2459]) ).
fof(f2537,plain,
! [X0,X1,X2] :
( leq(addition(one,X0),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(one,X0),addition(X1,addition(X2,multiplication(X1,X0)))) ),
inference(forward_demodulation,[status(thm)],[f97,f2536]) ).
fof(f2538,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(one,X1))),X0)
| ~ leq(addition(multiplication(X0,X1),addition(X0,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f103,f2460]) ).
fof(f2539,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(addition(one,X2))),X0)
| ~ leq(addition(X0,addition(X1,multiplication(X0,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f97,f2538]) ).
fof(f2540,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(one,X1))
| ~ leq(addition(multiplication(X0,X1),addition(X0,X2)),addition(one,X1)) ),
inference(forward_demodulation,[status(thm)],[f103,f2461]) ).
fof(f2541,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X1),addition(one,X2))
| ~ leq(addition(X0,addition(X1,multiplication(X0,X2))),addition(one,X2)) ),
inference(forward_demodulation,[status(thm)],[f97,f2540]) ).
fof(f2542,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X1,addition(one,X2)))),
inference(forward_demodulation,[status(thm)],[f103,f2463]) ).
fof(f2543,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X0,addition(multiplication(X1,addition(one,X2)),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f2542]) ).
fof(f2544,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f2464]) ).
fof(f2545,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f153,f2544]) ).
fof(f2546,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(addition(X0,multiplication(X0,X1)),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f2465]) ).
fof(f2547,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f2546]) ).
fof(f2548,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f2547]) ).
fof(f2549,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f153,f2548]) ).
fof(f2551,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f39,f2468]) ).
fof(f2552,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),X2))))
| ~ leq(X0,multiplication(X1,multiplication(X0,addition(one,X2)))) ),
inference(forward_demodulation,[status(thm)],[f39,f2469]) ).
fof(f2553,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,X2)))))
| ~ leq(X0,multiplication(X1,multiplication(X0,addition(one,X2)))) ),
inference(forward_demodulation,[status(thm)],[f39,f2552]) ).
fof(f2554,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f2470]) ).
fof(f2555,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f2554]) ).
fof(f2556,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X1)))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f2555]) ).
fof(f2557,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X1)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f2471]) ).
fof(f2558,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X1)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f2557]) ).
fof(f2560,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(one,X2)),X1),
inference(forward_demodulation,[status(thm)],[f97,f2480]) ).
fof(f2561,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(addition(one,X1),X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2481]) ).
fof(f2562,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,addition(one,X1)))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f2561]) ).
fof(f2563,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(one,X2))) = addition(X1,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f97,f2483]) ).
fof(f2567,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(antidomain(domain(X0)),X1),
inference(paramodulation,[status(thm)],[f67,f186]) ).
fof(f2568,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(antidomain(antidomain(X0)),X1),
inference(paramodulation,[status(thm)],[f62,f186]) ).
fof(f2580,plain,
! [X0] : multiplication(antidomain(c(X0)),one) = multiplication(antidomain(c(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f569,f186]) ).
fof(f2581,plain,
! [X0,X1] : multiplication(antidomain(coantidomain(multiplication(codomain(X0),X1))),coantidomain(multiplication(codomain(X0),X1))) = multiplication(antidomain(coantidomain(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f615,f186]) ).
fof(f2582,plain,
! [X0] : multiplication(antidomain(codomain(X0)),one) = multiplication(antidomain(codomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f683,f186]) ).
fof(f2583,plain,
! [X0,X1] : multiplication(antidomain(antidomain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,domain(X1)))) = multiplication(antidomain(antidomain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f479,f186]) ).
fof(f2584,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f558,f186]) ).
fof(f2585,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(X1,X2))) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f153,f186]) ).
fof(f2586,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(X2,X0),X1)) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f43,f186]) ).
fof(f2587,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(X2,X1))) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f42,f186]) ).
fof(f2588,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f103,f186]) ).
fof(f2589,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(paramodulation,[status(thm)],[f36,f186]) ).
fof(f2591,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(one,X1))) = multiplication(antidomain(multiplication(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f162,f186]) ).
fof(f2592,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,addition(X1,X0))),addition(X1,X0)) = multiplication(antidomain(addition(X0,addition(X1,X0))),X1),
inference(paramodulation,[status(thm)],[f99,f186]) ).
fof(f2593,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,X1)) = multiplication(antidomain(addition(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f105,f186]) ).
fof(f2594,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,addition(X1,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f97,f186]) ).
fof(f2595,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X1,addition(X2,X0))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f97,f186]) ).
fof(f2602,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X1,X0))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f186,f162]) ).
fof(f2604,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = addition(multiplication(antidomain(X0),X2),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f186,f153]) ).
fof(f2605,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,X0),coantidomain(multiplication(antidomain(X0),X1)))) = zero,
inference(paramodulation,[status(thm)],[f186,f144]) ).
fof(f2607,plain,
! [X0,X1] : addition(coantidomain(multiplication(antidomain(X0),X1)),coantidomain(multiplication(codomain(antidomain(X0)),addition(X1,X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),addition(X1,X0))),
inference(paramodulation,[status(thm)],[f186,f615]) ).
fof(f2608,plain,
! [X0,X1] : addition(antidomain(multiplication(antidomain(X0),X1)),antidomain(multiplication(antidomain(X0),domain(addition(X1,X0))))) = antidomain(multiplication(antidomain(X0),domain(addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f186,f479]) ).
fof(f2609,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),X2)))
| ~ leq(addition(X0,X1),addition(multiplication(antidomain(X1),X0),X2)) ),
inference(paramodulation,[status(thm)],[f186,f58]) ).
fof(f2610,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,X0))),antidomain(X0))
| ~ leq(addition(multiplication(antidomain(X0),X1),X2),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f186,f55]) ).
fof(f2611,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X0)),X2),addition(X1,X0))
| ~ leq(addition(multiplication(antidomain(X0),X1),X2),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f186,f53]) ).
fof(f2612,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X2,X1)) = addition(multiplication(X0,addition(X2,X1)),multiplication(antidomain(X1),X2)),
inference(paramodulation,[status(thm)],[f186,f43]) ).
fof(f2613,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X2,X0)) = addition(multiplication(antidomain(X0),X2),multiplication(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f186,f43]) ).
fof(f2614,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f186,f42]) ).
fof(f2615,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(addition(X1,X0),X2)) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f186,f42]) ).
fof(f2616,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X1,X0),X2)) = multiplication(multiplication(antidomain(X0),X1),X2),
inference(paramodulation,[status(thm)],[f186,f39]) ).
fof(f2621,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f67,f2567]) ).
fof(f2622,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f2568]) ).
fof(f2625,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f2580]) ).
fof(f2626,plain,
! [X0,X1] : zero = multiplication(antidomain(coantidomain(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f59,f2581]) ).
fof(f2627,plain,
! [X0] : antidomain(codomain(X0)) = multiplication(antidomain(codomain(X0)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f2582]) ).
fof(f2628,plain,
! [X0,X1] : zero = multiplication(antidomain(antidomain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f59,f2583]) ).
fof(f2629,plain,
! [X0,X1] : zero = multiplication(domain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f62,f2628]) ).
fof(f2630,plain,
! [X0,X1] : zero = domain_difference(multiplication(X0,domain(X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f68,f2629]) ).
fof(f2631,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f2584]) ).
fof(f2632,plain,
! [X0] : c(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f67,f2631]) ).
fof(f2633,plain,
! [X0] : c(X0) = multiplication(c(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f67,f2632]) ).
fof(f2635,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X0),
inference(forward_demodulation,[status(thm)],[f59,f2593]) ).
fof(f2637,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X1,X0))) = multiplication(antidomain(X0),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f162,f2602]) ).
fof(f2640,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f153,f2604]) ).
fof(f2641,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X2,X1)) = addition(multiplication(antidomain(X1),X2),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f35,f2612]) ).
fof(f2642,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2614]) ).
fof(f2643,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X0,addition(X1,X2))) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f103,f2615]) ).
fof(f2644,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,X2)) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f177,f2643]) ).
fof(f2645,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,X2)) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2644]) ).
fof(f2646,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X1,X0),X2)) = multiplication(antidomain(X0),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f2616]) ).
fof(f2648,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,omega(coantidomain(multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f39,f1813]) ).
fof(f2652,plain,
! [X0] : multiplication(coantidomain(X0),omega(codomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f66,f1813]) ).
fof(f2654,plain,
! [X0] : backward_diamond(omega(coantidomain(codomain(X0))),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f1813,f70]) ).
fof(f2657,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,omega(coantidomain(multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f1813,f39]) ).
fof(f2660,plain,
! [X0] : multiplication(X0,addition(one,omega(coantidomain(X0)))) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f1813,f162]) ).
fof(f2661,plain,
! [X0,X1] : multiplication(X0,addition(omega(coantidomain(X0)),X1)) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f1813,f153]) ).
fof(f2662,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(coantidomain(X0)))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f1813,f153]) ).
fof(f2665,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),omega(coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),omega(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f1813,f615]) ).
fof(f2666,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(X0,domain(omega(coantidomain(X0)))))) = antidomain(multiplication(X0,domain(omega(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f1813,f479]) ).
fof(f2667,plain,
! [X0,X1] :
( leq(omega(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(omega(coantidomain(X0)),addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f1813,f58]) ).
fof(f2668,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(coantidomain(X1)))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f1813,f55]) ).
fof(f2669,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),omega(coantidomain(X1)))
| ~ leq(addition(zero,X0),omega(coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f1813,f53]) ).
fof(f2670,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(coantidomain(X1))) = addition(multiplication(X0,omega(coantidomain(X1))),zero),
inference(paramodulation,[status(thm)],[f1813,f43]) ).
fof(f2671,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(coantidomain(X0))) = addition(zero,multiplication(X1,omega(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f1813,f43]) ).
fof(f2672,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(coantidomain(X0)))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f1813,f42]) ).
fof(f2673,plain,
! [X0,X1] : multiplication(X0,addition(omega(coantidomain(X0)),X1)) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f1813,f42]) ).
fof(f2674,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(coantidomain(X0)),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f1813,f39]) ).
fof(f2678,plain,
! [X0] : backward_diamond(omega(coantidomain(codomain(X0))),X0) = zero,
inference(forward_demodulation,[status(thm)],[f737,f2654]) ).
fof(f2684,plain,
! [X0] : multiplication(X0,addition(one,omega(coantidomain(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f37,f2660]) ).
fof(f2685,plain,
! [X0,X1] : multiplication(X0,addition(omega(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f2661]) ).
fof(f2686,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(coantidomain(X0)))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f2662]) ).
fof(f2689,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(X0),omega(coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),omega(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f696,f2665]) ).
fof(f2690,plain,
! [X0] : one = coantidomain(multiplication(codomain(X0),omega(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1377,f2689]) ).
fof(f2691,plain,
! [X0] : addition(one,antidomain(multiplication(X0,domain(omega(coantidomain(X0)))))) = antidomain(multiplication(X0,domain(omega(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f577,f2666]) ).
fof(f2692,plain,
! [X0] : one = antidomain(multiplication(X0,domain(omega(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f1379,f2691]) ).
fof(f2693,plain,
! [X0,X1] :
( leq(omega(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(omega(coantidomain(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f2667]) ).
fof(f2694,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(coantidomain(X1)))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f2668]) ).
fof(f2695,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),omega(coantidomain(X1)))
| ~ leq(X0,omega(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f80,f2669]) ).
fof(f2696,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(coantidomain(X1))) = multiplication(X0,omega(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f37,f2670]) ).
fof(f2697,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(coantidomain(X0))) = multiplication(X1,omega(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f80,f2671]) ).
fof(f2698,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(coantidomain(X0)))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f2672]) ).
fof(f2699,plain,
! [X0,X1] : multiplication(X0,addition(omega(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f2673]) ).
fof(f2700,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(coantidomain(X0)),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f2674]) ).
fof(f2701,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f39,f190]) ).
fof(f2708,plain,
! [X0,X1] : multiplication(multiplication(codomain(X0),X1),coantidomain(multiplication(codomain(X0),X1))) = multiplication(multiplication(codomain(X0),X1),coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f615,f190]) ).
fof(f2709,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f103,f190]) ).
fof(f2710,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f36,f190]) ).
fof(f2716,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(paramodulation,[status(thm)],[f66,f190]) ).
fof(f2718,plain,
! [X0,X1] : backward_diamond(addition(X0,coantidomain(codomain(X1))),X1) = codomain(multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f190,f70]) ).
fof(f2719,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,addition(X1,coantidomain(codomain(X0))))),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(codomain(X0),addition(X1,coantidomain(codomain(X0))))),
inference(paramodulation,[status(thm)],[f190,f615]) ).
fof(f2721,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f190,f39]) ).
fof(f2727,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,coantidomain(X0)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f190,f162]) ).
fof(f2729,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f190,f153]) ).
fof(f2730,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f190,f144]) ).
fof(f2732,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),addition(X1,coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),addition(X1,coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f190,f615]) ).
fof(f2733,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(addition(X1,coantidomain(X0)))))) = antidomain(multiplication(X0,domain(addition(X1,coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f190,f479]) ).
fof(f2734,plain,
! [X0,X1,X2] :
( leq(addition(X0,coantidomain(X1)),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,coantidomain(X1)),addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f190,f58]) ).
fof(f2735,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,coantidomain(X0)))),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f190,f55]) ).
fof(f2736,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(X1,coantidomain(X0)))
| ~ leq(addition(multiplication(X0,X1),X2),addition(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f190,f53]) ).
fof(f2737,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X1))) = addition(multiplication(X0,addition(X2,coantidomain(X1))),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f190,f43]) ).
fof(f2738,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X0))) = addition(multiplication(X0,X2),multiplication(X1,addition(X2,coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f190,f43]) ).
fof(f2739,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f190,f42]) ).
fof(f2741,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f190,f39]) ).
fof(f2742,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f2701]) ).
fof(f2748,plain,
! [X0,X1] : multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(codomain(X0),X1)))) = multiplication(multiplication(codomain(X0),X1),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f2708]) ).
fof(f2749,plain,
! [X0,X1] : zero = multiplication(multiplication(codomain(X0),X1),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f144,f2748]) ).
fof(f2750,plain,
! [X0,X1] : zero = multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f39,f2749]) ).
fof(f2755,plain,
! [X0,X1] : backward_diamond(addition(X0,coantidomain(codomain(X1))),X1) = backward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f70,f2718]) ).
fof(f2756,plain,
! [X0,X1] : addition(coantidomain(multiplication(codomain(X0),X1)),coantidomain(multiplication(X0,addition(X1,coantidomain(codomain(X0)))))) = coantidomain(multiplication(codomain(X0),addition(X1,coantidomain(codomain(X0))))),
inference(forward_demodulation,[status(thm)],[f35,f2719]) ).
fof(f2757,plain,
! [X0,X1] : addition(coantidomain(multiplication(codomain(X0),X1)),coantidomain(multiplication(X0,addition(X1,coantidomain(codomain(X0)))))) = coantidomain(multiplication(codomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f190,f2756]) ).
fof(f2758,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f2721]) ).
fof(f2766,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f153,f2729]) ).
fof(f2767,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X1))) = addition(multiplication(X1,X2),multiplication(X0,addition(X2,coantidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f35,f2737]) ).
fof(f2768,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2739]) ).
fof(f2771,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f2741]) ).
fof(f2772,plain,
! [X0,X1] : addition(divergence(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2232,f48]) ).
fof(f2786,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f97,f2232]) ).
fof(f2787,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f97,f2232]) ).
fof(f2792,plain,
! [X0,X1] : addition(one,addition(X0,divergence(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f2772]) ).
fof(f2793,plain,
! [X0,X1] : addition(codomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2247,f48]) ).
fof(f2794,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f70,f2247]) ).
fof(f2796,plain,
! [X0,X1] : leq(coantidomain(codomain(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f193,f2247]) ).
fof(f2810,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f97,f2247]) ).
fof(f2811,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f97,f2247]) ).
fof(f2816,plain,
! [X0,X1] : addition(one,addition(X0,codomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f2793]) ).
fof(f2822,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f103,f192]) ).
fof(f2823,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f192]) ).
fof(f2828,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(X1,one)) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f43,f192]) ).
fof(f2829,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X1,addition(X0,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f103,f192]) ).
fof(f2830,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f36,f192]) ).
fof(f2832,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = multiplication(X0,addition(one,X1)),
inference(paramodulation,[status(thm)],[f162,f192]) ).
fof(f2835,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X1),one)) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f68,f192]) ).
fof(f2836,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(X2,one)) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f39,f192]) ).
fof(f2838,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(addition(X0,X1),one)) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f177,f192]) ).
fof(f2839,plain,
! [X0] : multiplication(antidomain(X0),addition(omega(X0),one)) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f1569,f192]) ).
fof(f2840,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(multiplication(X0,X1),one)) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f136,f192]) ).
fof(f2845,plain,
! [X0,X1] : multiplication(X0,addition(addition(X1,one),one)) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f192]) ).
fof(f2847,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),one)) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f151,f192]) ).
fof(f2848,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),one)) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f144,f192]) ).
fof(f2849,plain,
! [X0] : multiplication(X0,addition(omega(coantidomain(X0)),one)) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f1813,f192]) ).
fof(f2850,plain,
! [X0] : multiplication(X0,addition(omega(X0),one)) = addition(X0,omega(X0)),
inference(paramodulation,[status(thm)],[f56,f192]) ).
fof(f2858,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f162]) ).
fof(f2859,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,one),X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f153]) ).
fof(f2860,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(addition(X0,multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f192,f153]) ).
fof(f2861,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(addition(X0,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f192,f144]) ).
fof(f2863,plain,
! [X0,X1] : addition(coantidomain(addition(X0,multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),addition(X1,one)))) = coantidomain(multiplication(codomain(X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f192,f615]) ).
fof(f2864,plain,
! [X0,X1] : addition(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(X1,one))))) = antidomain(multiplication(X0,domain(addition(X1,one)))),
inference(paramodulation,[status(thm)],[f192,f479]) ).
fof(f2865,plain,
! [X0,X1,X2] :
( leq(addition(X0,one),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,one),addition(addition(X1,multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f192,f58]) ).
fof(f2866,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,one))),X0)
| ~ leq(addition(addition(X0,multiplication(X0,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f192,f55]) ).
fof(f2867,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(X1,one))
| ~ leq(addition(addition(X0,multiplication(X0,X1)),X2),addition(X1,one)) ),
inference(paramodulation,[status(thm)],[f192,f53]) ).
fof(f2868,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(multiplication(X0,addition(X2,one)),addition(X1,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f192,f43]) ).
fof(f2869,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(addition(X0,multiplication(X0,X2)),multiplication(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f192,f43]) ).
fof(f2870,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f192,f42]) ).
fof(f2872,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,one),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f192,f39]) ).
fof(f2874,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(paramodulation,[status(thm)],[f192,f43]) ).
fof(f2875,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),X2))))
| ~ leq(X0,multiplication(multiplication(X1,X0),addition(X2,one))) ),
inference(paramodulation,[status(thm)],[f192,f58]) ).
fof(f2876,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(multiplication(multiplication(X0,X1),addition(X2,one)),X0) ),
inference(paramodulation,[status(thm)],[f192,f55]) ).
fof(f2877,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X1)
| ~ leq(multiplication(multiplication(X0,X1),addition(X2,one)),X1) ),
inference(paramodulation,[status(thm)],[f192,f53]) ).
fof(f2878,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),X2))) = multiplication(addition(X1,X0),addition(X2,one)),
inference(paramodulation,[status(thm)],[f192,f103]) ).
fof(f2879,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),X2))) = multiplication(addition(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f192,f36]) ).
fof(f2880,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = multiplication(X0,addition(X1,one)),
inference(paramodulation,[status(thm)],[f192,f162]) ).
fof(f2881,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(X1,one))) = multiplication(antidomain(multiplication(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f192,f186]) ).
fof(f2883,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f192,f1421]) ).
fof(f2884,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f192,f1420]) ).
fof(f2885,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f192,f1423]) ).
fof(f2886,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f192,f1324]) ).
fof(f2887,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f192,f105]) ).
fof(f2888,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f192,f103]) ).
fof(f2889,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,X1),multiplication(X0,addition(X1,one)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f192,f99]) ).
fof(f2890,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(X2,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f192,f97]) ).
fof(f2891,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(X2,one))) = addition(multiplication(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f192,f97]) ).
fof(f2892,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != X0
| leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f192,f246]) ).
fof(f2893,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != multiplication(X0,X1)
| leq(X0,multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f192,f49]) ).
fof(f2894,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f192,f36]) ).
fof(f2903,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f39,f2828]) ).
fof(f2910,plain,
! [X0,X1] : multiplication(domain(X0),addition(one,antidomain(X1))) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f2835]) ).
fof(f2911,plain,
! [X0,X1] : multiplication(domain(X0),one) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1379,f2910]) ).
fof(f2912,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f40,f2911]) ).
fof(f2913,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f2836]) ).
fof(f2914,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = multiplication(X0,addition(multiplication(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f153,f2913]) ).
fof(f2915,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = multiplication(X0,addition(X1,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f2914]) ).
fof(f2918,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,addition(X0,one))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f103,f2838]) ).
fof(f2919,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,addition(X0,one))) = multiplication(antidomain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f2918]) ).
fof(f2920,plain,
! [X0] : multiplication(antidomain(X0),addition(one,omega(X0))) = addition(antidomain(X0),zero),
inference(forward_demodulation,[status(thm)],[f35,f2839]) ).
fof(f2921,plain,
! [X0] : multiplication(antidomain(X0),addition(one,omega(X0))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f37,f2920]) ).
fof(f2922,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = addition(antidomain(X0),zero),
inference(forward_demodulation,[status(thm)],[f35,f2840]) ).
fof(f2923,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f37,f2922]) ).
fof(f2935,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f2845]) ).
fof(f2936,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f105,f2935]) ).
fof(f2939,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = addition(X0,zero),
inference(forward_demodulation,[status(thm)],[f35,f2847]) ).
fof(f2940,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = X0,
inference(forward_demodulation,[status(thm)],[f37,f2939]) ).
fof(f2941,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = addition(X0,zero),
inference(forward_demodulation,[status(thm)],[f35,f2848]) ).
fof(f2942,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f37,f2941]) ).
fof(f2943,plain,
! [X0] : multiplication(X0,addition(one,omega(coantidomain(X0)))) = addition(X0,zero),
inference(forward_demodulation,[status(thm)],[f35,f2849]) ).
fof(f2944,plain,
! [X0] : multiplication(X0,addition(one,omega(coantidomain(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f37,f2943]) ).
fof(f2945,plain,
! [X0] : multiplication(X0,addition(one,omega(X0))) = addition(X0,omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f2850]) ).
fof(f2956,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f105,f2858]) ).
fof(f2957,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f2859]) ).
fof(f2958,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(X0,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f2957]) ).
fof(f2959,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f2958]) ).
fof(f2960,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f2860]) ).
fof(f2961,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f2960]) ).
fof(f2962,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f2961]) ).
fof(f2964,plain,
! [X0,X1,X2] :
( leq(addition(X0,one),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,one),addition(multiplication(X1,X0),addition(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f103,f2865]) ).
fof(f2965,plain,
! [X0,X1,X2] :
( leq(addition(X0,one),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,one),addition(X1,addition(X2,multiplication(X1,X0)))) ),
inference(forward_demodulation,[status(thm)],[f97,f2964]) ).
fof(f2966,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,one))),X0)
| ~ leq(addition(multiplication(X0,X1),addition(X0,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f103,f2866]) ).
fof(f2967,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(addition(X2,one))),X0)
| ~ leq(addition(X0,addition(X1,multiplication(X0,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f97,f2966]) ).
fof(f2968,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(X1,one))
| ~ leq(addition(multiplication(X0,X1),addition(X0,X2)),addition(X1,one)) ),
inference(forward_demodulation,[status(thm)],[f103,f2867]) ).
fof(f2969,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X1),addition(X2,one))
| ~ leq(addition(X0,addition(X1,multiplication(X0,X2))),addition(X2,one)) ),
inference(forward_demodulation,[status(thm)],[f97,f2968]) ).
fof(f2970,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(multiplication(X0,X2),addition(X0,multiplication(X1,addition(X2,one)))),
inference(forward_demodulation,[status(thm)],[f103,f2869]) ).
fof(f2971,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X0,addition(multiplication(X1,addition(X2,one)),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f2970]) ).
fof(f2972,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f2870]) ).
fof(f2973,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f153,f2972]) ).
fof(f2979,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f39,f2874]) ).
fof(f2980,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),X2))))
| ~ leq(X0,multiplication(X1,multiplication(X0,addition(X2,one)))) ),
inference(forward_demodulation,[status(thm)],[f39,f2875]) ).
fof(f2981,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,X2)))))
| ~ leq(X0,multiplication(X1,multiplication(X0,addition(X2,one)))) ),
inference(forward_demodulation,[status(thm)],[f39,f2980]) ).
fof(f2982,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,one))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f2876]) ).
fof(f2983,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,one))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f2982]) ).
fof(f2984,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X1)))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,one))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f2983]) ).
fof(f2985,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X1)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,one))),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f2877]) ).
fof(f2986,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X1)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,one))),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f2985]) ).
fof(f2988,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,one)),X1),
inference(forward_demodulation,[status(thm)],[f97,f2888]) ).
fof(f2989,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(addition(X1,one),X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f153,f2889]) ).
fof(f2990,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,addition(X1,X1)))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f2989]) ).
fof(f2991,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f38,f2990]) ).
fof(f2992,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(X2,one))) = addition(X1,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f97,f2891]) ).
fof(f2993,plain,
! [X0,X1] : addition(c(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2264,f48]) ).
fof(f2994,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f72,f2264]) ).
fof(f2995,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f71,f2264]) ).
fof(f2997,plain,
! [X0,X1] : leq(antidomain(c(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f547,f2264]) ).
fof(f2998,plain,
! [X0,X1] : leq(domain(c(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f362,f2264]) ).
fof(f3012,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f97,f2264]) ).
fof(f3013,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f97,f2264]) ).
fof(f3018,plain,
! [X0,X1] : addition(one,addition(X0,c(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f2993]) ).
fof(f3021,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X3,X1)),X2),
inference(paramodulation,[status(thm)],[f97,f170]) ).
fof(f3022,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,X2),multiplication(X1,X3))) = addition(multiplication(X1,addition(X2,X3)),X0),
inference(paramodulation,[status(thm)],[f97,f170]) ).
fof(f3025,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(c(X0),X1),X2)) = addition(multiplication(c(X0),addition(domain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f197,f170]) ).
fof(f3026,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(coantidomain(X0),X1),X2)) = addition(multiplication(coantidomain(X0),addition(codomain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f195,f170]) ).
fof(f3027,plain,
! [X0,X1,X2,X3] : addition(domain_difference(X0,X1),addition(multiplication(domain(X0),X2),X3)) = addition(multiplication(domain(X0),addition(antidomain(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f68,f170]) ).
fof(f3028,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(multiplication(X0,X1),X3),X4)) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(paramodulation,[status(thm)],[f39,f170]) ).
fof(f3030,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),addition(multiplication(antidomain(X0),X2),X3)) = addition(multiplication(antidomain(X0),addition(addition(X0,X1),X2)),X3),
inference(paramodulation,[status(thm)],[f177,f170]) ).
fof(f3031,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(antidomain(X0),X1),X2)) = addition(multiplication(antidomain(X0),addition(omega(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f1569,f170]) ).
fof(f3032,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(antidomain(X0),X1),X2)) = addition(multiplication(antidomain(X0),addition(multiplication(X0,X3),X1)),X2),
inference(paramodulation,[status(thm)],[f136,f170]) ).
fof(f3036,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(codomain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f2309,f170]) ).
fof(f3037,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X0,X1)),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(addition(one,X1),X2)),X3),
inference(paramodulation,[status(thm)],[f162,f170]) ).
fof(f3038,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(addition(coantidomain(X0),X1),X2)),X3),
inference(paramodulation,[status(thm)],[f181,f170]) ).
fof(f3039,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X0,X1)),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(addition(X1,one),X2)),X3),
inference(paramodulation,[status(thm)],[f192,f170]) ).
fof(f3041,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(multiplication(coantidomain(X0),X3),X1)),X2),
inference(paramodulation,[status(thm)],[f151,f170]) ).
fof(f3042,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(multiplication(X3,coantidomain(multiplication(X0,X3))),X1)),X2),
inference(paramodulation,[status(thm)],[f144,f170]) ).
fof(f3043,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(omega(coantidomain(X0)),X1)),X2),
inference(paramodulation,[status(thm)],[f1813,f170]) ).
fof(f3044,plain,
! [X0,X1,X2] : addition(omega(X0),addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(omega(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f56,f170]) ).
fof(f3047,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f40,f170]) ).
fof(f3048,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X0,addition(X2,X3)),X4)) = addition(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X3),X4)),
inference(paramodulation,[status(thm)],[f170,f170]) ).
fof(f3049,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,addition(X2,X3))) = addition(multiplication(X0,addition(X1,X3)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f153,f170]) ).
fof(f3050,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f43,f170]) ).
fof(f3051,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,addition(X2,X3))) = addition(multiplication(X0,addition(X1,X2)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f42,f170]) ).
fof(f3052,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(multiplication(X0,X2),addition(X3,one))) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),X3)),
inference(paramodulation,[status(thm)],[f192,f170]) ).
fof(f3053,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(multiplication(X0,X2),addition(one,X3))) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),X3)),
inference(paramodulation,[status(thm)],[f162,f170]) ).
fof(f3054,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),addition(X3,addition(multiplication(X0,X2),X3))),
inference(paramodulation,[status(thm)],[f99,f170]) ).
fof(f3055,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),X3)),
inference(paramodulation,[status(thm)],[f105,f170]) ).
fof(f3056,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,X4)))) = addition(multiplication(X0,addition(X1,X4)),addition(X2,X3)),
inference(paramodulation,[status(thm)],[f97,f170]) ).
fof(f3057,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),X4))) = addition(multiplication(X0,addition(X1,X3)),addition(X4,X2)),
inference(paramodulation,[status(thm)],[f97,f170]) ).
fof(f3058,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f37,f170]) ).
fof(f3059,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),X2),
inference(paramodulation,[status(thm)],[f35,f170]) ).
fof(f3060,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),X2),
inference(paramodulation,[status(thm)],[f35,f170]) ).
fof(f3061,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f38,f170]) ).
fof(f3062,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(zero,X2)) = addition(multiplication(c(X0),addition(X1,domain(X0))),X2),
inference(paramodulation,[status(thm)],[f197,f170]) ).
fof(f3063,plain,
! [X0,X1,X2] : addition(multiplication(coantidomain(X0),X1),addition(zero,X2)) = addition(multiplication(coantidomain(X0),addition(X1,codomain(X0))),X2),
inference(paramodulation,[status(thm)],[f195,f170]) ).
fof(f3064,plain,
! [X0,X1,X2,X3] : addition(multiplication(domain(X0),X1),addition(domain_difference(X0,X2),X3)) = addition(multiplication(domain(X0),addition(X1,antidomain(X2))),X3),
inference(paramodulation,[status(thm)],[f68,f170]) ).
fof(f3065,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(multiplication(X0,X1),X2),addition(multiplication(X0,multiplication(X1,X3)),X4)) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(paramodulation,[status(thm)],[f39,f170]) ).
fof(f3066,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),addition(multiplication(antidomain(X0),X2),X3)) = addition(multiplication(antidomain(X0),addition(X1,addition(X2,X0))),X3),
inference(paramodulation,[status(thm)],[f186,f170]) ).
fof(f3067,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),addition(multiplication(antidomain(X0),X2),X3)) = addition(multiplication(antidomain(X0),addition(X1,addition(X0,X2))),X3),
inference(paramodulation,[status(thm)],[f177,f170]) ).
fof(f3068,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),addition(zero,X2)) = addition(multiplication(antidomain(X0),addition(X1,omega(X0))),X2),
inference(paramodulation,[status(thm)],[f1569,f170]) ).
fof(f3069,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),addition(zero,X2)) = addition(multiplication(antidomain(X0),addition(X1,multiplication(X0,X3))),X2),
inference(paramodulation,[status(thm)],[f136,f170]) ).
fof(f3073,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,codomain(X0))),X2),
inference(paramodulation,[status(thm)],[f2309,f170]) ).
fof(f3074,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(X0,multiplication(X0,X2)),X3)) = addition(multiplication(X0,addition(X1,addition(one,X2))),X3),
inference(paramodulation,[status(thm)],[f162,f170]) ).
fof(f3075,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,addition(coantidomain(X0),X2))),X3),
inference(paramodulation,[status(thm)],[f181,f170]) ).
fof(f3076,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(X0,multiplication(X0,X2)),X3)) = addition(multiplication(X0,addition(X1,addition(X2,one))),X3),
inference(paramodulation,[status(thm)],[f192,f170]) ).
fof(f3077,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))),X3),
inference(paramodulation,[status(thm)],[f190,f170]) ).
fof(f3078,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(X0,addition(X1,multiplication(coantidomain(X0),X3))),X2),
inference(paramodulation,[status(thm)],[f151,f170]) ).
fof(f3079,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(X0,addition(X1,multiplication(X3,coantidomain(multiplication(X0,X3))))),X2),
inference(paramodulation,[status(thm)],[f144,f170]) ).
fof(f3080,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(X0,addition(X1,omega(coantidomain(X0)))),X2),
inference(paramodulation,[status(thm)],[f1813,f170]) ).
fof(f3081,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(omega(X0),X2)) = addition(multiplication(X0,addition(X1,omega(X0))),X2),
inference(paramodulation,[status(thm)],[f56,f170]) ).
fof(f3084,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f40,f170]) ).
fof(f3085,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),addition(multiplication(X1,X2),X3))))
| ~ leq(X0,addition(multiplication(X1,addition(X0,X2)),X3)) ),
inference(paramodulation,[status(thm)],[f170,f58]) ).
fof(f3086,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(multiplication(X0,X2),X3),star(X1)),X0)
| ~ leq(addition(multiplication(X0,addition(X1,X2)),X3),X0) ),
inference(paramodulation,[status(thm)],[f170,f55]) ).
fof(f3087,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),addition(multiplication(X0,X2),X3)),X1)
| ~ leq(addition(multiplication(X0,addition(X1,X2)),X3),X1) ),
inference(paramodulation,[status(thm)],[f170,f53]) ).
fof(f3089,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(X0,addition(X2,X1)),X3)),
inference(paramodulation,[status(thm)],[f170,f1421]) ).
fof(f3093,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X3,X1)),X2),
inference(paramodulation,[status(thm)],[f170,f97]) ).
fof(f3094,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f170,f97]) ).
fof(f3095,plain,
! [X0,X1,X2,X3] : multiplication(antidomain(addition(multiplication(X0,X1),X2)),addition(multiplication(X0,addition(X3,X1)),X2)) = multiplication(antidomain(addition(multiplication(X0,X1),X2)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f170,f186]) ).
fof(f3096,plain,
! [X0,X1,X2,X3] : multiplication(antidomain(multiplication(X0,X1)),addition(multiplication(X0,addition(X1,X2)),X3)) = multiplication(antidomain(multiplication(X0,X1)),addition(multiplication(X0,X2),X3)),
inference(paramodulation,[status(thm)],[f170,f177]) ).
fof(f3097,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(X0,addition(X1,X3)),X4))),
inference(paramodulation,[status(thm)],[f170,f1421]) ).
fof(f3098,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),addition(X3,addition(multiplication(X0,addition(X4,X1)),X2))),
inference(paramodulation,[status(thm)],[f170,f1420]) ).
fof(f3099,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(X0,addition(X3,X1)),X2)),
inference(paramodulation,[status(thm)],[f170,f1423]) ).
fof(f3100,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(X0,addition(X1,X2)),X3)),
inference(paramodulation,[status(thm)],[f170,f1324]) ).
fof(f3102,plain,
! [X0,X1,X2,X3,X4] : addition(addition(multiplication(X0,X1),X2),addition(multiplication(X0,X3),X4)) = addition(addition(multiplication(X0,addition(X3,X1)),X2),X4),
inference(paramodulation,[status(thm)],[f170,f103]) ).
fof(f3103,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(multiplication(X0,X2),X3),addition(multiplication(X0,addition(X1,X2)),X3))) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)),
inference(paramodulation,[status(thm)],[f170,f99]) ).
fof(f3104,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(addition(multiplication(X0,X2),X3),X4)) = addition(X4,addition(multiplication(X0,addition(X1,X2)),X3)),
inference(paramodulation,[status(thm)],[f170,f97]) ).
fof(f3105,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) = addition(addition(multiplication(X1,X3),X4),addition(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f170,f97]) ).
fof(f3106,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X3,X1)),X2) != multiplication(X0,X3)
| leq(addition(multiplication(X0,X1),X2),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f170,f246]) ).
fof(f3107,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X1,X2)),X3) != addition(multiplication(X0,X2),X3)
| leq(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) ),
inference(paramodulation,[status(thm)],[f170,f49]) ).
fof(f3108,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(addition(multiplication(X0,X2),X3),X4)) = addition(addition(multiplication(X0,addition(X1,X2)),X3),X4),
inference(paramodulation,[status(thm)],[f170,f36]) ).
fof(f3116,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,addition(X3,X2)),X0),
inference(forward_demodulation,[status(thm)],[f153,f3022]) ).
fof(f3121,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),X2) = addition(multiplication(c(X0),addition(domain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f3025]) ).
fof(f3122,plain,
! [X0,X1,X2] : addition(multiplication(coantidomain(X0),X1),X2) = addition(multiplication(coantidomain(X0),addition(codomain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f3026]) ).
fof(f3123,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X0,multiplication(X1,X3)),X4)) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(forward_demodulation,[status(thm)],[f39,f3028]) ).
fof(f3124,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),X4) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(forward_demodulation,[status(thm)],[f170,f3123]) ).
fof(f3125,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,addition(X2,X3))),X4) = addition(multiplication(multiplication(X0,X1),addition(X3,X2)),X4),
inference(forward_demodulation,[status(thm)],[f153,f3124]) ).
fof(f3126,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,addition(X2,X3))),X4) = addition(multiplication(X0,multiplication(X1,addition(X3,X2))),X4),
inference(forward_demodulation,[status(thm)],[f39,f3125]) ).
fof(f3129,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),addition(X1,X2)),X3) = addition(multiplication(antidomain(X0),addition(addition(X0,X1),X2)),X3),
inference(forward_demodulation,[status(thm)],[f170,f3030]) ).
fof(f3130,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),addition(X1,X2)),X3) = addition(multiplication(antidomain(X0),addition(X1,addition(X0,X2))),X3),
inference(forward_demodulation,[status(thm)],[f103,f3129]) ).
fof(f3131,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),X2) = addition(multiplication(antidomain(X0),addition(omega(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f3031]) ).
fof(f3132,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),X2) = addition(multiplication(antidomain(X0),addition(multiplication(X0,X3),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f3032]) ).
fof(f3140,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X0,addition(multiplication(X0,X2),X3))) = addition(multiplication(X0,addition(addition(one,X1),X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f3037]) ).
fof(f3141,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(multiplication(X0,X1),X2),multiplication(X0,X3))) = addition(multiplication(X0,addition(addition(one,X3),X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f3140]) ).
fof(f3142,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(multiplication(X0,X2),multiplication(X0,X3)))) = addition(multiplication(X0,addition(addition(one,X3),X2)),X1),
inference(forward_demodulation,[status(thm)],[f103,f3141]) ).
fof(f3143,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(addition(one,X2),X3)),X1),
inference(forward_demodulation,[status(thm)],[f153,f3142]) ).
fof(f3144,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(X2,addition(one,X3))),X1),
inference(forward_demodulation,[status(thm)],[f103,f3143]) ).
fof(f3145,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(addition(coantidomain(X0),X1),X2)),X3),
inference(forward_demodulation,[status(thm)],[f170,f3038]) ).
fof(f3146,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X1,addition(coantidomain(X0),X2))),X3),
inference(forward_demodulation,[status(thm)],[f103,f3145]) ).
fof(f3147,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X0,addition(multiplication(X0,X2),X3))) = addition(multiplication(X0,addition(addition(X1,one),X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f3039]) ).
fof(f3148,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(multiplication(X0,X1),X2),multiplication(X0,X3))) = addition(multiplication(X0,addition(addition(X3,one),X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f3147]) ).
fof(f3149,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(multiplication(X0,X2),multiplication(X0,X3)))) = addition(multiplication(X0,addition(addition(X3,one),X2)),X1),
inference(forward_demodulation,[status(thm)],[f103,f3148]) ).
fof(f3150,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(addition(X2,one),X3)),X1),
inference(forward_demodulation,[status(thm)],[f153,f3149]) ).
fof(f3151,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(one,addition(X2,X3))),X1),
inference(forward_demodulation,[status(thm)],[f103,f3150]) ).
fof(f3154,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),X2) = addition(multiplication(X0,addition(multiplication(coantidomain(X0),X3),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f3041]) ).
fof(f3155,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),X2) = addition(multiplication(X0,addition(multiplication(X3,coantidomain(multiplication(X0,X3))),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f3042]) ).
fof(f3156,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),X2) = addition(multiplication(X0,addition(omega(coantidomain(X0)),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f3043]) ).
fof(f3159,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(X1,addition(X2,X3))),X4) = addition(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X3),X4)),
inference(forward_demodulation,[status(thm)],[f170,f3048]) ).
fof(f3160,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(X1,addition(X2,X3))),X4) = addition(multiplication(X0,addition(addition(X1,X2),X3)),X4),
inference(forward_demodulation,[status(thm)],[f170,f3159]) ).
fof(f3161,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(X1,addition(X2,X3))),X4) = addition(multiplication(X0,addition(X2,addition(X1,X3))),X4),
inference(forward_demodulation,[status(thm)],[f103,f3160]) ).
fof(f3162,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(addition(X1,X2),X3)) = addition(multiplication(X0,addition(X3,X2)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f153,f3049]) ).
fof(f3163,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = addition(multiplication(X0,addition(X3,X1)),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f3162]) ).
fof(f3164,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = multiplication(X0,addition(X2,addition(X3,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3163]) ).
fof(f3165,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(addition(X1,X2),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f153,f3051]) ).
fof(f3166,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = addition(multiplication(X0,addition(X3,X2)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f3165]) ).
fof(f3167,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = multiplication(X0,addition(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f153,f3166]) ).
fof(f3168,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,multiplication(X2,addition(X3,one)))) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f39,f3052]) ).
fof(f3169,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(X2,one)),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f153,f3168]) ).
fof(f3170,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(X2,one)),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f3169]) ).
fof(f3171,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(X2,one)),X3)) = multiplication(X0,addition(multiplication(X1,X2),addition(X3,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3170]) ).
fof(f3172,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(X2,one)),X3)) = multiplication(X0,addition(X1,addition(multiplication(X1,X2),X3))),
inference(forward_demodulation,[status(thm)],[f97,f3171]) ).
fof(f3173,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,multiplication(X2,addition(one,X3)))) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f39,f3053]) ).
fof(f3174,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(one,X2)),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f153,f3173]) ).
fof(f3175,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(one,X2)),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f3174]) ).
fof(f3176,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(one,X2)),X3)) = multiplication(X0,addition(multiplication(X1,X2),addition(X3,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3175]) ).
fof(f3177,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(one,X2)),X3)) = multiplication(X0,addition(X1,addition(multiplication(X1,X2),X3))),
inference(forward_demodulation,[status(thm)],[f97,f3176]) ).
fof(f3178,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X1,X2)),addition(X3,addition(multiplication(X0,X2),X3))),
inference(forward_demodulation,[status(thm)],[f170,f3054]) ).
fof(f3179,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f170,f3055]) ).
fof(f3180,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(addition(X1,X2),X2)),X3),
inference(forward_demodulation,[status(thm)],[f170,f3179]) ).
fof(f3181,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X2,addition(X1,X2))),X3),
inference(forward_demodulation,[status(thm)],[f103,f3180]) ).
fof(f3182,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),zero),
inference(forward_demodulation,[status(thm)],[f153,f3058]) ).
fof(f3183,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f37,f3182]) ).
fof(f3184,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f153,f3061]) ).
fof(f3185,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3184]) ).
fof(f3186,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(c(X1),X2))) = addition(multiplication(c(X1),addition(X2,domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f97,f3062]) ).
fof(f3187,plain,
! [X0,X1,X2] : addition(X0,multiplication(c(X1),X2)) = addition(multiplication(c(X1),addition(X2,domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f80,f3186]) ).
fof(f3188,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(coantidomain(X1),X2))) = addition(multiplication(coantidomain(X1),addition(X2,codomain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f97,f3063]) ).
fof(f3189,plain,
! [X0,X1,X2] : addition(X0,multiplication(coantidomain(X1),X2)) = addition(multiplication(coantidomain(X1),addition(X2,codomain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f80,f3188]) ).
fof(f3190,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X0,multiplication(X1,X3)),X4)) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(forward_demodulation,[status(thm)],[f39,f3065]) ).
fof(f3191,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),X4) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(forward_demodulation,[status(thm)],[f170,f3190]) ).
fof(f3192,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,addition(X2,X3))),X4) = addition(multiplication(multiplication(X0,X1),addition(X3,X2)),X4),
inference(forward_demodulation,[status(thm)],[f153,f3191]) ).
fof(f3193,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,addition(X2,X3))),X4) = addition(multiplication(X0,multiplication(X1,addition(X3,X2))),X4),
inference(forward_demodulation,[status(thm)],[f39,f3192]) ).
fof(f3194,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),addition(X1,X2)),X3) = addition(multiplication(antidomain(X0),addition(X1,addition(X2,X0))),X3),
inference(forward_demodulation,[status(thm)],[f170,f3066]) ).
fof(f3195,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),addition(X1,X2)),X3) = addition(multiplication(antidomain(X0),addition(X1,addition(X0,X2))),X3),
inference(forward_demodulation,[status(thm)],[f170,f3067]) ).
fof(f3196,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(antidomain(X1),X2))) = addition(multiplication(antidomain(X1),addition(X2,omega(X1))),X0),
inference(forward_demodulation,[status(thm)],[f97,f3068]) ).
fof(f3197,plain,
! [X0,X1,X2] : addition(X0,multiplication(antidomain(X1),X2)) = addition(multiplication(antidomain(X1),addition(X2,omega(X1))),X0),
inference(forward_demodulation,[status(thm)],[f80,f3196]) ).
fof(f3198,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(antidomain(X1),X2))) = addition(multiplication(antidomain(X1),addition(X2,multiplication(X1,X3))),X0),
inference(forward_demodulation,[status(thm)],[f97,f3069]) ).
fof(f3199,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(antidomain(X1),X2)) = addition(multiplication(antidomain(X1),addition(X2,multiplication(X1,X3))),X0),
inference(forward_demodulation,[status(thm)],[f80,f3198]) ).
fof(f3210,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,codomain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f97,f3073]) ).
fof(f3211,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),addition(X0,X3))) = addition(multiplication(X0,addition(X1,addition(one,X2))),X3),
inference(forward_demodulation,[status(thm)],[f103,f3074]) ).
fof(f3212,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),addition(X0,X3)) = addition(multiplication(X0,addition(X1,addition(one,X2))),X3),
inference(forward_demodulation,[status(thm)],[f170,f3211]) ).
fof(f3213,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(X2,addition(one,X3))),X1),
inference(forward_demodulation,[status(thm)],[f97,f3212]) ).
fof(f3214,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X1,addition(coantidomain(X0),X2))),X3),
inference(forward_demodulation,[status(thm)],[f170,f3075]) ).
fof(f3215,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),addition(X0,X3))) = addition(multiplication(X0,addition(X1,addition(X2,one))),X3),
inference(forward_demodulation,[status(thm)],[f103,f3076]) ).
fof(f3216,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),addition(X0,X3)) = addition(multiplication(X0,addition(X1,addition(X2,one))),X3),
inference(forward_demodulation,[status(thm)],[f170,f3215]) ).
fof(f3217,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(X2,addition(X3,one))),X1),
inference(forward_demodulation,[status(thm)],[f97,f3216]) ).
fof(f3218,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))),X3),
inference(forward_demodulation,[status(thm)],[f170,f3077]) ).
fof(f3219,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(X1,X2))) = addition(multiplication(X1,addition(X2,multiplication(coantidomain(X1),X3))),X0),
inference(forward_demodulation,[status(thm)],[f97,f3078]) ).
fof(f3220,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,X2)) = addition(multiplication(X1,addition(X2,multiplication(coantidomain(X1),X3))),X0),
inference(forward_demodulation,[status(thm)],[f80,f3219]) ).
fof(f3221,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(X1,X2))) = addition(multiplication(X1,addition(X2,multiplication(X3,coantidomain(multiplication(X1,X3))))),X0),
inference(forward_demodulation,[status(thm)],[f97,f3079]) ).
fof(f3222,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,X2)) = addition(multiplication(X1,addition(X2,multiplication(X3,coantidomain(multiplication(X1,X3))))),X0),
inference(forward_demodulation,[status(thm)],[f80,f3221]) ).
fof(f3223,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,X2))) = addition(multiplication(X1,addition(X2,omega(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f97,f3080]) ).
fof(f3224,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,X2)) = addition(multiplication(X1,addition(X2,omega(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f80,f3223]) ).
fof(f3225,plain,
! [X0,X1,X2] : addition(omega(X0),addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,omega(X0))),X1),
inference(forward_demodulation,[status(thm)],[f97,f3081]) ).
fof(f3232,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,one)),X1),
inference(forward_demodulation,[status(thm)],[f97,f3084]) ).
fof(f3241,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3094]) ).
fof(f3244,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4))) = addition(addition(multiplication(X1,addition(X3,X2)),X0),X4),
inference(forward_demodulation,[status(thm)],[f103,f3102]) ).
fof(f3245,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) = addition(addition(multiplication(X1,addition(X3,X2)),X0),X4),
inference(forward_demodulation,[status(thm)],[f170,f3244]) ).
fof(f3246,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) = addition(X0,addition(multiplication(X1,addition(X3,X2)),X4)),
inference(forward_demodulation,[status(thm)],[f103,f3245]) ).
fof(f3247,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),addition(multiplication(X0,addition(X1,X3)),X2)))) = addition(multiplication(X0,X1),addition(multiplication(X0,X3),X2)),
inference(forward_demodulation,[status(thm)],[f103,f3103]) ).
fof(f3248,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,addition(X3,addition(X1,X3))),X2))) = addition(multiplication(X0,X1),addition(multiplication(X0,X3),X2)),
inference(forward_demodulation,[status(thm)],[f170,f3247]) ).
fof(f3249,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,addition(X3,addition(X1,X3))),X2))) = addition(multiplication(X0,addition(X1,X3)),X2),
inference(forward_demodulation,[status(thm)],[f170,f3248]) ).
fof(f3250,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),X4))) = addition(X4,addition(multiplication(X0,addition(X1,X3)),X2)),
inference(forward_demodulation,[status(thm)],[f103,f3104]) ).
fof(f3251,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) = addition(X4,addition(multiplication(X1,X3),addition(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f103,f3105]) ).
fof(f3252,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),X4))) = addition(addition(multiplication(X0,addition(X1,X3)),X2),X4),
inference(forward_demodulation,[status(thm)],[f103,f3108]) ).
fof(f3253,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),X4))) = addition(X2,addition(multiplication(X0,addition(X1,X3)),X4)),
inference(forward_demodulation,[status(thm)],[f103,f3252]) ).
fof(f3258,plain,
! [X0,X1] : addition(antidomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2373,f48]) ).
fof(f3275,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f97,f2373]) ).
fof(f3276,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f97,f2373]) ).
fof(f3281,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f3258]) ).
fof(f3282,plain,
! [X0,X1] : addition(coantidomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2387,f48]) ).
fof(f3298,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f97,f2387]) ).
fof(f3299,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f97,f2387]) ).
fof(f3304,plain,
! [X0,X1] : addition(one,addition(X0,coantidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f3282]) ).
fof(f3305,plain,
! [X0,X1] : addition(domain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2403,f48]) ).
fof(f3306,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f69,f2403]) ).
fof(f3323,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f97,f2403]) ).
fof(f3324,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f97,f2403]) ).
fof(f3329,plain,
! [X0,X1] : addition(one,addition(X0,domain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f3305]) ).
fof(f3330,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),X0),
inference(resolution,[status(thm)],[f2492,f246]) ).
fof(f3333,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),divergence(X2)))),
inference(paramodulation,[status(thm)],[f103,f2492]) ).
fof(f3334,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),divergence(X2)))),
inference(paramodulation,[status(thm)],[f36,f2492]) ).
fof(f3352,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),divergence(X3))),
inference(paramodulation,[status(thm)],[f2492,f170]) ).
fof(f3353,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),divergence(X2)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2492,f58]) ).
fof(f3354,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),divergence(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2492,f55]) ).
fof(f3355,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),divergence(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2492,f53]) ).
fof(f3356,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),divergence(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2492,f103]) ).
fof(f3357,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),divergence(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2492,f36]) ).
fof(f3364,plain,
! [X0,X1,X2] : leq(multiplication(X0,divergence(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2492,f1420]) ).
fof(f3368,plain,
! [X0,X1,X2] : addition(multiplication(X0,divergence(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2492,f103]) ).
fof(f3370,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,divergence(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2492,f97]) ).
fof(f3371,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,divergence(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2492,f97]) ).
fof(f3373,plain,
! [X0,X1] :
( X0 != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(paramodulation,[status(thm)],[f2492,f49]) ).
fof(f3374,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,divergence(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2492,f36]) ).
fof(f3386,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),divergence(X3))),
inference(forward_demodulation,[status(thm)],[f153,f3352]) ).
fof(f3387,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,divergence(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f3386]) ).
fof(f3388,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,divergence(X3)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3387]) ).
fof(f3389,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,divergence(X3)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f3388]) ).
fof(f3390,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,divergence(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f3353]) ).
fof(f3391,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(divergence(X2),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3354]) ).
fof(f3392,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(divergence(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3391]) ).
fof(f3393,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,divergence(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f3355]) ).
fof(f3399,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,divergence(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f3368]) ).
fof(f3401,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,divergence(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f3371]) ).
fof(f3404,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,divergence(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f3330]) ).
fof(f3411,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),X0),
inference(resolution,[status(thm)],[f2493,f246]) ).
fof(f3414,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),codomain(X2)))),
inference(paramodulation,[status(thm)],[f103,f2493]) ).
fof(f3415,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),codomain(X2)))),
inference(paramodulation,[status(thm)],[f36,f2493]) ).
fof(f3427,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,coantidomain(codomain(X1)))),
inference(paramodulation,[status(thm)],[f193,f2493]) ).
fof(f3438,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),codomain(X3))),
inference(paramodulation,[status(thm)],[f2493,f170]) ).
fof(f3439,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),codomain(X2)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2493,f58]) ).
fof(f3440,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),codomain(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2493,f55]) ).
fof(f3441,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),codomain(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2493,f53]) ).
fof(f3442,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),codomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2493,f103]) ).
fof(f3443,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),codomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2493,f36]) ).
fof(f3450,plain,
! [X0,X1,X2] : leq(multiplication(X0,codomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2493,f1420]) ).
fof(f3454,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2493,f103]) ).
fof(f3456,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,codomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2493,f97]) ).
fof(f3457,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,codomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2493,f97]) ).
fof(f3459,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f2493,f49]) ).
fof(f3460,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,codomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2493,f36]) ).
fof(f3473,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),codomain(X3))),
inference(forward_demodulation,[status(thm)],[f153,f3438]) ).
fof(f3474,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,codomain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f3473]) ).
fof(f3475,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,codomain(X3)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3474]) ).
fof(f3476,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,codomain(X3)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f3475]) ).
fof(f3477,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,codomain(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f3439]) ).
fof(f3478,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(codomain(X2),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3440]) ).
fof(f3479,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(codomain(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3478]) ).
fof(f3480,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,codomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f3441]) ).
fof(f3486,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,codomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f3454]) ).
fof(f3488,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,codomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f3457]) ).
fof(f3492,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,codomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f3411]) ).
fof(f3497,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f70,f3411]) ).
fof(f3505,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f43,f201]) ).
fof(f3509,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(paramodulation,[status(thm)],[f192,f201]) ).
fof(f3510,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(paramodulation,[status(thm)],[f162,f201]) ).
fof(f3514,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = addition(zero,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f197,f201]) ).
fof(f3515,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = addition(zero,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f195,f201]) ).
fof(f3516,plain,
! [X0,X1,X2] : multiplication(addition(X0,domain(X1)),antidomain(X2)) = addition(domain_difference(X1,X2),multiplication(X0,antidomain(X2))),
inference(paramodulation,[status(thm)],[f68,f201]) ).
fof(f3517,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f39,f201]) ).
fof(f3518,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X2,X1)) = addition(multiplication(antidomain(X1),X2),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f186,f201]) ).
fof(f3519,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X1,X2)) = addition(multiplication(antidomain(X1),X2),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f177,f201]) ).
fof(f3520,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),omega(X1)) = addition(zero,multiplication(X0,omega(X1))),
inference(paramodulation,[status(thm)],[f1569,f201]) ).
fof(f3521,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = addition(zero,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f136,f201]) ).
fof(f3522,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f59,f201]) ).
fof(f3524,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f41,f201]) ).
fof(f3525,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(X1,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f2309,f201]) ).
fof(f3526,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(addition(X1,multiplication(X1,X2)),multiplication(X0,addition(one,X2))),
inference(paramodulation,[status(thm)],[f162,f201]) ).
fof(f3527,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X1),X2)) = addition(multiplication(X1,X2),multiplication(X0,addition(coantidomain(X1),X2))),
inference(paramodulation,[status(thm)],[f181,f201]) ).
fof(f3528,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(addition(X1,multiplication(X1,X2)),multiplication(X0,addition(X2,one))),
inference(paramodulation,[status(thm)],[f192,f201]) ).
fof(f3529,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X1))) = addition(multiplication(X1,X2),multiplication(X0,addition(X2,coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f190,f201]) ).
fof(f3530,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = addition(zero,multiplication(X0,multiplication(coantidomain(X1),X2))),
inference(paramodulation,[status(thm)],[f151,f201]) ).
fof(f3531,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = addition(zero,multiplication(X0,multiplication(X2,coantidomain(multiplication(X1,X2))))),
inference(paramodulation,[status(thm)],[f144,f201]) ).
fof(f3532,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(coantidomain(X1))) = addition(zero,multiplication(X0,omega(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f1813,f201]) ).
fof(f3533,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = addition(omega(X1),multiplication(X0,omega(X1))),
inference(paramodulation,[status(thm)],[f56,f201]) ).
fof(f3534,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(zero,multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f63,f201]) ).
fof(f3537,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = addition(multiplication(X1,domain(X0)),zero),
inference(paramodulation,[status(thm)],[f197,f201]) ).
fof(f3538,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = addition(multiplication(X1,codomain(X0)),zero),
inference(paramodulation,[status(thm)],[f195,f201]) ).
fof(f3539,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),X1),antidomain(X2)) = addition(multiplication(X1,antidomain(X2)),domain_difference(X0,X2)),
inference(paramodulation,[status(thm)],[f68,f201]) ).
fof(f3540,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f39,f201]) ).
fof(f3541,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X2,X0)) = addition(multiplication(X1,addition(X2,X0)),multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f186,f201]) ).
fof(f3542,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X0,X2)) = addition(multiplication(X1,addition(X0,X2)),multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f177,f201]) ).
fof(f3543,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),omega(X0)) = addition(multiplication(X1,omega(X0)),zero),
inference(paramodulation,[status(thm)],[f1569,f201]) ).
fof(f3544,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = addition(multiplication(X1,multiplication(X0,X2)),zero),
inference(paramodulation,[status(thm)],[f136,f201]) ).
fof(f3545,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(multiplication(X1,X0),zero),
inference(paramodulation,[status(thm)],[f59,f201]) ).
fof(f3547,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f41,f201]) ).
fof(f3548,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(multiplication(X1,codomain(X0)),X0),
inference(paramodulation,[status(thm)],[f2309,f201]) ).
fof(f3549,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(multiplication(X1,addition(one,X2)),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f162,f201]) ).
fof(f3550,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X0),X2)) = addition(multiplication(X1,addition(coantidomain(X0),X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f181,f201]) ).
fof(f3551,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(multiplication(X1,addition(X2,one)),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f192,f201]) ).
fof(f3552,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X0))) = addition(multiplication(X1,addition(X2,coantidomain(X0))),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f190,f201]) ).
fof(f3553,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = addition(multiplication(X1,multiplication(coantidomain(X0),X2)),zero),
inference(paramodulation,[status(thm)],[f151,f201]) ).
fof(f3554,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X0,X2)))) = addition(multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,X2)))),zero),
inference(paramodulation,[status(thm)],[f144,f201]) ).
fof(f3555,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(coantidomain(X0))) = addition(multiplication(X1,omega(coantidomain(X0))),zero),
inference(paramodulation,[status(thm)],[f1813,f201]) ).
fof(f3556,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = addition(multiplication(X1,omega(X0)),omega(X0)),
inference(paramodulation,[status(thm)],[f56,f201]) ).
fof(f3557,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(multiplication(X1,coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f63,f201]) ).
fof(f3561,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f201,f43]) ).
fof(f3563,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,X0),X3)) = addition(multiplication(X0,addition(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f201,f170]) ).
fof(f3564,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(X1,X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f201,f58]) ).
fof(f3565,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X2)),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f201,f55]) ).
fof(f3566,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f201,f53]) ).
fof(f3569,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(X1,one)) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f201,f192]) ).
fof(f3570,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(one,X1)) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f201,f162]) ).
fof(f3571,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(X0,X2),X1)) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f201,f186]) ).
fof(f3572,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(X2,X0),X1)) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f201,f177]) ).
fof(f3573,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f201,f1421]) ).
fof(f3574,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f201,f1420]) ).
fof(f3575,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f201,f1423]) ).
fof(f3576,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f201,f1324]) ).
fof(f3577,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(addition(X2,X0),X1)) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f201,f105]) ).
fof(f3578,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f201,f103]) ).
fof(f3580,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(X3,multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f201,f97]) ).
fof(f3581,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(X1,X3),addition(X0,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f201,f97]) ).
fof(f3582,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f201,f246]) ).
fof(f3583,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f201,f49]) ).
fof(f3584,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X2,X0),X1),X3),
inference(paramodulation,[status(thm)],[f201,f36]) ).
fof(f3592,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f35,f3509]) ).
fof(f3593,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f39,f3592]) ).
fof(f3594,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f35,f3510]) ).
fof(f3595,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f39,f3594]) ).
fof(f3596,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f80,f3514]) ).
fof(f3597,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f80,f3515]) ).
fof(f3598,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),omega(X1)) = multiplication(X0,omega(X1)),
inference(forward_demodulation,[status(thm)],[f80,f3520]) ).
fof(f3599,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f80,f3521]) ).
fof(f3600,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f3522]) ).
fof(f3602,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(multiplication(X1,X2),addition(X1,multiplication(X0,addition(one,X2)))),
inference(forward_demodulation,[status(thm)],[f103,f3526]) ).
fof(f3603,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X1,addition(multiplication(X0,addition(one,X2)),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f97,f3602]) ).
fof(f3604,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(multiplication(X1,X2),addition(X1,multiplication(X0,addition(X2,one)))),
inference(forward_demodulation,[status(thm)],[f103,f3528]) ).
fof(f3605,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X1,addition(multiplication(X0,addition(X2,one)),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f97,f3604]) ).
fof(f3606,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f80,f3530]) ).
fof(f3607,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(X0,multiplication(X2,coantidomain(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f80,f3531]) ).
fof(f3608,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(coantidomain(X1))) = multiplication(X0,omega(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f80,f3532]) ).
fof(f3609,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f80,f3534]) ).
fof(f3614,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f3537]) ).
fof(f3615,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f3538]) ).
fof(f3616,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X2,X0)) = addition(multiplication(antidomain(X0),X2),multiplication(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f35,f3541]) ).
fof(f3617,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X0,X2)) = addition(multiplication(antidomain(X0),X2),multiplication(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f35,f3542]) ).
fof(f3618,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),omega(X0)) = multiplication(X1,omega(X0)),
inference(forward_demodulation,[status(thm)],[f37,f3543]) ).
fof(f3619,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f37,f3544]) ).
fof(f3620,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f37,f3545]) ).
fof(f3622,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f3547]) ).
fof(f3623,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(X0,multiplication(X1,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f3548]) ).
fof(f3624,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X0),X2)) = addition(multiplication(X0,X2),multiplication(X1,addition(coantidomain(X0),X2))),
inference(forward_demodulation,[status(thm)],[f35,f3550]) ).
fof(f3625,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X0))) = addition(multiplication(X0,X2),multiplication(X1,addition(X2,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f3552]) ).
fof(f3626,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f37,f3553]) ).
fof(f3627,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X0,X2)))) = multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f37,f3554]) ).
fof(f3628,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(coantidomain(X0))) = multiplication(X1,omega(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f3555]) ).
fof(f3629,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = addition(omega(X0),multiplication(X1,omega(X0))),
inference(forward_demodulation,[status(thm)],[f35,f3556]) ).
fof(f3630,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f3557]) ).
fof(f3637,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f3565]) ).
fof(f3640,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f39,f3569]) ).
fof(f3641,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f35,f3640]) ).
fof(f3642,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f39,f3570]) ).
fof(f3643,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f35,f3642]) ).
fof(f3644,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f201,f3577]) ).
fof(f3645,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X0)),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f3644]) ).
fof(f3646,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f201,f3645]) ).
fof(f3652,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),X0),
inference(resolution,[status(thm)],[f2494,f246]) ).
fof(f3656,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),c(X2)))),
inference(paramodulation,[status(thm)],[f103,f2494]) ).
fof(f3657,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),c(X2)))),
inference(paramodulation,[status(thm)],[f36,f2494]) ).
fof(f3668,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f547,f2494]) ).
fof(f3669,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f362,f2494]) ).
fof(f3681,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),c(X3))),
inference(paramodulation,[status(thm)],[f2494,f170]) ).
fof(f3682,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),c(X2)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2494,f58]) ).
fof(f3683,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),c(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2494,f55]) ).
fof(f3684,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),c(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2494,f53]) ).
fof(f3685,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),c(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2494,f103]) ).
fof(f3686,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),c(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2494,f36]) ).
fof(f3693,plain,
! [X0,X1,X2] : leq(multiplication(X0,c(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2494,f1420]) ).
fof(f3697,plain,
! [X0,X1,X2] : addition(multiplication(X0,c(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2494,f103]) ).
fof(f3699,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,c(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2494,f97]) ).
fof(f3700,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,c(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2494,f97]) ).
fof(f3702,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f2494,f49]) ).
fof(f3703,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,c(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2494,f36]) ).
fof(f3718,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),c(X3))),
inference(forward_demodulation,[status(thm)],[f153,f3681]) ).
fof(f3719,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,c(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f3718]) ).
fof(f3720,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,c(X3)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3719]) ).
fof(f3721,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,c(X3)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f3720]) ).
fof(f3722,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,c(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f3682]) ).
fof(f3723,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(c(X2),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3683]) ).
fof(f3724,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(c(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3723]) ).
fof(f3725,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,c(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f3684]) ).
fof(f3731,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,c(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f3697]) ).
fof(f3733,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,c(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f3700]) ).
fof(f3736,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,c(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f3652]) ).
fof(f3740,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f72,f3652]) ).
fof(f3741,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f71,f3652]) ).
fof(f3749,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),X0),
inference(resolution,[status(thm)],[f2495,f246]) ).
fof(f3753,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),antidomain(X2)))),
inference(paramodulation,[status(thm)],[f103,f2495]) ).
fof(f3754,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),antidomain(X2)))),
inference(paramodulation,[status(thm)],[f36,f2495]) ).
fof(f3758,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f68,f2495]) ).
fof(f3777,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),antidomain(X3))),
inference(paramodulation,[status(thm)],[f2495,f170]) ).
fof(f3778,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),antidomain(X2)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2495,f58]) ).
fof(f3779,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),antidomain(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2495,f55]) ).
fof(f3780,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),antidomain(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2495,f53]) ).
fof(f3781,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),antidomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2495,f103]) ).
fof(f3782,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),antidomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2495,f36]) ).
fof(f3789,plain,
! [X0,X1,X2] : leq(multiplication(X0,antidomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2495,f1420]) ).
fof(f3793,plain,
! [X0,X1,X2] : addition(multiplication(X0,antidomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2495,f103]) ).
fof(f3795,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,antidomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2495,f97]) ).
fof(f3796,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,antidomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2495,f97]) ).
fof(f3798,plain,
! [X0,X1] :
( X0 != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f2495,f49]) ).
fof(f3799,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,antidomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2495,f36]) ).
fof(f3816,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),antidomain(X3))),
inference(forward_demodulation,[status(thm)],[f153,f3777]) ).
fof(f3817,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,antidomain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f3816]) ).
fof(f3818,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,antidomain(X3)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f3817]) ).
fof(f3819,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,antidomain(X3)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f3818]) ).
fof(f3820,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,antidomain(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f3778]) ).
fof(f3821,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(antidomain(X2),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3779]) ).
fof(f3822,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(antidomain(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3821]) ).
fof(f3823,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,antidomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f3780]) ).
fof(f3829,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,antidomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f3793]) ).
fof(f3831,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,antidomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f3796]) ).
fof(f3834,plain,
! [X0,X1] : leq(domain_difference(X0,X1),domain(X0)),
inference(paramodulation,[status(thm)],[f68,f3749]) ).
fof(f3835,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,antidomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f3749]) ).
fof(f3841,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),X0),
inference(paramodulation,[status(thm)],[f62,f3749]) ).
fof(f3847,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f153,f204]) ).
fof(f3848,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f42,f204]) ).
fof(f3853,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)),
inference(paramodulation,[status(thm)],[f192,f204]) ).
fof(f3854,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)),
inference(paramodulation,[status(thm)],[f162,f204]) ).
fof(f3855,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f35,f204]) ).
fof(f3856,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f35,f204]) ).
fof(f3857,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(multiplication(X0,X1),X2),X3),X4) = addition(multiplication(X0,multiplication(X1,multiplication(X2,X4))),multiplication(X3,X4)),
inference(paramodulation,[status(thm)],[f39,f204]) ).
fof(f3859,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(antidomain(multiplication(X0,X1)),X0),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f59,f204]) ).
fof(f3863,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(multiplication(X0,X1))) = addition(zero,multiplication(X2,coantidomain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f144,f204]) ).
fof(f3864,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),domain(X1)) = addition(multiplication(X0,zero),multiplication(X2,domain(X1))),
inference(paramodulation,[status(thm)],[f197,f204]) ).
fof(f3865,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,coantidomain(X1)),X2),codomain(X1)) = addition(multiplication(X0,zero),multiplication(X2,codomain(X1))),
inference(paramodulation,[status(thm)],[f195,f204]) ).
fof(f3866,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,domain(X1)),X2),antidomain(X3)) = addition(multiplication(X0,domain_difference(X1,X3)),multiplication(X2,antidomain(X3))),
inference(paramodulation,[status(thm)],[f68,f204]) ).
fof(f3867,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,multiplication(X1,X2)),X3),X4) = addition(multiplication(X0,multiplication(X1,multiplication(X2,X4))),multiplication(X3,X4)),
inference(paramodulation,[status(thm)],[f39,f204]) ).
fof(f3868,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),addition(X3,X1)) = addition(multiplication(X0,multiplication(antidomain(X1),X3)),multiplication(X2,addition(X3,X1))),
inference(paramodulation,[status(thm)],[f186,f204]) ).
fof(f3869,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),addition(X1,X3)) = addition(multiplication(X0,multiplication(antidomain(X1),X3)),multiplication(X2,addition(X1,X3))),
inference(paramodulation,[status(thm)],[f177,f204]) ).
fof(f3870,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),omega(X1)) = addition(multiplication(X0,zero),multiplication(X2,omega(X1))),
inference(paramodulation,[status(thm)],[f1569,f204]) ).
fof(f3871,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),multiplication(X1,X3)) = addition(multiplication(X0,zero),multiplication(X2,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f136,f204]) ).
fof(f3872,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = addition(multiplication(X0,zero),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f59,f204]) ).
fof(f3875,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),codomain(X1)) = addition(multiplication(X0,X1),multiplication(X2,codomain(X1))),
inference(paramodulation,[status(thm)],[f2309,f204]) ).
fof(f3876,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(one,X3)) = addition(multiplication(X0,addition(X1,multiplication(X1,X3))),multiplication(X2,addition(one,X3))),
inference(paramodulation,[status(thm)],[f162,f204]) ).
fof(f3877,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(coantidomain(X1),X3)) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,addition(coantidomain(X1),X3))),
inference(paramodulation,[status(thm)],[f181,f204]) ).
fof(f3878,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,one)) = addition(multiplication(X0,addition(X1,multiplication(X1,X3))),multiplication(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f192,f204]) ).
fof(f3879,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,coantidomain(X1))) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,addition(X3,coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f190,f204]) ).
fof(f3880,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(coantidomain(X1),X3)) = addition(multiplication(X0,zero),multiplication(X2,multiplication(coantidomain(X1),X3))),
inference(paramodulation,[status(thm)],[f151,f204]) ).
fof(f3881,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X1,X3)))) = addition(multiplication(X0,zero),multiplication(X2,multiplication(X3,coantidomain(multiplication(X1,X3))))),
inference(paramodulation,[status(thm)],[f144,f204]) ).
fof(f3882,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(coantidomain(X1))) = addition(multiplication(X0,zero),multiplication(X2,omega(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f1813,f204]) ).
fof(f3883,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(X1)) = addition(multiplication(X0,omega(X1)),multiplication(X2,omega(X1))),
inference(paramodulation,[status(thm)],[f56,f204]) ).
fof(f3884,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = addition(multiplication(X0,zero),multiplication(X2,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f63,f204]) ).
fof(f3887,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),domain(X2)) = addition(multiplication(X0,multiplication(X1,domain(X2))),zero),
inference(paramodulation,[status(thm)],[f197,f204]) ).
fof(f3888,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),coantidomain(X2)),codomain(X2)) = addition(multiplication(X0,multiplication(X1,codomain(X2))),zero),
inference(paramodulation,[status(thm)],[f195,f204]) ).
fof(f3889,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),domain(X2)),antidomain(X3)) = addition(multiplication(X0,multiplication(X1,antidomain(X3))),domain_difference(X2,X3)),
inference(paramodulation,[status(thm)],[f68,f204]) ).
fof(f3890,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),multiplication(X2,X3)),X4) = addition(multiplication(X0,multiplication(X1,X4)),multiplication(X2,multiplication(X3,X4))),
inference(paramodulation,[status(thm)],[f39,f204]) ).
fof(f3891,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),addition(X3,X2)) = addition(multiplication(X0,multiplication(X1,addition(X3,X2))),multiplication(antidomain(X2),X3)),
inference(paramodulation,[status(thm)],[f186,f204]) ).
fof(f3892,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,addition(X2,X3))),multiplication(antidomain(X2),X3)),
inference(paramodulation,[status(thm)],[f177,f204]) ).
fof(f3893,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),omega(X2)) = addition(multiplication(X0,multiplication(X1,omega(X2))),zero),
inference(paramodulation,[status(thm)],[f1569,f204]) ).
fof(f3894,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),multiplication(X2,X3)) = addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),zero),
inference(paramodulation,[status(thm)],[f136,f204]) ).
fof(f3895,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f59,f204]) ).
fof(f3897,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f41,f204]) ).
fof(f3898,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),codomain(X2)) = addition(multiplication(X0,multiplication(X1,codomain(X2))),X2),
inference(paramodulation,[status(thm)],[f2309,f204]) ).
fof(f3899,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(one,X3)) = addition(multiplication(X0,multiplication(X1,addition(one,X3))),addition(X2,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f162,f204]) ).
fof(f3900,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(coantidomain(X2),X3)) = addition(multiplication(X0,multiplication(X1,addition(coantidomain(X2),X3))),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f181,f204]) ).
fof(f3901,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,one)) = addition(multiplication(X0,multiplication(X1,addition(X3,one))),addition(X2,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f192,f204]) ).
fof(f3902,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,coantidomain(X2))) = addition(multiplication(X0,multiplication(X1,addition(X3,coantidomain(X2)))),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f190,f204]) ).
fof(f3903,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(coantidomain(X2),X3)) = addition(multiplication(X0,multiplication(X1,multiplication(coantidomain(X2),X3))),zero),
inference(paramodulation,[status(thm)],[f151,f204]) ).
fof(f3904,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X2,X3)))) = addition(multiplication(X0,multiplication(X1,multiplication(X3,coantidomain(multiplication(X2,X3))))),zero),
inference(paramodulation,[status(thm)],[f144,f204]) ).
fof(f3905,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(coantidomain(X2))) = addition(multiplication(X0,multiplication(X1,omega(coantidomain(X2)))),zero),
inference(paramodulation,[status(thm)],[f1813,f204]) ).
fof(f3906,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(X2)) = addition(multiplication(X0,multiplication(X1,omega(X2))),omega(X2)),
inference(paramodulation,[status(thm)],[f56,f204]) ).
fof(f3907,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X2)) = addition(multiplication(X0,multiplication(X1,coantidomain(X2))),zero),
inference(paramodulation,[status(thm)],[f63,f204]) ).
fof(f3910,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(multiplication(X0,X2),X0),X1),
inference(paramodulation,[status(thm)],[f204,f153]) ).
fof(f3911,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,X2),X2)) = multiplication(addition(multiplication(X0,X1),X0),X2),
inference(paramodulation,[status(thm)],[f204,f42]) ).
fof(f3912,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(addition(multiplication(X0,X2),X3),X4)) = addition(multiplication(X0,addition(X1,multiplication(X2,X4))),multiplication(X3,X4)),
inference(paramodulation,[status(thm)],[f204,f170]) ).
fof(f3913,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X3,X1))))
| ~ leq(multiplication(X0,X1),multiplication(addition(multiplication(X2,X0),X3),X1)) ),
inference(paramodulation,[status(thm)],[f204,f58]) ).
fof(f3914,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X2,X3),star(multiplication(X1,X3))),X0)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),X0) ),
inference(paramodulation,[status(thm)],[f204,f55]) ).
fof(f3915,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X2,X3)),multiplication(X1,X3))
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f204,f53]) ).
fof(f3920,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(paramodulation,[status(thm)],[f204,f192]) ).
fof(f3921,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(paramodulation,[status(thm)],[f204,f162]) ).
fof(f3922,plain,
! [X0,X1,X2,X3] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(multiplication(X2,X3),X0),X1)) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f204,f186]) ).
fof(f3923,plain,
! [X0,X1,X2,X3] : multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(addition(multiplication(X0,X1),X3),X2)) = multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(X3,X2)),
inference(paramodulation,[status(thm)],[f204,f177]) ).
fof(f3924,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),addition(X3,multiplication(addition(multiplication(X0,X1),X4),X2))),
inference(paramodulation,[status(thm)],[f204,f1421]) ).
fof(f3925,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(multiplication(X3,X4),X0),X1))),
inference(paramodulation,[status(thm)],[f204,f1420]) ).
fof(f3926,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(multiplication(X2,X3),X0),X1)),
inference(paramodulation,[status(thm)],[f204,f1423]) ).
fof(f3927,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f204,f1324]) ).
fof(f3929,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),X4)) = addition(multiplication(addition(multiplication(X2,X3),X0),X1),X4),
inference(paramodulation,[status(thm)],[f204,f103]) ).
fof(f3931,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) = addition(X4,multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f204,f97]) ).
fof(f3932,plain,
! [X0,X1,X2,X3,X4] : addition(X0,multiplication(addition(multiplication(X1,X2),X3),X4)) = addition(multiplication(X3,X4),addition(X0,multiplication(X1,multiplication(X2,X4)))),
inference(paramodulation,[status(thm)],[f204,f97]) ).
fof(f3933,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X2,X3),X0),X1) != multiplication(X2,multiplication(X3,X1))
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))) ),
inference(paramodulation,[status(thm)],[f204,f246]) ).
fof(f3934,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X0,X1),X3),X2) != multiplication(X3,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f204,f49]) ).
fof(f3935,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(multiplication(X0,X1),X3),X2),X4),
inference(paramodulation,[status(thm)],[f204,f36]) ).
fof(f3936,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))) = multiplication(addition(multiplication(X2,X3),X0),X1),
inference(paramodulation,[status(thm)],[f204,f35]) ).
fof(f3937,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f204,f35]) ).
fof(f3938,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f3847]) ).
fof(f3939,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f35,f3848]) ).
fof(f3940,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f3939]) ).
fof(f3953,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(multiplication(X1,X2),X1)),X2) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)),
inference(forward_demodulation,[status(thm)],[f153,f3853]) ).
fof(f3954,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(multiplication(X1,X2),X1),X2)) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)),
inference(forward_demodulation,[status(thm)],[f39,f3953]) ).
fof(f3955,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)),
inference(forward_demodulation,[status(thm)],[f35,f3954]) ).
fof(f3956,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(X0,multiplication(multiplication(X1,X2),addition(X2,one))),
inference(forward_demodulation,[status(thm)],[f39,f3955]) ).
fof(f3957,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))),
inference(forward_demodulation,[status(thm)],[f39,f3956]) ).
fof(f3958,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(multiplication(X1,X2),X1)),X2) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)),
inference(forward_demodulation,[status(thm)],[f153,f3854]) ).
fof(f3959,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(multiplication(X1,X2),X1),X2)) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)),
inference(forward_demodulation,[status(thm)],[f39,f3958]) ).
fof(f3960,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)),
inference(forward_demodulation,[status(thm)],[f35,f3959]) ).
fof(f3961,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(X0,multiplication(multiplication(X1,X2),addition(one,X2))),
inference(forward_demodulation,[status(thm)],[f39,f3960]) ).
fof(f3962,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f3961]) ).
fof(f3963,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,multiplication(X1,X2)),X3),X4) = addition(multiplication(X0,multiplication(X1,multiplication(X2,X4))),multiplication(X3,X4)),
inference(forward_demodulation,[status(thm)],[f39,f3857]) ).
fof(f3966,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(antidomain(multiplication(X0,X1)),X0),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f80,f3859]) ).
fof(f3972,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(multiplication(X0,X1))) = multiplication(X2,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f80,f3863]) ).
fof(f3973,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),domain(X1)) = addition(zero,multiplication(X2,domain(X1))),
inference(forward_demodulation,[status(thm)],[f44,f3864]) ).
fof(f3974,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),domain(X1)) = multiplication(X2,domain(X1)),
inference(forward_demodulation,[status(thm)],[f80,f3973]) ).
fof(f3975,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,coantidomain(X1)),X2),codomain(X1)) = addition(zero,multiplication(X2,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f44,f3865]) ).
fof(f3976,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,coantidomain(X1)),X2),codomain(X1)) = multiplication(X2,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f80,f3975]) ).
fof(f3977,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),omega(X1)) = addition(zero,multiplication(X2,omega(X1))),
inference(forward_demodulation,[status(thm)],[f44,f3870]) ).
fof(f3978,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),omega(X1)) = multiplication(X2,omega(X1)),
inference(forward_demodulation,[status(thm)],[f80,f3977]) ).
fof(f3979,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),multiplication(X1,X3)) = addition(zero,multiplication(X2,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f44,f3871]) ).
fof(f3980,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),multiplication(X1,X3)) = multiplication(X2,multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f80,f3979]) ).
fof(f3981,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f44,f3872]) ).
fof(f3982,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f80,f3981]) ).
fof(f3987,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(coantidomain(X1),X3)) = addition(zero,multiplication(X2,multiplication(coantidomain(X1),X3))),
inference(forward_demodulation,[status(thm)],[f44,f3880]) ).
fof(f3988,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(coantidomain(X1),X3)) = multiplication(X2,multiplication(coantidomain(X1),X3)),
inference(forward_demodulation,[status(thm)],[f80,f3987]) ).
fof(f3989,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X1,X3)))) = addition(zero,multiplication(X2,multiplication(X3,coantidomain(multiplication(X1,X3))))),
inference(forward_demodulation,[status(thm)],[f44,f3881]) ).
fof(f3990,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X1,X3)))) = multiplication(X2,multiplication(X3,coantidomain(multiplication(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f80,f3989]) ).
fof(f3991,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(coantidomain(X1))) = addition(zero,multiplication(X2,omega(coantidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f44,f3882]) ).
fof(f3992,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(coantidomain(X1))) = multiplication(X2,omega(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f80,f3991]) ).
fof(f3993,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(X1)) = multiplication(addition(X2,X0),omega(X1)),
inference(forward_demodulation,[status(thm)],[f201,f3883]) ).
fof(f3994,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = addition(zero,multiplication(X2,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f44,f3884]) ).
fof(f3995,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f80,f3994]) ).
fof(f3999,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),domain(X2)) = multiplication(X0,multiplication(X1,domain(X2))),
inference(forward_demodulation,[status(thm)],[f37,f3887]) ).
fof(f4000,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),coantidomain(X2)),codomain(X2)) = multiplication(X0,multiplication(X1,codomain(X2))),
inference(forward_demodulation,[status(thm)],[f37,f3888]) ).
fof(f4001,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),addition(X3,X2)) = addition(multiplication(antidomain(X2),X3),multiplication(X0,multiplication(X1,addition(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f35,f3891]) ).
fof(f4002,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),addition(X2,X3)) = addition(multiplication(antidomain(X2),X3),multiplication(X0,multiplication(X1,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f35,f3892]) ).
fof(f4003,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),omega(X2)) = multiplication(X0,multiplication(X1,omega(X2))),
inference(forward_demodulation,[status(thm)],[f37,f3893]) ).
fof(f4004,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),multiplication(X2,X3)) = multiplication(X0,multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f37,f3894]) ).
fof(f4005,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),X2) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f3895]) ).
fof(f4008,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(forward_demodulation,[status(thm)],[f35,f3897]) ).
fof(f4009,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f4008]) ).
fof(f4010,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),codomain(X2)) = addition(X2,multiplication(X0,multiplication(X1,codomain(X2)))),
inference(forward_demodulation,[status(thm)],[f35,f3898]) ).
fof(f4011,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(coantidomain(X2),X3)) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,addition(coantidomain(X2),X3)))),
inference(forward_demodulation,[status(thm)],[f35,f3900]) ).
fof(f4012,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,coantidomain(X2))) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,addition(X3,coantidomain(X2))))),
inference(forward_demodulation,[status(thm)],[f35,f3902]) ).
fof(f4013,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(coantidomain(X2),X3)) = multiplication(X0,multiplication(X1,multiplication(coantidomain(X2),X3))),
inference(forward_demodulation,[status(thm)],[f37,f3903]) ).
fof(f4014,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X2,X3)))) = multiplication(X0,multiplication(X1,multiplication(X3,coantidomain(multiplication(X2,X3))))),
inference(forward_demodulation,[status(thm)],[f37,f3904]) ).
fof(f4015,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(coantidomain(X2))) = multiplication(X0,multiplication(X1,omega(coantidomain(X2)))),
inference(forward_demodulation,[status(thm)],[f37,f3905]) ).
fof(f4016,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(X2)) = addition(omega(X2),multiplication(X0,multiplication(X1,omega(X2)))),
inference(forward_demodulation,[status(thm)],[f35,f3906]) ).
fof(f4017,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X2)) = multiplication(X0,multiplication(X1,coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f37,f3907]) ).
fof(f4022,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f35,f3910]) ).
fof(f4023,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(multiplication(X0,X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f3911]) ).
fof(f4024,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f35,f4023]) ).
fof(f4025,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X2,multiplication(X3,star(multiplication(X1,X3)))),X0)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f3914]) ).
fof(f4038,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(multiplication(X1,X2),addition(X2,one))) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(forward_demodulation,[status(thm)],[f39,f3920]) ).
fof(f4039,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(forward_demodulation,[status(thm)],[f39,f4038]) ).
fof(f4040,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))) = multiplication(multiplication(X0,addition(multiplication(X1,X2),X1)),X2),
inference(forward_demodulation,[status(thm)],[f153,f4039]) ).
fof(f4041,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))) = multiplication(X0,multiplication(addition(multiplication(X1,X2),X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f4040]) ).
fof(f4042,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))) = multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)),
inference(forward_demodulation,[status(thm)],[f35,f4041]) ).
fof(f4043,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(multiplication(X1,X2),addition(one,X2))) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(forward_demodulation,[status(thm)],[f39,f3921]) ).
fof(f4044,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(forward_demodulation,[status(thm)],[f39,f4043]) ).
fof(f4045,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))) = multiplication(multiplication(X0,addition(multiplication(X1,X2),X1)),X2),
inference(forward_demodulation,[status(thm)],[f153,f4044]) ).
fof(f4046,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))) = multiplication(X0,multiplication(addition(multiplication(X1,X2),X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f4045]) ).
fof(f4047,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))) = multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)),
inference(forward_demodulation,[status(thm)],[f35,f4046]) ).
fof(f4055,plain,
! [X0,X1] : addition(domain_difference(X0,X1),domain(X0)) = domain(X0),
inference(resolution,[status(thm)],[f3834,f48]) ).
fof(f4061,plain,
! [X0,X1,X2] : leq(domain_difference(multiplication(X0,domain(X1)),X2),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f69,f3834]) ).
fof(f4063,plain,
! [X0,X1] : leq(domain_difference(domain(X0),X1),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f196,f3834]) ).
fof(f4064,plain,
! [X0,X1] : leq(domain_difference(antidomain(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f361,f3834]) ).
fof(f4066,plain,
! [X0,X1] : addition(domain(X0),domain_difference(X0,X1)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f35,f4055]) ).
fof(f4073,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,domain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f3841]) ).
fof(f4077,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f69,f3841]) ).
fof(f4089,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f558,f224]) ).
fof(f4090,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),antidomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2495,f224]) ).
fof(f4091,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),c(X1)),X0),
inference(paramodulation,[status(thm)],[f2494,f224]) ).
fof(f4092,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),codomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2493,f224]) ).
fof(f4093,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),divergence(X1)),X0),
inference(paramodulation,[status(thm)],[f2492,f224]) ).
fof(f4094,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),addition(X1,one)),X0) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f192,f224]) ).
fof(f4095,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),addition(one,X1)),X0) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f162,f224]) ).
fof(f4096,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(addition(X1,addition(antidomain(X0),X1)),X0),
inference(paramodulation,[status(thm)],[f99,f224]) ).
fof(f4098,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f97,f224]) ).
fof(f4099,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f97,f224]) ).
fof(f4101,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f35,f224]) ).
fof(f4102,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f35,f224]) ).
fof(f4105,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(paramodulation,[status(thm)],[f67,f224]) ).
fof(f4106,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(paramodulation,[status(thm)],[f62,f224]) ).
fof(f4108,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(antidomain(antidomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f224,f3749]) ).
fof(f4109,plain,
! [X0,X1] : addition(antidomain(antidomain(X0)),X1) = addition(addition(antidomain(antidomain(X0)),X1),multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f224,f2495]) ).
fof(f4110,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),addition(antidomain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f224,f3652]) ).
fof(f4111,plain,
! [X0,X1] : addition(antidomain(c(X0)),X1) = addition(addition(antidomain(c(X0)),X1),multiplication(X1,c(X0))),
inference(paramodulation,[status(thm)],[f224,f2494]) ).
fof(f4112,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),addition(antidomain(divergence(X1)),X0)),
inference(paramodulation,[status(thm)],[f224,f3330]) ).
fof(f4113,plain,
! [X0,X1] : addition(antidomain(divergence(X0)),X1) = addition(addition(antidomain(divergence(X0)),X1),multiplication(X1,divergence(X0))),
inference(paramodulation,[status(thm)],[f224,f2492]) ).
fof(f4114,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),addition(antidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f224,f3411]) ).
fof(f4115,plain,
! [X0,X1] : addition(antidomain(codomain(X0)),X1) = addition(addition(antidomain(codomain(X0)),X1),multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f224,f2493]) ).
fof(f4116,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(antidomain(multiplication(X0,X1)),X2),X0),X3),X1) = addition(multiplication(X2,multiplication(X0,X1)),multiplication(X3,X1)),
inference(paramodulation,[status(thm)],[f224,f204]) ).
fof(f4117,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(antidomain(domain(X1)),X0)),
inference(paramodulation,[status(thm)],[f224,f3841]) ).
fof(f4118,plain,
! [X0,X1] : forward_diamond(addition(antidomain(domain(X0)),X1),X0) = domain(multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f224,f69]) ).
fof(f4119,plain,
! [X0,X1] : addition(antidomain(multiplication(addition(antidomain(domain(X0)),X1),X0)),antidomain(multiplication(X1,domain(X0)))) = antidomain(multiplication(addition(antidomain(domain(X0)),X1),domain(X0))),
inference(paramodulation,[status(thm)],[f224,f479]) ).
fof(f4122,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(antidomain(X2),X3)),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),
inference(paramodulation,[status(thm)],[f224,f204]) ).
fof(f4123,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(antidomain(X1),X2)),X3),X1) = addition(multiplication(X0,multiplication(X2,X1)),multiplication(X3,X1)),
inference(paramodulation,[status(thm)],[f224,f204]) ).
fof(f4124,plain,
! [X0,X1,X2] : multiplication(addition(addition(antidomain(X0),X1),X2),X0) = addition(multiplication(X2,X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f224,f201]) ).
fof(f4125,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f224,f201]) ).
fof(f4126,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(antidomain(X0),X1),X2),addition(multiplication(X1,X0),X3)) = addition(multiplication(addition(antidomain(X0),X1),addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f224,f170]) ).
fof(f4127,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(addition(antidomain(X1),X0),X2),X3)) = addition(multiplication(addition(antidomain(X1),X0),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f224,f170]) ).
fof(f4128,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(X0,one)) = addition(addition(antidomain(X0),X1),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f224,f192]) ).
fof(f4129,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(one,X0)) = addition(addition(antidomain(X0),X1),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f224,f162]) ).
fof(f4130,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X0,X2)) = addition(multiplication(addition(antidomain(X0),X1),X2),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f224,f153]) ).
fof(f4131,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X2,X0)) = addition(multiplication(X1,X0),multiplication(addition(antidomain(X0),X1),X2)),
inference(paramodulation,[status(thm)],[f224,f153]) ).
fof(f4132,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),multiplication(X0,coantidomain(multiplication(X1,X0)))) = zero,
inference(paramodulation,[status(thm)],[f224,f144]) ).
fof(f4133,plain,
! [X0,X1] : multiplication(antidomain(addition(antidomain(X0),X1)),multiplication(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f224,f136]) ).
fof(f4134,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(addition(antidomain(X1),X0)),X1))) = coantidomain(multiplication(codomain(addition(antidomain(X1),X0)),X1)),
inference(paramodulation,[status(thm)],[f224,f615]) ).
fof(f4135,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(addition(antidomain(X1),X0),domain(X1)))) = antidomain(multiplication(addition(antidomain(X1),X0),domain(X1))),
inference(paramodulation,[status(thm)],[f224,f479]) ).
fof(f4136,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(antidomain(X0),X1)),multiplication(star(addition(antidomain(X0),X1)),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f224,f58]) ).
fof(f4137,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),addition(antidomain(X1),X0))
| ~ leq(addition(multiplication(X0,X1),X2),addition(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f224,f55]) ).
fof(f4138,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(antidomain(X1),X0)),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f224,f53]) ).
fof(f4139,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f224,f43]) ).
fof(f4140,plain,
! [X0,X1,X2] : multiplication(addition(addition(antidomain(X0),X1),X2),X0) = addition(multiplication(X1,X0),multiplication(X2,X0)),
inference(paramodulation,[status(thm)],[f224,f43]) ).
fof(f4141,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X2,X0)) = addition(multiplication(addition(antidomain(X0),X1),X2),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f224,f42]) ).
fof(f4142,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X0,X2)) = addition(multiplication(X1,X0),multiplication(addition(antidomain(X0),X1),X2)),
inference(paramodulation,[status(thm)],[f224,f42]) ).
fof(f4143,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(multiplication(X1,X0),X2),
inference(paramodulation,[status(thm)],[f224,f39]) ).
fof(f4146,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f41,f4089]) ).
fof(f4147,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),antidomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f59,f4090]) ).
fof(f4148,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4147]) ).
fof(f4149,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),c(X1)),X0),
inference(forward_demodulation,[status(thm)],[f59,f4091]) ).
fof(f4150,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4149]) ).
fof(f4151,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),codomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f59,f4092]) ).
fof(f4152,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4151]) ).
fof(f4153,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),divergence(X1)),X0),
inference(forward_demodulation,[status(thm)],[f59,f4093]) ).
fof(f4154,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4153]) ).
fof(f4155,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(forward_demodulation,[status(thm)],[f39,f4094]) ).
fof(f4156,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f39,f4155]) ).
fof(f4157,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(forward_demodulation,[status(thm)],[f39,f4095]) ).
fof(f4158,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f39,f4157]) ).
fof(f4159,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,addition(antidomain(X1),X0)),X1),
inference(forward_demodulation,[status(thm)],[f224,f4096]) ).
fof(f4164,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f62,f4108]) ).
fof(f4165,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(addition(antidomain(antidomain(X0)),X1),multiplication(X1,antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f4109]) ).
fof(f4166,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(X1,addition(antidomain(antidomain(X0)),multiplication(X1,antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4165]) ).
fof(f4167,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(X1,addition(domain(X0),multiplication(X1,antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f4166]) ).
fof(f4168,plain,
! [X0,X1] : addition(antidomain(c(X0)),X1) = addition(X1,addition(antidomain(c(X0)),multiplication(X1,c(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4111]) ).
fof(f4169,plain,
! [X0,X1] : addition(antidomain(divergence(X0)),X1) = addition(X1,addition(antidomain(divergence(X0)),multiplication(X1,divergence(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4113]) ).
fof(f4170,plain,
! [X0,X1] : addition(antidomain(codomain(X0)),X1) = addition(X1,addition(antidomain(codomain(X0)),multiplication(X1,codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4115]) ).
fof(f4171,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(antidomain(multiplication(X0,X1)),X2),X0),X3),X1) = multiplication(addition(multiplication(X2,X0),X3),X1),
inference(forward_demodulation,[status(thm)],[f204,f4116]) ).
fof(f4172,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f67,f4117]) ).
fof(f4173,plain,
! [X0,X1] : forward_diamond(addition(c(X0),X1),X0) = domain(multiplication(X1,domain(X0))),
inference(forward_demodulation,[status(thm)],[f67,f4118]) ).
fof(f4174,plain,
! [X0,X1] : forward_diamond(addition(c(X0),X1),X0) = forward_diamond(X1,X0),
inference(forward_demodulation,[status(thm)],[f69,f4173]) ).
fof(f4175,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(addition(antidomain(domain(X1)),X0),X1))) = antidomain(multiplication(addition(antidomain(domain(X1)),X0),domain(X1))),
inference(forward_demodulation,[status(thm)],[f35,f4119]) ).
fof(f4176,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(addition(c(X1),X0),X1))) = antidomain(multiplication(addition(antidomain(domain(X1)),X0),domain(X1))),
inference(forward_demodulation,[status(thm)],[f67,f4175]) ).
fof(f4177,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(addition(c(X1),X0),X1))) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f224,f4176]) ).
fof(f4180,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(antidomain(X2),X3)),X2) = multiplication(addition(multiplication(X0,X1),X3),X2),
inference(forward_demodulation,[status(thm)],[f204,f4122]) ).
fof(f4181,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(antidomain(X1),X2)),X3),X1) = multiplication(addition(multiplication(X0,X2),X3),X1),
inference(forward_demodulation,[status(thm)],[f204,f4123]) ).
fof(f4182,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f4124]) ).
fof(f4183,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f201,f4182]) ).
fof(f4184,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f201,f4125]) ).
fof(f4185,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(addition(antidomain(X1),X0),X3))) = addition(multiplication(addition(antidomain(X1),X0),addition(X3,X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f4126]) ).
fof(f4186,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(X0,one)) = addition(X1,addition(antidomain(X0),multiplication(X1,X0))),
inference(forward_demodulation,[status(thm)],[f103,f4128]) ).
fof(f4187,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(one,X0)) = addition(X1,addition(antidomain(X0),multiplication(X1,X0))),
inference(forward_demodulation,[status(thm)],[f103,f4129]) ).
fof(f4188,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X0,X2)) = addition(multiplication(X1,X0),multiplication(addition(antidomain(X0),X1),X2)),
inference(forward_demodulation,[status(thm)],[f35,f4130]) ).
fof(f4189,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f201,f4139]) ).
fof(f4190,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f103,f4140]) ).
fof(f4191,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f201,f4190]) ).
fof(f4192,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),addition(X2,X0)) = addition(multiplication(X1,X0),multiplication(addition(antidomain(X0),X1),X2)),
inference(forward_demodulation,[status(thm)],[f35,f4141]) ).
fof(f4193,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f39,f4143]) ).
fof(f4195,plain,
! [X0] : antidomain(X0) = domain_difference(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f68,f4146]) ).
fof(f4198,plain,
! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(forward_diamond(X0,X1),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f69,f4146]) ).
fof(f4200,plain,
! [X0] : domain(X0) = multiplication(antidomain(c(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f196,f4146]) ).
fof(f4201,plain,
! [X0] : antidomain(X0) = multiplication(c(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f361,f4146]) ).
fof(f4204,plain,
! [X0] : leq(antidomain(X0),domain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f4146,f3749]) ).
fof(f4206,plain,
! [X0] : leq(c(X0),domain(c(X0))),
inference(paramodulation,[status(thm)],[f4146,f3652]) ).
fof(f4207,plain,
! [X0] : domain(c(X0)) = addition(domain(c(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f4146,f2494]) ).
fof(f4208,plain,
! [X0] : leq(divergence(X0),domain(divergence(X0))),
inference(paramodulation,[status(thm)],[f4146,f3330]) ).
fof(f4209,plain,
! [X0] : domain(divergence(X0)) = addition(domain(divergence(X0)),divergence(X0)),
inference(paramodulation,[status(thm)],[f4146,f2492]) ).
fof(f4210,plain,
! [X0] : leq(codomain(X0),domain(codomain(X0))),
inference(paramodulation,[status(thm)],[f4146,f3411]) ).
fof(f4211,plain,
! [X0] : domain(codomain(X0)) = addition(domain(codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f4146,f2493]) ).
fof(f4212,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(domain(multiplication(X0,X1)),X0),X2),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f4146,f204]) ).
fof(f4213,plain,
! [X0] : leq(domain(X0),domain(domain(X0))),
inference(paramodulation,[status(thm)],[f4146,f3841]) ).
fof(f4214,plain,
! [X0] : forward_diamond(domain(domain(X0)),X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f4146,f69]) ).
fof(f4215,plain,
! [X0] : addition(antidomain(multiplication(domain(domain(X0)),X0)),antidomain(domain(X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f4146,f479]) ).
fof(f4218,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f4146,f204]) ).
fof(f4219,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f4146,f204]) ).
fof(f4220,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f4146,f201]) ).
fof(f4221,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f4146,f201]) ).
fof(f4222,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),addition(X0,X2)) = addition(multiplication(domain(X0),addition(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f4146,f170]) ).
fof(f4223,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X0),X1),X2)) = addition(multiplication(domain(X0),addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f4146,f170]) ).
fof(f4224,plain,
! [X0] : multiplication(domain(X0),addition(X0,one)) = addition(domain(X0),X0),
inference(paramodulation,[status(thm)],[f4146,f192]) ).
fof(f4225,plain,
! [X0] : multiplication(domain(X0),addition(one,X0)) = addition(domain(X0),X0),
inference(paramodulation,[status(thm)],[f4146,f162]) ).
fof(f4226,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(multiplication(domain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f4146,f153]) ).
fof(f4227,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(X0,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f4146,f153]) ).
fof(f4229,plain,
! [X0] : multiplication(antidomain(domain(X0)),X0) = zero,
inference(paramodulation,[status(thm)],[f4146,f136]) ).
fof(f4230,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(domain(X0)),X0))) = coantidomain(multiplication(codomain(domain(X0)),X0)),
inference(paramodulation,[status(thm)],[f4146,f615]) ).
fof(f4231,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(domain(X0),domain(X0)))) = antidomain(multiplication(domain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f4146,f479]) ).
fof(f4232,plain,
! [X0,X1] :
( leq(X0,addition(omega(domain(X0)),multiplication(star(domain(X0)),X1)))
| ~ leq(X0,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4146,f58]) ).
fof(f4233,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),domain(X0))
| ~ leq(addition(X0,X1),domain(X0)) ),
inference(paramodulation,[status(thm)],[f4146,f55]) ).
fof(f4234,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X0)),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4146,f53]) ).
fof(f4235,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f4146,f43]) ).
fof(f4236,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f4146,f43]) ).
fof(f4237,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(multiplication(domain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f4146,f42]) ).
fof(f4238,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f4146,f42]) ).
fof(f4239,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(X0,X1)) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f4146,f39]) ).
fof(f4241,plain,
! [X0] : leq(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f361,f4204]) ).
fof(f4245,plain,
! [X0] : domain(c(X0)) = addition(c(X0),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4207]) ).
fof(f4246,plain,
! [X0] : domain(divergence(X0)) = addition(divergence(X0),domain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4209]) ).
fof(f4247,plain,
! [X0] : domain(codomain(X0)) = addition(codomain(X0),domain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4211]) ).
fof(f4248,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(domain(multiplication(X0,X1)),X0),X2),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f201,f4212]) ).
fof(f4249,plain,
! [X0] : leq(domain(X0),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f196,f4213]) ).
fof(f4250,plain,
! [X0] : forward_diamond(antidomain(c(X0)),X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f196,f4214]) ).
fof(f4251,plain,
! [X0] : forward_diamond(antidomain(c(X0)),X0) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f196,f4250]) ).
fof(f4252,plain,
! [X0] : addition(antidomain(domain(X0)),antidomain(multiplication(domain(domain(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4215]) ).
fof(f4253,plain,
! [X0] : addition(c(X0),antidomain(multiplication(domain(domain(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f67,f4252]) ).
fof(f4254,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f196,f4253]) ).
fof(f4255,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f4146,f4254]) ).
fof(f4256,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = c(X0),
inference(forward_demodulation,[status(thm)],[f67,f4255]) ).
fof(f4257,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f4218]) ).
fof(f4258,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f201,f4219]) ).
fof(f4259,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f4220]) ).
fof(f4260,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X0),X2))) = addition(multiplication(domain(X0),addition(X2,X0)),X1),
inference(forward_demodulation,[status(thm)],[f97,f4222]) ).
fof(f4261,plain,
! [X0] : multiplication(domain(X0),addition(X0,one)) = addition(X0,domain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f4224]) ).
fof(f4262,plain,
! [X0] : multiplication(domain(X0),addition(one,X0)) = addition(X0,domain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f4225]) ).
fof(f4263,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f4226]) ).
fof(f4265,plain,
! [X0] : multiplication(c(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f67,f4229]) ).
fof(f4266,plain,
! [X0,X1] : leq(X0,addition(omega(domain(X0)),multiplication(star(domain(X0)),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f4232,f1324]) ).
fof(f4267,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f4235]) ).
fof(f4268,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(X0,multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f4237]) ).
fof(f4274,plain,
! [X0,X1] : leq(antidomain(backward_diamond(X0,c(X1))),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f72,f4241]) ).
fof(f4275,plain,
! [X0,X1] : leq(antidomain(forward_diamond(X0,c(X1))),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f71,f4241]) ).
fof(f4291,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f72,f4265]) ).
fof(f4292,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f71,f4265]) ).
fof(f4294,plain,
! [X0] : multiplication(antidomain(c(X0)),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f547,f4265]) ).
fof(f4295,plain,
! [X0] : multiplication(domain(c(X0)),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f362,f4265]) ).
fof(f4305,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(c(multiplication(X0,X1)),X0),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f4265,f204]) ).
fof(f4307,plain,
! [X0] : forward_diamond(c(domain(X0)),X0) = domain(zero),
inference(paramodulation,[status(thm)],[f4265,f69]) ).
fof(f4311,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f4265,f204]) ).
fof(f4312,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = addition(multiplication(X0,zero),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f4265,f204]) ).
fof(f4313,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = addition(multiplication(X1,X0),zero),
inference(paramodulation,[status(thm)],[f4265,f201]) ).
fof(f4314,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f4265,f201]) ).
fof(f4315,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(zero,X2)) = addition(multiplication(c(X0),addition(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f4265,f170]) ).
fof(f4316,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(c(X0),X1),X2)) = addition(multiplication(c(X0),addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f4265,f170]) ).
fof(f4317,plain,
! [X0] : multiplication(c(X0),addition(X0,one)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f4265,f192]) ).
fof(f4318,plain,
! [X0] : multiplication(c(X0),addition(one,X0)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f4265,f162]) ).
fof(f4319,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f4265,f153]) ).
fof(f4320,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f4265,f153]) ).
fof(f4323,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(c(X0)),X0))) = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(paramodulation,[status(thm)],[f4265,f615]) ).
fof(f4325,plain,
! [X0,X1] :
( leq(X0,addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f4265,f58]) ).
fof(f4326,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),c(X1))
| ~ leq(addition(zero,X0),c(X1)) ),
inference(paramodulation,[status(thm)],[f4265,f55]) ).
fof(f4327,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f4265,f53]) ).
fof(f4328,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f4265,f43]) ).
fof(f4329,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f4265,f43]) ).
fof(f4330,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f4265,f42]) ).
fof(f4331,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f4265,f42]) ).
fof(f4337,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(c(multiplication(X0,X1)),X0),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f80,f4305]) ).
fof(f4339,plain,
! [X0] : forward_diamond(domain(c(X0)),X0) = domain(zero),
inference(forward_demodulation,[status(thm)],[f362,f4307]) ).
fof(f4340,plain,
! [X0] : forward_diamond(domain(c(X0)),X0) = zero,
inference(forward_demodulation,[status(thm)],[f607,f4339]) ).
fof(f4345,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),X2) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f4311]) ).
fof(f4346,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f44,f4312]) ).
fof(f4347,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f80,f4346]) ).
fof(f4348,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f37,f4313]) ).
fof(f4349,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f4314]) ).
fof(f4350,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(c(X1),X2))) = addition(multiplication(c(X1),addition(X2,X1)),X0),
inference(forward_demodulation,[status(thm)],[f97,f4315]) ).
fof(f4351,plain,
! [X0,X1,X2] : addition(X0,multiplication(c(X1),X2)) = addition(multiplication(c(X1),addition(X2,X1)),X0),
inference(forward_demodulation,[status(thm)],[f80,f4350]) ).
fof(f4352,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),X2) = addition(multiplication(c(X0),addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f4316]) ).
fof(f4353,plain,
! [X0] : multiplication(c(X0),addition(X0,one)) = c(X0),
inference(forward_demodulation,[status(thm)],[f37,f4317]) ).
fof(f4354,plain,
! [X0] : multiplication(c(X0),addition(one,X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f37,f4318]) ).
fof(f4355,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f4319]) ).
fof(f4356,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f4320]) ).
fof(f4359,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(c(X0)),X0))) = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f696,f4323]) ).
fof(f4360,plain,
! [X0] : one = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f1377,f4359]) ).
fof(f4364,plain,
! [X0,X1] :
( leq(X0,addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f4325]) ).
fof(f4365,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f4326]) ).
fof(f4366,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f4327]) ).
fof(f4367,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f4328]) ).
fof(f4368,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f80,f4329]) ).
fof(f4369,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f4330]) ).
fof(f4370,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f4331]) ).
fof(f4376,plain,
! [X0] : antidomain(antidomain(X0)) = domain_difference(domain(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f62,f4195]) ).
fof(f4386,plain,
! [X0] : domain(X0) = domain_difference(domain(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f4376]) ).
fof(f4394,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1504,f207]) ).
fof(f4395,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1497,f207]) ).
fof(f4396,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1492,f207]) ).
fof(f4397,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1485,f207]) ).
fof(f4398,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(divergence(X1),X0)),
inference(paramodulation,[status(thm)],[f1488,f207]) ).
fof(f4399,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1477,f207]) ).
fof(f4400,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(c(X1),X0)),
inference(paramodulation,[status(thm)],[f1471,f207]) ).
fof(f4401,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1379,f207]) ).
fof(f4402,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(coantidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1377,f207]) ).
fof(f4403,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f1375,f207]) ).
fof(f4408,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(X0,addition(one,X0)),X1)),
inference(paramodulation,[status(thm)],[f99,f207]) ).
fof(f4409,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f105,f207]) ).
fof(f4410,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f97,f207]) ).
fof(f4411,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f97,f207]) ).
fof(f4413,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f207]) ).
fof(f4414,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f207]) ).
fof(f4416,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f153,f207]) ).
fof(f4417,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f42,f207]) ).
fof(f4418,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X2,addition(X1,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f103,f207]) ).
fof(f4419,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X1,addition(X2,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f36,f207]) ).
fof(f4425,plain,
! [X0] : multiplication(addition(one,X0),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f192,f207]) ).
fof(f4426,plain,
! [X0] : multiplication(addition(one,X0),X0) = multiplication(X0,addition(one,X0)),
inference(paramodulation,[status(thm)],[f162,f207]) ).
fof(f4428,plain,
! [X0,X1] : multiplication(addition(one,addition(antidomain(X0),X1)),X0) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f224,f207]) ).
fof(f4432,plain,
! [X0,X1] : multiplication(addition(one,domain(X0)),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f68,f207]) ).
fof(f4434,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f39,f207]) ).
fof(f4435,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f186,f207]) ).
fof(f4436,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f177,f207]) ).
fof(f4442,plain,
! [X0] : multiplication(addition(one,X0),codomain(X0)) = addition(codomain(X0),X0),
inference(paramodulation,[status(thm)],[f2309,f207]) ).
fof(f4443,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(addition(one,X1),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f162,f207]) ).
fof(f4444,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(coantidomain(X0),X1)) = addition(addition(coantidomain(X0),X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f181,f207]) ).
fof(f4445,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(addition(X1,one),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f207]) ).
fof(f4446,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,coantidomain(X0))) = addition(addition(X1,coantidomain(X0)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f190,f207]) ).
fof(f4447,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(coantidomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f151,f207]) ).
fof(f4448,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(multiplication(X0,X1)))) = addition(multiplication(X1,coantidomain(multiplication(X0,X1))),zero),
inference(paramodulation,[status(thm)],[f144,f207]) ).
fof(f4449,plain,
! [X0] : multiplication(addition(one,X0),omega(coantidomain(X0))) = addition(omega(coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f1813,f207]) ).
fof(f4450,plain,
! [X0] : multiplication(addition(one,X0),omega(X0)) = addition(omega(X0),omega(X0)),
inference(paramodulation,[status(thm)],[f56,f207]) ).
fof(f4451,plain,
! [X0] : multiplication(addition(one,X0),coantidomain(X0)) = addition(coantidomain(X0),zero),
inference(paramodulation,[status(thm)],[f63,f207]) ).
fof(f4454,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(one,X2)),X3) = addition(multiplication(X0,multiplication(X1,X3)),addition(X3,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f207,f204]) ).
fof(f4455,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(one,X1)),X2),X3) = addition(multiplication(X0,addition(X3,multiplication(X1,X3))),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f207,f204]) ).
fof(f4456,plain,
! [X0,X1,X2] : multiplication(addition(addition(one,X0),X1),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f207,f201]) ).
fof(f4457,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(addition(X2,multiplication(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f207,f201]) ).
fof(f4458,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,X0),X1),addition(addition(X2,multiplication(X0,X2)),X3)) = addition(multiplication(addition(one,X0),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f207,f170]) ).
fof(f4459,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X1,X0)),addition(multiplication(addition(one,X1),X2),X3)) = addition(multiplication(addition(one,X1),addition(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f207,f170]) ).
fof(f4460,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(addition(one,X0),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f207,f192]) ).
fof(f4461,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(addition(one,X0),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f207,f162]) ).
fof(f4462,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(multiplication(addition(one,X0),X2),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f207,f153]) ).
fof(f4463,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(addition(X2,multiplication(X0,X2)),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f207,f153]) ).
fof(f4464,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(addition(X1,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f207,f144]) ).
fof(f4465,plain,
! [X0,X1] : multiplication(antidomain(addition(one,X0)),addition(X1,multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f207,f136]) ).
fof(f4466,plain,
! [X0,X1] : addition(coantidomain(addition(X0,multiplication(X1,X0))),coantidomain(multiplication(codomain(addition(one,X1)),X0))) = coantidomain(multiplication(codomain(addition(one,X1)),X0)),
inference(paramodulation,[status(thm)],[f207,f615]) ).
fof(f4467,plain,
! [X0,X1] : addition(antidomain(addition(X0,multiplication(X1,X0))),antidomain(multiplication(addition(one,X1),domain(X0)))) = antidomain(multiplication(addition(one,X1),domain(X0))),
inference(paramodulation,[status(thm)],[f207,f479]) ).
fof(f4468,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(one,X1)),multiplication(star(addition(one,X1)),X2)))
| ~ leq(X0,addition(addition(X0,multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f207,f58]) ).
fof(f4469,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X0)),addition(one,X1))
| ~ leq(addition(addition(X0,multiplication(X1,X0)),X2),addition(one,X1)) ),
inference(paramodulation,[status(thm)],[f207,f55]) ).
fof(f4470,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(one,X1)),X2),X0)
| ~ leq(addition(addition(X0,multiplication(X1,X0)),X2),X0) ),
inference(paramodulation,[status(thm)],[f207,f53]) ).
fof(f4471,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f207,f43]) ).
fof(f4472,plain,
! [X0,X1,X2] : multiplication(addition(addition(one,X0),X1),X2) = addition(addition(X2,multiplication(X0,X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f207,f43]) ).
fof(f4473,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(multiplication(addition(one,X0),X1),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f207,f42]) ).
fof(f4474,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(addition(X1,multiplication(X0,X1)),multiplication(addition(one,X0),X2)),
inference(paramodulation,[status(thm)],[f207,f42]) ).
fof(f4475,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f207,f39]) ).
fof(f4476,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f207,f181]) ).
fof(f4478,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X0,X1),X1)) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f207,f153]) ).
fof(f4479,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f207,f42]) ).
fof(f4480,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(one,X2),multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),multiplication(X2,multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f207,f170]) ).
fof(f4481,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(addition(one,X1),multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f207,f58]) ).
fof(f4482,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),star(X2)),X1)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f207,f55]) ).
fof(f4483,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f207,f53]) ).
fof(f4484,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X1,X0)))) = multiplication(addition(one,X2),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f207,f103]) ).
fof(f4485,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X0,X1)))) = multiplication(addition(one,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f207,f36]) ).
fof(f4490,plain,
! [X0] : multiplication(X0,addition(X0,one)) = multiplication(addition(one,X0),X0),
inference(paramodulation,[status(thm)],[f207,f192]) ).
fof(f4491,plain,
! [X0] : multiplication(X0,addition(one,X0)) = multiplication(addition(one,X0),X0),
inference(paramodulation,[status(thm)],[f207,f162]) ).
fof(f4492,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(one,X0),X1)) = multiplication(antidomain(multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f207,f186]) ).
fof(f4493,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f207,f177]) ).
fof(f4494,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(one,X2),X0))),
inference(paramodulation,[status(thm)],[f207,f1421]) ).
fof(f4495,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(one,X0),X1))),
inference(paramodulation,[status(thm)],[f207,f1420]) ).
fof(f4496,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f207,f1423]) ).
fof(f4497,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f207,f1324]) ).
fof(f4498,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f207,f105]) ).
fof(f4499,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(one,X0),X1),X2),
inference(paramodulation,[status(thm)],[f207,f103]) ).
fof(f4500,plain,
! [X0,X1] : addition(X0,addition(multiplication(X1,X0),multiplication(addition(one,X1),X0))) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f207,f99]) ).
fof(f4501,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(X2,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f207,f97]) ).
fof(f4502,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(one,X1),X2)) = addition(multiplication(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f207,f97]) ).
fof(f4503,plain,
! [X0,X1] :
( multiplication(addition(one,X0),X1) != X1
| leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f207,f246]) ).
fof(f4504,plain,
! [X0,X1] :
( multiplication(addition(one,X1),X0) != multiplication(X1,X0)
| leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f207,f49]) ).
fof(f4505,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(one,X1),X0),X2),
inference(paramodulation,[status(thm)],[f207,f36]) ).
fof(f4507,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4394]) ).
fof(f4508,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4395]) ).
fof(f4509,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4396]) ).
fof(f4510,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4397]) ).
fof(f4511,plain,
! [X0,X1] : X0 = addition(X0,multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4398]) ).
fof(f4512,plain,
! [X0,X1] : X0 = addition(X0,multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4399]) ).
fof(f4513,plain,
! [X0,X1] : X0 = addition(X0,multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4400]) ).
fof(f4514,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4401]) ).
fof(f4515,plain,
! [X0,X1] : X0 = addition(X0,multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4402]) ).
fof(f4516,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4403]) ).
fof(f4533,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f4416]) ).
fof(f4546,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1375,f4432]) ).
fof(f4547,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f4546]) ).
fof(f4550,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f1379,f4435]) ).
fof(f4551,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f41,f4550]) ).
fof(f4552,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f103,f4551]) ).
fof(f4553,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1379,f4436]) ).
fof(f4554,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f41,f4553]) ).
fof(f4555,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f4554]) ).
fof(f4566,plain,
! [X0] : multiplication(addition(one,X0),codomain(X0)) = addition(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f4442]) ).
fof(f4567,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(X1,addition(one,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f4443]) ).
fof(f4568,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(coantidomain(X0),X1)) = addition(X1,addition(coantidomain(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f4444]) ).
fof(f4569,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(one,addition(X1,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f4445]) ).
fof(f4570,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,coantidomain(X0))) = addition(coantidomain(X0),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f4446]) ).
fof(f4571,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(coantidomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f4447]) ).
fof(f4572,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f37,f4448]) ).
fof(f4573,plain,
! [X0] : multiplication(addition(one,X0),omega(coantidomain(X0))) = omega(coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f4449]) ).
fof(f4574,plain,
! [X0] : multiplication(addition(one,X0),omega(X0)) = omega(X0),
inference(forward_demodulation,[status(thm)],[f38,f4450]) ).
fof(f4575,plain,
! [X0] : multiplication(addition(one,X0),coantidomain(X0)) = coantidomain(X0),
inference(forward_demodulation,[status(thm)],[f37,f4451]) ).
fof(f4577,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),X3) = addition(multiplication(X1,multiplication(X2,X3)),addition(X3,multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f97,f4454]) ).
fof(f4578,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),X3) = addition(X3,addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f97,f4577]) ).
fof(f4579,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f4456]) ).
fof(f4580,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f97,f4579]) ).
fof(f4581,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f4580]) ).
fof(f4582,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f4457]) ).
fof(f4583,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f97,f4582]) ).
fof(f4584,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f4583]) ).
fof(f4585,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,X0),X1),addition(multiplication(X0,X2),addition(X2,X3))) = addition(multiplication(addition(one,X0),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f4458]) ).
fof(f4586,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,X0),X1),addition(X2,addition(X3,multiplication(X0,X2)))) = addition(multiplication(addition(one,X0),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f97,f4585]) ).
fof(f4587,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X1,addition(multiplication(addition(one,X0),X2),X3))) = addition(multiplication(addition(one,X0),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f4459]) ).
fof(f4588,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(multiplication(addition(one,X1),X2),X3),multiplication(X1,X0))) = addition(multiplication(addition(one,X1),addition(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f97,f4587]) ).
fof(f4589,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(multiplication(addition(one,X2),X3),multiplication(X2,X0)))) = addition(multiplication(addition(one,X2),addition(X0,X3)),X1),
inference(forward_demodulation,[status(thm)],[f103,f4588]) ).
fof(f4590,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(X0,addition(one,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f4460]) ).
fof(f4591,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(X0,addition(one,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f4461]) ).
fof(f4592,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(multiplication(X0,X2),addition(X2,multiplication(addition(one,X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f4463]) ).
fof(f4593,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X2,addition(multiplication(addition(one,X0),X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f4592]) ).
fof(f4594,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(one,X1)),multiplication(star(addition(one,X1)),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),addition(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f103,f4468]) ).
fof(f4595,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(one,X2)),multiplication(star(addition(one,X2)),X1)))
| ~ leq(X0,addition(X0,addition(X1,multiplication(X2,X0)))) ),
inference(forward_demodulation,[status(thm)],[f97,f4594]) ).
fof(f4596,plain,
! [X0,X1,X2] : leq(X0,addition(omega(addition(one,X1)),multiplication(star(addition(one,X1)),X2))),
inference(forward_subsumption_resolution,[status(thm)],[f4595,f1324]) ).
fof(f4597,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),addition(one,X0))
| ~ leq(addition(multiplication(X0,X1),addition(X1,X2)),addition(one,X0)) ),
inference(forward_demodulation,[status(thm)],[f103,f4469]) ).
fof(f4598,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X0)),addition(one,X2))
| ~ leq(addition(X0,addition(X1,multiplication(X2,X0))),addition(one,X2)) ),
inference(forward_demodulation,[status(thm)],[f97,f4597]) ).
fof(f4599,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(one,X0)),X2),X1)
| ~ leq(addition(multiplication(X0,X1),addition(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f103,f4470]) ).
fof(f4600,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(one,X2)),X1),X0)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X0))),X0) ),
inference(forward_demodulation,[status(thm)],[f97,f4599]) ).
fof(f4601,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,addition(multiplication(X1,X2),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f4471]) ).
fof(f4602,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f201,f4601]) ).
fof(f4603,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(addition(X2,multiplication(X0,X2)),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f4472]) ).
fof(f4604,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f103,f4603]) ).
fof(f4605,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,addition(multiplication(X1,X2),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f4604]) ).
fof(f4606,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f201,f4605]) ).
fof(f4607,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(multiplication(X0,X1),addition(X1,multiplication(addition(one,X0),X2))),
inference(forward_demodulation,[status(thm)],[f103,f4474]) ).
fof(f4608,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X1,addition(multiplication(addition(one,X0),X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f4607]) ).
fof(f4616,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f4478]) ).
fof(f4617,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(X2))),X1)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f4482]) ).
fof(f4618,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X1)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f4617]) ).
fof(f4623,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(one,X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f97,f4499]) ).
fof(f4624,plain,
! [X0,X1] : addition(X0,multiplication(addition(addition(one,X1),X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f201,f4500]) ).
fof(f4625,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,addition(one,X1)),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f4624]) ).
fof(f4626,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(one,X1),X2)) = addition(X2,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f97,f4502]) ).
fof(f4627,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),X0),
inference(resolution,[status(thm)],[f2496,f246]) ).
fof(f4632,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),coantidomain(X2)))),
inference(paramodulation,[status(thm)],[f103,f2496]) ).
fof(f4633,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),coantidomain(X2)))),
inference(paramodulation,[status(thm)],[f36,f2496]) ).
fof(f4638,plain,
! [X0,X1] : addition(antidomain(coantidomain(X0)),X1) = addition(addition(antidomain(coantidomain(X0)),X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f224,f2496]) ).
fof(f4640,plain,
! [X0] : domain(coantidomain(X0)) = addition(domain(coantidomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f4146,f2496]) ).
fof(f4650,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),coantidomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2496,f224]) ).
fof(f4662,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),coantidomain(X3))),
inference(paramodulation,[status(thm)],[f2496,f170]) ).
fof(f4663,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),coantidomain(X2)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2496,f58]) ).
fof(f4664,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),coantidomain(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2496,f55]) ).
fof(f4665,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),coantidomain(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2496,f53]) ).
fof(f4666,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),coantidomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2496,f103]) ).
fof(f4667,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),coantidomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2496,f36]) ).
fof(f4675,plain,
! [X0,X1,X2] : leq(multiplication(X0,coantidomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2496,f1420]) ).
fof(f4679,plain,
! [X0,X1,X2] : addition(multiplication(X0,coantidomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2496,f103]) ).
fof(f4681,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,coantidomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2496,f97]) ).
fof(f4682,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,coantidomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2496,f97]) ).
fof(f4684,plain,
! [X0,X1] :
( X0 != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f2496,f49]) ).
fof(f4685,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,coantidomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2496,f36]) ).
fof(f4696,plain,
! [X0,X1] : addition(antidomain(coantidomain(X0)),X1) = addition(X1,addition(antidomain(coantidomain(X0)),multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4638]) ).
fof(f4697,plain,
! [X0] : domain(coantidomain(X0)) = addition(coantidomain(X0),domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4640]) ).
fof(f4703,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),coantidomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f59,f4650]) ).
fof(f4704,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4703]) ).
fof(f4714,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),coantidomain(X3))),
inference(forward_demodulation,[status(thm)],[f153,f4662]) ).
fof(f4715,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,coantidomain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f4714]) ).
fof(f4716,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,coantidomain(X3)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f4715]) ).
fof(f4717,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,coantidomain(X3)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f4716]) ).
fof(f4718,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,coantidomain(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f4663]) ).
fof(f4719,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(coantidomain(X2),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f4664]) ).
fof(f4720,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(coantidomain(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f4719]) ).
fof(f4721,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,coantidomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f4665]) ).
fof(f4728,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,coantidomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f4679]) ).
fof(f4730,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,coantidomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f4682]) ).
fof(f4733,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(antidomain(coantidomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f224,f4627]) ).
fof(f4735,plain,
! [X0] : leq(coantidomain(X0),domain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4146,f4627]) ).
fof(f4736,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,coantidomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f4627]) ).
fof(f4757,plain,
! [X0] : multiplication(one,coantidomain(domain(X0))) = multiplication(c(X0),coantidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f569,f226]) ).
fof(f4759,plain,
! [X0] : multiplication(one,coantidomain(coantidomain(X0))) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f683,f226]) ).
fof(f4761,plain,
! [X0] : multiplication(one,coantidomain(antidomain(X0))) = multiplication(domain(X0),coantidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f558,f226]) ).
fof(f4762,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(addition(multiplication(X0,X1),X2),X3),coantidomain(multiplication(X0,multiplication(X1,X3)))) = multiplication(multiplication(X2,X3),coantidomain(multiplication(X0,multiplication(X1,X3)))),
inference(paramodulation,[status(thm)],[f204,f226]) ).
fof(f4763,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),coantidomain(multiplication(X0,X1))) = multiplication(addition(multiplication(X0,X2),X3),coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f170,f226]) ).
fof(f4764,plain,
! [X0,X1,X2] : multiplication(multiplication(addition(X0,X1),X2),coantidomain(multiplication(X1,X2))) = multiplication(multiplication(X0,X2),coantidomain(multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f201,f226]) ).
fof(f4765,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,X2)),coantidomain(multiplication(X0,X2))) = multiplication(multiplication(X0,X1),coantidomain(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f153,f226]) ).
fof(f4766,plain,
! [X0,X1,X2] : multiplication(multiplication(addition(X0,X1),X2),coantidomain(multiplication(X0,X2))) = multiplication(multiplication(X1,X2),coantidomain(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f43,f226]) ).
fof(f4767,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,X2)),coantidomain(multiplication(X0,X1))) = multiplication(multiplication(X0,X2),coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f42,f226]) ).
fof(f4768,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X1,X0))) = multiplication(X2,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f103,f226]) ).
fof(f4769,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X0,X1))) = multiplication(X2,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f226]) ).
fof(f4771,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,coantidomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2496,f226]) ).
fof(f4772,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,antidomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2495,f226]) ).
fof(f4773,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,c(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2494,f226]) ).
fof(f4774,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,codomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2493,f226]) ).
fof(f4775,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,divergence(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2492,f226]) ).
fof(f4777,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(X1,one)),coantidomain(X0)) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f192,f226]) ).
fof(f4778,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(one,X1)),coantidomain(X0)) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f162,f226]) ).
fof(f4779,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(addition(X1,addition(X0,X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f99,f226]) ).
fof(f4781,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f97,f226]) ).
fof(f4782,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(paramodulation,[status(thm)],[f97,f226]) ).
fof(f4784,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(paramodulation,[status(thm)],[f35,f226]) ).
fof(f4785,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(paramodulation,[status(thm)],[f35,f226]) ).
fof(f4788,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,coantidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f66,f226]) ).
fof(f4790,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f226,f4627]) ).
fof(f4791,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f2496]) ).
fof(f4792,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X0)) = addition(coantidomain(X0),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f207]) ).
fof(f4793,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),coantidomain(X2)) = addition(multiplication(X0,multiplication(X1,coantidomain(X2))),multiplication(X3,coantidomain(X2))),
inference(paramodulation,[status(thm)],[f226,f204]) ).
fof(f4794,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),coantidomain(X1)) = addition(multiplication(X0,multiplication(X2,coantidomain(X1))),multiplication(X3,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f226,f204]) ).
fof(f4795,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),coantidomain(X0)) = addition(multiplication(X2,coantidomain(X0)),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f201]) ).
fof(f4796,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = addition(multiplication(X2,coantidomain(X1)),multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f226,f201]) ).
fof(f4797,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),addition(multiplication(X1,coantidomain(X0)),X3)) = addition(multiplication(addition(X0,X1),addition(X2,coantidomain(X0))),X3),
inference(paramodulation,[status(thm)],[f226,f170]) ).
fof(f4798,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,coantidomain(X1)),addition(multiplication(addition(X1,X0),X2),X3)) = addition(multiplication(addition(X1,X0),addition(coantidomain(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f226,f170]) ).
fof(f4799,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(coantidomain(X0),one)) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f192]) ).
fof(f4800,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,coantidomain(X0))) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f162]) ).
fof(f4801,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X0),X2)) = addition(multiplication(addition(X0,X1),X2),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f153]) ).
fof(f4802,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X0))) = addition(multiplication(X1,coantidomain(X0)),multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f226,f153]) ).
fof(f4803,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),coantidomain(multiplication(X1,coantidomain(X0))))) = zero,
inference(paramodulation,[status(thm)],[f226,f144]) ).
fof(f4804,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),multiplication(X1,coantidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f226,f136]) ).
fof(f4805,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,coantidomain(X1))),coantidomain(multiplication(codomain(addition(X1,X0)),coantidomain(X1)))) = coantidomain(multiplication(codomain(addition(X1,X0)),coantidomain(X1))),
inference(paramodulation,[status(thm)],[f226,f615]) ).
fof(f4806,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,coantidomain(X1))),antidomain(multiplication(addition(X1,X0),domain(coantidomain(X1))))) = antidomain(multiplication(addition(X1,X0),domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f226,f479]) ).
fof(f4807,plain,
! [X0,X1,X2] :
( leq(coantidomain(X0),addition(omega(addition(X0,X1)),multiplication(star(addition(X0,X1)),X2)))
| ~ leq(coantidomain(X0),addition(multiplication(X1,coantidomain(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f226,f58]) ).
fof(f4808,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(coantidomain(X1))),addition(X1,X0))
| ~ leq(addition(multiplication(X0,coantidomain(X1)),X2),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f226,f55]) ).
fof(f4809,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,X0)),X2),coantidomain(X1))
| ~ leq(addition(multiplication(X0,coantidomain(X1)),X2),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f226,f53]) ).
fof(f4810,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),multiplication(X2,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f226,f43]) ).
fof(f4811,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),coantidomain(X0)) = addition(multiplication(X1,coantidomain(X0)),multiplication(X2,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f43]) ).
fof(f4812,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X0))) = addition(multiplication(addition(X0,X1),X2),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f42]) ).
fof(f4813,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X0),X2)) = addition(multiplication(X1,coantidomain(X0)),multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f226,f42]) ).
fof(f4814,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(multiplication(X1,coantidomain(X0)),X2),
inference(paramodulation,[status(thm)],[f226,f39]) ).
fof(f4845,plain,
! [X0] : coantidomain(domain(X0)) = multiplication(c(X0),coantidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f41,f4757]) ).
fof(f4846,plain,
! [X0] : coantidomain(coantidomain(X0)) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f41,f4759]) ).
fof(f4847,plain,
! [X0] : codomain(X0) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f66,f4846]) ).
fof(f4848,plain,
! [X0] : codomain(X0) = multiplication(codomain(X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f66,f4847]) ).
fof(f4849,plain,
! [X0] : coantidomain(antidomain(X0)) = multiplication(domain(X0),coantidomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f41,f4761]) ).
fof(f4850,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X0,multiplication(X1,X3))))) = multiplication(multiplication(X2,X3),coantidomain(multiplication(X0,multiplication(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f39,f4762]) ).
fof(f4851,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X0,multiplication(X1,X3))))) = multiplication(X2,multiplication(X3,coantidomain(multiplication(X0,multiplication(X1,X3))))),
inference(forward_demodulation,[status(thm)],[f39,f4850]) ).
fof(f4852,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(multiplication(X0,X2),coantidomain(multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f4764]) ).
fof(f4853,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(X0,multiplication(X2,coantidomain(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f4852]) ).
fof(f4854,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),coantidomain(multiplication(X0,X2)))) = multiplication(multiplication(X0,X1),coantidomain(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f4765]) ).
fof(f4855,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),coantidomain(multiplication(X0,X2)))) = multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f4854]) ).
fof(f4856,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X0,X2)))) = multiplication(multiplication(X1,X2),coantidomain(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f4766]) ).
fof(f4857,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X0,X2)))) = multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f4856]) ).
fof(f4858,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),coantidomain(multiplication(X0,X1)))) = multiplication(multiplication(X0,X2),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f4767]) ).
fof(f4859,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),coantidomain(multiplication(X0,X1)))) = multiplication(X0,multiplication(X2,coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f39,f4858]) ).
fof(f4860,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,coantidomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f4771]) ).
fof(f4861,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4860]) ).
fof(f4862,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,antidomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f4772]) ).
fof(f4863,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4862]) ).
fof(f4864,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,c(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f4773]) ).
fof(f4865,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4864]) ).
fof(f4866,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,codomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f4774]) ).
fof(f4867,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4866]) ).
fof(f4868,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,divergence(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f4775]) ).
fof(f4869,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4868]) ).
fof(f4877,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f4777]) ).
fof(f4878,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4877]) ).
fof(f4879,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f4778]) ).
fof(f4880,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4879]) ).
fof(f4881,plain,
! [X0,X1] : multiplication(X0,coantidomain(X1)) = multiplication(addition(X0,addition(X1,X0)),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f226,f4779]) ).
fof(f4886,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f66,f4788]) ).
fof(f4891,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4791]) ).
fof(f4892,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X0)) = multiplication(addition(one,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f207,f4792]) ).
fof(f4893,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),coantidomain(X2)) = multiplication(addition(multiplication(X0,X1),X3),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f204,f4793]) ).
fof(f4894,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),coantidomain(X1)) = multiplication(addition(multiplication(X0,X2),X3),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f204,f4794]) ).
fof(f4895,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = addition(multiplication(X2,coantidomain(X1)),multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f103,f4795]) ).
fof(f4896,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X0,X2),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f201,f4895]) ).
fof(f4897,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X0,X2),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f201,f4796]) ).
fof(f4898,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,coantidomain(X1)),addition(X2,multiplication(addition(X1,X0),X3))) = addition(multiplication(addition(X1,X0),addition(X3,coantidomain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f97,f4797]) ).
fof(f4899,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,coantidomain(X0))) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4799]) ).
fof(f4900,plain,
! [X0,X1] : multiplication(addition(X0,X1),one) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f1377,f4899]) ).
fof(f4901,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f40,f4900]) ).
fof(f4902,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4901]) ).
fof(f4903,plain,
! [X0,X1] : multiplication(addition(X0,X1),one) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f1377,f4800]) ).
fof(f4904,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f40,f4903]) ).
fof(f4905,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4904]) ).
fof(f4906,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X0),X2)) = addition(multiplication(X1,coantidomain(X0)),multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f35,f4801]) ).
fof(f4907,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f201,f4810]) ).
fof(f4908,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),multiplication(X2,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f103,f4811]) ).
fof(f4909,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f201,f4908]) ).
fof(f4910,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X0))) = addition(multiplication(X1,coantidomain(X0)),multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f35,f4812]) ).
fof(f4911,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f39,f4814]) ).
fof(f4917,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f103,f2497]) ).
fof(f4918,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f36,f2497]) ).
fof(f4923,plain,
! [X0,X1] : addition(antidomain(domain(X0)),X1) = addition(addition(antidomain(domain(X0)),X1),multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f224,f2497]) ).
fof(f4926,plain,
! [X0] : domain(domain(X0)) = addition(domain(domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f4146,f2497]) ).
fof(f4931,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f69,f2497]) ).
fof(f4937,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),domain(X1)),X0),
inference(paramodulation,[status(thm)],[f2497,f224]) ).
fof(f4949,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),domain(X3))),
inference(paramodulation,[status(thm)],[f2497,f170]) ).
fof(f4950,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),domain(X2)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2497,f58]) ).
fof(f4951,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),domain(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2497,f55]) ).
fof(f4952,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),domain(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2497,f53]) ).
fof(f4953,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),domain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2497,f103]) ).
fof(f4954,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),domain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2497,f36]) ).
fof(f4959,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,domain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2497,f226]) ).
fof(f4963,plain,
! [X0,X1,X2] : leq(multiplication(X0,domain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2497,f1420]) ).
fof(f4967,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2497,f103]) ).
fof(f4969,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,domain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2497,f97]) ).
fof(f4970,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,domain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2497,f97]) ).
fof(f4972,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f2497,f49]) ).
fof(f4973,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,domain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2497,f36]) ).
fof(f4984,plain,
! [X0,X1] : addition(c(X0),X1) = addition(addition(antidomain(domain(X0)),X1),multiplication(X1,domain(X0))),
inference(forward_demodulation,[status(thm)],[f67,f4923]) ).
fof(f4985,plain,
! [X0,X1] : addition(c(X0),X1) = addition(X1,addition(antidomain(domain(X0)),multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f4984]) ).
fof(f4986,plain,
! [X0,X1] : addition(c(X0),X1) = addition(X1,addition(c(X0),multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f67,f4985]) ).
fof(f4989,plain,
! [X0] : antidomain(c(X0)) = addition(domain(domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f196,f4926]) ).
fof(f4990,plain,
! [X0] : antidomain(c(X0)) = addition(domain(X0),domain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4989]) ).
fof(f4991,plain,
! [X0] : antidomain(c(X0)) = addition(domain(X0),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f196,f4990]) ).
fof(f4999,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),domain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f59,f4937]) ).
fof(f5000,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4999]) ).
fof(f5010,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),domain(X3))),
inference(forward_demodulation,[status(thm)],[f153,f4949]) ).
fof(f5011,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,domain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f5010]) ).
fof(f5012,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,domain(X3)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f5011]) ).
fof(f5013,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,domain(X3)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f5012]) ).
fof(f5014,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,domain(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f4950]) ).
fof(f5015,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(domain(X2),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f4951]) ).
fof(f5016,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(domain(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f5015]) ).
fof(f5017,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,domain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f4952]) ).
fof(f5022,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,domain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f4959]) ).
fof(f5023,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f5022]) ).
fof(f5026,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,domain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f4967]) ).
fof(f5028,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,domain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f4970]) ).
fof(f5030,plain,
! [X0,X1,X2] : addition(multiplication(X0,backward_diamond(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3497,f48]) ).
fof(f5031,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(antidomain(backward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f224,f3497]) ).
fof(f5033,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f4146,f3497]) ).
fof(f5034,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,backward_diamond(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f3497]) ).
fof(f5043,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,backward_diamond(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f5030]) ).
fof(f5047,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f153,f211]) ).
fof(f5048,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f42,f211]) ).
fof(f5049,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(addition(one,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f207,f211]) ).
fof(f5050,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1) = multiplication(multiplication(X0,X1),addition(multiplication(X2,X1),one)),
inference(paramodulation,[status(thm)],[f192,f211]) ).
fof(f5051,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1) = multiplication(multiplication(X0,X1),addition(one,multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f162,f211]) ).
fof(f5052,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f35,f211]) ).
fof(f5053,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f35,f211]) ).
fof(f5054,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(one,X0),multiplication(X1,X2)),X3) = addition(addition(X3,multiplication(X0,X3)),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f207,f211]) ).
fof(f5055,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(antidomain(X0),X1),multiplication(X2,X3)),X0) = addition(multiplication(X1,X0),multiplication(X2,multiplication(X3,X0))),
inference(paramodulation,[status(thm)],[f224,f211]) ).
fof(f5056,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,X1),multiplication(X2,X3)),coantidomain(X0)) = addition(multiplication(X1,coantidomain(X0)),multiplication(X2,multiplication(X3,coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f226,f211]) ).
fof(f5057,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),domain(X0)) = addition(zero,multiplication(X1,multiplication(X2,domain(X0)))),
inference(paramodulation,[status(thm)],[f197,f211]) ).
fof(f5058,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),X0) = addition(zero,multiplication(X1,multiplication(X2,X0))),
inference(paramodulation,[status(thm)],[f4265,f211]) ).
fof(f5059,plain,
! [X0,X1,X2] : multiplication(addition(coantidomain(X0),multiplication(X1,X2)),codomain(X0)) = addition(zero,multiplication(X1,multiplication(X2,codomain(X0)))),
inference(paramodulation,[status(thm)],[f195,f211]) ).
fof(f5060,plain,
! [X0,X1,X2,X3] : multiplication(addition(domain(X0),multiplication(X1,X2)),antidomain(X3)) = addition(domain_difference(X0,X3),multiplication(X1,multiplication(X2,antidomain(X3)))),
inference(paramodulation,[status(thm)],[f68,f211]) ).
fof(f5061,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),multiplication(X1,X2)),X0) = addition(X0,multiplication(X1,multiplication(X2,X0))),
inference(paramodulation,[status(thm)],[f4146,f211]) ).
fof(f5062,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),multiplication(X2,X3)),X4) = addition(multiplication(X0,multiplication(X1,X4)),multiplication(X2,multiplication(X3,X4))),
inference(paramodulation,[status(thm)],[f39,f211]) ).
fof(f5063,plain,
! [X0,X1,X2,X3] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),addition(X3,X0)) = addition(multiplication(antidomain(X0),X3),multiplication(X1,multiplication(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f186,f211]) ).
fof(f5064,plain,
! [X0,X1,X2,X3] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),addition(X0,X3)) = addition(multiplication(antidomain(X0),X3),multiplication(X1,multiplication(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f177,f211]) ).
fof(f5065,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),omega(X0)) = addition(zero,multiplication(X1,multiplication(X2,omega(X0)))),
inference(paramodulation,[status(thm)],[f1569,f211]) ).
fof(f5066,plain,
! [X0,X1,X2,X3] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),multiplication(X0,X3)) = addition(zero,multiplication(X1,multiplication(X2,multiplication(X0,X3)))),
inference(paramodulation,[status(thm)],[f136,f211]) ).
fof(f5069,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f41,f211]) ).
fof(f5070,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),codomain(X0)) = addition(X0,multiplication(X1,multiplication(X2,codomain(X0)))),
inference(paramodulation,[status(thm)],[f2309,f211]) ).
fof(f5071,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(one,X3)) = addition(addition(X0,multiplication(X0,X3)),multiplication(X1,multiplication(X2,addition(one,X3)))),
inference(paramodulation,[status(thm)],[f162,f211]) ).
fof(f5072,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(coantidomain(X0),X3)) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,addition(coantidomain(X0),X3)))),
inference(paramodulation,[status(thm)],[f181,f211]) ).
fof(f5073,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,one)) = addition(addition(X0,multiplication(X0,X3)),multiplication(X1,multiplication(X2,addition(X3,one)))),
inference(paramodulation,[status(thm)],[f192,f211]) ).
fof(f5074,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,coantidomain(X0))) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,addition(X3,coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f190,f211]) ).
fof(f5075,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(coantidomain(X0),X3)) = addition(zero,multiplication(X1,multiplication(X2,multiplication(coantidomain(X0),X3)))),
inference(paramodulation,[status(thm)],[f151,f211]) ).
fof(f5076,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X0,X3)))) = addition(zero,multiplication(X1,multiplication(X2,multiplication(X3,coantidomain(multiplication(X0,X3)))))),
inference(paramodulation,[status(thm)],[f144,f211]) ).
fof(f5077,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(coantidomain(X0))) = addition(zero,multiplication(X1,multiplication(X2,omega(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f1813,f211]) ).
fof(f5078,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(X0)) = addition(omega(X0),multiplication(X1,multiplication(X2,omega(X0)))),
inference(paramodulation,[status(thm)],[f56,f211]) ).
fof(f5082,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(antidomain(multiplication(X1,X2)),X3),X1)),X2) = addition(multiplication(X0,X2),multiplication(X3,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f224,f211]) ).
fof(f5083,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(c(multiplication(X1,X2)),X1)),X2) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f4265,f211]) ).
fof(f5084,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(domain(multiplication(X1,X2)),X1)),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f4146,f211]) ).
fof(f5085,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,multiplication(multiplication(X1,X2),X3)),X4) = addition(multiplication(X0,X4),multiplication(X1,multiplication(X2,multiplication(X3,X4)))),
inference(paramodulation,[status(thm)],[f39,f211]) ).
fof(f5087,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(antidomain(multiplication(X1,X2)),X1)),X2) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f59,f211]) ).
fof(f5091,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(multiplication(X1,X2))) = addition(multiplication(X0,coantidomain(multiplication(X1,X2))),zero),
inference(paramodulation,[status(thm)],[f144,f211]) ).
fof(f5092,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(one,X2))),X3) = addition(multiplication(X0,X3),multiplication(X1,addition(X3,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f207,f211]) ).
fof(f5093,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(antidomain(X2),X3))),X2) = addition(multiplication(X0,X2),multiplication(X1,multiplication(X3,X2))),
inference(paramodulation,[status(thm)],[f224,f211]) ).
fof(f5094,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,X3))),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),multiplication(X1,multiplication(X3,coantidomain(X2)))),
inference(paramodulation,[status(thm)],[f226,f211]) ).
fof(f5095,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f197,f211]) ).
fof(f5096,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f4265,f211]) ).
fof(f5097,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,coantidomain(X2))),codomain(X2)) = addition(multiplication(X0,codomain(X2)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f195,f211]) ).
fof(f5098,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,domain(X2))),antidomain(X3)) = addition(multiplication(X0,antidomain(X3)),multiplication(X1,domain_difference(X2,X3))),
inference(paramodulation,[status(thm)],[f68,f211]) ).
fof(f5099,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f4146,f211]) ).
fof(f5100,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,multiplication(X1,multiplication(X2,X3))),X4) = addition(multiplication(X0,X4),multiplication(X1,multiplication(X2,multiplication(X3,X4)))),
inference(paramodulation,[status(thm)],[f39,f211]) ).
fof(f5101,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),addition(X3,X2)) = addition(multiplication(X0,addition(X3,X2)),multiplication(X1,multiplication(antidomain(X2),X3))),
inference(paramodulation,[status(thm)],[f186,f211]) ).
fof(f5102,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),addition(X2,X3)) = addition(multiplication(X0,addition(X2,X3)),multiplication(X1,multiplication(antidomain(X2),X3))),
inference(paramodulation,[status(thm)],[f177,f211]) ).
fof(f5103,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),omega(X2)) = addition(multiplication(X0,omega(X2)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f1569,f211]) ).
fof(f5104,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),multiplication(X2,X3)) = addition(multiplication(X0,multiplication(X2,X3)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f136,f211]) ).
fof(f5105,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f59,f211]) ).
fof(f5108,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),codomain(X2)) = addition(multiplication(X0,codomain(X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f2309,f211]) ).
fof(f5109,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(one,X3)) = addition(multiplication(X0,addition(one,X3)),multiplication(X1,addition(X2,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f162,f211]) ).
fof(f5110,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(coantidomain(X2),X3)) = addition(multiplication(X0,addition(coantidomain(X2),X3)),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f181,f211]) ).
fof(f5111,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,one)) = addition(multiplication(X0,addition(X3,one)),multiplication(X1,addition(X2,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f192,f211]) ).
fof(f5112,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,coantidomain(X2))) = addition(multiplication(X0,addition(X3,coantidomain(X2))),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f190,f211]) ).
fof(f5113,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(coantidomain(X2),X3)) = addition(multiplication(X0,multiplication(coantidomain(X2),X3)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f151,f211]) ).
fof(f5114,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X2,X3)))) = addition(multiplication(X0,multiplication(X3,coantidomain(multiplication(X2,X3)))),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f144,f211]) ).
fof(f5115,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(coantidomain(X2))) = addition(multiplication(X0,omega(coantidomain(X2))),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f1813,f211]) ).
fof(f5116,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(X2)) = addition(multiplication(X0,omega(X2)),multiplication(X1,omega(X2))),
inference(paramodulation,[status(thm)],[f56,f211]) ).
fof(f5117,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f63,f211]) ).
fof(f5120,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,X2),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f211,f153]) ).
fof(f5121,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(paramodulation,[status(thm)],[f211,f42]) ).
fof(f5122,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(addition(X0,multiplication(X2,X3)),X4)) = addition(multiplication(X0,addition(X1,X4)),multiplication(X2,multiplication(X3,X4))),
inference(paramodulation,[status(thm)],[f211,f170]) ).
fof(f5123,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X2,multiplication(X3,X0)))))
| ~ leq(X0,multiplication(addition(X1,multiplication(X2,X3)),X0)) ),
inference(paramodulation,[status(thm)],[f211,f58]) ).
fof(f5124,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X1,multiplication(X2,X3)),star(X3)),X0)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X0) ),
inference(paramodulation,[status(thm)],[f211,f55]) ).
fof(f5125,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X1,multiplication(X2,X3))),X3)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X3) ),
inference(paramodulation,[status(thm)],[f211,f53]) ).
fof(f5126,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f211,f207]) ).
fof(f5127,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(multiplication(X2,X1),one)) = multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1),
inference(paramodulation,[status(thm)],[f211,f192]) ).
fof(f5128,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(one,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1),
inference(paramodulation,[status(thm)],[f211,f162]) ).
fof(f5129,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(addition(X0,multiplication(X1,X2)),X3),coantidomain(multiplication(X0,X3))) = multiplication(multiplication(X1,multiplication(X2,X3)),coantidomain(multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f211,f226]) ).
fof(f5130,plain,
! [X0,X1,X2,X3] : multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(addition(X3,multiplication(X0,X1)),X2)) = multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(X3,X2)),
inference(paramodulation,[status(thm)],[f211,f186]) ).
fof(f5131,plain,
! [X0,X1,X2,X3] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(X0,multiplication(X2,X3)),X1)) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f211,f177]) ).
fof(f5132,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,multiplication(X3,X4)),X1))),
inference(paramodulation,[status(thm)],[f211,f1421]) ).
fof(f5133,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),addition(X3,multiplication(addition(X4,multiplication(X0,X1)),X2))),
inference(paramodulation,[status(thm)],[f211,f1420]) ).
fof(f5134,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f211,f1423]) ).
fof(f5135,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(X0,multiplication(X2,X3)),X1)),
inference(paramodulation,[status(thm)],[f211,f1324]) ).
fof(f5136,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X0,multiplication(X2,X3)),X1)) = addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f211,f105]) ).
fof(f5137,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(X3,multiplication(X0,X1)),X2),X4),
inference(paramodulation,[status(thm)],[f211,f103]) ).
fof(f5138,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),multiplication(addition(X0,multiplication(X2,X3)),X1))) = addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f211,f99]) ).
fof(f5139,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),X4)) = addition(X4,multiplication(addition(X0,multiplication(X2,X3)),X1)),
inference(paramodulation,[status(thm)],[f211,f97]) ).
fof(f5140,plain,
! [X0,X1,X2,X3,X4] : addition(X0,multiplication(addition(X1,multiplication(X2,X3)),X4)) = addition(multiplication(X2,multiplication(X3,X4)),addition(X0,multiplication(X1,X4))),
inference(paramodulation,[status(thm)],[f211,f97]) ).
fof(f5141,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,multiplication(X0,X1)),X2) != multiplication(X3,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f211,f246]) ).
fof(f5142,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X0,multiplication(X2,X3)),X1) != multiplication(X2,multiplication(X3,X1))
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))) ),
inference(paramodulation,[status(thm)],[f211,f49]) ).
fof(f5143,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),X4)) = addition(multiplication(addition(X0,multiplication(X2,X3)),X1),X4),
inference(paramodulation,[status(thm)],[f211,f36]) ).
fof(f5144,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) = multiplication(addition(X3,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f211,f35]) ).
fof(f5145,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f211,f35]) ).
fof(f5146,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f5047]) ).
fof(f5147,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1) = multiplication(multiplication(X0,X1),addition(multiplication(X2,X1),one)),
inference(forward_demodulation,[status(thm)],[f39,f5050]) ).
fof(f5148,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1) = multiplication(X0,multiplication(X1,addition(multiplication(X2,X1),one))),
inference(forward_demodulation,[status(thm)],[f39,f5147]) ).
fof(f5149,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1) = multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f35,f5148]) ).
fof(f5150,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1) = multiplication(multiplication(X0,X1),addition(one,multiplication(X2,X1))),
inference(forward_demodulation,[status(thm)],[f39,f5051]) ).
fof(f5151,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1) = multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f39,f5150]) ).
fof(f5152,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(one,multiplication(X1,X2))),X3) = addition(addition(X3,multiplication(X0,X3)),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f103,f5054]) ).
fof(f5153,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(one,multiplication(X1,X2))),X3) = addition(multiplication(X0,X3),addition(X3,multiplication(X1,multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f103,f5152]) ).
fof(f5154,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(one,multiplication(X1,X2))),X3) = addition(X3,addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f97,f5153]) ).
fof(f5155,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(one,multiplication(X1,X2))),X3) = addition(X3,multiplication(addition(multiplication(X1,X2),X0),X3)),
inference(forward_demodulation,[status(thm)],[f204,f5154]) ).
fof(f5156,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(antidomain(X1),multiplication(X2,X3))),X1) = addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),
inference(forward_demodulation,[status(thm)],[f103,f5055]) ).
fof(f5157,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(antidomain(X1),multiplication(X2,X3))),X1) = multiplication(addition(X0,multiplication(X2,X3)),X1),
inference(forward_demodulation,[status(thm)],[f211,f5156]) ).
fof(f5158,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,multiplication(X2,X3))),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),multiplication(X2,multiplication(X3,coantidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f103,f5056]) ).
fof(f5159,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,multiplication(X2,X3))),coantidomain(X1)) = multiplication(addition(X0,multiplication(X2,X3)),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f211,f5158]) ).
fof(f5160,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),domain(X0)) = multiplication(X1,multiplication(X2,domain(X0))),
inference(forward_demodulation,[status(thm)],[f80,f5057]) ).
fof(f5161,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),X0) = multiplication(X1,multiplication(X2,X0)),
inference(forward_demodulation,[status(thm)],[f80,f5058]) ).
fof(f5162,plain,
! [X0,X1,X2] : multiplication(addition(coantidomain(X0),multiplication(X1,X2)),codomain(X0)) = multiplication(X1,multiplication(X2,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f80,f5059]) ).
fof(f5163,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),omega(X0)) = multiplication(X1,multiplication(X2,omega(X0))),
inference(forward_demodulation,[status(thm)],[f80,f5065]) ).
fof(f5164,plain,
! [X0,X1,X2,X3] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),multiplication(X0,X3)) = multiplication(X1,multiplication(X2,multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f80,f5066]) ).
fof(f5169,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(one,X3)) = addition(multiplication(X0,X3),addition(X0,multiplication(X1,multiplication(X2,addition(one,X3))))),
inference(forward_demodulation,[status(thm)],[f103,f5071]) ).
fof(f5170,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(one,X3)) = addition(X0,addition(multiplication(X1,multiplication(X2,addition(one,X3))),multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f97,f5169]) ).
fof(f5171,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,one)) = addition(multiplication(X0,X3),addition(X0,multiplication(X1,multiplication(X2,addition(X3,one))))),
inference(forward_demodulation,[status(thm)],[f103,f5073]) ).
fof(f5172,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,one)) = addition(X0,addition(multiplication(X1,multiplication(X2,addition(X3,one))),multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f97,f5171]) ).
fof(f5173,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(coantidomain(X0),X3)) = multiplication(X1,multiplication(X2,multiplication(coantidomain(X0),X3))),
inference(forward_demodulation,[status(thm)],[f80,f5075]) ).
fof(f5174,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X0,X3)))) = multiplication(X1,multiplication(X2,multiplication(X3,coantidomain(multiplication(X0,X3))))),
inference(forward_demodulation,[status(thm)],[f80,f5076]) ).
fof(f5175,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(coantidomain(X0))) = multiplication(X1,multiplication(X2,omega(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f80,f5077]) ).
fof(f5182,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(antidomain(multiplication(X1,X2)),X3),X1)),X2) = multiplication(addition(X0,multiplication(X3,X1)),X2),
inference(forward_demodulation,[status(thm)],[f211,f5082]) ).
fof(f5183,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(c(multiplication(X1,X2)),X1)),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f37,f5083]) ).
fof(f5184,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(domain(multiplication(X1,X2)),X1)),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f201,f5084]) ).
fof(f5185,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,multiplication(X1,multiplication(X2,X3))),X4) = addition(multiplication(X0,X4),multiplication(X1,multiplication(X2,multiplication(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f5085]) ).
fof(f5188,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(antidomain(multiplication(X1,X2)),X1)),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f37,f5087]) ).
fof(f5194,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(multiplication(X1,X2))) = multiplication(X0,coantidomain(multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f37,f5091]) ).
fof(f5195,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(antidomain(X2),X3))),X2) = multiplication(addition(X0,multiplication(X1,X3)),X2),
inference(forward_demodulation,[status(thm)],[f211,f5093]) ).
fof(f5196,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,X3))),coantidomain(X2)) = multiplication(addition(X0,multiplication(X1,X3)),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f211,f5094]) ).
fof(f5197,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f44,f5095]) ).
fof(f5198,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),domain(X2)) = multiplication(X0,domain(X2)),
inference(forward_demodulation,[status(thm)],[f37,f5197]) ).
fof(f5199,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = addition(multiplication(X0,X2),zero),
inference(forward_demodulation,[status(thm)],[f44,f5096]) ).
fof(f5200,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f37,f5199]) ).
fof(f5201,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,coantidomain(X2))),codomain(X2)) = addition(multiplication(X0,codomain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f44,f5097]) ).
fof(f5202,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,coantidomain(X2))),codomain(X2)) = multiplication(X0,codomain(X2)),
inference(forward_demodulation,[status(thm)],[f37,f5201]) ).
fof(f5203,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f201,f5099]) ).
fof(f5204,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),omega(X2)) = addition(multiplication(X0,omega(X2)),zero),
inference(forward_demodulation,[status(thm)],[f44,f5103]) ).
fof(f5205,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),omega(X2)) = multiplication(X0,omega(X2)),
inference(forward_demodulation,[status(thm)],[f37,f5204]) ).
fof(f5206,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),multiplication(X2,X3)) = addition(multiplication(X0,multiplication(X2,X3)),zero),
inference(forward_demodulation,[status(thm)],[f44,f5104]) ).
fof(f5207,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),multiplication(X2,X3)) = multiplication(X0,multiplication(X2,X3)),
inference(forward_demodulation,[status(thm)],[f37,f5206]) ).
fof(f5208,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),zero),
inference(forward_demodulation,[status(thm)],[f44,f5105]) ).
fof(f5209,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f37,f5208]) ).
fof(f5214,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(coantidomain(X2),X3)) = addition(multiplication(X0,multiplication(coantidomain(X2),X3)),zero),
inference(forward_demodulation,[status(thm)],[f44,f5113]) ).
fof(f5215,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(coantidomain(X2),X3)) = multiplication(X0,multiplication(coantidomain(X2),X3)),
inference(forward_demodulation,[status(thm)],[f37,f5214]) ).
fof(f5216,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X2,X3)))) = addition(multiplication(X0,multiplication(X3,coantidomain(multiplication(X2,X3)))),zero),
inference(forward_demodulation,[status(thm)],[f44,f5114]) ).
fof(f5217,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X2,X3)))) = multiplication(X0,multiplication(X3,coantidomain(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f37,f5216]) ).
fof(f5218,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(coantidomain(X2))) = addition(multiplication(X0,omega(coantidomain(X2))),zero),
inference(forward_demodulation,[status(thm)],[f44,f5115]) ).
fof(f5219,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(coantidomain(X2))) = multiplication(X0,omega(coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f37,f5218]) ).
fof(f5220,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(X2)) = multiplication(addition(X1,X0),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f5116]) ).
fof(f5221,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f44,f5117]) ).
fof(f5222,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = multiplication(X0,coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f37,f5221]) ).
fof(f5226,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f35,f5120]) ).
fof(f5227,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(multiplication(X2,X3),star(X3))),X0)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f5124]) ).
fof(f5228,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(X2,multiplication(X3,star(X3)))),X0)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f5227]) ).
fof(f5229,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(multiplication(X2,X1),one))) = multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1),
inference(forward_demodulation,[status(thm)],[f39,f5127]) ).
fof(f5230,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))) = multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1),
inference(forward_demodulation,[status(thm)],[f35,f5229]) ).
fof(f5231,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))) = multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1),
inference(forward_demodulation,[status(thm)],[f39,f5230]) ).
fof(f5232,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))) = multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1),
inference(forward_demodulation,[status(thm)],[f39,f5128]) ).
fof(f5233,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))) = multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1),
inference(forward_demodulation,[status(thm)],[f39,f5232]) ).
fof(f5234,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X0,X3)))) = multiplication(multiplication(X1,multiplication(X2,X3)),coantidomain(multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f39,f5129]) ).
fof(f5235,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X0,X3)))) = multiplication(X1,multiplication(multiplication(X2,X3),coantidomain(multiplication(X0,X3)))),
inference(forward_demodulation,[status(thm)],[f39,f5234]) ).
fof(f5236,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X0,X3)))) = multiplication(X1,multiplication(X2,multiplication(X3,coantidomain(multiplication(X0,X3))))),
inference(forward_demodulation,[status(thm)],[f39,f5235]) ).
fof(f5237,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,multiplication(X1,X2)),X0),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f201,f5136]) ).
fof(f5238,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X2)),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f103,f5237]) ).
fof(f5239,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f38,f5238]) ).
fof(f5240,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(multiplication(X2,X3),addition(X0,multiplication(X2,X3))),X1)) = addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),
inference(forward_demodulation,[status(thm)],[f204,f5138]) ).
fof(f5241,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(multiplication(X0,X1),addition(X2,multiplication(X0,X1))),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f201,f5240]) ).
fof(f5242,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,multiplication(X1,X2)),addition(multiplication(X1,X2),X0)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f103,f5241]) ).
fof(f5243,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X1),X2))),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f103,f5242]) ).
fof(f5244,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f99,f5243]) ).
fof(f5245,plain,
! [X0,X1,X2] : addition(multiplication(X0,backward_box(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3740,f48]) ).
fof(f5246,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),addition(antidomain(backward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f224,f3740]) ).
fof(f5248,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f4146,f3740]) ).
fof(f5249,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,backward_box(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f3740]) ).
fof(f5255,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,backward_box(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f5245]) ).
fof(f5258,plain,
! [X0,X1,X2] : addition(multiplication(X0,forward_box(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3741,f48]) ).
fof(f5259,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),addition(antidomain(forward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f224,f3741]) ).
fof(f5261,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f4146,f3741]) ).
fof(f5262,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,forward_box(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f3741]) ).
fof(f5269,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,forward_box(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f5258]) ).
fof(f5279,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))) = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f479,f230]) ).
fof(f5280,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f103,f230]) ).
fof(f5281,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f36,f230]) ).
fof(f5287,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f67,f230]) ).
fof(f5288,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = multiplication(X0,antidomain(X1)),
inference(paramodulation,[status(thm)],[f62,f230]) ).
fof(f5293,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),addition(X0,antidomain(forward_box(X1,X2)))),
inference(paramodulation,[status(thm)],[f230,f3741]) ).
fof(f5294,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),addition(X0,antidomain(backward_box(X1,X2)))),
inference(paramodulation,[status(thm)],[f230,f3740]) ).
fof(f5295,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(X0,antidomain(backward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f230,f3497]) ).
fof(f5296,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(X0,antidomain(antidomain(X1)))),
inference(paramodulation,[status(thm)],[f230,f3749]) ).
fof(f5298,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),addition(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f230,f3652]) ).
fof(f5300,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),addition(X0,antidomain(divergence(X1)))),
inference(paramodulation,[status(thm)],[f230,f3330]) ).
fof(f5302,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),addition(X0,antidomain(codomain(X1)))),
inference(paramodulation,[status(thm)],[f230,f3411]) ).
fof(f5304,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(X1,antidomain(multiplication(X2,X3))),X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f230,f211]) ).
fof(f5305,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,antidomain(multiplication(X1,X2))),X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),
inference(paramodulation,[status(thm)],[f230,f204]) ).
fof(f5307,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(X0,antidomain(domain(X1)))),
inference(paramodulation,[status(thm)],[f230,f3841]) ).
fof(f5308,plain,
! [X0,X1] : forward_diamond(addition(X0,antidomain(domain(X1))),X1) = domain(multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f230,f69]) ).
fof(f5309,plain,
! [X0,X1] : addition(antidomain(multiplication(addition(X0,antidomain(domain(X1))),X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(addition(X0,antidomain(domain(X1))),domain(X1))),
inference(paramodulation,[status(thm)],[f230,f479]) ).
fof(f5310,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X0,antidomain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f230,f4627]) ).
fof(f5314,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,antidomain(X3)))),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f230,f211]) ).
fof(f5316,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,antidomain(X1))),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f230,f207]) ).
fof(f5317,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,antidomain(X3))),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f230,f204]) ).
fof(f5318,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,antidomain(X2))),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),
inference(paramodulation,[status(thm)],[f230,f204]) ).
fof(f5320,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f230,f201]) ).
fof(f5321,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,antidomain(X1)),X2),addition(multiplication(X0,X1),X3)) = addition(multiplication(addition(X0,antidomain(X1)),addition(X2,X1)),X3),
inference(paramodulation,[status(thm)],[f230,f170]) ).
fof(f5322,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(addition(X0,antidomain(X1)),X2),X3)) = addition(multiplication(addition(X0,antidomain(X1)),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f230,f170]) ).
fof(f5323,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(X1,one)) = addition(addition(X0,antidomain(X1)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f230,f192]) ).
fof(f5324,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(one,X1)) = addition(addition(X0,antidomain(X1)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f230,f162]) ).
fof(f5325,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X1,X2)) = addition(multiplication(addition(X0,antidomain(X1)),X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f230,f153]) ).
fof(f5326,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X2,X1)) = addition(multiplication(X0,X1),multiplication(addition(X0,antidomain(X1)),X2)),
inference(paramodulation,[status(thm)],[f230,f153]) ).
fof(f5327,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f230,f144]) ).
fof(f5328,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,antidomain(X1))),multiplication(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f230,f136]) ).
fof(f5329,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(addition(X0,antidomain(X1))),X1))) = coantidomain(multiplication(codomain(addition(X0,antidomain(X1))),X1)),
inference(paramodulation,[status(thm)],[f230,f615]) ).
fof(f5330,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(addition(X0,antidomain(X1)),domain(X1)))) = antidomain(multiplication(addition(X0,antidomain(X1)),domain(X1))),
inference(paramodulation,[status(thm)],[f230,f479]) ).
fof(f5331,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(X1,antidomain(X0))),multiplication(star(addition(X1,antidomain(X0))),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f230,f58]) ).
fof(f5332,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),addition(X0,antidomain(X1)))
| ~ leq(addition(multiplication(X0,X1),X2),addition(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f230,f55]) ).
fof(f5333,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,antidomain(X1))),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f230,f53]) ).
fof(f5334,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f230,f43]) ).
fof(f5336,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X2,X1)) = addition(multiplication(addition(X0,antidomain(X1)),X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f230,f42]) ).
fof(f5337,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(addition(X0,antidomain(X1)),X2)),
inference(paramodulation,[status(thm)],[f230,f42]) ).
fof(f5338,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f230,f39]) ).
fof(f5344,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f59,f5279]) ).
fof(f5352,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f62,f5296]) ).
fof(f5363,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(X1,antidomain(multiplication(X2,X3))),X2)),X3) = multiplication(addition(X0,multiplication(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f211,f5304]) ).
fof(f5364,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,antidomain(multiplication(X1,X2))),X1),X3),X2) = multiplication(addition(multiplication(X0,X1),X3),X2),
inference(forward_demodulation,[status(thm)],[f204,f5305]) ).
fof(f5369,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f67,f5307]) ).
fof(f5370,plain,
! [X0,X1] : forward_diamond(addition(X0,c(X1)),X1) = domain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f67,f5308]) ).
fof(f5371,plain,
! [X0,X1] : forward_diamond(addition(X0,c(X1)),X1) = forward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f69,f5370]) ).
fof(f5372,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(addition(X0,antidomain(domain(X1))),X1))) = antidomain(multiplication(addition(X0,antidomain(domain(X1))),domain(X1))),
inference(forward_demodulation,[status(thm)],[f35,f5309]) ).
fof(f5373,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(addition(X0,c(X1)),X1))) = antidomain(multiplication(addition(X0,antidomain(domain(X1))),domain(X1))),
inference(forward_demodulation,[status(thm)],[f67,f5372]) ).
fof(f5374,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(addition(X0,c(X1)),X1))) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f230,f5373]) ).
fof(f5379,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,antidomain(X3)))),X3) = multiplication(addition(X0,multiplication(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f211,f5314]) ).
fof(f5382,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,antidomain(X3))),X3) = multiplication(addition(multiplication(X0,X1),X2),X3),
inference(forward_demodulation,[status(thm)],[f204,f5317]) ).
fof(f5383,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,antidomain(X2))),X3),X2) = multiplication(addition(multiplication(X0,X1),X3),X2),
inference(forward_demodulation,[status(thm)],[f204,f5318]) ).
fof(f5386,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f201,f5320]) ).
fof(f5387,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(addition(X0,antidomain(X1)),X3))) = addition(multiplication(addition(X0,antidomain(X1)),addition(X3,X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f5321]) ).
fof(f5388,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(X1,one)) = addition(antidomain(X1),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f5323]) ).
fof(f5389,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(one,X1)) = addition(antidomain(X1),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f5324]) ).
fof(f5390,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(addition(X0,antidomain(X1)),X2)),
inference(forward_demodulation,[status(thm)],[f35,f5325]) ).
fof(f5391,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f201,f5334]) ).
fof(f5394,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),addition(X2,X1)) = addition(multiplication(X0,X1),multiplication(addition(X0,antidomain(X1)),X2)),
inference(forward_demodulation,[status(thm)],[f35,f5336]) ).
fof(f5395,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f39,f5338]) ).
fof(f5396,plain,
! [X0,X1,X2] : addition(multiplication(X0,forward_diamond(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f4077,f48]) ).
fof(f5397,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(antidomain(forward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f224,f4077]) ).
fof(f5398,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(X0,antidomain(forward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f230,f4077]) ).
fof(f5400,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),domain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f4146,f4077]) ).
fof(f5401,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,forward_diamond(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f4077]) ).
fof(f5411,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,forward_diamond(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f5396]) ).
fof(f5415,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(resolution,[status(thm)],[f4206,f48]) ).
fof(f5416,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(c(backward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f72,f4206]) ).
fof(f5417,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(c(forward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f71,f4206]) ).
fof(f5420,plain,
! [X0] : leq(domain(c(X0)),domain(c(domain(X0)))),
inference(paramodulation,[status(thm)],[f362,f4206]) ).
fof(f5422,plain,
! [X0,X1] : leq(c(backward_diamond(X0,c(X1))),domain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f72,f4206]) ).
fof(f5423,plain,
! [X0,X1] : leq(c(forward_diamond(X0,c(X1))),domain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f71,f4206]) ).
fof(f5426,plain,
! [X0] : leq(c(domain(X0)),domain(domain(c(X0)))),
inference(paramodulation,[status(thm)],[f362,f4206]) ).
fof(f5428,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f72,f5416]) ).
fof(f5429,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f71,f5417]) ).
fof(f5434,plain,
! [X0] : leq(domain(c(X0)),domain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f362,f5420]) ).
fof(f5435,plain,
! [X0] : leq(domain(c(X0)),antidomain(c(c(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f5434]) ).
fof(f5438,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f72,f5422]) ).
fof(f5439,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f71,f5423]) ).
fof(f5444,plain,
! [X0] : leq(domain(c(X0)),domain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f362,f5426]) ).
fof(f5445,plain,
! [X0] : leq(domain(c(X0)),antidomain(c(c(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f5444]) ).
fof(f5448,plain,
! [X0] : addition(divergence(X0),domain(divergence(X0))) = domain(divergence(X0)),
inference(resolution,[status(thm)],[f4208,f48]) ).
fof(f5455,plain,
! [X0] : addition(codomain(X0),domain(codomain(X0))) = domain(codomain(X0)),
inference(resolution,[status(thm)],[f4210,f48]) ).
fof(f5456,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(codomain(multiplication(codomain(X1),X0)))),
inference(paramodulation,[status(thm)],[f70,f4210]) ).
fof(f5458,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(codomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f193,f4210]) ).
fof(f5460,plain,
! [X0,X1] : leq(codomain(multiplication(codomain(X0),X1)),domain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f70,f4210]) ).
fof(f5462,plain,
! [X0] : leq(codomain(coantidomain(X0)),domain(coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f193,f4210]) ).
fof(f5464,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f70,f5456]) ).
fof(f5467,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f193,f5458]) ).
fof(f5470,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f70,f5460]) ).
fof(f5473,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f193,f5462]) ).
fof(f5481,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f103,f232]) ).
fof(f5482,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f36,f232]) ).
fof(f5487,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f211,f232]) ).
fof(f5488,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f153,f232]) ).
fof(f5489,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f42,f232]) ).
fof(f5490,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X2,addition(X1,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f103,f232]) ).
fof(f5491,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X1,addition(X2,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f36,f232]) ).
fof(f5499,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = multiplication(addition(one,X0),X1),
inference(paramodulation,[status(thm)],[f207,f232]) ).
fof(f5500,plain,
! [X0] : multiplication(addition(X0,one),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f192,f232]) ).
fof(f5501,plain,
! [X0] : multiplication(addition(X0,one),X0) = multiplication(X0,addition(one,X0)),
inference(paramodulation,[status(thm)],[f162,f232]) ).
fof(f5504,plain,
! [X0,X1] : multiplication(addition(addition(X0,one),one),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f232,f232]) ).
fof(f5506,plain,
! [X0,X1] : multiplication(addition(addition(X0,X1),one),coantidomain(X0)) = addition(coantidomain(X0),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f232]) ).
fof(f5510,plain,
! [X0,X1] : multiplication(addition(domain(X0),one),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f68,f232]) ).
fof(f5512,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f39,f232]) ).
fof(f5513,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),one),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f186,f232]) ).
fof(f5514,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),one),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f177,f232]) ).
fof(f5520,plain,
! [X0] : multiplication(addition(X0,one),codomain(X0)) = addition(codomain(X0),X0),
inference(paramodulation,[status(thm)],[f2309,f232]) ).
fof(f5521,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(addition(one,X1),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f162,f232]) ).
fof(f5522,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(coantidomain(X0),X1)) = addition(addition(coantidomain(X0),X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f181,f232]) ).
fof(f5523,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(addition(X1,one),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f232]) ).
fof(f5524,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,coantidomain(X0))) = addition(addition(X1,coantidomain(X0)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f190,f232]) ).
fof(f5525,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(coantidomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f151,f232]) ).
fof(f5526,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(multiplication(X0,X1)))) = addition(multiplication(X1,coantidomain(multiplication(X0,X1))),zero),
inference(paramodulation,[status(thm)],[f144,f232]) ).
fof(f5527,plain,
! [X0] : multiplication(addition(X0,one),omega(coantidomain(X0))) = addition(omega(coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f1813,f232]) ).
fof(f5528,plain,
! [X0] : multiplication(addition(X0,one),omega(X0)) = addition(omega(X0),omega(X0)),
inference(paramodulation,[status(thm)],[f56,f232]) ).
fof(f5534,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,one))),X3) = addition(multiplication(X0,X3),multiplication(X1,addition(X3,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f232,f211]) ).
fof(f5535,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,one),multiplication(X1,X2)),X3) = addition(addition(X3,multiplication(X0,X3)),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f232,f211]) ).
fof(f5536,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f232,f207]) ).
fof(f5537,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,one)),X3) = addition(multiplication(X0,multiplication(X1,X3)),addition(X3,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f232,f204]) ).
fof(f5538,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,one)),X2),X3) = addition(multiplication(X0,addition(X3,multiplication(X1,X3))),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f232,f204]) ).
fof(f5539,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f232,f201]) ).
fof(f5540,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(addition(X2,multiplication(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f232,f201]) ).
fof(f5541,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),X1),addition(addition(X2,multiplication(X0,X2)),X3)) = addition(multiplication(addition(X0,one),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f232,f170]) ).
fof(f5542,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X1,X0)),addition(multiplication(addition(X1,one),X2),X3)) = addition(multiplication(addition(X1,one),addition(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f232,f170]) ).
fof(f5543,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(addition(X0,one),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f232,f192]) ).
fof(f5544,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(addition(X0,one),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f232,f162]) ).
fof(f5545,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(multiplication(addition(X0,one),X2),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f232,f153]) ).
fof(f5546,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(addition(X2,multiplication(X0,X2)),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f232,f153]) ).
fof(f5547,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(addition(X1,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f232,f144]) ).
fof(f5548,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,one)),addition(X1,multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f232,f136]) ).
fof(f5549,plain,
! [X0,X1] : addition(coantidomain(addition(X0,multiplication(X1,X0))),coantidomain(multiplication(codomain(addition(X1,one)),X0))) = coantidomain(multiplication(codomain(addition(X1,one)),X0)),
inference(paramodulation,[status(thm)],[f232,f615]) ).
fof(f5550,plain,
! [X0,X1] : addition(antidomain(addition(X0,multiplication(X1,X0))),antidomain(multiplication(addition(X1,one),domain(X0)))) = antidomain(multiplication(addition(X1,one),domain(X0))),
inference(paramodulation,[status(thm)],[f232,f479]) ).
fof(f5551,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),X2)))
| ~ leq(X0,addition(addition(X0,multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f232,f58]) ).
fof(f5552,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X0)),addition(X1,one))
| ~ leq(addition(addition(X0,multiplication(X1,X0)),X2),addition(X1,one)) ),
inference(paramodulation,[status(thm)],[f232,f55]) ).
fof(f5553,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,one)),X2),X0)
| ~ leq(addition(addition(X0,multiplication(X1,X0)),X2),X0) ),
inference(paramodulation,[status(thm)],[f232,f53]) ).
fof(f5554,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f232,f43]) ).
fof(f5556,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f232,f42]) ).
fof(f5557,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(addition(X1,multiplication(X0,X1)),multiplication(addition(X0,one),X2)),
inference(paramodulation,[status(thm)],[f232,f42]) ).
fof(f5558,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f232,f39]) ).
fof(f5559,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f232,f181]) ).
fof(f5561,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(addition(X1,one),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f232,f211]) ).
fof(f5562,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X0,X1),X1)) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f232,f153]) ).
fof(f5563,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f232,f42]) ).
fof(f5564,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,one),multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),multiplication(X2,multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f232,f170]) ).
fof(f5565,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(addition(X1,one),multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f232,f58]) ).
fof(f5566,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),star(X2)),X1)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f232,f55]) ).
fof(f5567,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f232,f53]) ).
fof(f5568,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X1,X0)))) = multiplication(addition(X2,one),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f232,f103]) ).
fof(f5569,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X0,X1)))) = multiplication(addition(X2,one),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f232,f36]) ).
fof(f5576,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = multiplication(addition(X0,one),X1),
inference(paramodulation,[status(thm)],[f232,f207]) ).
fof(f5577,plain,
! [X0] : multiplication(X0,addition(X0,one)) = multiplication(addition(X0,one),X0),
inference(paramodulation,[status(thm)],[f232,f192]) ).
fof(f5578,plain,
! [X0] : multiplication(X0,addition(one,X0)) = multiplication(addition(X0,one),X0),
inference(paramodulation,[status(thm)],[f232,f162]) ).
fof(f5580,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(X0,one),X1)) = multiplication(antidomain(multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f232,f186]) ).
fof(f5581,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f232,f177]) ).
fof(f5582,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(X2,one),X0))),
inference(paramodulation,[status(thm)],[f232,f1421]) ).
fof(f5583,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,one),X1))),
inference(paramodulation,[status(thm)],[f232,f1420]) ).
fof(f5584,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f232,f1423]) ).
fof(f5585,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f232,f1324]) ).
fof(f5586,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f232,f105]) ).
fof(f5587,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),X2),
inference(paramodulation,[status(thm)],[f232,f103]) ).
fof(f5588,plain,
! [X0,X1] : addition(X0,addition(multiplication(X1,X0),multiplication(addition(X1,one),X0))) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f232,f99]) ).
fof(f5589,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(X2,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f232,f97]) ).
fof(f5590,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X1,one),X2)) = addition(multiplication(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f232,f97]) ).
fof(f5591,plain,
! [X0,X1] :
( multiplication(addition(X0,one),X1) != X1
| leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f232,f246]) ).
fof(f5592,plain,
! [X0,X1] :
( multiplication(addition(X1,one),X0) != multiplication(X1,X0)
| leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f232,f49]) ).
fof(f5593,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(X1,one),X0),X2),
inference(paramodulation,[status(thm)],[f232,f36]) ).
fof(f5602,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f5488]) ).
fof(f5621,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f5504]) ).
fof(f5622,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f105,f5621]) ).
fof(f5625,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),coantidomain(X1)) = addition(coantidomain(X1),multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f103,f5506]) ).
fof(f5626,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),coantidomain(X1)) = multiplication(addition(X0,one),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f232,f5625]) ).
fof(f5636,plain,
! [X0,X1] : multiplication(addition(one,domain(X0)),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f5510]) ).
fof(f5637,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1375,f5636]) ).
fof(f5638,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f5637]) ).
fof(f5642,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f5512]) ).
fof(f5643,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f5513]) ).
fof(f5644,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f1379,f5643]) ).
fof(f5645,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f41,f5644]) ).
fof(f5646,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f103,f5645]) ).
fof(f5647,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f5514]) ).
fof(f5648,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1379,f5647]) ).
fof(f5649,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f41,f5648]) ).
fof(f5650,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f5649]) ).
fof(f5663,plain,
! [X0] : multiplication(addition(X0,one),codomain(X0)) = addition(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f5520]) ).
fof(f5664,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(X1,addition(one,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f5521]) ).
fof(f5665,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(coantidomain(X0),X1)) = addition(X1,addition(coantidomain(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f5522]) ).
fof(f5666,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(one,addition(X1,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f5523]) ).
fof(f5667,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,coantidomain(X0))) = addition(coantidomain(X0),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f5524]) ).
fof(f5668,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(coantidomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f5525]) ).
fof(f5669,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f37,f5526]) ).
fof(f5670,plain,
! [X0] : multiplication(addition(X0,one),omega(coantidomain(X0))) = omega(coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f5527]) ).
fof(f5671,plain,
! [X0] : multiplication(addition(X0,one),omega(X0)) = omega(X0),
inference(forward_demodulation,[status(thm)],[f38,f5528]) ).
fof(f5678,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),X3) = addition(addition(X3,multiplication(X0,X3)),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f103,f5535]) ).
fof(f5679,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),X3) = addition(multiplication(X0,X3),addition(X3,multiplication(X1,multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f103,f5678]) ).
fof(f5680,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),X3) = addition(X3,addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f97,f5679]) ).
fof(f5681,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),X3) = addition(X3,multiplication(addition(multiplication(X1,X2),X0),X3)),
inference(forward_demodulation,[status(thm)],[f204,f5680]) ).
fof(f5682,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f105,f5536]) ).
fof(f5683,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(multiplication(X0,X1),X2)),X3) = addition(multiplication(X0,multiplication(X1,X3)),addition(X3,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f97,f5537]) ).
fof(f5684,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(multiplication(X0,X1),X2)),X3) = addition(X3,addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f97,f5683]) ).
fof(f5685,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(multiplication(X0,X1),X2)),X3) = addition(X3,multiplication(addition(X2,multiplication(X0,X1)),X3)),
inference(forward_demodulation,[status(thm)],[f211,f5684]) ).
fof(f5686,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f5539]) ).
fof(f5687,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(X2,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f97,f5686]) ).
fof(f5688,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f5687]) ).
fof(f5689,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f5540]) ).
fof(f5690,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f97,f5689]) ).
fof(f5691,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f5690]) ).
fof(f5692,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),X1),addition(multiplication(X0,X2),addition(X2,X3))) = addition(multiplication(addition(X0,one),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f5541]) ).
fof(f5693,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),X1),addition(X2,addition(X3,multiplication(X0,X2)))) = addition(multiplication(addition(X0,one),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f97,f5692]) ).
fof(f5694,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X1,addition(multiplication(addition(X0,one),X2),X3))) = addition(multiplication(addition(X0,one),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f5542]) ).
fof(f5695,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(multiplication(addition(X1,one),X2),X3),multiplication(X1,X0))) = addition(multiplication(addition(X1,one),addition(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f97,f5694]) ).
fof(f5696,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(multiplication(addition(X2,one),X3),multiplication(X2,X0)))) = addition(multiplication(addition(X2,one),addition(X0,X3)),X1),
inference(forward_demodulation,[status(thm)],[f103,f5695]) ).
fof(f5697,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(one,addition(X0,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f5543]) ).
fof(f5698,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(one,addition(X0,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f5544]) ).
fof(f5699,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(multiplication(X0,X2),addition(X2,multiplication(addition(X0,one),X1))),
inference(forward_demodulation,[status(thm)],[f103,f5546]) ).
fof(f5700,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X2,addition(multiplication(addition(X0,one),X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f5699]) ).
fof(f5701,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),addition(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f103,f5551]) ).
fof(f5702,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(X2,one)),multiplication(star(addition(X2,one)),X1)))
| ~ leq(X0,addition(X0,addition(X1,multiplication(X2,X0)))) ),
inference(forward_demodulation,[status(thm)],[f97,f5701]) ).
fof(f5703,plain,
! [X0,X1,X2] : leq(X0,addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),X2))),
inference(forward_subsumption_resolution,[status(thm)],[f5702,f1324]) ).
fof(f5704,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),addition(X0,one))
| ~ leq(addition(multiplication(X0,X1),addition(X1,X2)),addition(X0,one)) ),
inference(forward_demodulation,[status(thm)],[f103,f5552]) ).
fof(f5705,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X0)),addition(X2,one))
| ~ leq(addition(X0,addition(X1,multiplication(X2,X0))),addition(X2,one)) ),
inference(forward_demodulation,[status(thm)],[f97,f5704]) ).
fof(f5706,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,one)),X2),X1)
| ~ leq(addition(multiplication(X0,X1),addition(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f103,f5553]) ).
fof(f5707,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X2,one)),X1),X0)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X0))),X0) ),
inference(forward_demodulation,[status(thm)],[f97,f5706]) ).
fof(f5708,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,addition(multiplication(X1,X2),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f5554]) ).
fof(f5709,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f201,f5708]) ).
fof(f5714,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(multiplication(X0,X1),addition(X1,multiplication(addition(X0,one),X2))),
inference(forward_demodulation,[status(thm)],[f103,f5557]) ).
fof(f5715,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X1,addition(multiplication(addition(X0,one),X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f5714]) ).
fof(f5723,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f5562]) ).
fof(f5724,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(X2))),X1)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f5566]) ).
fof(f5725,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X1)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f5724]) ).
fof(f5745,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,one),X0),X1),
inference(forward_demodulation,[status(thm)],[f97,f5587]) ).
fof(f5746,plain,
! [X0,X1] : addition(X0,multiplication(addition(addition(X1,one),X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f201,f5588]) ).
fof(f5747,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,addition(X1,X1)),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f5746]) ).
fof(f5748,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f38,f5747]) ).
fof(f5749,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X1,one),X2)) = addition(X2,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f97,f5590]) ).
fof(f5750,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(resolution,[status(thm)],[f4249,f48]) ).
fof(f5751,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),antidomain(c(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f69,f4249]) ).
fof(f5756,plain,
! [X0,X1] : leq(domain(backward_diamond(X0,c(X1))),antidomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f72,f4249]) ).
fof(f5757,plain,
! [X0,X1] : leq(domain(forward_diamond(X0,c(X1))),antidomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f71,f4249]) ).
fof(f5790,plain,
! [X0] : multiplication(one,coantidomain(c(X0))) = multiplication(domain(X0),coantidomain(c(X0))),
inference(paramodulation,[status(thm)],[f569,f233]) ).
fof(f5791,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(codomain(X0),X1)),coantidomain(coantidomain(multiplication(codomain(X0),X1)))) = multiplication(coantidomain(multiplication(X0,X1)),coantidomain(coantidomain(multiplication(codomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f615,f233]) ).
fof(f5792,plain,
! [X0] : multiplication(one,coantidomain(codomain(X0))) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f683,f233]) ).
fof(f5793,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),coantidomain(antidomain(multiplication(X0,domain(X1))))) = multiplication(antidomain(multiplication(X0,X1)),coantidomain(antidomain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f479,f233]) ).
fof(f5794,plain,
! [X0] : multiplication(one,coantidomain(domain(X0))) = multiplication(antidomain(X0),coantidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f558,f233]) ).
fof(f5795,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(addition(multiplication(X0,X1),X2),X3),coantidomain(multiplication(X2,X3))) = multiplication(multiplication(X0,multiplication(X1,X3)),coantidomain(multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f204,f233]) ).
fof(f5796,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),coantidomain(addition(multiplication(X0,X2),X3))) = multiplication(multiplication(X0,X1),coantidomain(addition(multiplication(X0,X2),X3))),
inference(paramodulation,[status(thm)],[f170,f233]) ).
fof(f5797,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(addition(X0,multiplication(X1,X2)),X3),coantidomain(multiplication(X1,multiplication(X2,X3)))) = multiplication(multiplication(X0,X3),coantidomain(multiplication(X1,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f211,f233]) ).
fof(f5798,plain,
! [X0,X1,X2] : multiplication(multiplication(addition(X0,X1),X2),coantidomain(multiplication(X0,X2))) = multiplication(multiplication(X1,X2),coantidomain(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f201,f233]) ).
fof(f5799,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,X2)),coantidomain(multiplication(X0,X1))) = multiplication(multiplication(X0,X2),coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f153,f233]) ).
fof(f5800,plain,
! [X0,X1,X2] : multiplication(multiplication(addition(X0,X1),X2),coantidomain(multiplication(X1,X2))) = multiplication(multiplication(X0,X2),coantidomain(multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f43,f233]) ).
fof(f5801,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,X2)),coantidomain(multiplication(X0,X2))) = multiplication(multiplication(X0,X1),coantidomain(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f42,f233]) ).
fof(f5802,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f103,f233]) ).
fof(f5803,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f36,f233]) ).
fof(f5811,plain,
! [X0,X1] : multiplication(multiplication(addition(X0,one),X1),coantidomain(multiplication(X0,X1))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f232,f233]) ).
fof(f5812,plain,
! [X0,X1] : multiplication(multiplication(addition(one,X0),X1),coantidomain(multiplication(X0,X1))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f207,f233]) ).
fof(f5813,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(X1,one)),coantidomain(multiplication(X0,X1))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f233]) ).
fof(f5814,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(one,X1)),coantidomain(multiplication(X0,X1))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f162,f233]) ).
fof(f5815,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X1,addition(X0,X1)))) = multiplication(X0,coantidomain(addition(X1,addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f99,f233]) ).
fof(f5816,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X0,X1))) = multiplication(X0,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f105,f233]) ).
fof(f5817,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X0,X1))) = multiplication(X2,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f97,f233]) ).
fof(f5818,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X2,X0))) = multiplication(X1,coantidomain(addition(X2,X0))),
inference(paramodulation,[status(thm)],[f97,f233]) ).
fof(f5824,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,coantidomain(coantidomain(X1))),
inference(paramodulation,[status(thm)],[f66,f233]) ).
fof(f5828,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f233,f4627]) ).
fof(f5831,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,X3))),coantidomain(X3)) = addition(multiplication(X0,coantidomain(X3)),multiplication(X1,multiplication(X2,coantidomain(X3)))),
inference(paramodulation,[status(thm)],[f233,f211]) ).
fof(f5833,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X1)) = addition(coantidomain(X1),multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f233,f207]) ).
fof(f5834,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),coantidomain(X3)) = addition(multiplication(X0,multiplication(X1,coantidomain(X3))),multiplication(X2,coantidomain(X3))),
inference(paramodulation,[status(thm)],[f233,f204]) ).
fof(f5835,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),coantidomain(X2)) = addition(multiplication(X0,multiplication(X1,coantidomain(X2))),multiplication(X3,coantidomain(X2))),
inference(paramodulation,[status(thm)],[f233,f204]) ).
fof(f5837,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = addition(multiplication(X1,coantidomain(X2)),multiplication(X0,coantidomain(X2))),
inference(paramodulation,[status(thm)],[f233,f201]) ).
fof(f5838,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),addition(multiplication(X0,coantidomain(X1)),X3)) = addition(multiplication(addition(X0,X1),addition(X2,coantidomain(X1))),X3),
inference(paramodulation,[status(thm)],[f233,f170]) ).
fof(f5839,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,coantidomain(X1)),addition(multiplication(addition(X0,X1),X2),X3)) = addition(multiplication(addition(X0,X1),addition(coantidomain(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f233,f170]) ).
fof(f5842,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X1),X2)) = addition(multiplication(addition(X0,X1),X2),multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f233,f153]) ).
fof(f5843,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X1))) = addition(multiplication(X0,coantidomain(X1)),multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f233,f153]) ).
fof(f5844,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),coantidomain(multiplication(X0,coantidomain(X1))))) = zero,
inference(paramodulation,[status(thm)],[f233,f144]) ).
fof(f5845,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),multiplication(X0,coantidomain(X1))) = zero,
inference(paramodulation,[status(thm)],[f233,f136]) ).
fof(f5846,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,coantidomain(X1))),coantidomain(multiplication(codomain(addition(X0,X1)),coantidomain(X1)))) = coantidomain(multiplication(codomain(addition(X0,X1)),coantidomain(X1))),
inference(paramodulation,[status(thm)],[f233,f615]) ).
fof(f5847,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,coantidomain(X1))),antidomain(multiplication(addition(X0,X1),domain(coantidomain(X1))))) = antidomain(multiplication(addition(X0,X1),domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f233,f479]) ).
fof(f5848,plain,
! [X0,X1,X2] :
( leq(coantidomain(X0),addition(omega(addition(X1,X0)),multiplication(star(addition(X1,X0)),X2)))
| ~ leq(coantidomain(X0),addition(multiplication(X1,coantidomain(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f233,f58]) ).
fof(f5849,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(coantidomain(X1))),addition(X0,X1))
| ~ leq(addition(multiplication(X0,coantidomain(X1)),X2),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f233,f55]) ).
fof(f5850,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,X1)),X2),coantidomain(X1))
| ~ leq(addition(multiplication(X0,coantidomain(X1)),X2),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f233,f53]) ).
fof(f5851,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),multiplication(X1,coantidomain(X2))),
inference(paramodulation,[status(thm)],[f233,f43]) ).
fof(f5852,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),multiplication(X2,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f233,f43]) ).
fof(f5853,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X1))) = addition(multiplication(addition(X0,X1),X2),multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f233,f42]) ).
fof(f5854,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X1),X2)) = addition(multiplication(X0,coantidomain(X1)),multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f233,f42]) ).
fof(f5855,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(multiplication(X0,coantidomain(X1)),X2),
inference(paramodulation,[status(thm)],[f233,f39]) ).
fof(f5857,plain,
! [X0] : coantidomain(c(X0)) = multiplication(domain(X0),coantidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f41,f5790]) ).
fof(f5858,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),coantidomain(coantidomain(multiplication(codomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f63,f5791]) ).
fof(f5859,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),codomain(multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f66,f5858]) ).
fof(f5860,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),backward_diamond(X1,X0)),
inference(forward_demodulation,[status(thm)],[f70,f5859]) ).
fof(f5861,plain,
! [X0] : coantidomain(codomain(X0)) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f41,f5792]) ).
fof(f5862,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),coantidomain(antidomain(multiplication(X0,domain(X1))))),
inference(forward_demodulation,[status(thm)],[f63,f5793]) ).
fof(f5863,plain,
! [X0] : coantidomain(domain(X0)) = multiplication(antidomain(X0),coantidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f41,f5794]) ).
fof(f5864,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X2,X3)))) = multiplication(multiplication(X0,multiplication(X1,X3)),coantidomain(multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f39,f5795]) ).
fof(f5865,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X2,X3)))) = multiplication(X0,multiplication(multiplication(X1,X3),coantidomain(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f39,f5864]) ).
fof(f5866,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,coantidomain(multiplication(X2,X3)))) = multiplication(X0,multiplication(X1,multiplication(X3,coantidomain(multiplication(X2,X3))))),
inference(forward_demodulation,[status(thm)],[f39,f5865]) ).
fof(f5867,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),coantidomain(addition(multiplication(X0,X2),X3))) = multiplication(X0,multiplication(X1,coantidomain(addition(multiplication(X0,X2),X3)))),
inference(forward_demodulation,[status(thm)],[f39,f5796]) ).
fof(f5868,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X1,multiplication(X2,X3))))) = multiplication(multiplication(X0,X3),coantidomain(multiplication(X1,multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f39,f5797]) ).
fof(f5869,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,coantidomain(multiplication(X1,multiplication(X2,X3))))) = multiplication(X0,multiplication(X3,coantidomain(multiplication(X1,multiplication(X2,X3))))),
inference(forward_demodulation,[status(thm)],[f39,f5868]) ).
fof(f5870,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X0,X2)))) = multiplication(multiplication(X1,X2),coantidomain(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f5798]) ).
fof(f5871,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X0,X2)))) = multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f5870]) ).
fof(f5872,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),coantidomain(multiplication(X0,X1)))) = multiplication(multiplication(X0,X2),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f5799]) ).
fof(f5873,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),coantidomain(multiplication(X0,X1)))) = multiplication(X0,multiplication(X2,coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f39,f5872]) ).
fof(f5874,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(multiplication(X0,X2),coantidomain(multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f5800]) ).
fof(f5875,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(X0,multiplication(X2,coantidomain(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f5874]) ).
fof(f5876,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),coantidomain(multiplication(X0,X2)))) = multiplication(multiplication(X0,X1),coantidomain(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f5801]) ).
fof(f5877,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),coantidomain(multiplication(X0,X2)))) = multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f5876]) ).
fof(f5879,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f5811]) ).
fof(f5880,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f5812]) ).
fof(f5881,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(multiplication(X0,X1)))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f5813]) ).
fof(f5882,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(multiplication(X0,X1)))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f5814]) ).
fof(f5883,plain,
! [X0,X1] : zero = multiplication(X0,coantidomain(addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f63,f5816]) ).
fof(f5887,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f66,f5824]) ).
fof(f5897,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,X3))),coantidomain(X3)) = multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X3)),
inference(forward_demodulation,[status(thm)],[f211,f5831]) ).
fof(f5900,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X1)) = multiplication(addition(X0,one),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f232,f5833]) ).
fof(f5901,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),coantidomain(X3)) = multiplication(addition(multiplication(X0,X1),X2),coantidomain(X3)),
inference(forward_demodulation,[status(thm)],[f204,f5834]) ).
fof(f5902,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),coantidomain(X2)) = multiplication(addition(multiplication(X0,X1),X3),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f204,f5835]) ).
fof(f5905,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f201,f5837]) ).
fof(f5906,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,coantidomain(X1)),addition(X2,multiplication(addition(X0,X1),X3))) = addition(multiplication(addition(X0,X1),addition(X3,coantidomain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f97,f5838]) ).
fof(f5916,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(coantidomain(X1),X2)) = addition(multiplication(X0,coantidomain(X1)),multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f35,f5842]) ).
fof(f5917,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f201,f5851]) ).
fof(f5918,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X0)) = addition(multiplication(X1,coantidomain(X0)),multiplication(X2,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f103,f5852]) ).
fof(f5919,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),multiplication(X1,coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f226,f5918]) ).
fof(f5920,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f201,f5919]) ).
fof(f5921,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,coantidomain(X1))) = addition(multiplication(X0,coantidomain(X1)),multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f35,f5853]) ).
fof(f5922,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f5855]) ).
fof(f5926,plain,
! [X0,X1] : forward_diamond(domain(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f72,f4340]) ).
fof(f5927,plain,
! [X0,X1] : forward_diamond(domain(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f71,f4340]) ).
fof(f5929,plain,
! [X0] : forward_diamond(domain(antidomain(c(X0))),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f547,f4340]) ).
fof(f5930,plain,
! [X0] : forward_diamond(domain(domain(c(X0))),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f362,f4340]) ).
fof(f5933,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(domain(c(domain(X0)))),forward_diamond(star(domain(c(domain(X0)))),domain(X1)))) = addition(divergence(domain(c(domain(X0)))),forward_diamond(star(domain(c(domain(X0)))),domain(X1)))
| addition(domain(X0),addition(zero,domain(X1))) != addition(forward_diamond(domain(c(domain(X0))),domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f4340,f75]) ).
fof(f5934,plain,
! [X0] : forward_box(domain(c(c(X0))),X0) = c(zero),
inference(paramodulation,[status(thm)],[f4340,f71]) ).
fof(f5943,plain,
! [X0] : forward_diamond(c(c(X0)),antidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f361,f5929]) ).
fof(f5944,plain,
! [X0] : forward_diamond(antidomain(c(c(X0))),domain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f196,f5930]) ).
fof(f5951,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))) = addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(zero,addition(domain(X0),domain(X1))) != addition(forward_diamond(domain(c(domain(X1))),domain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f5933]) ).
fof(f5952,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))) = addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != addition(forward_diamond(domain(c(domain(X1))),domain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f5951]) ).
fof(f5953,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))) = addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != addition(zero,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f4340,f5952]) ).
fof(f5954,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))) = addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f80,f5953]) ).
fof(f5955,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(domain(domain(c(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))) = addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f362,f5954]) ).
fof(f5956,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))) = addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f196,f5955]) ).
fof(f5957,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(domain(domain(c(X1)))),domain(X0)))) = addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f362,f5956]) ).
fof(f5958,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(antidomain(c(c(X1)))),domain(X0)))) = addition(divergence(domain(c(domain(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f196,f5957]) ).
fof(f5959,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(antidomain(c(c(X1)))),domain(X0)))) = addition(divergence(domain(domain(c(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f362,f5958]) ).
fof(f5960,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(antidomain(c(c(X1)))),domain(X0)))) = addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(domain(c(domain(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f196,f5959]) ).
fof(f5961,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(antidomain(c(c(X1)))),domain(X0)))) = addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(domain(domain(c(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f362,f5960]) ).
fof(f5962,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(antidomain(c(c(X1)))),domain(X0)))) = addition(divergence(antidomain(c(c(X1)))),forward_diamond(star(antidomain(c(c(X1)))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f196,f5961]) ).
fof(f5963,plain,
! [X0] : forward_box(domain(c(c(X0))),X0) = one,
inference(forward_demodulation,[status(thm)],[f597,f5934]) ).
fof(f5965,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),X1),
inference(resolution,[status(thm)],[f4511,f246]) ).
fof(f5970,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(divergence(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4511]) ).
fof(f5971,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(divergence(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4511]) ).
fof(f5978,plain,
! [X0] : codomain(divergence(X0)) = addition(codomain(divergence(X0)),divergence(X0)),
inference(paramodulation,[status(thm)],[f2309,f4511]) ).
fof(f5979,plain,
! [X0,X1] : addition(coantidomain(divergence(X0)),X1) = addition(addition(coantidomain(divergence(X0)),X1),multiplication(divergence(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f4511]) ).
fof(f5989,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4511,f181]) ).
fof(f6002,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(divergence(X3),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4511,f170]) ).
fof(f6003,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(divergence(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4511,f58]) ).
fof(f6004,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(divergence(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4511,f55]) ).
fof(f6005,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(divergence(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4511,f53]) ).
fof(f6006,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4511,f103]) ).
fof(f6007,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4511,f36]) ).
fof(f6017,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(paramodulation,[status(thm)],[f4511,f177]) ).
fof(f6019,plain,
! [X0,X1,X2] : leq(multiplication(divergence(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4511,f1420]) ).
fof(f6023,plain,
! [X0,X1,X2] : addition(multiplication(divergence(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4511,f103]) ).
fof(f6025,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(divergence(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4511,f97]) ).
fof(f6026,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(divergence(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4511,f97]) ).
fof(f6028,plain,
! [X0,X1] :
( X0 != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4511,f49]) ).
fof(f6029,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(divergence(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4511,f36]) ).
fof(f6039,plain,
! [X0] : codomain(divergence(X0)) = addition(divergence(X0),codomain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f35,f5978]) ).
fof(f6040,plain,
! [X0,X1] : addition(coantidomain(divergence(X0)),X1) = addition(X1,addition(coantidomain(divergence(X0)),multiplication(divergence(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f5979]) ).
fof(f6044,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f5989]) ).
fof(f6054,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(divergence(X3),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f6002]) ).
fof(f6055,plain,
! [X0,X1,X2] :
( leq(multiplication(divergence(X2),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f6004]) ).
fof(f6056,plain,
! [X0,X1,X2] :
( leq(multiplication(divergence(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f6055]) ).
fof(f6066,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f59,f6017]) ).
fof(f6068,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f6023]) ).
fof(f6070,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(divergence(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f6026]) ).
fof(f6073,plain,
! [X0] : leq(divergence(X0),codomain(divergence(X0))),
inference(paramodulation,[status(thm)],[f2309,f5965]) ).
fof(f6074,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),addition(coantidomain(divergence(X0)),X1)),
inference(paramodulation,[status(thm)],[f181,f5965]) ).
fof(f6075,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),addition(X1,coantidomain(divergence(X0)))),
inference(paramodulation,[status(thm)],[f190,f5965]) ).
fof(f6089,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X3,X0),X1),X2),
inference(paramodulation,[status(thm)],[f97,f219]) ).
fof(f6090,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,X2),multiplication(X3,X2))) = addition(multiplication(addition(X1,X3),X2),X0),
inference(paramodulation,[status(thm)],[f97,f219]) ).
fof(f6093,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X1,X0)),addition(multiplication(X2,X0),X3)) = addition(multiplication(addition(addition(one,X1),X2),X0),X3),
inference(paramodulation,[status(thm)],[f207,f219]) ).
fof(f6094,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(addition(antidomain(X1),X0),X2),X1),X3),
inference(paramodulation,[status(thm)],[f224,f219]) ).
fof(f6095,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X1,X0)),addition(multiplication(X2,X0),X3)) = addition(multiplication(addition(addition(X1,one),X2),X0),X3),
inference(paramodulation,[status(thm)],[f232,f219]) ).
fof(f6098,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,coantidomain(X1)),addition(multiplication(X2,coantidomain(X1)),X3)) = addition(multiplication(addition(addition(X1,X0),X2),coantidomain(X1)),X3),
inference(paramodulation,[status(thm)],[f226,f219]) ).
fof(f6099,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,domain(X1)),X2)) = addition(multiplication(addition(c(X1),X0),domain(X1)),X2),
inference(paramodulation,[status(thm)],[f197,f219]) ).
fof(f6100,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(addition(c(X1),X0),X1),X2),
inference(paramodulation,[status(thm)],[f4265,f219]) ).
fof(f6101,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,codomain(X1)),X2)) = addition(multiplication(addition(coantidomain(X1),X0),codomain(X1)),X2),
inference(paramodulation,[status(thm)],[f195,f219]) ).
fof(f6102,plain,
! [X0,X1,X2,X3] : addition(domain_difference(X0,X1),addition(multiplication(X2,antidomain(X1)),X3)) = addition(multiplication(addition(domain(X0),X2),antidomain(X1)),X3),
inference(paramodulation,[status(thm)],[f68,f219]) ).
fof(f6103,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(domain(X0),X1),X0),X2),
inference(paramodulation,[status(thm)],[f4146,f219]) ).
fof(f6104,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(multiplication(X0,X1),X3),X2),X4),
inference(paramodulation,[status(thm)],[f39,f219]) ).
fof(f6105,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),addition(multiplication(X2,addition(X1,X0)),X3)) = addition(multiplication(addition(antidomain(X0),X2),addition(X1,X0)),X3),
inference(paramodulation,[status(thm)],[f186,f219]) ).
fof(f6106,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),addition(multiplication(X2,addition(X0,X1)),X3)) = addition(multiplication(addition(antidomain(X0),X2),addition(X0,X1)),X3),
inference(paramodulation,[status(thm)],[f177,f219]) ).
fof(f6107,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,omega(X1)),X2)) = addition(multiplication(addition(antidomain(X1),X0),omega(X1)),X2),
inference(paramodulation,[status(thm)],[f1569,f219]) ).
fof(f6108,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(X0,multiplication(X1,X2)),X3)) = addition(multiplication(addition(antidomain(X1),X0),multiplication(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f136,f219]) ).
fof(f6111,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(one,X1),X0),X2),
inference(paramodulation,[status(thm)],[f41,f219]) ).
fof(f6112,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,codomain(X0)),X2)) = addition(multiplication(addition(X0,X1),codomain(X0)),X2),
inference(paramodulation,[status(thm)],[f2309,f219]) ).
fof(f6113,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X0,X1)),addition(multiplication(X2,addition(one,X1)),X3)) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(paramodulation,[status(thm)],[f162,f219]) ).
fof(f6114,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,addition(coantidomain(X0),X1)),X3)) = addition(multiplication(addition(X0,X2),addition(coantidomain(X0),X1)),X3),
inference(paramodulation,[status(thm)],[f181,f219]) ).
fof(f6115,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X0,X1)),addition(multiplication(X2,addition(X1,one)),X3)) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(paramodulation,[status(thm)],[f192,f219]) ).
fof(f6116,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,addition(X1,coantidomain(X0))),X3)) = addition(multiplication(addition(X0,X2),addition(X1,coantidomain(X0))),X3),
inference(paramodulation,[status(thm)],[f190,f219]) ).
fof(f6117,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(X0,multiplication(coantidomain(X1),X2)),X3)) = addition(multiplication(addition(X1,X0),multiplication(coantidomain(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f151,f219]) ).
fof(f6118,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(X0,multiplication(X1,coantidomain(multiplication(X2,X1)))),X3)) = addition(multiplication(addition(X2,X0),multiplication(X1,coantidomain(multiplication(X2,X1)))),X3),
inference(paramodulation,[status(thm)],[f144,f219]) ).
fof(f6119,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,omega(coantidomain(X1))),X2)) = addition(multiplication(addition(X1,X0),omega(coantidomain(X1))),X2),
inference(paramodulation,[status(thm)],[f1813,f219]) ).
fof(f6120,plain,
! [X0,X1,X2] : addition(omega(X0),addition(multiplication(X1,omega(X0)),X2)) = addition(multiplication(addition(X0,X1),omega(X0)),X2),
inference(paramodulation,[status(thm)],[f56,f219]) ).
fof(f6125,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(addition(X2,X3),X1),X4)) = addition(multiplication(addition(X0,X2),X1),addition(multiplication(X3,X1),X4)),
inference(paramodulation,[status(thm)],[f219,f219]) ).
fof(f6126,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,addition(X1,X3)),X4)) = addition(multiplication(addition(X0,X2),X1),addition(multiplication(X2,X3),X4)),
inference(paramodulation,[status(thm)],[f170,f219]) ).
fof(f6127,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(addition(X2,multiplication(X3,X4)),X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(X3,multiplication(X4,X1))),
inference(paramodulation,[status(thm)],[f211,f219]) ).
fof(f6128,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,X3),X1)) = addition(multiplication(addition(X0,X3),X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f201,f219]) ).
fof(f6129,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,addition(X3,X1))) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f153,f219]) ).
fof(f6130,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,X3),X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(X3,X1)),
inference(paramodulation,[status(thm)],[f43,f219]) ).
fof(f6131,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,addition(X1,X3))) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f42,f219]) ).
fof(f6132,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(divergence(X3),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4511,f219]) ).
fof(f6133,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),domain(X3))),
inference(paramodulation,[status(thm)],[f2497,f219]) ).
fof(f6134,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),coantidomain(X3))),
inference(paramodulation,[status(thm)],[f2496,f219]) ).
fof(f6135,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),antidomain(X3))),
inference(paramodulation,[status(thm)],[f2495,f219]) ).
fof(f6136,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),c(X3))),
inference(paramodulation,[status(thm)],[f2494,f219]) ).
fof(f6137,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),codomain(X3))),
inference(paramodulation,[status(thm)],[f2493,f219]) ).
fof(f6138,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),divergence(X3))),
inference(paramodulation,[status(thm)],[f2492,f219]) ).
fof(f6139,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,one),multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f232,f219]) ).
fof(f6140,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(one,X2),multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f207,f219]) ).
fof(f6141,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(multiplication(X2,X1),addition(X3,one))) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),X3)),
inference(paramodulation,[status(thm)],[f192,f219]) ).
fof(f6142,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(multiplication(X2,X1),addition(one,X3))) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),X3)),
inference(paramodulation,[status(thm)],[f162,f219]) ).
fof(f6143,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),addition(X3,addition(multiplication(X2,X1),X3))),
inference(paramodulation,[status(thm)],[f99,f219]) ).
fof(f6144,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),addition(multiplication(X2,X1),X3)),
inference(paramodulation,[status(thm)],[f105,f219]) ).
fof(f6145,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X4,X1)))) = addition(multiplication(addition(X0,X4),X1),addition(X2,X3)),
inference(paramodulation,[status(thm)],[f97,f219]) ).
fof(f6146,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),X4))) = addition(multiplication(addition(X0,X3),X1),addition(X4,X2)),
inference(paramodulation,[status(thm)],[f97,f219]) ).
fof(f6147,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),zero),
inference(paramodulation,[status(thm)],[f37,f219]) ).
fof(f6148,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),X2),
inference(paramodulation,[status(thm)],[f35,f219]) ).
fof(f6149,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),X2),
inference(paramodulation,[status(thm)],[f35,f219]) ).
fof(f6150,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f38,f219]) ).
fof(f6151,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(X1,multiplication(X2,X1)),X3)) = addition(multiplication(addition(X0,addition(one,X2)),X1),X3),
inference(paramodulation,[status(thm)],[f207,f219]) ).
fof(f6152,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,addition(antidomain(X1),X2)),X1),X3),
inference(paramodulation,[status(thm)],[f224,f219]) ).
fof(f6153,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(X1,multiplication(X2,X1)),X3)) = addition(multiplication(addition(X0,addition(X2,one)),X1),X3),
inference(paramodulation,[status(thm)],[f232,f219]) ).
fof(f6154,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,addition(X2,antidomain(X1))),X1),X3),
inference(paramodulation,[status(thm)],[f230,f219]) ).
fof(f6155,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,coantidomain(X1)),addition(multiplication(X2,coantidomain(X1)),X3)) = addition(multiplication(addition(X0,addition(X2,X1)),coantidomain(X1)),X3),
inference(paramodulation,[status(thm)],[f233,f219]) ).
fof(f6156,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,coantidomain(X1)),addition(multiplication(X2,coantidomain(X1)),X3)) = addition(multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)),X3),
inference(paramodulation,[status(thm)],[f226,f219]) ).
fof(f6157,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),addition(zero,X2)) = addition(multiplication(addition(X0,c(X1)),domain(X1)),X2),
inference(paramodulation,[status(thm)],[f197,f219]) ).
fof(f6158,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(addition(X0,c(X1)),X1),X2),
inference(paramodulation,[status(thm)],[f4265,f219]) ).
fof(f6159,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),addition(zero,X2)) = addition(multiplication(addition(X0,coantidomain(X1)),codomain(X1)),X2),
inference(paramodulation,[status(thm)],[f195,f219]) ).
fof(f6160,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,antidomain(X1)),addition(domain_difference(X2,X1),X3)) = addition(multiplication(addition(X0,domain(X2)),antidomain(X1)),X3),
inference(paramodulation,[status(thm)],[f68,f219]) ).
fof(f6161,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,domain(X1)),X1),X2),
inference(paramodulation,[status(thm)],[f4146,f219]) ).
fof(f6162,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),X4)) = addition(multiplication(addition(X0,multiplication(X2,X3)),X1),X4),
inference(paramodulation,[status(thm)],[f39,f219]) ).
fof(f6163,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),addition(multiplication(antidomain(X2),X1),X3)) = addition(multiplication(addition(X0,antidomain(X2)),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f186,f219]) ).
fof(f6164,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),addition(multiplication(antidomain(X1),X2),X3)) = addition(multiplication(addition(X0,antidomain(X1)),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f177,f219]) ).
fof(f6165,plain,
! [X0,X1,X2] : addition(multiplication(X0,omega(X1)),addition(zero,X2)) = addition(multiplication(addition(X0,antidomain(X1)),omega(X1)),X2),
inference(paramodulation,[status(thm)],[f1569,f219]) ).
fof(f6166,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,X2)),addition(zero,X3)) = addition(multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f136,f219]) ).
fof(f6169,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),X2),
inference(paramodulation,[status(thm)],[f41,f219]) ).
fof(f6170,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),addition(X1,X2)) = addition(multiplication(addition(X0,X1),codomain(X1)),X2),
inference(paramodulation,[status(thm)],[f2309,f219]) ).
fof(f6171,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(one,X1)),addition(addition(X2,multiplication(X2,X1)),X3)) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(paramodulation,[status(thm)],[f162,f219]) ).
fof(f6172,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(coantidomain(X1),X2)),addition(multiplication(X1,X2),X3)) = addition(multiplication(addition(X0,X1),addition(coantidomain(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f181,f219]) ).
fof(f6173,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,one)),addition(addition(X2,multiplication(X2,X1)),X3)) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(paramodulation,[status(thm)],[f192,f219]) ).
fof(f6174,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,coantidomain(X2))),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),addition(X1,coantidomain(X2))),X3),
inference(paramodulation,[status(thm)],[f190,f219]) ).
fof(f6175,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(coantidomain(X1),X2)),addition(zero,X3)) = addition(multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f151,f219]) ).
fof(f6176,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,coantidomain(multiplication(X2,X1)))),addition(zero,X3)) = addition(multiplication(addition(X0,X2),multiplication(X1,coantidomain(multiplication(X2,X1)))),X3),
inference(paramodulation,[status(thm)],[f144,f219]) ).
fof(f6177,plain,
! [X0,X1,X2] : addition(multiplication(X0,omega(coantidomain(X1))),addition(zero,X2)) = addition(multiplication(addition(X0,X1),omega(coantidomain(X1))),X2),
inference(paramodulation,[status(thm)],[f1813,f219]) ).
fof(f6178,plain,
! [X0,X1,X2] : addition(multiplication(X0,omega(X1)),addition(omega(X1),X2)) = addition(multiplication(addition(X0,X1),omega(X1)),X2),
inference(paramodulation,[status(thm)],[f56,f219]) ).
fof(f6183,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X3),X4)) = addition(multiplication(X0,addition(X1,X3)),addition(multiplication(X2,X3),X4)),
inference(paramodulation,[status(thm)],[f219,f170]) ).
fof(f6184,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),addition(multiplication(X2,X0),X3))))
| ~ leq(X0,addition(multiplication(addition(X1,X2),X0),X3)) ),
inference(paramodulation,[status(thm)],[f219,f58]) ).
fof(f6185,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(multiplication(X1,X2),X3),star(X2)),X0)
| ~ leq(addition(multiplication(addition(X0,X1),X2),X3),X0) ),
inference(paramodulation,[status(thm)],[f219,f55]) ).
fof(f6186,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),addition(multiplication(X1,X2),X3)),X2)
| ~ leq(addition(multiplication(addition(X0,X1),X2),X3),X2) ),
inference(paramodulation,[status(thm)],[f219,f53]) ).
fof(f6188,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(addition(X2,X0),X1),X3)),
inference(paramodulation,[status(thm)],[f219,f1421]) ).
fof(f6192,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X3,X0),X1),X2),
inference(paramodulation,[status(thm)],[f219,f97]) ).
fof(f6193,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f219,f97]) ).
fof(f6194,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X1),X2),X3),coantidomain(addition(multiplication(X1,X2),X3))) = multiplication(multiplication(X0,X2),coantidomain(addition(multiplication(X1,X2),X3))),
inference(paramodulation,[status(thm)],[f219,f233]) ).
fof(f6195,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X1),X2),X3),coantidomain(multiplication(X0,X2))) = multiplication(addition(multiplication(X1,X2),X3),coantidomain(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f219,f226]) ).
fof(f6196,plain,
! [X0,X1,X2,X3] : multiplication(antidomain(addition(multiplication(X0,X1),X2)),addition(multiplication(addition(X3,X0),X1),X2)) = multiplication(antidomain(addition(multiplication(X0,X1),X2)),multiplication(X3,X1)),
inference(paramodulation,[status(thm)],[f219,f186]) ).
fof(f6197,plain,
! [X0,X1,X2,X3] : multiplication(antidomain(multiplication(X0,X1)),addition(multiplication(addition(X0,X2),X1),X3)) = multiplication(antidomain(multiplication(X0,X1)),addition(multiplication(X2,X1),X3)),
inference(paramodulation,[status(thm)],[f219,f177]) ).
fof(f6198,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(addition(X0,X3),X1),X4))),
inference(paramodulation,[status(thm)],[f219,f1421]) ).
fof(f6199,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),addition(X3,addition(multiplication(addition(X4,X0),X1),X2))),
inference(paramodulation,[status(thm)],[f219,f1420]) ).
fof(f6200,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(addition(X3,X0),X1),X2)),
inference(paramodulation,[status(thm)],[f219,f1423]) ).
fof(f6201,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f219,f1324]) ).
fof(f6203,plain,
! [X0,X1,X2,X3,X4] : addition(addition(multiplication(X0,X1),X2),addition(multiplication(X3,X1),X4)) = addition(addition(multiplication(addition(X3,X0),X1),X2),X4),
inference(paramodulation,[status(thm)],[f219,f103]) ).
fof(f6204,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(multiplication(X2,X1),X3),addition(multiplication(addition(X0,X2),X1),X3))) = addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)),
inference(paramodulation,[status(thm)],[f219,f99]) ).
fof(f6205,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(addition(multiplication(X2,X1),X3),X4)) = addition(X4,addition(multiplication(addition(X0,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f219,f97]) ).
fof(f6206,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(addition(X1,X2),X3),X4)) = addition(addition(multiplication(X2,X3),X4),addition(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f219,f97]) ).
fof(f6207,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X3,X0),X1),X2) != multiplication(X3,X1)
| leq(addition(multiplication(X0,X1),X2),multiplication(X3,X1)) ),
inference(paramodulation,[status(thm)],[f219,f246]) ).
fof(f6208,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X0,X2),X1),X3) != addition(multiplication(X2,X1),X3)
| leq(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) ),
inference(paramodulation,[status(thm)],[f219,f49]) ).
fof(f6209,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(addition(multiplication(X2,X1),X3),X4)) = addition(addition(multiplication(addition(X0,X2),X1),X3),X4),
inference(paramodulation,[status(thm)],[f219,f36]) ).
fof(f6218,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(addition(X2,X1),X3),X0),
inference(forward_demodulation,[status(thm)],[f201,f6090]) ).
fof(f6223,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X1,addition(multiplication(X2,X1),X3))) = addition(multiplication(addition(addition(one,X0),X2),X1),X3),
inference(forward_demodulation,[status(thm)],[f103,f6093]) ).
fof(f6224,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(multiplication(X1,X0),X2),multiplication(X3,X0))) = addition(multiplication(addition(addition(one,X3),X1),X0),X2),
inference(forward_demodulation,[status(thm)],[f97,f6223]) ).
fof(f6225,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(multiplication(X2,X0),multiplication(X3,X0)))) = addition(multiplication(addition(addition(one,X3),X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f103,f6224]) ).
fof(f6226,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X2,X3),X0))) = addition(multiplication(addition(addition(one,X2),X3),X0),X1),
inference(forward_demodulation,[status(thm)],[f201,f6225]) ).
fof(f6227,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X2,X3),X0))) = addition(multiplication(addition(X2,addition(one,X3)),X0),X1),
inference(forward_demodulation,[status(thm)],[f103,f6226]) ).
fof(f6228,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(addition(antidomain(X2),X0),X1),X2),X3),
inference(forward_demodulation,[status(thm)],[f219,f6094]) ).
fof(f6229,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X0,addition(antidomain(X2),X1)),X2),X3),
inference(forward_demodulation,[status(thm)],[f103,f6228]) ).
fof(f6230,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X1,addition(multiplication(X2,X1),X3))) = addition(multiplication(addition(addition(X0,one),X2),X1),X3),
inference(forward_demodulation,[status(thm)],[f103,f6095]) ).
fof(f6231,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(multiplication(X1,X0),X2),multiplication(X3,X0))) = addition(multiplication(addition(addition(X3,one),X1),X0),X2),
inference(forward_demodulation,[status(thm)],[f97,f6230]) ).
fof(f6232,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(multiplication(X2,X0),multiplication(X3,X0)))) = addition(multiplication(addition(addition(X3,one),X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f103,f6231]) ).
fof(f6233,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X2,X3),X0))) = addition(multiplication(addition(addition(X2,one),X3),X0),X1),
inference(forward_demodulation,[status(thm)],[f201,f6232]) ).
fof(f6234,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X2,X3),X0))) = addition(multiplication(addition(one,addition(X2,X3)),X0),X1),
inference(forward_demodulation,[status(thm)],[f103,f6233]) ).
fof(f6239,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),coantidomain(X2)),X3) = addition(multiplication(addition(addition(X2,X0),X1),coantidomain(X2)),X3),
inference(forward_demodulation,[status(thm)],[f219,f6098]) ).
fof(f6240,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),coantidomain(X2)),X3) = addition(multiplication(addition(X0,addition(X2,X1)),coantidomain(X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f6239]) ).
fof(f6241,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),X2) = addition(multiplication(addition(c(X1),X0),domain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f6099]) ).
fof(f6242,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),X2) = addition(multiplication(addition(c(X1),X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f80,f6100]) ).
fof(f6243,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),X2) = addition(multiplication(addition(coantidomain(X1),X0),codomain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f6101]) ).
fof(f6244,plain,
! [X0,X1,X2] : addition(multiplication(X0,omega(X1)),X2) = addition(multiplication(addition(antidomain(X1),X0),omega(X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f6107]) ).
fof(f6245,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,X2)),X3) = addition(multiplication(addition(antidomain(X1),X0),multiplication(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f80,f6108]) ).
fof(f6248,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X0,addition(multiplication(X2,addition(one,X1)),X3))) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(forward_demodulation,[status(thm)],[f103,f6113]) ).
fof(f6249,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(multiplication(X1,addition(one,X2)),X3),multiplication(X0,X2))) = addition(multiplication(addition(X0,X1),addition(one,X2)),X3),
inference(forward_demodulation,[status(thm)],[f97,f6248]) ).
fof(f6250,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(multiplication(X2,addition(one,X3)),multiplication(X0,X3)))) = addition(multiplication(addition(X0,X2),addition(one,X3)),X1),
inference(forward_demodulation,[status(thm)],[f103,f6249]) ).
fof(f6251,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X0,addition(multiplication(X2,addition(X1,one)),X3))) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(forward_demodulation,[status(thm)],[f103,f6115]) ).
fof(f6252,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(multiplication(X1,addition(X2,one)),X3),multiplication(X0,X2))) = addition(multiplication(addition(X0,X1),addition(X2,one)),X3),
inference(forward_demodulation,[status(thm)],[f97,f6251]) ).
fof(f6253,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(multiplication(X2,addition(X3,one)),multiplication(X0,X3)))) = addition(multiplication(addition(X0,X2),addition(X3,one)),X1),
inference(forward_demodulation,[status(thm)],[f103,f6252]) ).
fof(f6254,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(coantidomain(X1),X2)),X3) = addition(multiplication(addition(X1,X0),multiplication(coantidomain(X1),X2)),X3),
inference(forward_demodulation,[status(thm)],[f80,f6117]) ).
fof(f6255,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,coantidomain(multiplication(X2,X1)))),X3) = addition(multiplication(addition(X2,X0),multiplication(X1,coantidomain(multiplication(X2,X1)))),X3),
inference(forward_demodulation,[status(thm)],[f80,f6118]) ).
fof(f6256,plain,
! [X0,X1,X2] : addition(multiplication(X0,omega(coantidomain(X1))),X2) = addition(multiplication(addition(X1,X0),omega(coantidomain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f80,f6119]) ).
fof(f6266,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(addition(X0,addition(X1,X2)),X3),X4) = addition(multiplication(addition(X0,X1),X3),addition(multiplication(X2,X3),X4)),
inference(forward_demodulation,[status(thm)],[f219,f6125]) ).
fof(f6267,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(addition(X0,addition(X1,X2)),X3),X4) = addition(multiplication(addition(addition(X0,X1),X2),X3),X4),
inference(forward_demodulation,[status(thm)],[f219,f6266]) ).
fof(f6268,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(addition(X0,addition(X1,X2)),X3),X4) = addition(multiplication(addition(X1,addition(X0,X2)),X3),X4),
inference(forward_demodulation,[status(thm)],[f103,f6267]) ).
fof(f6269,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(addition(X0,multiplication(X1,X2)),X3),X4) = addition(multiplication(addition(X3,X0),X4),multiplication(X1,multiplication(X2,X4))),
inference(forward_demodulation,[status(thm)],[f201,f6127]) ).
fof(f6270,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),X4) = addition(multiplication(addition(X3,X2),X4),multiplication(X0,multiplication(X1,X4))),
inference(forward_demodulation,[status(thm)],[f103,f6269]) ).
fof(f6271,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),X4) = multiplication(addition(addition(X3,X2),multiplication(X0,X1)),X4),
inference(forward_demodulation,[status(thm)],[f211,f6270]) ).
fof(f6272,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),X4) = multiplication(addition(X2,addition(X3,multiplication(X0,X1))),X4),
inference(forward_demodulation,[status(thm)],[f103,f6271]) ).
fof(f6273,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,X1),X2),X3) = addition(multiplication(addition(X2,X1),X3),multiplication(X0,X3)),
inference(forward_demodulation,[status(thm)],[f201,f6128]) ).
fof(f6274,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = addition(multiplication(addition(X2,X0),X3),multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f103,f6273]) ).
fof(f6275,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f201,f6274]) ).
fof(f6276,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,X1),X2),X3) = addition(multiplication(addition(X2,X0),X3),multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f201,f6130]) ).
fof(f6277,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = addition(multiplication(addition(X2,X1),X3),multiplication(X0,X3)),
inference(forward_demodulation,[status(thm)],[f103,f6276]) ).
fof(f6278,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f201,f6277]) ).
fof(f6279,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(divergence(X3),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f6132]) ).
fof(f6280,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(divergence(X3),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f6279]) ).
fof(f6281,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(divergence(X3),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f6280]) ).
fof(f6282,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),domain(X3))),
inference(forward_demodulation,[status(thm)],[f201,f6133]) ).
fof(f6283,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,domain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f6282]) ).
fof(f6284,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),coantidomain(X3))),
inference(forward_demodulation,[status(thm)],[f201,f6134]) ).
fof(f6285,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,coantidomain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f6284]) ).
fof(f6286,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),antidomain(X3))),
inference(forward_demodulation,[status(thm)],[f201,f6135]) ).
fof(f6287,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,antidomain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f6286]) ).
fof(f6288,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),c(X3))),
inference(forward_demodulation,[status(thm)],[f201,f6136]) ).
fof(f6289,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,c(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f6288]) ).
fof(f6290,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),codomain(X3))),
inference(forward_demodulation,[status(thm)],[f201,f6137]) ).
fof(f6291,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,codomain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f6290]) ).
fof(f6292,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),divergence(X3))),
inference(forward_demodulation,[status(thm)],[f201,f6138]) ).
fof(f6293,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,divergence(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f6292]) ).
fof(f6294,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(X1,one),X2)),X3) = addition(multiplication(addition(X0,X2),X3),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f211,f6139]) ).
fof(f6295,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(X1,one),X2)),X3) = multiplication(addition(addition(X0,X2),multiplication(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f211,f6294]) ).
fof(f6296,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(X1,one),X2)),X3) = multiplication(addition(X2,addition(X0,multiplication(X1,X2))),X3),
inference(forward_demodulation,[status(thm)],[f103,f6295]) ).
fof(f6297,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(one,X1),X2)),X3) = addition(multiplication(addition(X0,X2),X3),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f211,f6140]) ).
fof(f6298,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(one,X1),X2)),X3) = multiplication(addition(addition(X0,X2),multiplication(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f211,f6297]) ).
fof(f6299,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(one,X1),X2)),X3) = multiplication(addition(X2,addition(X0,multiplication(X1,X2))),X3),
inference(forward_demodulation,[status(thm)],[f103,f6298]) ).
fof(f6300,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,multiplication(X1,addition(X3,one)))) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),X3)),
inference(forward_demodulation,[status(thm)],[f39,f6141]) ).
fof(f6301,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,multiplication(X1,addition(X3,one)))) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f39,f6300]) ).
fof(f6302,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,multiplication(X1,addition(one,X3)))) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),X3)),
inference(forward_demodulation,[status(thm)],[f39,f6142]) ).
fof(f6303,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,multiplication(X1,addition(one,X3)))) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f39,f6302]) ).
fof(f6304,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X0,X1),X2),addition(X3,addition(multiplication(X1,X2),X3))),
inference(forward_demodulation,[status(thm)],[f219,f6143]) ).
fof(f6305,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),X3)),
inference(forward_demodulation,[status(thm)],[f219,f6144]) ).
fof(f6306,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(addition(X0,X1),X1),X2),X3),
inference(forward_demodulation,[status(thm)],[f219,f6305]) ).
fof(f6307,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X1,addition(X0,X1)),X2),X3),
inference(forward_demodulation,[status(thm)],[f103,f6306]) ).
fof(f6308,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),zero),
inference(forward_demodulation,[status(thm)],[f201,f6147]) ).
fof(f6309,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f37,f6308]) ).
fof(f6310,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f201,f6150]) ).
fof(f6311,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f201,f6310]) ).
fof(f6312,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),addition(X1,X3))) = addition(multiplication(addition(X0,addition(one,X2)),X1),X3),
inference(forward_demodulation,[status(thm)],[f103,f6151]) ).
fof(f6313,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),addition(X2,X3)) = addition(multiplication(addition(X0,addition(one,X1)),X2),X3),
inference(forward_demodulation,[status(thm)],[f219,f6312]) ).
fof(f6314,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X2,X3),X0))) = addition(multiplication(addition(X2,addition(one,X3)),X0),X1),
inference(forward_demodulation,[status(thm)],[f97,f6313]) ).
fof(f6315,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X0,addition(antidomain(X2),X1)),X2),X3),
inference(forward_demodulation,[status(thm)],[f219,f6152]) ).
fof(f6316,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),addition(X1,X3))) = addition(multiplication(addition(X0,addition(X2,one)),X1),X3),
inference(forward_demodulation,[status(thm)],[f103,f6153]) ).
fof(f6317,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),addition(X2,X3)) = addition(multiplication(addition(X0,addition(X1,one)),X2),X3),
inference(forward_demodulation,[status(thm)],[f219,f6316]) ).
fof(f6318,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X2,X3),X0))) = addition(multiplication(addition(X2,addition(X3,one)),X0),X1),
inference(forward_demodulation,[status(thm)],[f97,f6317]) ).
fof(f6319,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X0,addition(X1,antidomain(X2))),X2),X3),
inference(forward_demodulation,[status(thm)],[f219,f6154]) ).
fof(f6320,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),coantidomain(X2)),X3) = addition(multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)),X3),
inference(forward_demodulation,[status(thm)],[f219,f6155]) ).
fof(f6321,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),coantidomain(X2)),X3) = addition(multiplication(addition(X0,addition(X2,X1)),coantidomain(X2)),X3),
inference(forward_demodulation,[status(thm)],[f219,f6156]) ).
fof(f6322,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,domain(X2)))) = addition(multiplication(addition(X1,c(X2)),domain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f97,f6157]) ).
fof(f6323,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,domain(X2))) = addition(multiplication(addition(X1,c(X2)),domain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f80,f6322]) ).
fof(f6324,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,X2))) = addition(multiplication(addition(X1,c(X2)),X2),X0),
inference(forward_demodulation,[status(thm)],[f97,f6158]) ).
fof(f6325,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,X2)) = addition(multiplication(addition(X1,c(X2)),X2),X0),
inference(forward_demodulation,[status(thm)],[f80,f6324]) ).
fof(f6326,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,codomain(X2)))) = addition(multiplication(addition(X1,coantidomain(X2)),codomain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f97,f6159]) ).
fof(f6327,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,codomain(X2))) = addition(multiplication(addition(X1,coantidomain(X2)),codomain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f80,f6326]) ).
fof(f6328,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,domain(X0)),X0),X1),
inference(forward_demodulation,[status(thm)],[f97,f6161]) ).
fof(f6329,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),addition(X2,multiplication(X3,addition(X1,X0)))) = addition(multiplication(addition(X3,antidomain(X0)),addition(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f97,f6163]) ).
fof(f6330,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(X0),X1),addition(X2,multiplication(X3,addition(X0,X1)))) = addition(multiplication(addition(X3,antidomain(X0)),addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f6164]) ).
fof(f6331,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,omega(X2)))) = addition(multiplication(addition(X1,antidomain(X2)),omega(X2)),X0),
inference(forward_demodulation,[status(thm)],[f97,f6165]) ).
fof(f6332,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,omega(X2))) = addition(multiplication(addition(X1,antidomain(X2)),omega(X2)),X0),
inference(forward_demodulation,[status(thm)],[f80,f6331]) ).
fof(f6333,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(X1,multiplication(X2,X3)))) = addition(multiplication(addition(X1,antidomain(X2)),multiplication(X2,X3)),X0),
inference(forward_demodulation,[status(thm)],[f97,f6166]) ).
fof(f6334,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,multiplication(X2,X3))) = addition(multiplication(addition(X1,antidomain(X2)),multiplication(X2,X3)),X0),
inference(forward_demodulation,[status(thm)],[f80,f6333]) ).
fof(f6341,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,one),X0),X1),
inference(forward_demodulation,[status(thm)],[f97,f6169]) ).
fof(f6342,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,codomain(X0)))) = addition(multiplication(addition(X2,X0),codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f97,f6170]) ).
fof(f6343,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(one,X1)),addition(multiplication(X2,X1),addition(X2,X3))) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(forward_demodulation,[status(thm)],[f103,f6171]) ).
fof(f6344,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(one,X1)),addition(X2,addition(X3,multiplication(X2,X1)))) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(forward_demodulation,[status(thm)],[f97,f6343]) ).
fof(f6345,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,addition(coantidomain(X0),X1)))) = addition(multiplication(addition(X3,X0),addition(coantidomain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f6172]) ).
fof(f6346,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,one)),addition(multiplication(X2,X1),addition(X2,X3))) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(forward_demodulation,[status(thm)],[f103,f6173]) ).
fof(f6347,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,one)),addition(X2,addition(X3,multiplication(X2,X1)))) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(forward_demodulation,[status(thm)],[f97,f6346]) ).
fof(f6348,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,addition(X1,coantidomain(X0))))) = addition(multiplication(addition(X3,X0),addition(X1,coantidomain(X0))),X2),
inference(forward_demodulation,[status(thm)],[f97,f6174]) ).
fof(f6349,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(X1,multiplication(coantidomain(X2),X3)))) = addition(multiplication(addition(X1,X2),multiplication(coantidomain(X2),X3)),X0),
inference(forward_demodulation,[status(thm)],[f97,f6175]) ).
fof(f6350,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,multiplication(coantidomain(X2),X3))) = addition(multiplication(addition(X1,X2),multiplication(coantidomain(X2),X3)),X0),
inference(forward_demodulation,[status(thm)],[f80,f6349]) ).
fof(f6351,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X3,X2)))))) = addition(multiplication(addition(X1,X3),multiplication(X2,coantidomain(multiplication(X3,X2)))),X0),
inference(forward_demodulation,[status(thm)],[f97,f6176]) ).
fof(f6352,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X3,X2))))) = addition(multiplication(addition(X1,X3),multiplication(X2,coantidomain(multiplication(X3,X2)))),X0),
inference(forward_demodulation,[status(thm)],[f80,f6351]) ).
fof(f6353,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,omega(coantidomain(X2))))) = addition(multiplication(addition(X1,X2),omega(coantidomain(X2))),X0),
inference(forward_demodulation,[status(thm)],[f97,f6177]) ).
fof(f6354,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,omega(coantidomain(X2)))) = addition(multiplication(addition(X1,X2),omega(coantidomain(X2))),X0),
inference(forward_demodulation,[status(thm)],[f80,f6353]) ).
fof(f6355,plain,
! [X0,X1,X2] : addition(omega(X0),addition(X1,multiplication(X2,omega(X0)))) = addition(multiplication(addition(X2,X0),omega(X0)),X1),
inference(forward_demodulation,[status(thm)],[f97,f6178]) ).
fof(f6375,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f6193]) ).
fof(f6376,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X1),X2),X3),coantidomain(addition(multiplication(X1,X2),X3))) = multiplication(X0,multiplication(X2,coantidomain(addition(multiplication(X1,X2),X3)))),
inference(forward_demodulation,[status(thm)],[f39,f6194]) ).
fof(f6379,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,X2),addition(multiplication(X3,X2),X4))) = addition(addition(multiplication(addition(X3,X1),X2),X0),X4),
inference(forward_demodulation,[status(thm)],[f103,f6203]) ).
fof(f6380,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(addition(X1,X2),X3),X4)) = addition(addition(multiplication(addition(X2,X1),X3),X0),X4),
inference(forward_demodulation,[status(thm)],[f219,f6379]) ).
fof(f6381,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(addition(X1,X2),X3),X4)) = addition(X0,addition(multiplication(addition(X2,X1),X3),X4)),
inference(forward_demodulation,[status(thm)],[f103,f6380]) ).
fof(f6382,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),addition(multiplication(addition(X0,X3),X1),X2)))) = addition(multiplication(X0,X1),addition(multiplication(X3,X1),X2)),
inference(forward_demodulation,[status(thm)],[f103,f6204]) ).
fof(f6383,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(addition(X3,addition(X0,X3)),X1),X2))) = addition(multiplication(X0,X1),addition(multiplication(X3,X1),X2)),
inference(forward_demodulation,[status(thm)],[f219,f6382]) ).
fof(f6384,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(addition(X3,addition(X0,X3)),X1),X2))) = addition(multiplication(addition(X0,X3),X1),X2),
inference(forward_demodulation,[status(thm)],[f219,f6383]) ).
fof(f6385,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),X4))) = addition(X4,addition(multiplication(addition(X0,X3),X1),X2)),
inference(forward_demodulation,[status(thm)],[f103,f6205]) ).
fof(f6386,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(addition(X1,X2),X3),X4)) = addition(X4,addition(multiplication(X2,X3),addition(X0,multiplication(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f103,f6206]) ).
fof(f6387,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),X4))) = addition(addition(multiplication(addition(X0,X3),X1),X2),X4),
inference(forward_demodulation,[status(thm)],[f103,f6209]) ).
fof(f6388,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),X4))) = addition(X2,addition(multiplication(addition(X0,X3),X1),X4)),
inference(forward_demodulation,[status(thm)],[f103,f6387]) ).
fof(f6393,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4512,f246]) ).
fof(f6398,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(codomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4512]) ).
fof(f6399,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(codomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4512]) ).
fof(f6406,plain,
! [X0] : codomain(codomain(X0)) = addition(codomain(codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f2309,f4512]) ).
fof(f6407,plain,
! [X0,X1] : addition(coantidomain(codomain(X0)),X1) = addition(addition(coantidomain(codomain(X0)),X1),multiplication(codomain(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f4512]) ).
fof(f6416,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f70,f4512]) ).
fof(f6418,plain,
! [X0,X1] : X0 = addition(X0,multiplication(coantidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f193,f4512]) ).
fof(f6420,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4512,f181]) ).
fof(f6433,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(codomain(X3),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4512,f219]) ).
fof(f6434,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(codomain(X3),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4512,f170]) ).
fof(f6435,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(codomain(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4512,f58]) ).
fof(f6436,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(codomain(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4512,f55]) ).
fof(f6437,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(codomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4512,f53]) ).
fof(f6438,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4512,f103]) ).
fof(f6439,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4512,f36]) ).
fof(f6449,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4512,f177]) ).
fof(f6451,plain,
! [X0,X1,X2] : leq(multiplication(codomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4512,f1420]) ).
fof(f6455,plain,
! [X0,X1,X2] : addition(multiplication(codomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4512,f103]) ).
fof(f6457,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(codomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4512,f97]) ).
fof(f6458,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(codomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4512,f97]) ).
fof(f6460,plain,
! [X0,X1] :
( X0 != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4512,f49]) ).
fof(f6461,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(codomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4512,f36]) ).
fof(f6471,plain,
! [X0] : codomain(codomain(X0)) = addition(codomain(X0),codomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f6406]) ).
fof(f6472,plain,
! [X0,X1] : addition(coantidomain(codomain(X0)),X1) = addition(X1,addition(coantidomain(codomain(X0)),multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f6407]) ).
fof(f6477,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f6420]) ).
fof(f6487,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(codomain(X3),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f6433]) ).
fof(f6488,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(codomain(X3),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f6487]) ).
fof(f6489,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(codomain(X3),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f6488]) ).
fof(f6490,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(codomain(X3),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f6434]) ).
fof(f6491,plain,
! [X0,X1,X2] :
( leq(multiplication(codomain(X2),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f6436]) ).
fof(f6492,plain,
! [X0,X1,X2] :
( leq(multiplication(codomain(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f6491]) ).
fof(f6502,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f59,f6449]) ).
fof(f6504,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f6455]) ).
fof(f6506,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(codomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f6458]) ).
fof(f6509,plain,
! [X0] : leq(codomain(X0),codomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f2309,f6393]) ).
fof(f6510,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),addition(coantidomain(codomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f181,f6393]) ).
fof(f6511,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),addition(X1,coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f190,f6393]) ).
fof(f6519,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f70,f6393]) ).
fof(f6521,plain,
! [X0,X1] : leq(multiplication(coantidomain(codomain(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f193,f6393]) ).
fof(f6526,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),X1),
inference(resolution,[status(thm)],[f4513,f246]) ).
fof(f6531,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(c(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4513]) ).
fof(f6532,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(c(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4513]) ).
fof(f6541,plain,
! [X0] : codomain(c(X0)) = addition(codomain(c(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f2309,f4513]) ).
fof(f6542,plain,
! [X0,X1] : addition(coantidomain(c(X0)),X1) = addition(addition(coantidomain(c(X0)),X1),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f4513]) ).
fof(f6551,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f72,f4513]) ).
fof(f6552,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f71,f4513]) ).
fof(f6554,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f547,f4513]) ).
fof(f6555,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f362,f4513]) ).
fof(f6557,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4513,f181]) ).
fof(f6570,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(c(X3),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4513,f219]) ).
fof(f6571,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(c(X3),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4513,f170]) ).
fof(f6572,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(c(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4513,f58]) ).
fof(f6573,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(c(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4513,f55]) ).
fof(f6574,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(c(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4513,f53]) ).
fof(f6575,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4513,f103]) ).
fof(f6576,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4513,f36]) ).
fof(f6586,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(paramodulation,[status(thm)],[f4513,f177]) ).
fof(f6588,plain,
! [X0,X1,X2] : leq(multiplication(c(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4513,f1420]) ).
fof(f6592,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4513,f103]) ).
fof(f6594,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(c(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4513,f97]) ).
fof(f6595,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(c(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4513,f97]) ).
fof(f6597,plain,
! [X0,X1] :
( X0 != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4513,f49]) ).
fof(f6598,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(c(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4513,f36]) ).
fof(f6608,plain,
! [X0] : codomain(c(X0)) = addition(c(X0),codomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f35,f6541]) ).
fof(f6609,plain,
! [X0,X1] : addition(coantidomain(c(X0)),X1) = addition(X1,addition(coantidomain(c(X0)),multiplication(c(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f6542]) ).
fof(f6614,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f6557]) ).
fof(f6624,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(c(X3),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f6570]) ).
fof(f6625,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(c(X3),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f6624]) ).
fof(f6626,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(c(X3),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f6625]) ).
fof(f6627,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(c(X3),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f6571]) ).
fof(f6628,plain,
! [X0,X1,X2] :
( leq(multiplication(c(X2),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f6573]) ).
fof(f6629,plain,
! [X0,X1,X2] :
( leq(multiplication(c(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f6628]) ).
fof(f6639,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f59,f6586]) ).
fof(f6641,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f6592]) ).
fof(f6643,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(c(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f6595]) ).
fof(f6648,plain,
! [X0] : leq(c(X0),codomain(c(X0))),
inference(paramodulation,[status(thm)],[f2309,f6526]) ).
fof(f6649,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),addition(coantidomain(c(X0)),X1)),
inference(paramodulation,[status(thm)],[f181,f6526]) ).
fof(f6650,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),addition(X1,coantidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f190,f6526]) ).
fof(f6658,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f72,f6526]) ).
fof(f6659,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f71,f6526]) ).
fof(f6661,plain,
! [X0,X1] : leq(multiplication(antidomain(c(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f547,f6526]) ).
fof(f6662,plain,
! [X0,X1] : leq(multiplication(domain(c(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f362,f6526]) ).
fof(f6667,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4514,f246]) ).
fof(f6672,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4514]) ).
fof(f6673,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(antidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4514]) ).
fof(f6681,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f177,f4514]) ).
fof(f6685,plain,
! [X0] : codomain(antidomain(X0)) = addition(codomain(antidomain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f2309,f4514]) ).
fof(f6686,plain,
! [X0,X1] : addition(coantidomain(antidomain(X0)),X1) = addition(addition(coantidomain(antidomain(X0)),X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f4514]) ).
fof(f6699,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4514,f181]) ).
fof(f6712,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(antidomain(X3),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4514,f219]) ).
fof(f6713,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(antidomain(X3),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4514,f170]) ).
fof(f6714,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(antidomain(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4514,f58]) ).
fof(f6715,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(antidomain(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4514,f55]) ).
fof(f6716,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(antidomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4514,f53]) ).
fof(f6717,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4514,f103]) ).
fof(f6718,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4514,f36]) ).
fof(f6728,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4514,f177]) ).
fof(f6730,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4514,f1420]) ).
fof(f6734,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4514,f103]) ).
fof(f6736,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(antidomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4514,f97]) ).
fof(f6737,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(antidomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4514,f97]) ).
fof(f6739,plain,
! [X0,X1] :
( X0 != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4514,f49]) ).
fof(f6740,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(antidomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4514,f36]) ).
fof(f6752,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f6681]) ).
fof(f6753,plain,
! [X0] : codomain(antidomain(X0)) = addition(antidomain(X0),codomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f6685]) ).
fof(f6754,plain,
! [X0,X1] : addition(coantidomain(antidomain(X0)),X1) = addition(X1,addition(coantidomain(antidomain(X0)),multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f6686]) ).
fof(f6759,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f6699]) ).
fof(f6769,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(antidomain(X3),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f6712]) ).
fof(f6770,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(antidomain(X3),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f6769]) ).
fof(f6771,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(antidomain(X3),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f6770]) ).
fof(f6772,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(antidomain(X3),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f6713]) ).
fof(f6773,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(X2),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f6715]) ).
fof(f6774,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f6773]) ).
fof(f6784,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f59,f6728]) ).
fof(f6786,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f6734]) ).
fof(f6788,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(antidomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f6737]) ).
fof(f6791,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f186,f6667]) ).
fof(f6792,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f177,f6667]) ).
fof(f6796,plain,
! [X0] : leq(antidomain(X0),codomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f2309,f6667]) ).
fof(f6797,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(coantidomain(antidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f181,f6667]) ).
fof(f6798,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X1,coantidomain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f190,f6667]) ).
fof(f6808,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),X1),
inference(paramodulation,[status(thm)],[f62,f6667]) ).
fof(f6823,plain,
! [X0,X1] :
( addition(X0,X1) != multiplication(X1,codomain(addition(X0,X1)))
| leq(multiplication(X0,codomain(addition(X0,X1))),multiplication(X1,codomain(addition(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f2309,f241]) ).
fof(f6824,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X1),X2) != multiplication(X1,addition(coantidomain(addition(X0,X1)),X2))
| leq(multiplication(X0,addition(coantidomain(addition(X0,X1)),X2)),multiplication(X1,addition(coantidomain(addition(X0,X1)),X2))) ),
inference(paramodulation,[status(thm)],[f181,f241]) ).
fof(f6825,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,addition(X1,coantidomain(addition(X0,X2))))
| leq(multiplication(X0,addition(X1,coantidomain(addition(X0,X2)))),multiplication(X2,addition(X1,coantidomain(addition(X0,X2))))) ),
inference(paramodulation,[status(thm)],[f190,f241]) ).
fof(f6826,plain,
! [X0,X1,X2] :
( zero != multiplication(X1,multiplication(coantidomain(addition(X0,X1)),X2))
| leq(multiplication(X0,multiplication(coantidomain(addition(X0,X1)),X2)),multiplication(X1,multiplication(coantidomain(addition(X0,X1)),X2))) ),
inference(paramodulation,[status(thm)],[f151,f241]) ).
fof(f6827,plain,
! [X0,X1,X2] :
( zero != multiplication(X2,multiplication(X1,coantidomain(multiplication(addition(X0,X2),X1))))
| leq(multiplication(X0,multiplication(X1,coantidomain(multiplication(addition(X0,X2),X1)))),multiplication(X2,multiplication(X1,coantidomain(multiplication(addition(X0,X2),X1))))) ),
inference(paramodulation,[status(thm)],[f144,f241]) ).
fof(f6828,plain,
! [X0,X1] :
( zero != multiplication(X1,omega(coantidomain(addition(X0,X1))))
| leq(multiplication(X0,omega(coantidomain(addition(X0,X1)))),multiplication(X1,omega(coantidomain(addition(X0,X1))))) ),
inference(paramodulation,[status(thm)],[f1813,f241]) ).
fof(f6829,plain,
! [X0,X1] :
( omega(addition(X0,X1)) != multiplication(X1,omega(addition(X0,X1)))
| leq(multiplication(X0,omega(addition(X0,X1))),multiplication(X1,omega(addition(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f56,f241]) ).
fof(f6830,plain,
! [X0,X1] :
( zero != multiplication(X1,coantidomain(addition(X0,X1)))
| leq(multiplication(X0,coantidomain(addition(X0,X1))),multiplication(X1,coantidomain(addition(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f63,f241]) ).
fof(f6833,plain,
! [X0,X1,X2] :
( multiplication(one,X0) != multiplication(backward_diamond(X1,X2),X0)
| leq(multiplication(one,X0),multiplication(backward_diamond(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f1504,f241]) ).
fof(f6834,plain,
! [X0,X1,X2] :
( multiplication(one,X0) != multiplication(forward_box(X1,X2),X0)
| leq(multiplication(one,X0),multiplication(forward_box(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f1497,f241]) ).
fof(f6835,plain,
! [X0,X1,X2] :
( multiplication(one,X0) != multiplication(backward_box(X1,X2),X0)
| leq(multiplication(one,X0),multiplication(backward_box(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f1492,f241]) ).
fof(f6836,plain,
! [X0,X1,X2] :
( multiplication(one,X0) != multiplication(forward_diamond(X1,X2),X0)
| leq(multiplication(one,X0),multiplication(forward_diamond(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f1485,f241]) ).
fof(f6837,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(divergence(X1),X0)
| leq(multiplication(one,X0),multiplication(divergence(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1488,f241]) ).
fof(f6838,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(codomain(X1),X0)
| leq(multiplication(one,X0),multiplication(codomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1477,f241]) ).
fof(f6839,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(c(X1),X0)
| leq(multiplication(one,X0),multiplication(c(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1471,f241]) ).
fof(f6840,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(antidomain(X1),X0)
| leq(multiplication(one,X0),multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1379,f241]) ).
fof(f6841,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(coantidomain(X1),X0)
| leq(multiplication(one,X0),multiplication(coantidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1377,f241]) ).
fof(f6842,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(domain(X1),X0)
| leq(multiplication(one,X0),multiplication(domain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1375,f241]) ).
fof(f6843,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(c(X0),X1)
| leq(multiplication(domain(X0),X1),multiplication(c(X0),X1)) ),
inference(paramodulation,[status(thm)],[f569,f241]) ).
fof(f6844,plain,
! [X0,X1,X2] :
( multiplication(coantidomain(multiplication(codomain(X0),X1)),X2) != multiplication(coantidomain(multiplication(codomain(X0),X1)),X2)
| leq(multiplication(coantidomain(multiplication(X0,X1)),X2),multiplication(coantidomain(multiplication(codomain(X0),X1)),X2)) ),
inference(paramodulation,[status(thm)],[f615,f241]) ).
fof(f6845,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(codomain(X0),X1)
| leq(multiplication(coantidomain(X0),X1),multiplication(codomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f683,f241]) ).
fof(f6846,plain,
! [X0,X1,X2] :
( multiplication(antidomain(multiplication(X0,domain(X1))),X2) != multiplication(antidomain(multiplication(X0,domain(X1))),X2)
| leq(multiplication(antidomain(multiplication(X0,X1)),X2),multiplication(antidomain(multiplication(X0,domain(X1))),X2)) ),
inference(paramodulation,[status(thm)],[f479,f241]) ).
fof(f6847,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(domain(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(domain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f558,f241]) ).
fof(f6848,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(multiplication(X0,multiplication(X1,X2)),X3),multiplication(multiplication(X4,X2),X3)) ),
inference(paramodulation,[status(thm)],[f204,f241]) ).
fof(f6849,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(addition(X0,X3),X1),X4),X2) != multiplication(addition(multiplication(X3,X1),X4),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(addition(multiplication(X3,X1),X4),X2)) ),
inference(paramodulation,[status(thm)],[f219,f241]) ).
fof(f6850,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(X0,addition(X1,X3)),X4),X2) != multiplication(addition(multiplication(X0,X3),X4),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(addition(multiplication(X0,X3),X4),X2)) ),
inference(paramodulation,[status(thm)],[f170,f241]) ).
fof(f6851,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(X0,multiplication(X3,X4)),X1),X2) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X3,multiplication(X4,X1)),X2)) ),
inference(paramodulation,[status(thm)],[f211,f241]) ).
fof(f6852,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(addition(X3,X0),X1),X2) != multiplication(multiplication(X3,X1),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X3,X1),X2)) ),
inference(paramodulation,[status(thm)],[f201,f241]) ).
fof(f6853,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X3,X1)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,X3),X2)) ),
inference(paramodulation,[status(thm)],[f153,f241]) ).
fof(f6855,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X1,X3)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,X3),X2)) ),
inference(paramodulation,[status(thm)],[f42,f241]) ).
fof(f6856,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X1,addition(X0,X3)),X2) != multiplication(X3,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f103,f241]) ).
fof(f6857,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X0,addition(X1,X3)),X2) != multiplication(X3,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f36,f241]) ).
fof(f6859,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(antidomain(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(antidomain(X2),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4514,f241]) ).
fof(f6860,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(c(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(c(X2),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4513,f241]) ).
fof(f6861,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(codomain(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(codomain(X2),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4512,f241]) ).
fof(f6862,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(divergence(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(divergence(X2),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4511,f241]) ).
fof(f6863,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,domain(X2)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,domain(X2)),X1)) ),
inference(paramodulation,[status(thm)],[f2497,f241]) ).
fof(f6864,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,coantidomain(X2)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,coantidomain(X2)),X1)) ),
inference(paramodulation,[status(thm)],[f2496,f241]) ).
fof(f6865,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,antidomain(X2)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,antidomain(X2)),X1)) ),
inference(paramodulation,[status(thm)],[f2495,f241]) ).
fof(f6866,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,c(X2)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,c(X2)),X1)) ),
inference(paramodulation,[status(thm)],[f2494,f241]) ).
fof(f6867,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,codomain(X2)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,codomain(X2)),X1)) ),
inference(paramodulation,[status(thm)],[f2493,f241]) ).
fof(f6868,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,divergence(X2)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,divergence(X2)),X1)) ),
inference(paramodulation,[status(thm)],[f2492,f241]) ).
fof(f6869,plain,
! [X0,X1,X2] :
( multiplication(multiplication(addition(X2,one),X0),X1) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X2,X0),X1)) ),
inference(paramodulation,[status(thm)],[f232,f241]) ).
fof(f6870,plain,
! [X0,X1,X2] :
( multiplication(multiplication(addition(one,X2),X0),X1) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X2,X0),X1)) ),
inference(paramodulation,[status(thm)],[f207,f241]) ).
fof(f6871,plain,
! [X0,X1,X2] :
( multiplication(multiplication(X0,addition(X2,one)),X1) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,X2),X1)) ),
inference(paramodulation,[status(thm)],[f192,f241]) ).
fof(f6872,plain,
! [X0,X1,X2] :
( multiplication(multiplication(X0,addition(one,X2)),X1) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,X2),X1)) ),
inference(paramodulation,[status(thm)],[f162,f241]) ).
fof(f6873,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(addition(X2,addition(X0,X2)),X1)
| leq(multiplication(X0,X1),multiplication(addition(X2,addition(X0,X2)),X1)) ),
inference(paramodulation,[status(thm)],[f99,f241]) ).
fof(f6874,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)) ),
inference(paramodulation,[status(thm)],[f105,f241]) ).
fof(f6875,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X2,addition(X3,X0)),X1) != multiplication(addition(X2,X3),X1)
| leq(multiplication(X0,X1),multiplication(addition(X2,X3),X1)) ),
inference(paramodulation,[status(thm)],[f97,f241]) ).
fof(f6876,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,addition(X0,X2)),X1) != multiplication(addition(X2,X3),X1)
| leq(multiplication(X0,X1),multiplication(addition(X2,X3),X1)) ),
inference(paramodulation,[status(thm)],[f97,f241]) ).
fof(f6878,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f35,f241]) ).
fof(f6879,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f35,f241]) ).
fof(f6905,plain,
! [X0,X1,X2] :
( multiplication(one,X0) != multiplication(backward_diamond(X1,X2),X0)
| leq(X0,multiplication(backward_diamond(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6833]) ).
fof(f6906,plain,
! [X0,X1,X2] :
( X0 != multiplication(backward_diamond(X1,X2),X0)
| leq(X0,multiplication(backward_diamond(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6905]) ).
fof(f6907,plain,
! [X0,X1,X2] :
( multiplication(one,X0) != multiplication(forward_box(X1,X2),X0)
| leq(X0,multiplication(forward_box(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6834]) ).
fof(f6908,plain,
! [X0,X1,X2] :
( X0 != multiplication(forward_box(X1,X2),X0)
| leq(X0,multiplication(forward_box(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6907]) ).
fof(f6909,plain,
! [X0,X1,X2] :
( multiplication(one,X0) != multiplication(backward_box(X1,X2),X0)
| leq(X0,multiplication(backward_box(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6835]) ).
fof(f6910,plain,
! [X0,X1,X2] :
( X0 != multiplication(backward_box(X1,X2),X0)
| leq(X0,multiplication(backward_box(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6909]) ).
fof(f6911,plain,
! [X0,X1,X2] :
( multiplication(one,X0) != multiplication(forward_diamond(X1,X2),X0)
| leq(X0,multiplication(forward_diamond(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6836]) ).
fof(f6912,plain,
! [X0,X1,X2] :
( X0 != multiplication(forward_diamond(X1,X2),X0)
| leq(X0,multiplication(forward_diamond(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6911]) ).
fof(f6913,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6837]) ).
fof(f6914,plain,
! [X0,X1] :
( X0 != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6913]) ).
fof(f6915,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6838]) ).
fof(f6916,plain,
! [X0,X1] :
( X0 != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6915]) ).
fof(f6917,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6839]) ).
fof(f6918,plain,
! [X0,X1] :
( X0 != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6917]) ).
fof(f6919,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6840]) ).
fof(f6920,plain,
! [X0,X1] :
( X0 != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6919]) ).
fof(f6921,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6841]) ).
fof(f6922,plain,
! [X0,X1] :
( X0 != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6921]) ).
fof(f6923,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6842]) ).
fof(f6924,plain,
! [X0,X1] :
( X0 != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f6923]) ).
fof(f6925,plain,
! [X0,X1] :
( X1 != multiplication(c(X0),X1)
| leq(multiplication(domain(X0),X1),multiplication(c(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f6843]) ).
fof(f6926,plain,
! [X0,X1,X2] : leq(multiplication(coantidomain(multiplication(X0,X1)),X2),multiplication(coantidomain(multiplication(codomain(X0),X1)),X2)),
inference(trivial_equality_resolution,[status(thm)],[f6844]) ).
fof(f6927,plain,
! [X0,X1] :
( X1 != multiplication(codomain(X0),X1)
| leq(multiplication(coantidomain(X0),X1),multiplication(codomain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f6845]) ).
fof(f6928,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(multiplication(X0,X1)),X2),multiplication(antidomain(multiplication(X0,domain(X1))),X2)),
inference(trivial_equality_resolution,[status(thm)],[f6846]) ).
fof(f6929,plain,
! [X0,X1] :
( X1 != multiplication(domain(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(domain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f6847]) ).
fof(f6930,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(X0,multiplication(multiplication(X1,X2),X3)),multiplication(multiplication(X4,X2),X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f6848]) ).
fof(f6931,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(multiplication(X4,X2),X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f6930]) ).
fof(f6932,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X4,multiplication(X2,X3))) ),
inference(forward_demodulation,[status(thm)],[f39,f6931]) ).
fof(f6933,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(X0,X1),X4),multiplication(X2,X3)) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X4,multiplication(X2,X3))) ),
inference(forward_demodulation,[status(thm)],[f39,f6932]) ).
fof(f6934,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(X0,X1),X4),multiplication(X2,X3)) != multiplication(X4,multiplication(X2,X3))
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X4,multiplication(X2,X3))) ),
inference(forward_demodulation,[status(thm)],[f39,f6933]) ).
fof(f6935,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(addition(X0,X3),X1),X4),X2) != multiplication(addition(multiplication(X3,X1),X4),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X3,X1),X4),X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f6849]) ).
fof(f6936,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(X0,addition(X1,X3)),X4),X2) != multiplication(addition(multiplication(X0,X3),X4),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X3),X4),X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f6850]) ).
fof(f6937,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(X0,multiplication(X3,X4)),X1),X2) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X3,multiplication(X4,X1)),X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f6851]) ).
fof(f6938,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(X0,multiplication(X3,X4)),X1),X2) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(multiplication(X4,X1),X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6937]) ).
fof(f6939,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(X0,multiplication(X3,X4)),X1),X2) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,multiplication(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f39,f6938]) ).
fof(f6940,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(X0,multiplication(X3,X4)),multiplication(X1,X2)) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,multiplication(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f39,f6939]) ).
fof(f6941,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(X0,multiplication(X3,X4)),multiplication(X1,X2)) != multiplication(X3,multiplication(multiplication(X4,X1),X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,multiplication(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f39,f6940]) ).
fof(f6942,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(X0,multiplication(X3,X4)),multiplication(X1,X2)) != multiplication(X3,multiplication(X4,multiplication(X1,X2)))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,multiplication(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f39,f6941]) ).
fof(f6943,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(addition(X3,X0),X1),X2) != multiplication(multiplication(X3,X1),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X3,X1),X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f6852]) ).
fof(f6944,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(addition(X3,X0),X1),X2) != multiplication(multiplication(X3,X1),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6943]) ).
fof(f6945,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,X0),multiplication(X1,X2)) != multiplication(multiplication(X3,X1),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6944]) ).
fof(f6946,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,X0),multiplication(X1,X2)) != multiplication(X3,multiplication(X1,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6945]) ).
fof(f6947,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X3,X1)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X3),X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f6853]) ).
fof(f6948,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X3,X1)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6947]) ).
fof(f6949,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X3,X1),X2)) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6948]) ).
fof(f6950,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X3,X1),X2)) != multiplication(X0,multiplication(X3,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6949]) ).
fof(f6955,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X1,X3)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X3),X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f6855]) ).
fof(f6956,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X1,X3)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6955]) ).
fof(f6957,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X1,X3),X2)) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6956]) ).
fof(f6958,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X1,X3),X2)) != multiplication(X0,multiplication(X3,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f6957]) ).
fof(f6961,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(antidomain(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(antidomain(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6859]) ).
fof(f6962,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(antidomain(X2),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(antidomain(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6961]) ).
fof(f6963,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(c(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(c(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6860]) ).
fof(f6964,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(c(X2),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(c(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6963]) ).
fof(f6965,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(codomain(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(codomain(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6861]) ).
fof(f6966,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(codomain(X2),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(codomain(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6965]) ).
fof(f6967,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(divergence(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(divergence(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6862]) ).
fof(f6968,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(divergence(X2),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(divergence(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6967]) ).
fof(f6969,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,domain(X2)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(domain(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6863]) ).
fof(f6970,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(domain(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(domain(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6969]) ).
fof(f6971,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,coantidomain(X2)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(coantidomain(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6864]) ).
fof(f6972,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(coantidomain(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(coantidomain(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6971]) ).
fof(f6973,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,antidomain(X2)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(antidomain(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6865]) ).
fof(f6974,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(antidomain(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(antidomain(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6973]) ).
fof(f6975,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,c(X2)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(c(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6866]) ).
fof(f6976,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(c(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(c(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6975]) ).
fof(f6977,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,codomain(X2)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(codomain(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6867]) ).
fof(f6978,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(codomain(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(codomain(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6977]) ).
fof(f6979,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(X0,divergence(X2)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(divergence(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6868]) ).
fof(f6980,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(divergence(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(divergence(X2),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6979]) ).
fof(f6981,plain,
! [X0,X1,X2] :
( multiplication(multiplication(addition(X2,one),X0),X1) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6869]) ).
fof(f6982,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,one),multiplication(X0,X1)) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6981]) ).
fof(f6983,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,one),multiplication(X0,X1)) != multiplication(X2,multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6982]) ).
fof(f6984,plain,
! [X0,X1,X2] :
( multiplication(multiplication(addition(one,X2),X0),X1) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6870]) ).
fof(f6985,plain,
! [X0,X1,X2] :
( multiplication(addition(one,X2),multiplication(X0,X1)) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6984]) ).
fof(f6986,plain,
! [X0,X1,X2] :
( multiplication(addition(one,X2),multiplication(X0,X1)) != multiplication(X2,multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6985]) ).
fof(f6987,plain,
! [X0,X1,X2] :
( multiplication(multiplication(X0,addition(X2,one)),X1) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6871]) ).
fof(f6988,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(X2,one),X1)) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6987]) ).
fof(f6989,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(X2,one),X1)) != multiplication(X0,multiplication(X2,X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6988]) ).
fof(f6990,plain,
! [X0,X1,X2] :
( multiplication(multiplication(X0,addition(one,X2)),X1) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6872]) ).
fof(f6991,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(one,X2),X1)) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6990]) ).
fof(f6992,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(one,X2),X1)) != multiplication(X0,multiplication(X2,X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f6991]) ).
fof(f6993,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(trivial_equality_resolution,[status(thm)],[f6874]) ).
fof(f6998,plain,
! [X0,X1] : leq(domain_difference(X0,X1),antidomain(X1)),
inference(paramodulation,[status(thm)],[f68,f6808]) ).
fof(f7000,plain,
! [X0] : leq(domain(X0),codomain(domain(X0))),
inference(paramodulation,[status(thm)],[f2309,f6808]) ).
fof(f7001,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),addition(coantidomain(domain(X0)),X1)),
inference(paramodulation,[status(thm)],[f181,f6808]) ).
fof(f7002,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),addition(X1,coantidomain(domain(X0)))),
inference(paramodulation,[status(thm)],[f190,f6808]) ).
fof(f7010,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f69,f6808]) ).
fof(f7018,plain,
! [X0,X1] : addition(domain_difference(X0,X1),antidomain(X1)) = antidomain(X1),
inference(resolution,[status(thm)],[f6998,f48]) ).
fof(f7026,plain,
! [X0,X1] : leq(domain_difference(X0,domain(X1)),c(X1)),
inference(paramodulation,[status(thm)],[f67,f6998]) ).
fof(f7027,plain,
! [X0,X1] : leq(domain_difference(X0,antidomain(X1)),domain(X1)),
inference(paramodulation,[status(thm)],[f62,f6998]) ).
fof(f7029,plain,
! [X0,X1] : addition(antidomain(X0),domain_difference(X1,X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f7018]) ).
fof(f7038,plain,
! [X0,X1,X2] :
( multiplication(X2,addition(X0,X1)) != multiplication(addition(antidomain(addition(X0,X1)),X2),X1)
| leq(multiplication(addition(antidomain(addition(X0,X1)),X2),X0),multiplication(addition(antidomain(addition(X0,X1)),X2),X1)) ),
inference(paramodulation,[status(thm)],[f224,f242]) ).
fof(f7039,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(addition(X0,antidomain(addition(X1,X2))),X2)
| leq(multiplication(addition(X0,antidomain(addition(X1,X2))),X1),multiplication(addition(X0,antidomain(addition(X1,X2))),X2)) ),
inference(paramodulation,[status(thm)],[f230,f242]) ).
fof(f7040,plain,
! [X0,X1] :
( zero != multiplication(c(addition(X0,X1)),X1)
| leq(multiplication(c(addition(X0,X1)),X0),multiplication(c(addition(X0,X1)),X1)) ),
inference(paramodulation,[status(thm)],[f4265,f242]) ).
fof(f7041,plain,
! [X0,X1] :
( addition(X0,X1) != multiplication(domain(addition(X0,X1)),X1)
| leq(multiplication(domain(addition(X0,X1)),X0),multiplication(domain(addition(X0,X1)),X1)) ),
inference(paramodulation,[status(thm)],[f4146,f242]) ).
fof(f7042,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(multiplication(X0,X1),X3)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,X1),X3)) ),
inference(paramodulation,[status(thm)],[f39,f242]) ).
fof(f7045,plain,
! [X0,X1] :
( zero != multiplication(antidomain(addition(X0,X1)),X1)
| leq(multiplication(antidomain(addition(X0,X1)),X0),multiplication(antidomain(addition(X0,X1)),X1)) ),
inference(paramodulation,[status(thm)],[f59,f242]) ).
fof(f7052,plain,
! [X0,X1,X2] :
( multiplication(X0,one) != multiplication(X0,backward_diamond(X1,X2))
| leq(multiplication(X0,one),multiplication(X0,backward_diamond(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1504,f242]) ).
fof(f7053,plain,
! [X0,X1,X2] :
( multiplication(X0,one) != multiplication(X0,forward_box(X1,X2))
| leq(multiplication(X0,one),multiplication(X0,forward_box(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1497,f242]) ).
fof(f7054,plain,
! [X0,X1,X2] :
( multiplication(X0,one) != multiplication(X0,backward_box(X1,X2))
| leq(multiplication(X0,one),multiplication(X0,backward_box(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1492,f242]) ).
fof(f7055,plain,
! [X0,X1,X2] :
( multiplication(X0,one) != multiplication(X0,forward_diamond(X1,X2))
| leq(multiplication(X0,one),multiplication(X0,forward_diamond(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1485,f242]) ).
fof(f7056,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,divergence(X1))
| leq(multiplication(X0,one),multiplication(X0,divergence(X1))) ),
inference(paramodulation,[status(thm)],[f1488,f242]) ).
fof(f7057,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(multiplication(X0,one),multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f1477,f242]) ).
fof(f7058,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(multiplication(X0,one),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f1471,f242]) ).
fof(f7059,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,antidomain(X1))
| leq(multiplication(X0,one),multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f1379,f242]) ).
fof(f7060,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,coantidomain(X1))
| leq(multiplication(X0,one),multiplication(X0,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f1377,f242]) ).
fof(f7061,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(multiplication(X0,one),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f1375,f242]) ).
fof(f7062,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(multiplication(X0,domain(X1)),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f569,f242]) ).
fof(f7063,plain,
! [X0,X1,X2] :
( multiplication(X0,coantidomain(multiplication(codomain(X1),X2))) != multiplication(X0,coantidomain(multiplication(codomain(X1),X2)))
| leq(multiplication(X0,coantidomain(multiplication(X1,X2))),multiplication(X0,coantidomain(multiplication(codomain(X1),X2)))) ),
inference(paramodulation,[status(thm)],[f615,f242]) ).
fof(f7064,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(multiplication(X0,coantidomain(X1)),multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f683,f242]) ).
fof(f7065,plain,
! [X0,X1,X2] :
( multiplication(X0,antidomain(multiplication(X1,domain(X2)))) != multiplication(X0,antidomain(multiplication(X1,domain(X2))))
| leq(multiplication(X0,antidomain(multiplication(X1,X2))),multiplication(X0,antidomain(multiplication(X1,domain(X2))))) ),
inference(paramodulation,[status(thm)],[f479,f242]) ).
fof(f7066,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f558,f242]) ).
fof(f7067,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(X0,multiplication(addition(multiplication(X1,X2),X4),X3)) != multiplication(X0,multiplication(X4,X3))
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X0,multiplication(X4,X3))) ),
inference(paramodulation,[status(thm)],[f204,f242]) ).
fof(f7068,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(X0,addition(multiplication(addition(X1,X3),X2),X4)) != multiplication(X0,addition(multiplication(X3,X2),X4))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,addition(multiplication(X3,X2),X4))) ),
inference(paramodulation,[status(thm)],[f219,f242]) ).
fof(f7069,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(X0,addition(multiplication(X1,addition(X2,X3)),X4)) != multiplication(X0,addition(multiplication(X1,X3),X4))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,addition(multiplication(X1,X3),X4))) ),
inference(paramodulation,[status(thm)],[f170,f242]) ).
fof(f7070,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(X0,multiplication(addition(X1,multiplication(X3,X4)),X2)) != multiplication(X0,multiplication(X3,multiplication(X4,X2)))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,multiplication(X4,X2)))) ),
inference(paramodulation,[status(thm)],[f211,f242]) ).
fof(f7071,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X3,X1),X2)) != multiplication(X0,multiplication(X3,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(paramodulation,[status(thm)],[f201,f242]) ).
fof(f7072,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X3,X2))) != multiplication(X0,multiplication(X1,X3))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) ),
inference(paramodulation,[status(thm)],[f153,f242]) ).
fof(f7073,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X1,X3),X2)) != multiplication(X0,multiplication(X3,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(paramodulation,[status(thm)],[f43,f242]) ).
fof(f7074,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(X0,multiplication(X1,X3))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) ),
inference(paramodulation,[status(thm)],[f42,f242]) ).
fof(f7075,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(X2,addition(X1,X3))) != multiplication(X0,X3)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f103,f242]) ).
fof(f7076,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(X1,addition(X2,X3))) != multiplication(X0,X3)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f36,f242]) ).
fof(f7078,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(antidomain(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(antidomain(X2),X1))) ),
inference(paramodulation,[status(thm)],[f4514,f242]) ).
fof(f7079,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(c(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(c(X2),X1))) ),
inference(paramodulation,[status(thm)],[f4513,f242]) ).
fof(f7080,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(codomain(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(codomain(X2),X1))) ),
inference(paramodulation,[status(thm)],[f4512,f242]) ).
fof(f7081,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(divergence(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(divergence(X2),X1))) ),
inference(paramodulation,[status(thm)],[f4511,f242]) ).
fof(f7082,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,domain(X2)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,domain(X2)))) ),
inference(paramodulation,[status(thm)],[f2497,f242]) ).
fof(f7083,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,coantidomain(X2)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,coantidomain(X2)))) ),
inference(paramodulation,[status(thm)],[f2496,f242]) ).
fof(f7084,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,antidomain(X2)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,antidomain(X2)))) ),
inference(paramodulation,[status(thm)],[f2495,f242]) ).
fof(f7085,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,c(X2)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,c(X2)))) ),
inference(paramodulation,[status(thm)],[f2494,f242]) ).
fof(f7086,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,codomain(X2)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,codomain(X2)))) ),
inference(paramodulation,[status(thm)],[f2493,f242]) ).
fof(f7087,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,divergence(X2)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,divergence(X2)))) ),
inference(paramodulation,[status(thm)],[f2492,f242]) ).
fof(f7088,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(X2,one),X1)) != multiplication(X0,multiplication(X2,X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(paramodulation,[status(thm)],[f232,f242]) ).
fof(f7089,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(one,X2),X1)) != multiplication(X0,multiplication(X2,X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(paramodulation,[status(thm)],[f207,f242]) ).
fof(f7090,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(X1,addition(X2,one))) != multiplication(X0,multiplication(X1,X2))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f192,f242]) ).
fof(f7091,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(X1,addition(one,X2))) != multiplication(X0,multiplication(X1,X2))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f162,f242]) ).
fof(f7092,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,addition(X2,addition(X1,X2)))
| leq(multiplication(X0,X1),multiplication(X0,addition(X2,addition(X1,X2)))) ),
inference(paramodulation,[status(thm)],[f99,f242]) ).
fof(f7093,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,addition(X1,X2))
| leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f105,f242]) ).
fof(f7094,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(X2,addition(X3,X1))) != multiplication(X0,addition(X2,X3))
| leq(multiplication(X0,X1),multiplication(X0,addition(X2,X3))) ),
inference(paramodulation,[status(thm)],[f97,f242]) ).
fof(f7095,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(X3,addition(X1,X2))) != multiplication(X0,addition(X2,X3))
| leq(multiplication(X0,X1),multiplication(X0,addition(X2,X3))) ),
inference(paramodulation,[status(thm)],[f97,f242]) ).
fof(f7097,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f35,f242]) ).
fof(f7098,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f35,f242]) ).
fof(f7106,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(multiplication(X0,X1),X3)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X1),X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f7042]) ).
fof(f7107,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(multiplication(X0,X1),X3)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) ),
inference(forward_demodulation,[status(thm)],[f39,f7106]) ).
fof(f7108,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(X0,multiplication(X1,X3))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) ),
inference(forward_demodulation,[status(thm)],[f39,f7107]) ).
fof(f7127,plain,
! [X0,X1,X2] :
( multiplication(X0,one) != multiplication(X0,backward_diamond(X1,X2))
| leq(X0,multiplication(X0,backward_diamond(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f40,f7052]) ).
fof(f7128,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_diamond(X1,X2))
| leq(X0,multiplication(X0,backward_diamond(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f40,f7127]) ).
fof(f7129,plain,
! [X0,X1,X2] :
( multiplication(X0,one) != multiplication(X0,forward_box(X1,X2))
| leq(X0,multiplication(X0,forward_box(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f40,f7053]) ).
fof(f7130,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_box(X1,X2))
| leq(X0,multiplication(X0,forward_box(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f40,f7129]) ).
fof(f7131,plain,
! [X0,X1,X2] :
( multiplication(X0,one) != multiplication(X0,backward_box(X1,X2))
| leq(X0,multiplication(X0,backward_box(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f40,f7054]) ).
fof(f7132,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_box(X1,X2))
| leq(X0,multiplication(X0,backward_box(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f40,f7131]) ).
fof(f7133,plain,
! [X0,X1,X2] :
( multiplication(X0,one) != multiplication(X0,forward_diamond(X1,X2))
| leq(X0,multiplication(X0,forward_diamond(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f40,f7055]) ).
fof(f7134,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_diamond(X1,X2))
| leq(X0,multiplication(X0,forward_diamond(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f40,f7133]) ).
fof(f7135,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7056]) ).
fof(f7136,plain,
! [X0,X1] :
( X0 != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7135]) ).
fof(f7137,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7057]) ).
fof(f7138,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7137]) ).
fof(f7139,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7058]) ).
fof(f7140,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7139]) ).
fof(f7141,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7059]) ).
fof(f7142,plain,
! [X0,X1] :
( X0 != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7141]) ).
fof(f7143,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7060]) ).
fof(f7144,plain,
! [X0,X1] :
( X0 != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7143]) ).
fof(f7145,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7061]) ).
fof(f7146,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7145]) ).
fof(f7147,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(multiplication(X0,domain(X1)),multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7062]) ).
fof(f7148,plain,
! [X0,X1,X2] : leq(multiplication(X0,coantidomain(multiplication(X1,X2))),multiplication(X0,coantidomain(multiplication(codomain(X1),X2)))),
inference(trivial_equality_resolution,[status(thm)],[f7063]) ).
fof(f7149,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(multiplication(X0,coantidomain(X1)),multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7064]) ).
fof(f7150,plain,
! [X0,X1,X2] : leq(multiplication(X0,antidomain(multiplication(X1,X2))),multiplication(X0,antidomain(multiplication(X1,domain(X2))))),
inference(trivial_equality_resolution,[status(thm)],[f7065]) ).
fof(f7151,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f7066]) ).
fof(f7154,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(trivial_equality_resolution,[status(thm)],[f7093]) ).
fof(f7158,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4515,f246]) ).
fof(f7163,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(coantidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4515]) ).
fof(f7164,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4515]) ).
fof(f7172,plain,
! [X0] : codomain(coantidomain(X0)) = addition(codomain(coantidomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2309,f4515]) ).
fof(f7173,plain,
! [X0,X1] : addition(coantidomain(coantidomain(X0)),X1) = addition(addition(coantidomain(coantidomain(X0)),X1),multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f4515]) ).
fof(f7185,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4515,f181]) ).
fof(f7198,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(coantidomain(X3),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4515,f219]) ).
fof(f7199,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(coantidomain(X3),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4515,f170]) ).
fof(f7200,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(coantidomain(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4515,f58]) ).
fof(f7201,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(coantidomain(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4515,f55]) ).
fof(f7202,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(coantidomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4515,f53]) ).
fof(f7203,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4515,f103]) ).
fof(f7204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4515,f36]) ).
fof(f7211,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(coantidomain(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(coantidomain(X2),X1))) ),
inference(paramodulation,[status(thm)],[f4515,f242]) ).
fof(f7212,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(coantidomain(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(coantidomain(X2),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4515,f241]) ).
fof(f7216,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4515,f177]) ).
fof(f7218,plain,
! [X0,X1,X2] : leq(multiplication(coantidomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4515,f1420]) ).
fof(f7222,plain,
! [X0,X1,X2] : addition(multiplication(coantidomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4515,f103]) ).
fof(f7224,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(coantidomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4515,f97]) ).
fof(f7225,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(coantidomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4515,f97]) ).
fof(f7227,plain,
! [X0,X1] :
( X0 != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4515,f49]) ).
fof(f7228,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(coantidomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4515,f36]) ).
fof(f7238,plain,
! [X0] : coantidomain(codomain(X0)) = addition(codomain(coantidomain(X0)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f193,f7172]) ).
fof(f7239,plain,
! [X0] : coantidomain(codomain(X0)) = addition(coantidomain(X0),codomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f7238]) ).
fof(f7240,plain,
! [X0] : coantidomain(codomain(X0)) = addition(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f193,f7239]) ).
fof(f7241,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(addition(coantidomain(coantidomain(X0)),X1),multiplication(coantidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f66,f7173]) ).
fof(f7242,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(X1,addition(coantidomain(coantidomain(X0)),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f7241]) ).
fof(f7243,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(X1,addition(codomain(X0),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f66,f7242]) ).
fof(f7256,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f7185]) ).
fof(f7266,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(coantidomain(X3),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f7198]) ).
fof(f7267,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(coantidomain(X3),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f7266]) ).
fof(f7268,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(coantidomain(X3),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f7267]) ).
fof(f7269,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(coantidomain(X3),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f7199]) ).
fof(f7270,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(X2),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7201]) ).
fof(f7271,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7270]) ).
fof(f7278,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(coantidomain(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(coantidomain(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f7212]) ).
fof(f7279,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(coantidomain(X2),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(coantidomain(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f7278]) ).
fof(f7283,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f59,f7216]) ).
fof(f7285,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f7222]) ).
fof(f7287,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(coantidomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f7225]) ).
fof(f7291,plain,
! [X0] : leq(coantidomain(X0),codomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f2309,f7158]) ).
fof(f7292,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(coantidomain(coantidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f181,f7158]) ).
fof(f7293,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(X1,coantidomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f190,f7158]) ).
fof(f7305,plain,
! [X0] : leq(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f193,f7291]) ).
fof(f7306,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(codomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f66,f7292]) ).
fof(f7307,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(X1,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f66,f7293]) ).
fof(f7314,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X0,X2),X1),X3) != X3
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),X3) ),
inference(paramodulation,[status(thm)],[f219,f243]) ).
fof(f7315,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X1,X2)),X3) != X3
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),X3) ),
inference(paramodulation,[status(thm)],[f170,f243]) ).
fof(f7316,plain,
! [X0,X1,X2,X3] :
( addition(X1,addition(X0,addition(X2,X3))) != X3
| leq(addition(addition(X0,X1),X2),X3) ),
inference(paramodulation,[status(thm)],[f103,f243]) ).
fof(f7317,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(addition(X0,X1),X2),X3) ),
inference(paramodulation,[status(thm)],[f36,f243]) ).
fof(f7321,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f97,f243]) ).
fof(f7323,plain,
! [X0,X1,X2] :
( addition(addition(X1,X2),X0) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f35,f243]) ).
fof(f7324,plain,
! [X0,X1,X2] :
( addition(addition(X1,X2),X0) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f35,f243]) ).
fof(f7325,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(addition(X0,X1),X0),X1) ),
inference(paramodulation,[status(thm)],[f38,f243]) ).
fof(f7326,plain,
! [X0,X1,X2] :
( addition(X0,one) != backward_diamond(X1,X2)
| leq(addition(X0,one),backward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1504,f243]) ).
fof(f7327,plain,
! [X0,X1,X2] :
( addition(X0,one) != forward_box(X1,X2)
| leq(addition(X0,one),forward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1497,f243]) ).
fof(f7328,plain,
! [X0,X1,X2] :
( addition(X0,one) != backward_box(X1,X2)
| leq(addition(X0,one),backward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1492,f243]) ).
fof(f7329,plain,
! [X0,X1,X2] :
( addition(X0,one) != forward_diamond(X1,X2)
| leq(addition(X0,one),forward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1485,f243]) ).
fof(f7330,plain,
! [X0,X1] :
( addition(X0,one) != divergence(X1)
| leq(addition(X0,one),divergence(X1)) ),
inference(paramodulation,[status(thm)],[f1488,f243]) ).
fof(f7331,plain,
! [X0,X1] :
( addition(X0,one) != codomain(X1)
| leq(addition(X0,one),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f1477,f243]) ).
fof(f7332,plain,
! [X0,X1] :
( addition(X0,one) != c(X1)
| leq(addition(X0,one),c(X1)) ),
inference(paramodulation,[status(thm)],[f1471,f243]) ).
fof(f7333,plain,
! [X0,X1] :
( addition(X0,one) != antidomain(X1)
| leq(addition(X0,one),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f1379,f243]) ).
fof(f7334,plain,
! [X0,X1] :
( addition(X0,one) != coantidomain(X1)
| leq(addition(X0,one),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f1377,f243]) ).
fof(f7335,plain,
! [X0,X1] :
( addition(X0,one) != domain(X1)
| leq(addition(X0,one),domain(X1)) ),
inference(paramodulation,[status(thm)],[f1375,f243]) ).
fof(f7336,plain,
! [X0,X1] :
( addition(X0,one) != c(X1)
| leq(addition(X0,domain(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f569,f243]) ).
fof(f7337,plain,
! [X0,X1,X2] :
( addition(X0,coantidomain(multiplication(codomain(X1),X2))) != coantidomain(multiplication(codomain(X1),X2))
| leq(addition(X0,coantidomain(multiplication(X1,X2))),coantidomain(multiplication(codomain(X1),X2))) ),
inference(paramodulation,[status(thm)],[f615,f243]) ).
fof(f7338,plain,
! [X0,X1] :
( addition(X0,one) != codomain(X1)
| leq(addition(X0,coantidomain(X1)),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f683,f243]) ).
fof(f7339,plain,
! [X0,X1,X2] :
( addition(X0,antidomain(multiplication(X1,domain(X2)))) != antidomain(multiplication(X1,domain(X2)))
| leq(addition(X0,antidomain(multiplication(X1,X2))),antidomain(multiplication(X1,domain(X2)))) ),
inference(paramodulation,[status(thm)],[f479,f243]) ).
fof(f7340,plain,
! [X0,X1] :
( addition(X0,one) != domain(X1)
| leq(addition(X0,antidomain(X1)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f558,f243]) ).
fof(f7341,plain,
! [X0,X1,X2,X3,X4] :
( addition(X0,multiplication(addition(multiplication(X1,X2),X4),X3)) != multiplication(X4,X3)
| leq(addition(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X4,X3)) ),
inference(paramodulation,[status(thm)],[f204,f243]) ).
fof(f7342,plain,
! [X0,X1,X2,X3,X4] :
( addition(X0,addition(multiplication(addition(X1,X3),X2),X4)) != addition(multiplication(X3,X2),X4)
| leq(addition(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) ),
inference(paramodulation,[status(thm)],[f219,f243]) ).
fof(f7343,plain,
! [X0,X1,X2,X3,X4] :
( addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) != addition(multiplication(X1,X3),X4)
| leq(addition(X0,multiplication(X1,X2)),addition(multiplication(X1,X3),X4)) ),
inference(paramodulation,[status(thm)],[f170,f243]) ).
fof(f7344,plain,
! [X0,X1,X2,X3,X4] :
( addition(X0,multiplication(addition(X1,multiplication(X3,X4)),X2)) != multiplication(X3,multiplication(X4,X2))
| leq(addition(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,X2))) ),
inference(paramodulation,[status(thm)],[f211,f243]) ).
fof(f7345,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(addition(X3,X1),X2)) != multiplication(X3,X2)
| leq(addition(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f201,f243]) ).
fof(f7346,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(X1,addition(X3,X2))) != multiplication(X1,X3)
| leq(addition(X0,multiplication(X1,X2)),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f153,f243]) ).
fof(f7347,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(addition(X1,X3),X2)) != multiplication(X3,X2)
| leq(addition(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f43,f243]) ).
fof(f7348,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(X1,addition(X2,X3))) != multiplication(X1,X3)
| leq(addition(X0,multiplication(X1,X2)),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f42,f243]) ).
fof(f7349,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X2,addition(X1,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(paramodulation,[status(thm)],[f103,f243]) ).
fof(f7350,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(paramodulation,[status(thm)],[f36,f243]) ).
fof(f7352,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(coantidomain(X2),X1)
| leq(addition(X0,X1),multiplication(coantidomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4515,f243]) ).
fof(f7353,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(antidomain(X2),X1)
| leq(addition(X0,X1),multiplication(antidomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4514,f243]) ).
fof(f7354,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(c(X2),X1)
| leq(addition(X0,X1),multiplication(c(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4513,f243]) ).
fof(f7355,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(codomain(X2),X1)
| leq(addition(X0,X1),multiplication(codomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4512,f243]) ).
fof(f7356,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(divergence(X2),X1)
| leq(addition(X0,X1),multiplication(divergence(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4511,f243]) ).
fof(f7357,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,domain(X2))
| leq(addition(X0,X1),multiplication(X1,domain(X2))) ),
inference(paramodulation,[status(thm)],[f2497,f243]) ).
fof(f7358,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,coantidomain(X2))
| leq(addition(X0,X1),multiplication(X1,coantidomain(X2))) ),
inference(paramodulation,[status(thm)],[f2496,f243]) ).
fof(f7359,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,antidomain(X2))
| leq(addition(X0,X1),multiplication(X1,antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f2495,f243]) ).
fof(f7360,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,c(X2))
| leq(addition(X0,X1),multiplication(X1,c(X2))) ),
inference(paramodulation,[status(thm)],[f2494,f243]) ).
fof(f7361,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,codomain(X2))
| leq(addition(X0,X1),multiplication(X1,codomain(X2))) ),
inference(paramodulation,[status(thm)],[f2493,f243]) ).
fof(f7362,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,divergence(X2))
| leq(addition(X0,X1),multiplication(X1,divergence(X2))) ),
inference(paramodulation,[status(thm)],[f2492,f243]) ).
fof(f7363,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(addition(X2,one),X1)) != multiplication(X2,X1)
| leq(addition(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f232,f243]) ).
fof(f7364,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(addition(one,X2),X1)) != multiplication(X2,X1)
| leq(addition(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f207,f243]) ).
fof(f7365,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(X1,addition(X2,one))) != multiplication(X1,X2)
| leq(addition(X0,X1),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f192,f243]) ).
fof(f7366,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(X1,addition(one,X2))) != multiplication(X1,X2)
| leq(addition(X0,X1),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f162,f243]) ).
fof(f7367,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X2,addition(X1,X2))
| leq(addition(X0,X1),addition(X2,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f99,f243]) ).
fof(f7368,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X1,X2)
| leq(addition(X0,X1),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f105,f243]) ).
fof(f7369,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X2,addition(X3,X1))) != addition(X2,X3)
| leq(addition(X0,X1),addition(X2,X3)) ),
inference(paramodulation,[status(thm)],[f97,f243]) ).
fof(f7370,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X3,addition(X1,X2))) != addition(X2,X3)
| leq(addition(X0,X1),addition(X2,X3)) ),
inference(paramodulation,[status(thm)],[f97,f243]) ).
fof(f7372,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f35,f243]) ).
fof(f7373,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f35,f243]) ).
fof(f7374,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f38,f243]) ).
fof(f7375,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X1,X0),X2),X3) != X3
| leq(multiplication(addition(X0,X1),X2),X3) ),
inference(forward_demodulation,[status(thm)],[f201,f7314]) ).
fof(f7376,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X2,X1)),X3) != X3
| leq(multiplication(X0,addition(X1,X2)),X3) ),
inference(forward_demodulation,[status(thm)],[f153,f7315]) ).
fof(f7377,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(forward_demodulation,[status(thm)],[f103,f7316]) ).
fof(f7378,plain,
! [X0,X1,X2,X3] :
( addition(X1,addition(X0,addition(X2,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(forward_demodulation,[status(thm)],[f103,f7317]) ).
fof(f7382,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f103,f7323]) ).
fof(f7383,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f103,f7324]) ).
fof(f7384,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,addition(X1,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f103,f7325]) ).
fof(f7385,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f38,f7384]) ).
fof(f7392,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(domain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4516]) ).
fof(f7393,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(domain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4516]) ).
fof(f7400,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(paramodulation,[status(thm)],[f68,f4516]) ).
fof(f7402,plain,
! [X0] : codomain(domain(X0)) = addition(codomain(domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f2309,f4516]) ).
fof(f7403,plain,
! [X0,X1] : addition(coantidomain(domain(X0)),X1) = addition(addition(coantidomain(domain(X0)),X1),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f4516]) ).
fof(f7412,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f69,f4516]) ).
fof(f7417,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4516,f181]) ).
fof(f7430,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(domain(X3),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4516,f219]) ).
fof(f7431,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(domain(X3),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4516,f170]) ).
fof(f7432,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(domain(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4516,f58]) ).
fof(f7433,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(domain(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4516,f55]) ).
fof(f7434,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(domain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4516,f53]) ).
fof(f7435,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4516,f103]) ).
fof(f7436,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4516,f36]) ).
fof(f7443,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(domain(X2),X1)
| leq(addition(X0,X1),multiplication(domain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4516,f243]) ).
fof(f7444,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(X0,multiplication(domain(X2),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(domain(X2),X1))) ),
inference(paramodulation,[status(thm)],[f4516,f242]) ).
fof(f7445,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(domain(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(domain(X2),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4516,f241]) ).
fof(f7449,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f4516,f177]) ).
fof(f7451,plain,
! [X0,X1,X2] : leq(multiplication(domain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4516,f1420]) ).
fof(f7455,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4516,f103]) ).
fof(f7457,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4516,f97]) ).
fof(f7458,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(domain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4516,f97]) ).
fof(f7460,plain,
! [X0,X1] :
( X0 != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4516,f49]) ).
fof(f7461,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4516,f36]) ).
fof(f7471,plain,
! [X0] : codomain(domain(X0)) = addition(domain(X0),codomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f7402]) ).
fof(f7472,plain,
! [X0,X1] : addition(coantidomain(domain(X0)),X1) = addition(X1,addition(coantidomain(domain(X0)),multiplication(domain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f103,f7403]) ).
fof(f7477,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f7417]) ).
fof(f7487,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(domain(X3),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f7430]) ).
fof(f7488,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(domain(X3),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f7487]) ).
fof(f7489,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(domain(X3),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f7488]) ).
fof(f7490,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(domain(X3),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f7431]) ).
fof(f7491,plain,
! [X0,X1,X2] :
( leq(multiplication(domain(X2),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7433]) ).
fof(f7492,plain,
! [X0,X1,X2] :
( leq(multiplication(domain(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7491]) ).
fof(f7499,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(multiplication(domain(X2),X0),X1)
| leq(multiplication(X0,X1),multiplication(domain(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f7445]) ).
fof(f7500,plain,
! [X0,X1,X2] :
( multiplication(X0,X1) != multiplication(domain(X2),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(domain(X2),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f7499]) ).
fof(f7504,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f59,f7449]) ).
fof(f7506,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f7455]) ).
fof(f7508,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(domain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f7458]) ).
fof(f7510,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f232,f256]) ).
fof(f7511,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,addition(X1,one)),star(addition(X1,X0)))) = star(addition(X1,X0)),
inference(paramodulation,[status(thm)],[f103,f7510]) ).
fof(f7512,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,addition(X1,one)),star(addition(X0,X1)))) = star(addition(X0,X1)),
inference(paramodulation,[status(thm)],[f36,f7510]) ).
fof(f7513,plain,
addition(one,multiplication(one,star(zero))) = star(zero),
inference(paramodulation,[status(thm)],[f80,f7510]) ).
fof(f7514,plain,
! [X0] : addition(one,multiplication(addition(one,X0),star(X0))) = star(X0),
inference(paramodulation,[status(thm)],[f35,f7510]) ).
fof(f7515,plain,
! [X0] : addition(one,multiplication(addition(one,X0),star(X0))) = star(X0),
inference(paramodulation,[status(thm)],[f35,f7510]) ).
fof(f7516,plain,
addition(one,multiplication(one,star(one))) = star(one),
inference(paramodulation,[status(thm)],[f38,f7510]) ).
fof(f7517,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(addition(X0,one),star(X0)),X1)),
inference(paramodulation,[status(thm)],[f7510,f207]) ).
fof(f7518,plain,
! [X0,X1] : leq(domain(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7510,f2403]) ).
fof(f7519,plain,
! [X0,X1] : leq(coantidomain(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7510,f2387]) ).
fof(f7520,plain,
! [X0,X1] : leq(antidomain(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7510,f2373]) ).
fof(f7521,plain,
! [X0,X1] : leq(c(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7510,f2264]) ).
fof(f7522,plain,
! [X0,X1] : leq(codomain(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7510,f2247]) ).
fof(f7523,plain,
! [X0,X1] : leq(divergence(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7510,f2232]) ).
fof(f7524,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,multiplication(addition(X1,one),star(X1)))),
inference(paramodulation,[status(thm)],[f7510,f162]) ).
fof(f7525,plain,
! [X0,X1] :
( addition(X0,star(X1)) != multiplication(addition(X1,one),star(X1))
| leq(addition(X0,one),multiplication(addition(X1,one),star(X1))) ),
inference(paramodulation,[status(thm)],[f7510,f243]) ).
fof(f7526,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,multiplication(addition(X1,one),star(X1)))
| leq(multiplication(X0,one),multiplication(X0,multiplication(addition(X1,one),star(X1)))) ),
inference(paramodulation,[status(thm)],[f7510,f242]) ).
fof(f7527,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(addition(X1,one),star(X1)),X0)
| leq(multiplication(one,X0),multiplication(multiplication(addition(X1,one),star(X1)),X0)) ),
inference(paramodulation,[status(thm)],[f7510,f241]) ).
fof(f7528,plain,
! [X0] : multiplication(star(X0),coantidomain(multiplication(addition(X0,one),star(X0)))) = multiplication(one,coantidomain(multiplication(addition(X0,one),star(X0)))),
inference(paramodulation,[status(thm)],[f7510,f233]) ).
fof(f7530,plain,
! [X0] : multiplication(antidomain(multiplication(addition(X0,one),star(X0))),star(X0)) = multiplication(antidomain(multiplication(addition(X0,one),star(X0))),one),
inference(paramodulation,[status(thm)],[f7510,f186]) ).
fof(f7532,plain,
! [X0,X1] : leq(one,addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f7510,f1421]) ).
fof(f7533,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),star(X0)),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f7510,f1420]) ).
fof(f7534,plain,
! [X0] : leq(multiplication(addition(X0,one),star(X0)),star(X0)),
inference(paramodulation,[status(thm)],[f7510,f1423]) ).
fof(f7535,plain,
! [X0] : leq(one,star(X0)),
inference(paramodulation,[status(thm)],[f7510,f1324]) ).
fof(f7536,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(paramodulation,[status(thm)],[f7510,f105]) ).
fof(f7537,plain,
! [X0,X1] : addition(multiplication(addition(X0,one),star(X0)),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7510,f103]) ).
fof(f7538,plain,
! [X0] : addition(one,addition(multiplication(addition(X0,one),star(X0)),star(X0))) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(paramodulation,[status(thm)],[f7510,f99]) ).
fof(f7539,plain,
! [X0,X1] : addition(one,addition(multiplication(addition(X0,one),star(X0)),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f7510,f97]) ).
fof(f7540,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(multiplication(addition(X1,one),star(X1)),addition(X0,one)),
inference(paramodulation,[status(thm)],[f7510,f97]) ).
fof(f7541,plain,
! [X0] :
( star(X0) != one
| leq(multiplication(addition(X0,one),star(X0)),one) ),
inference(paramodulation,[status(thm)],[f7510,f246]) ).
fof(f7542,plain,
! [X0] :
( star(X0) != multiplication(addition(X0,one),star(X0))
| leq(one,multiplication(addition(X0,one),star(X0))) ),
inference(paramodulation,[status(thm)],[f7510,f49]) ).
fof(f7543,plain,
! [X0,X1] : addition(one,addition(multiplication(addition(X0,one),star(X0)),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7510,f36]) ).
fof(f7544,plain,
addition(one,star(zero)) = star(zero),
inference(forward_demodulation,[status(thm)],[f41,f7513]) ).
fof(f7545,plain,
addition(one,star(one)) = star(one),
inference(forward_demodulation,[status(thm)],[f41,f7516]) ).
fof(f7546,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(addition(X0,one),multiplication(star(X0),X1))),
inference(forward_demodulation,[status(thm)],[f39,f7517]) ).
fof(f7547,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,multiplication(addition(X1,one),star(X1)))
| leq(X0,multiplication(X0,multiplication(addition(X1,one),star(X1)))) ),
inference(forward_demodulation,[status(thm)],[f40,f7526]) ).
fof(f7548,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(addition(X1,one),star(X1)),X0)
| leq(X0,multiplication(multiplication(addition(X1,one),star(X1)),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f7527]) ).
fof(f7549,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(addition(X1,one),star(X1)),X0)
| leq(X0,multiplication(addition(X1,one),multiplication(star(X1),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f7548]) ).
fof(f7550,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(addition(X1,one),multiplication(star(X1),X0))
| leq(X0,multiplication(addition(X1,one),multiplication(star(X1),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f7549]) ).
fof(f7551,plain,
! [X0] : multiplication(star(X0),coantidomain(multiplication(addition(X0,one),star(X0)))) = coantidomain(multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f41,f7528]) ).
fof(f7559,plain,
! [X0] : multiplication(antidomain(multiplication(addition(X0,one),star(X0))),star(X0)) = antidomain(multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f40,f7530]) ).
fof(f7563,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f7510,f7536]) ).
fof(f7564,plain,
! [X0,X1] : addition(one,addition(X0,multiplication(addition(X1,one),star(X1)))) = addition(star(X1),X0),
inference(forward_demodulation,[status(thm)],[f97,f7537]) ).
fof(f7565,plain,
! [X0] : addition(one,addition(star(X0),multiplication(addition(X0,one),star(X0)))) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f35,f7538]) ).
fof(f7566,plain,
! [X0] : addition(one,multiplication(addition(addition(X0,one),one),star(X0))) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f232,f7565]) ).
fof(f7567,plain,
! [X0] : addition(one,multiplication(addition(one,addition(X0,one)),star(X0))) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f103,f7566]) ).
fof(f7568,plain,
! [X0] : addition(one,multiplication(addition(one,addition(X0,one)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f7510,f7567]) ).
fof(f7569,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(multiplication(addition(X1,one),star(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f7540]) ).
fof(f7571,plain,
! [X0,X1] : addition(domain(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7518,f48]) ).
fof(f7572,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),star(X2)),
inference(paramodulation,[status(thm)],[f69,f7518]) ).
fof(f7577,plain,
! [X0,X1] : addition(coantidomain(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7519,f48]) ).
fof(f7581,plain,
! [X0,X1] : addition(antidomain(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7520,f48]) ).
fof(f7586,plain,
! [X0,X1] : addition(addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(X0,X1))) = star(multiplication(X0,X1)),
inference(resolution,[status(thm)],[f252,f48]) ).
fof(f7587,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(multiplication(X0,X1),X2)))))),star(multiplication(multiplication(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f39,f252]) ).
fof(f7592,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))),star(multiplication(X0,multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f39,f252]) ).
fof(f7595,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(one,X0),multiplication(X1,star(addition(X1,multiplication(X0,X1)))))),star(multiplication(addition(one,X0),X1))),
inference(paramodulation,[status(thm)],[f207,f252]) ).
fof(f7596,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(antidomain(X0),X1),multiplication(X0,star(multiplication(X1,X0))))),star(multiplication(addition(antidomain(X0),X1),X0))),
inference(paramodulation,[status(thm)],[f224,f252]) ).
fof(f7597,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,one),multiplication(X1,star(addition(X1,multiplication(X0,X1)))))),star(multiplication(addition(X0,one),X1))),
inference(paramodulation,[status(thm)],[f232,f252]) ).
fof(f7598,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,antidomain(X1)),multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(addition(X0,antidomain(X1)),X1))),
inference(paramodulation,[status(thm)],[f230,f252]) ).
fof(f7599,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(coantidomain(X1),star(multiplication(X0,coantidomain(X1)))))),star(multiplication(addition(X0,X1),coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f233,f252]) ).
fof(f7600,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(coantidomain(X0),star(multiplication(X1,coantidomain(X0)))))),star(multiplication(addition(X0,X1),coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f226,f252]) ).
fof(f7601,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(domain(X0),star(zero)))),star(multiplication(c(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f197,f252]) ).
fof(f7602,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(X0,star(zero)))),star(multiplication(c(X0),X0))),
inference(paramodulation,[status(thm)],[f4265,f252]) ).
fof(f7603,plain,
! [X0] : leq(addition(one,multiplication(coantidomain(X0),multiplication(codomain(X0),star(zero)))),star(multiplication(coantidomain(X0),codomain(X0)))),
inference(paramodulation,[status(thm)],[f195,f252]) ).
fof(f7604,plain,
! [X0,X1] : leq(addition(one,multiplication(domain(X0),multiplication(antidomain(X1),star(domain_difference(X0,X1))))),star(multiplication(domain(X0),antidomain(X1)))),
inference(paramodulation,[status(thm)],[f68,f252]) ).
fof(f7605,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(X0,star(X0)))),star(multiplication(domain(X0),X0))),
inference(paramodulation,[status(thm)],[f4146,f252]) ).
fof(f7606,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(multiplication(X0,X1),multiplication(X2,star(multiplication(X0,multiplication(X1,X2)))))),star(multiplication(multiplication(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f39,f252]) ).
fof(f7607,plain,
! [X0,X1] : leq(addition(one,multiplication(antidomain(X0),multiplication(addition(X1,X0),star(multiplication(antidomain(X0),X1))))),star(multiplication(antidomain(X0),addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f186,f252]) ).
fof(f7608,plain,
! [X0,X1] : leq(addition(one,multiplication(antidomain(X0),multiplication(addition(X0,X1),star(multiplication(antidomain(X0),X1))))),star(multiplication(antidomain(X0),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f177,f252]) ).
fof(f7609,plain,
! [X0] : leq(addition(one,multiplication(antidomain(X0),multiplication(omega(X0),star(zero)))),star(multiplication(antidomain(X0),omega(X0)))),
inference(paramodulation,[status(thm)],[f1569,f252]) ).
fof(f7614,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(codomain(X0),star(X0)))),star(multiplication(X0,codomain(X0)))),
inference(paramodulation,[status(thm)],[f2309,f252]) ).
fof(f7615,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(one,X1),star(addition(X0,multiplication(X0,X1)))))),star(multiplication(X0,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f162,f252]) ).
fof(f7616,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(coantidomain(X0),X1),star(multiplication(X0,X1))))),star(multiplication(X0,addition(coantidomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f181,f252]) ).
fof(f7617,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,one),star(addition(X0,multiplication(X0,X1)))))),star(multiplication(X0,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f192,f252]) ).
fof(f7618,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,coantidomain(X0)),star(multiplication(X0,X1))))),star(multiplication(X0,addition(X1,coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f190,f252]) ).
fof(f7620,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(multiplication(X1,coantidomain(multiplication(X0,X1))),star(zero)))),star(multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f144,f252]) ).
fof(f7621,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(omega(coantidomain(X0)),star(zero)))),star(multiplication(X0,omega(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f1813,f252]) ).
fof(f7622,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(omega(X0),star(omega(X0))))),star(multiplication(X0,omega(X0)))),
inference(paramodulation,[status(thm)],[f56,f252]) ).
fof(f7626,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(one,X0),multiplication(X1,star(multiplication(addition(one,X0),X1))))),star(addition(X1,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f207,f252]) ).
fof(f7627,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(antidomain(X0),X1),multiplication(X0,star(multiplication(addition(antidomain(X0),X1),X0))))),star(multiplication(X1,X0))),
inference(paramodulation,[status(thm)],[f224,f252]) ).
fof(f7628,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,one),multiplication(X1,star(multiplication(addition(X0,one),X1))))),star(addition(X1,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f232,f252]) ).
fof(f7629,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,antidomain(X1)),multiplication(X1,star(multiplication(addition(X0,antidomain(X1)),X1))))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f230,f252]) ).
fof(f7630,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(coantidomain(X1),star(multiplication(addition(X0,X1),coantidomain(X1)))))),star(multiplication(X0,coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f233,f252]) ).
fof(f7631,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(coantidomain(X0),star(multiplication(addition(X0,X1),coantidomain(X0)))))),star(multiplication(X1,coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f226,f252]) ).
fof(f7632,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(domain(X0),star(multiplication(c(X0),domain(X0)))))),star(zero)),
inference(paramodulation,[status(thm)],[f197,f252]) ).
fof(f7633,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(X0,star(multiplication(c(X0),X0))))),star(zero)),
inference(paramodulation,[status(thm)],[f4265,f252]) ).
fof(f7634,plain,
! [X0] : leq(addition(one,multiplication(coantidomain(X0),multiplication(codomain(X0),star(multiplication(coantidomain(X0),codomain(X0)))))),star(zero)),
inference(paramodulation,[status(thm)],[f195,f252]) ).
fof(f7635,plain,
! [X0,X1] : leq(addition(one,multiplication(domain(X0),multiplication(antidomain(X1),star(multiplication(domain(X0),antidomain(X1)))))),star(domain_difference(X0,X1))),
inference(paramodulation,[status(thm)],[f68,f252]) ).
fof(f7636,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(X0,star(multiplication(domain(X0),X0))))),star(X0)),
inference(paramodulation,[status(thm)],[f4146,f252]) ).
fof(f7637,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(multiplication(X0,X1),multiplication(X2,star(multiplication(multiplication(X0,X1),X2))))),star(multiplication(X0,multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f39,f252]) ).
fof(f7638,plain,
! [X0,X1] : leq(addition(one,multiplication(antidomain(X0),multiplication(addition(X1,X0),star(multiplication(antidomain(X0),addition(X1,X0)))))),star(multiplication(antidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f186,f252]) ).
fof(f7639,plain,
! [X0,X1] : leq(addition(one,multiplication(antidomain(X0),multiplication(addition(X0,X1),star(multiplication(antidomain(X0),addition(X0,X1)))))),star(multiplication(antidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f177,f252]) ).
fof(f7640,plain,
! [X0] : leq(addition(one,multiplication(antidomain(X0),multiplication(omega(X0),star(multiplication(antidomain(X0),omega(X0)))))),star(zero)),
inference(paramodulation,[status(thm)],[f1569,f252]) ).
fof(f7645,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(codomain(X0),star(multiplication(X0,codomain(X0)))))),star(X0)),
inference(paramodulation,[status(thm)],[f2309,f252]) ).
fof(f7646,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(one,X1),star(multiplication(X0,addition(one,X1)))))),star(addition(X0,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f162,f252]) ).
fof(f7647,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(coantidomain(X0),X1),star(multiplication(X0,addition(coantidomain(X0),X1)))))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f181,f252]) ).
fof(f7648,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,one),star(multiplication(X0,addition(X1,one)))))),star(addition(X0,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f192,f252]) ).
fof(f7649,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,coantidomain(X0)),star(multiplication(X0,addition(X1,coantidomain(X0))))))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f190,f252]) ).
fof(f7651,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(multiplication(X1,coantidomain(multiplication(X0,X1))),star(multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))))))),star(zero)),
inference(paramodulation,[status(thm)],[f144,f252]) ).
fof(f7652,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(omega(coantidomain(X0)),star(multiplication(X0,omega(coantidomain(X0))))))),star(zero)),
inference(paramodulation,[status(thm)],[f1813,f252]) ).
fof(f7653,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(omega(X0),star(multiplication(X0,omega(X0)))))),star(omega(X0))),
inference(paramodulation,[status(thm)],[f56,f252]) ).
fof(f7657,plain,
! [X0,X1] : addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),addition(one,star(multiplication(X0,X1)))) = star(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f7586]) ).
fof(f7658,plain,
! [X0,X1] : addition(one,addition(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))))) = star(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f97,f7657]) ).
fof(f7659,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))),star(multiplication(multiplication(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f39,f7587]) ).
fof(f7660,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))),star(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f7659]) ).
fof(f7674,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(antidomain(X0),X1),multiplication(X0,star(multiplication(X1,X0))))),star(multiplication(X1,X0))),
inference(forward_demodulation,[status(thm)],[f224,f7596]) ).
fof(f7675,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,antidomain(X1)),multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f230,f7598]) ).
fof(f7676,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(coantidomain(X1),star(multiplication(X0,coantidomain(X1)))))),star(multiplication(X0,coantidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f233,f7599]) ).
fof(f7677,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(coantidomain(X0),star(multiplication(X1,coantidomain(X0)))))),star(multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f226,f7600]) ).
fof(f7678,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(domain(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f197,f7601]) ).
fof(f7679,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(X0,star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f4265,f7602]) ).
fof(f7680,plain,
! [X0] : leq(addition(one,multiplication(coantidomain(X0),multiplication(codomain(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f195,f7603]) ).
fof(f7681,plain,
! [X0,X1] : leq(addition(one,multiplication(domain(X0),multiplication(antidomain(X1),star(domain_difference(X0,X1))))),star(domain_difference(X0,X1))),
inference(forward_demodulation,[status(thm)],[f68,f7604]) ).
fof(f7682,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(X0,star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f4146,f7605]) ).
fof(f7683,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))),star(multiplication(multiplication(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f39,f7606]) ).
fof(f7684,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))),star(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f7683]) ).
fof(f7685,plain,
! [X0,X1] : leq(addition(one,multiplication(antidomain(X0),multiplication(addition(X1,X0),star(multiplication(antidomain(X0),X1))))),star(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f186,f7607]) ).
fof(f7686,plain,
! [X0,X1] : leq(addition(one,multiplication(antidomain(X0),multiplication(addition(X0,X1),star(multiplication(antidomain(X0),X1))))),star(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f177,f7608]) ).
fof(f7687,plain,
! [X0] : leq(addition(one,multiplication(antidomain(X0),multiplication(omega(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f1569,f7609]) ).
fof(f7700,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(codomain(X0),star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f2309,f7614]) ).
fof(f7701,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(coantidomain(X0),X1),star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f181,f7616]) ).
fof(f7702,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,coantidomain(X0)),star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f190,f7618]) ).
fof(f7707,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),star(zero))))),star(multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f39,f7620]) ).
fof(f7708,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),star(zero))))),star(zero)),
inference(forward_demodulation,[status(thm)],[f144,f7707]) ).
fof(f7709,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(omega(coantidomain(X0)),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f1813,f7621]) ).
fof(f7710,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(omega(X0),star(omega(X0))))),star(omega(X0))),
inference(forward_demodulation,[status(thm)],[f56,f7622]) ).
fof(f7720,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(antidomain(X0),X1),multiplication(X0,star(multiplication(X1,X0))))),star(multiplication(X1,X0))),
inference(forward_demodulation,[status(thm)],[f224,f7627]) ).
fof(f7721,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,antidomain(X1)),multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f230,f7629]) ).
fof(f7722,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(coantidomain(X1),star(multiplication(X0,coantidomain(X1)))))),star(multiplication(X0,coantidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f233,f7630]) ).
fof(f7723,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(coantidomain(X0),star(multiplication(X1,coantidomain(X0)))))),star(multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f226,f7631]) ).
fof(f7724,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(domain(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f197,f7632]) ).
fof(f7725,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(X0,star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f4265,f7633]) ).
fof(f7726,plain,
! [X0] : leq(addition(one,multiplication(coantidomain(X0),multiplication(codomain(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f195,f7634]) ).
fof(f7727,plain,
! [X0,X1] : leq(addition(one,multiplication(domain(X0),multiplication(antidomain(X1),star(domain_difference(X0,X1))))),star(domain_difference(X0,X1))),
inference(forward_demodulation,[status(thm)],[f68,f7635]) ).
fof(f7728,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(X0,star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f4146,f7636]) ).
fof(f7729,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(multiplication(X0,X1),X2)))))),star(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f7637]) ).
fof(f7730,plain,
! [X0,X1,X2] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))),star(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f39,f7729]) ).
fof(f7731,plain,
! [X0,X1] : leq(addition(one,multiplication(antidomain(X0),multiplication(addition(X1,X0),star(multiplication(antidomain(X0),X1))))),star(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f186,f7638]) ).
fof(f7732,plain,
! [X0,X1] : leq(addition(one,multiplication(antidomain(X0),multiplication(addition(X0,X1),star(multiplication(antidomain(X0),X1))))),star(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f177,f7639]) ).
fof(f7733,plain,
! [X0] : leq(addition(one,multiplication(antidomain(X0),multiplication(omega(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f1569,f7640]) ).
fof(f7743,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(codomain(X0),star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f2309,f7645]) ).
fof(f7744,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(coantidomain(X0),X1),star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f181,f7647]) ).
fof(f7745,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,coantidomain(X0)),star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f190,f7649]) ).
fof(f7749,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),star(multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1))))))))),star(zero)),
inference(forward_demodulation,[status(thm)],[f39,f7651]) ).
fof(f7750,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),star(zero))))),star(zero)),
inference(forward_demodulation,[status(thm)],[f144,f7749]) ).
fof(f7751,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(omega(coantidomain(X0)),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f1813,f7652]) ).
fof(f7752,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(omega(X0),star(omega(X0))))),star(omega(X0))),
inference(forward_demodulation,[status(thm)],[f56,f7653]) ).
fof(f7760,plain,
! [X0,X1] : addition(c(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7521,f48]) ).
fof(f7761,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),star(X2)),
inference(paramodulation,[status(thm)],[f72,f7521]) ).
fof(f7762,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),star(X2)),
inference(paramodulation,[status(thm)],[f71,f7521]) ).
fof(f7767,plain,
! [X0,X1] : addition(codomain(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7522,f48]) ).
fof(f7768,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),star(X2)),
inference(paramodulation,[status(thm)],[f70,f7522]) ).
fof(f7772,plain,
! [X0,X1] : addition(divergence(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7523,f48]) ).
fof(f7774,plain,
addition(addition(one,star(one)),star(one)) = star(one),
inference(resolution,[status(thm)],[f254,f48]) ).
fof(f7775,plain,
addition(star(one),addition(one,star(one))) = star(one),
inference(forward_demodulation,[status(thm)],[f103,f7774]) ).
fof(f7776,plain,
addition(one,addition(star(one),star(one))) = star(one),
inference(forward_demodulation,[status(thm)],[f97,f7775]) ).
fof(f7777,plain,
addition(one,star(one)) = star(one),
inference(forward_demodulation,[status(thm)],[f38,f7776]) ).
fof(f7778,plain,
! [X0,X1,X2] : addition(forward_diamond(X0,X1),star(X2)) = star(X2),
inference(resolution,[status(thm)],[f7572,f48]) ).
fof(f7786,plain,
! [X0,X1,X2] : addition(backward_box(X0,X1),star(X2)) = star(X2),
inference(resolution,[status(thm)],[f7761,f48]) ).
fof(f7789,plain,
! [X0] : addition(one,multiplication(star(X0),addition(X0,one))) = star(X0),
inference(forward_demodulation,[status(thm)],[f192,f264]) ).
fof(f7790,plain,
! [X0,X1] : addition(one,multiplication(star(addition(X0,X1)),addition(X1,addition(X0,one)))) = star(addition(X0,X1)),
inference(paramodulation,[status(thm)],[f103,f7789]) ).
fof(f7791,plain,
! [X0,X1] : addition(one,multiplication(star(addition(X0,X1)),addition(X0,addition(X1,one)))) = star(addition(X0,X1)),
inference(paramodulation,[status(thm)],[f36,f7789]) ).
fof(f7792,plain,
addition(one,multiplication(star(zero),one)) = star(zero),
inference(paramodulation,[status(thm)],[f80,f7789]) ).
fof(f7793,plain,
! [X0] : addition(one,multiplication(star(X0),addition(one,X0))) = star(X0),
inference(paramodulation,[status(thm)],[f35,f7789]) ).
fof(f7794,plain,
! [X0] : addition(one,multiplication(star(X0),addition(one,X0))) = star(X0),
inference(paramodulation,[status(thm)],[f35,f7789]) ).
fof(f7795,plain,
addition(one,multiplication(star(one),one)) = star(one),
inference(paramodulation,[status(thm)],[f38,f7789]) ).
fof(f7796,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(star(X0),addition(X0,one)),X1)),
inference(paramodulation,[status(thm)],[f7789,f207]) ).
fof(f7803,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,multiplication(star(X1),addition(X1,one)))),
inference(paramodulation,[status(thm)],[f7789,f162]) ).
fof(f7804,plain,
! [X0,X1] :
( addition(X0,star(X1)) != multiplication(star(X1),addition(X1,one))
| leq(addition(X0,one),multiplication(star(X1),addition(X1,one))) ),
inference(paramodulation,[status(thm)],[f7789,f243]) ).
fof(f7805,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,multiplication(star(X1),addition(X1,one)))
| leq(multiplication(X0,one),multiplication(X0,multiplication(star(X1),addition(X1,one)))) ),
inference(paramodulation,[status(thm)],[f7789,f242]) ).
fof(f7806,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(star(X1),addition(X1,one)),X0)
| leq(multiplication(one,X0),multiplication(multiplication(star(X1),addition(X1,one)),X0)) ),
inference(paramodulation,[status(thm)],[f7789,f241]) ).
fof(f7807,plain,
! [X0] : multiplication(star(X0),coantidomain(multiplication(star(X0),addition(X0,one)))) = multiplication(one,coantidomain(multiplication(star(X0),addition(X0,one)))),
inference(paramodulation,[status(thm)],[f7789,f233]) ).
fof(f7809,plain,
! [X0] : multiplication(antidomain(multiplication(star(X0),addition(X0,one))),star(X0)) = multiplication(antidomain(multiplication(star(X0),addition(X0,one))),one),
inference(paramodulation,[status(thm)],[f7789,f186]) ).
fof(f7812,plain,
! [X0,X1] : leq(multiplication(star(X0),addition(X0,one)),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f7789,f1420]) ).
fof(f7813,plain,
! [X0] : leq(multiplication(star(X0),addition(X0,one)),star(X0)),
inference(paramodulation,[status(thm)],[f7789,f1423]) ).
fof(f7816,plain,
! [X0,X1] : addition(multiplication(star(X0),addition(X0,one)),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7789,f103]) ).
fof(f7817,plain,
! [X0] : addition(one,addition(multiplication(star(X0),addition(X0,one)),star(X0))) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(paramodulation,[status(thm)],[f7789,f99]) ).
fof(f7818,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),addition(X0,one)),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f7789,f97]) ).
fof(f7819,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(multiplication(star(X1),addition(X1,one)),addition(X0,one)),
inference(paramodulation,[status(thm)],[f7789,f97]) ).
fof(f7820,plain,
! [X0] :
( star(X0) != one
| leq(multiplication(star(X0),addition(X0,one)),one) ),
inference(paramodulation,[status(thm)],[f7789,f246]) ).
fof(f7821,plain,
! [X0] :
( star(X0) != multiplication(star(X0),addition(X0,one))
| leq(one,multiplication(star(X0),addition(X0,one))) ),
inference(paramodulation,[status(thm)],[f7789,f49]) ).
fof(f7822,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),addition(X0,one)),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7789,f36]) ).
fof(f7823,plain,
addition(one,star(zero)) = star(zero),
inference(forward_demodulation,[status(thm)],[f40,f7792]) ).
fof(f7824,plain,
addition(one,star(one)) = star(one),
inference(forward_demodulation,[status(thm)],[f40,f7795]) ).
fof(f7825,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),multiplication(addition(X0,one),X1))),
inference(forward_demodulation,[status(thm)],[f39,f7796]) ).
fof(f7826,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,multiplication(star(X1),addition(X1,one)))
| leq(X0,multiplication(X0,multiplication(star(X1),addition(X1,one)))) ),
inference(forward_demodulation,[status(thm)],[f40,f7805]) ).
fof(f7827,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(star(X1),addition(X1,one)),X0)
| leq(X0,multiplication(multiplication(star(X1),addition(X1,one)),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f7806]) ).
fof(f7828,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(star(X1),addition(X1,one)),X0)
| leq(X0,multiplication(star(X1),multiplication(addition(X1,one),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f7827]) ).
fof(f7829,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(star(X1),multiplication(addition(X1,one),X0))
| leq(X0,multiplication(star(X1),multiplication(addition(X1,one),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f7828]) ).
fof(f7830,plain,
! [X0] : multiplication(star(X0),coantidomain(multiplication(star(X0),addition(X0,one)))) = coantidomain(multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f41,f7807]) ).
fof(f7837,plain,
! [X0] : multiplication(antidomain(multiplication(star(X0),addition(X0,one))),star(X0)) = antidomain(multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f40,f7809]) ).
fof(f7842,plain,
! [X0,X1] : addition(one,addition(X0,multiplication(star(X1),addition(X1,one)))) = addition(star(X1),X0),
inference(forward_demodulation,[status(thm)],[f97,f7816]) ).
fof(f7843,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),addition(X0,one)))) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f35,f7817]) ).
fof(f7844,plain,
! [X0] : addition(one,multiplication(star(X0),addition(addition(X0,one),one))) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f192,f7843]) ).
fof(f7845,plain,
! [X0] : addition(one,multiplication(star(X0),addition(one,addition(X0,one)))) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f103,f7844]) ).
fof(f7846,plain,
! [X0] : addition(one,multiplication(star(X0),addition(one,addition(X0,one)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f7789,f7845]) ).
fof(f7847,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(multiplication(star(X1),addition(X1,one)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f7819]) ).
fof(f7848,plain,
! [X0,X1,X2] : addition(forward_box(X0,X1),star(X2)) = star(X2),
inference(resolution,[status(thm)],[f7762,f48]) ).
fof(f7852,plain,
! [X0,X1,X2] : addition(backward_diamond(X0,X1),star(X2)) = star(X2),
inference(resolution,[status(thm)],[f7768,f48]) ).
fof(f7858,plain,
! [X0] : addition(coantidomain(X0),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(resolution,[status(thm)],[f4735,f48]) ).
fof(f7875,plain,
! [X0] : addition(divergence(X0),codomain(divergence(X0))) = codomain(divergence(X0)),
inference(resolution,[status(thm)],[f6073,f48]) ).
fof(f7882,plain,
! [X0] : addition(codomain(X0),codomain(codomain(X0))) = codomain(codomain(X0)),
inference(resolution,[status(thm)],[f6509,f48]) ).
fof(f7883,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(codomain(multiplication(codomain(X1),X0)))),
inference(paramodulation,[status(thm)],[f70,f6509]) ).
fof(f7885,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(codomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f193,f6509]) ).
fof(f7887,plain,
! [X0,X1] : leq(codomain(multiplication(codomain(X0),X1)),codomain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f70,f6509]) ).
fof(f7889,plain,
! [X0] : leq(codomain(coantidomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f193,f6509]) ).
fof(f7891,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f70,f7883]) ).
fof(f7894,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f193,f7885]) ).
fof(f7895,plain,
! [X0] : leq(coantidomain(codomain(X0)),coantidomain(codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f193,f7894]) ).
fof(f7898,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f70,f7887]) ).
fof(f7901,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f193,f7889]) ).
fof(f7902,plain,
! [X0] : leq(coantidomain(codomain(X0)),coantidomain(codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f193,f7901]) ).
fof(f7905,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X1,X0)),X0)
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(paramodulation,[status(thm)],[f207,f290]) ).
fof(f7906,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f224,f290]) ).
fof(f7907,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(one,X0)),X0)
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(paramodulation,[status(thm)],[f232,f290]) ).
fof(f7910,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,coantidomain(X1))),coantidomain(X1))
| ~ leq(multiplication(X0,coantidomain(X1)),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f226,f290]) ).
fof(f7911,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,codomain(addition(X0,X1)))),codomain(addition(X0,X1)))
| ~ leq(addition(X0,X1),codomain(addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f2309,f290]) ).
fof(f7912,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,addition(coantidomain(addition(X0,X1)),X2))),addition(coantidomain(addition(X0,X1)),X2))
| ~ leq(multiplication(addition(X0,X1),X2),addition(coantidomain(addition(X0,X1)),X2)) ),
inference(paramodulation,[status(thm)],[f181,f290]) ).
fof(f7913,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,addition(X2,coantidomain(addition(X0,X1))))),addition(X2,coantidomain(addition(X0,X1))))
| ~ leq(multiplication(addition(X0,X1),X2),addition(X2,coantidomain(addition(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f190,f290]) ).
fof(f7914,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,multiplication(coantidomain(addition(X0,X1)),X2))),multiplication(coantidomain(addition(X0,X1)),X2))
| ~ leq(zero,multiplication(coantidomain(addition(X0,X1)),X2)) ),
inference(paramodulation,[status(thm)],[f151,f290]) ).
fof(f7915,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X2,multiplication(X0,coantidomain(multiplication(addition(X1,X2),X0))))),multiplication(X0,coantidomain(multiplication(addition(X1,X2),X0))))
| ~ leq(zero,multiplication(X0,coantidomain(multiplication(addition(X1,X2),X0)))) ),
inference(paramodulation,[status(thm)],[f144,f290]) ).
fof(f7916,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,omega(coantidomain(addition(X0,X1))))),omega(coantidomain(addition(X0,X1))))
| ~ leq(zero,omega(coantidomain(addition(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f1813,f290]) ).
fof(f7917,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,omega(addition(X0,X1)))),omega(addition(X0,X1)))
| ~ leq(omega(addition(X0,X1)),omega(addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f56,f290]) ).
fof(f7918,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,coantidomain(addition(X0,X1)))),coantidomain(addition(X0,X1)))
| ~ leq(zero,coantidomain(addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f63,f290]) ).
fof(f7919,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,zero)),zero)
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f44,f290]) ).
fof(f7920,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,one)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f40,f290]) ).
fof(f7921,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(multiplication(star(X0),addition(X0,one)),X1)),X1)
| ~ leq(multiplication(star(X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f7789,f290]) ).
fof(f7922,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(multiplication(addition(X0,one),star(X0)),X1)),X1)
| ~ leq(multiplication(star(X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f7510,f290]) ).
fof(f7923,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(backward_diamond(X1,X2),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1504,f290]) ).
fof(f7924,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(forward_box(X1,X2),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1497,f290]) ).
fof(f7925,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(backward_box(X1,X2),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1492,f290]) ).
fof(f7926,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(forward_diamond(X1,X2),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1485,f290]) ).
fof(f7927,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(divergence(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1488,f290]) ).
fof(f7928,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(codomain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1477,f290]) ).
fof(f7929,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(c(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1471,f290]) ).
fof(f7930,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(antidomain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1379,f290]) ).
fof(f7931,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(coantidomain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1377,f290]) ).
fof(f7932,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(domain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1375,f290]) ).
fof(f7933,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),multiplication(c(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f569,f290]) ).
fof(f7934,plain,
! [X0,X1,X2] :
( leq(multiplication(star(coantidomain(multiplication(X0,X1))),multiplication(coantidomain(multiplication(codomain(X0),X1)),X2)),X2)
| ~ leq(multiplication(coantidomain(multiplication(codomain(X0),X1)),X2),X2) ),
inference(paramodulation,[status(thm)],[f615,f290]) ).
fof(f7935,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),multiplication(codomain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f683,f290]) ).
fof(f7936,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(multiplication(X0,X1))),multiplication(antidomain(multiplication(X0,domain(X1))),X2)),X2)
| ~ leq(multiplication(antidomain(multiplication(X0,domain(X1))),X2),X2) ),
inference(paramodulation,[status(thm)],[f479,f290]) ).
fof(f7937,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),multiplication(domain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f558,f290]) ).
fof(f7938,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,multiplication(X1,X3))),multiplication(multiplication(X2,X3),X4)),X4)
| ~ leq(multiplication(multiplication(addition(multiplication(X0,X1),X2),X3),X4),X4) ),
inference(paramodulation,[status(thm)],[f204,f290]) ).
fof(f7939,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(addition(multiplication(X1,X2),X3),X4)),X4)
| ~ leq(multiplication(addition(multiplication(addition(X0,X1),X2),X3),X4),X4) ),
inference(paramodulation,[status(thm)],[f219,f290]) ).
fof(f7940,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(addition(multiplication(X0,X2),X3),X4)),X4)
| ~ leq(multiplication(addition(multiplication(X0,addition(X1,X2)),X3),X4),X4) ),
inference(paramodulation,[status(thm)],[f170,f290]) ).
fof(f7941,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X3)),multiplication(multiplication(X1,multiplication(X2,X3)),X4)),X4)
| ~ leq(multiplication(multiplication(addition(X0,multiplication(X1,X2)),X3),X4),X4) ),
inference(paramodulation,[status(thm)],[f211,f290]) ).
fof(f7942,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X0,X2),X3)),X3)
| ~ leq(multiplication(multiplication(addition(X0,X1),X2),X3),X3) ),
inference(paramodulation,[status(thm)],[f201,f290]) ).
fof(f7943,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(multiplication(X0,X1),X3)),X3)
| ~ leq(multiplication(multiplication(X0,addition(X1,X2)),X3),X3) ),
inference(paramodulation,[status(thm)],[f153,f290]) ).
fof(f7944,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(multiplication(X1,X2),X3)),X3)
| ~ leq(multiplication(multiplication(addition(X0,X1),X2),X3),X3) ),
inference(paramodulation,[status(thm)],[f43,f290]) ).
fof(f7945,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,X2),X3)),X3)
| ~ leq(multiplication(multiplication(X0,addition(X1,X2)),X3),X3) ),
inference(paramodulation,[status(thm)],[f42,f290]) ).
fof(f7946,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(addition(X1,X0)),multiplication(X2,X3)),X3)
| ~ leq(multiplication(addition(X0,addition(X1,X2)),X3),X3) ),
inference(paramodulation,[status(thm)],[f103,f290]) ).
fof(f7947,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(addition(X0,X1)),multiplication(X2,X3)),X3)
| ~ leq(multiplication(addition(X0,addition(X1,X2)),X3),X3) ),
inference(paramodulation,[status(thm)],[f36,f290]) ).
fof(f7948,plain,
! [X0,X1] :
( leq(multiplication(star(zero),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f80,f290]) ).
fof(f7949,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(domain(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4516,f290]) ).
fof(f7950,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(coantidomain(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4515,f290]) ).
fof(f7951,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(antidomain(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4514,f290]) ).
fof(f7952,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(c(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4513,f290]) ).
fof(f7953,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(codomain(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4512,f290]) ).
fof(f7954,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(divergence(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4511,f290]) ).
fof(f7955,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,domain(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2497,f290]) ).
fof(f7956,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,coantidomain(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2496,f290]) ).
fof(f7957,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,antidomain(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2495,f290]) ).
fof(f7958,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,c(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2494,f290]) ).
fof(f7959,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,codomain(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2493,f290]) ).
fof(f7960,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,divergence(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2492,f290]) ).
fof(f7961,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(multiplication(addition(X0,one),X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f232,f290]) ).
fof(f7962,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(multiplication(addition(one,X0),X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f207,f290]) ).
fof(f7963,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(multiplication(X0,addition(X1,one)),X2),X2) ),
inference(paramodulation,[status(thm)],[f192,f290]) ).
fof(f7964,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(multiplication(X0,addition(one,X1)),X2),X2) ),
inference(paramodulation,[status(thm)],[f162,f290]) ).
fof(f7965,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(addition(X1,addition(X0,X1)),X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f99,f290]) ).
fof(f7966,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(addition(X0,X1),X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f105,f290]) ).
fof(f7967,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X2),multiplication(addition(X0,X1),X3)),X3)
| ~ leq(multiplication(addition(X0,addition(X1,X2)),X3),X3) ),
inference(paramodulation,[status(thm)],[f97,f290]) ).
fof(f7968,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X1),multiplication(addition(X2,X0),X3)),X3)
| ~ leq(multiplication(addition(X0,addition(X1,X2)),X3),X3) ),
inference(paramodulation,[status(thm)],[f97,f290]) ).
fof(f7970,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f35,f290]) ).
fof(f7971,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f35,f290]) ).
fof(f7972,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f38,f290]) ).
fof(f7973,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),X0)
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7907]) ).
fof(f7978,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(X1,multiplication(coantidomain(addition(X0,X1)),X2))),multiplication(coantidomain(addition(X0,X1)),X2)),
inference(forward_subsumption_resolution,[status(thm)],[f7914,f240]) ).
fof(f7979,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(X1,multiplication(X2,coantidomain(multiplication(addition(X0,X1),X2))))),multiplication(X2,coantidomain(multiplication(addition(X0,X1),X2)))),
inference(forward_subsumption_resolution,[status(thm)],[f7915,f240]) ).
fof(f7980,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(X1,omega(coantidomain(addition(X0,X1))))),omega(coantidomain(addition(X0,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[f7916,f240]) ).
fof(f7981,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(X1,omega(addition(X0,X1)))),omega(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f7917,f239]) ).
fof(f7982,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(X1,coantidomain(addition(X0,X1)))),coantidomain(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f7918,f240]) ).
fof(f7983,definition,
( sQ11_spl
<=> leq(zero,zero) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f7985,plain,
( sQ11_spl
| ~ leq(zero,zero) ),
inference(component_clause,[status(thm)],[f7983]) ).
fof(f7986,definition,
! [X0,X1] :
( sQ12_spl
<=> leq(multiplication(star(X0),multiplication(X1,zero)),zero) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f7989,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7919,f7983,f7986]) ).
fof(f7990,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(forward_demodulation,[status(thm)],[f40,f7920]) ).
fof(f7991,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(star(X0),multiplication(addition(X0,one),X1))),X1)
| ~ leq(multiplication(star(X0),X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7921]) ).
fof(f7992,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(addition(X0,one),multiplication(star(X0),X1))),X1)
| ~ leq(multiplication(star(X0),X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7922]) ).
fof(f7993,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(backward_diamond(X1,X2),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7923]) ).
fof(f7994,plain,
! [X0,X1,X2] : leq(multiplication(star(one),multiplication(backward_diamond(X0,X1),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7993,f239]) ).
fof(f7995,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(forward_box(X1,X2),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7924]) ).
fof(f7996,plain,
! [X0,X1,X2] : leq(multiplication(star(one),multiplication(forward_box(X0,X1),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7995,f239]) ).
fof(f7997,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(backward_box(X1,X2),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7925]) ).
fof(f7998,plain,
! [X0,X1,X2] : leq(multiplication(star(one),multiplication(backward_box(X0,X1),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7997,f239]) ).
fof(f7999,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(forward_diamond(X1,X2),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7926]) ).
fof(f8000,plain,
! [X0,X1,X2] : leq(multiplication(star(one),multiplication(forward_diamond(X0,X1),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7999,f239]) ).
fof(f8001,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(divergence(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7927]) ).
fof(f8002,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(divergence(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8001,f239]) ).
fof(f8003,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(codomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7928]) ).
fof(f8004,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(codomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8003,f239]) ).
fof(f8005,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(c(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7929]) ).
fof(f8006,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(c(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8005,f239]) ).
fof(f8007,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(antidomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7930]) ).
fof(f8008,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(antidomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8007,f239]) ).
fof(f8009,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(coantidomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7931]) ).
fof(f8010,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(coantidomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8009,f239]) ).
fof(f8011,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(domain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7932]) ).
fof(f8012,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(domain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8011,f239]) ).
fof(f8013,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),multiplication(c(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7933]) ).
fof(f8014,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),multiplication(c(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8013,f239]) ).
fof(f8015,plain,
! [X0,X1,X2] : leq(multiplication(star(coantidomain(multiplication(X0,X1))),multiplication(coantidomain(multiplication(codomain(X0),X1)),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7934,f7158]) ).
fof(f8016,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),multiplication(codomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7935]) ).
fof(f8017,plain,
! [X0,X1] : leq(multiplication(star(coantidomain(X0)),multiplication(codomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8016,f239]) ).
fof(f8018,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(multiplication(X0,X1))),multiplication(antidomain(multiplication(X0,domain(X1))),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7936,f6667]) ).
fof(f8019,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),multiplication(domain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f7937]) ).
fof(f8020,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(domain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8019,f239]) ).
fof(f8021,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,multiplication(X1,X3))),multiplication(multiplication(X2,X3),X4)),X4)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,X4)),X4) ),
inference(forward_demodulation,[status(thm)],[f39,f7938]) ).
fof(f8022,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,multiplication(X1,X3))),multiplication(X2,multiplication(X3,X4))),X4)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,X4)),X4) ),
inference(forward_demodulation,[status(thm)],[f39,f8021]) ).
fof(f8023,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X3)),multiplication(multiplication(X1,multiplication(X2,X3)),X4)),X4)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),X4) ),
inference(forward_demodulation,[status(thm)],[f39,f7941]) ).
fof(f8024,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X3)),multiplication(X1,multiplication(multiplication(X2,X3),X4))),X4)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),X4) ),
inference(forward_demodulation,[status(thm)],[f39,f8023]) ).
fof(f8025,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X3)),multiplication(X1,multiplication(X2,multiplication(X3,X4)))),X4)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),X4) ),
inference(forward_demodulation,[status(thm)],[f39,f8024]) ).
fof(f8026,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X0,X2),X3)),X3)
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f7942]) ).
fof(f8027,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),multiplication(X0,multiplication(X2,X3))),X3)
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f8026]) ).
fof(f8028,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(multiplication(X0,X1),X3)),X3)
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f7943]) ).
fof(f8029,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(X0,multiplication(X1,X3))),X3)
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f8028]) ).
fof(f8030,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(multiplication(X1,X2),X3)),X3)
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f7944]) ).
fof(f8031,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(X1,multiplication(X2,X3))),X3)
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f8030]) ).
fof(f8032,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,X2),X3)),X3)
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f7945]) ).
fof(f8033,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X2,X3))),X3)
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f8032]) ).
fof(f8034,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(domain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7949]) ).
fof(f8035,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(coantidomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7950]) ).
fof(f8036,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(antidomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7951]) ).
fof(f8037,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(c(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7952]) ).
fof(f8038,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(codomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7953]) ).
fof(f8039,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(divergence(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7954]) ).
fof(f8040,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(domain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7955]) ).
fof(f8041,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(coantidomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7956]) ).
fof(f8042,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(antidomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7957]) ).
fof(f8043,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(c(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7958]) ).
fof(f8044,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(codomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7959]) ).
fof(f8045,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(divergence(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f7960]) ).
fof(f8046,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f7961]) ).
fof(f8047,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8046]) ).
fof(f8048,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f7962]) ).
fof(f8049,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8048]) ).
fof(f8050,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(X0,multiplication(addition(X1,one),X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f7963]) ).
fof(f8051,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(X0,multiplication(addition(X1,one),X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8050]) ).
fof(f8052,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(X0,multiplication(addition(one,X1),X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f7964]) ).
fof(f8053,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(X0,multiplication(addition(one,X1),X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8052]) ).
fof(f8056,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7985,f240]) ).
fof(f8057,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f8056]) ).
fof(f8060,plain,
! [X0,X1,X2] : addition(multiplication(backward_diamond(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6519,f48]) ).
fof(f8061,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f2309,f6519]) ).
fof(f8062,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),addition(coantidomain(backward_diamond(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f181,f6519]) ).
fof(f8063,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),addition(X2,coantidomain(backward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f190,f6519]) ).
fof(f8076,plain,
! [X0,X1,X2] : addition(X0,multiplication(backward_diamond(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f35,f8060]) ).
fof(f8080,plain,
! [X0] : addition(c(X0),codomain(c(X0))) = codomain(c(X0)),
inference(resolution,[status(thm)],[f6648,f48]) ).
fof(f8081,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(c(backward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f72,f6648]) ).
fof(f8082,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(c(forward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f71,f6648]) ).
fof(f8084,plain,
! [X0] : leq(antidomain(c(X0)),codomain(c(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f547,f6648]) ).
fof(f8085,plain,
! [X0] : leq(domain(c(X0)),codomain(c(domain(X0)))),
inference(paramodulation,[status(thm)],[f362,f6648]) ).
fof(f8087,plain,
! [X0,X1] : leq(c(backward_diamond(X0,c(X1))),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f72,f6648]) ).
fof(f8088,plain,
! [X0,X1] : leq(c(forward_diamond(X0,c(X1))),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f71,f6648]) ).
fof(f8090,plain,
! [X0] : leq(c(antidomain(X0)),codomain(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f547,f6648]) ).
fof(f8091,plain,
! [X0] : leq(c(domain(X0)),codomain(domain(c(X0)))),
inference(paramodulation,[status(thm)],[f362,f6648]) ).
fof(f8093,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f72,f8081]) ).
fof(f8094,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f71,f8082]) ).
fof(f8097,plain,
! [X0] : leq(antidomain(c(X0)),codomain(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f547,f8084]) ).
fof(f8098,plain,
! [X0] : leq(domain(c(X0)),codomain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f362,f8085]) ).
fof(f8101,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f72,f8087]) ).
fof(f8102,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f71,f8088]) ).
fof(f8105,plain,
! [X0] : leq(antidomain(c(X0)),codomain(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f547,f8090]) ).
fof(f8106,plain,
! [X0] : leq(domain(c(X0)),codomain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f362,f8091]) ).
fof(f8109,plain,
! [X0,X1,X2] : addition(multiplication(backward_box(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6658,f48]) ).
fof(f8110,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f2309,f6658]) ).
fof(f8111,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),addition(coantidomain(backward_box(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f181,f6658]) ).
fof(f8112,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),addition(X2,coantidomain(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f190,f6658]) ).
fof(f8122,plain,
! [X0,X1,X2] : addition(X0,multiplication(backward_box(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f35,f8109]) ).
fof(f8125,plain,
! [X0,X1,X2] : addition(multiplication(forward_box(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6659,f48]) ).
fof(f8126,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f2309,f6659]) ).
fof(f8127,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),addition(coantidomain(forward_box(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f181,f6659]) ).
fof(f8128,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),addition(X2,coantidomain(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f190,f6659]) ).
fof(f8139,plain,
! [X0,X1,X2] : addition(X0,multiplication(forward_box(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f35,f8125]) ).
fof(f8143,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(antidomain(addition(X1,X2)),X0)),multiplication(addition(antidomain(addition(X1,X2)),X0),X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f224,f291]) ).
fof(f8144,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,antidomain(addition(X1,X2)))),multiplication(addition(X0,antidomain(addition(X1,X2))),X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f230,f291]) ).
fof(f8145,plain,
! [X0,X1] :
( leq(multiplication(star(c(addition(X0,X1))),multiplication(c(addition(X0,X1)),X1)),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f4265,f291]) ).
fof(f8146,plain,
! [X0,X1] :
( leq(multiplication(star(domain(addition(X0,X1))),multiplication(domain(addition(X0,X1)),X1)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4146,f291]) ).
fof(f8147,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,X1),X3)),X2)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),X2) ),
inference(paramodulation,[status(thm)],[f39,f291]) ).
fof(f8149,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X1)),X0)
| ~ leq(multiplication(antidomain(X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f177,f291]) ).
fof(f8150,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(addition(X0,X1))),multiplication(antidomain(addition(X0,X1)),X1)),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f59,f291]) ).
fof(f8152,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(one,X1)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f41,f291]) ).
fof(f8153,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),one)
| ~ leq(addition(X0,multiplication(X0,X1)),one) ),
inference(paramodulation,[status(thm)],[f162,f291]) ).
fof(f8154,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),coantidomain(X0))
| ~ leq(multiplication(X0,X1),coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f181,f291]) ).
fof(f8155,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,one)),X1)
| ~ leq(addition(X0,multiplication(X0,X1)),X1) ),
inference(paramodulation,[status(thm)],[f192,f291]) ).
fof(f8157,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(star(X1),addition(X1,one)))),one)
| ~ leq(multiplication(X0,star(X1)),one) ),
inference(paramodulation,[status(thm)],[f7789,f291]) ).
fof(f8158,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(addition(X1,one),star(X1)))),one)
| ~ leq(multiplication(X0,star(X1)),one) ),
inference(paramodulation,[status(thm)],[f7510,f291]) ).
fof(f8159,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1504,f291]) ).
fof(f8160,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_box(X1,X2))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1497,f291]) ).
fof(f8161,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_box(X1,X2))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1492,f291]) ).
fof(f8162,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1485,f291]) ).
fof(f8163,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,divergence(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1488,f291]) ).
fof(f8164,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1477,f291]) ).
fof(f8165,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1471,f291]) ).
fof(f8166,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1379,f291]) ).
fof(f8167,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,coantidomain(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1377,f291]) ).
fof(f8168,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1375,f291]) ).
fof(f8169,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),domain(X1))
| ~ leq(multiplication(X0,one),domain(X1)) ),
inference(paramodulation,[status(thm)],[f569,f291]) ).
fof(f8170,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,coantidomain(multiplication(codomain(X1),X2)))),coantidomain(multiplication(X1,X2)))
| ~ leq(multiplication(X0,coantidomain(multiplication(codomain(X1),X2))),coantidomain(multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f615,f291]) ).
fof(f8171,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),coantidomain(X1))
| ~ leq(multiplication(X0,one),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f683,f291]) ).
fof(f8172,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(multiplication(X1,domain(X2))))),antidomain(multiplication(X1,X2)))
| ~ leq(multiplication(X0,antidomain(multiplication(X1,domain(X2)))),antidomain(multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f479,f291]) ).
fof(f8173,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),antidomain(X1))
| ~ leq(multiplication(X0,one),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f558,f291]) ).
fof(f8174,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X3,X4))),multiplication(X1,multiplication(X2,X4)))
| ~ leq(multiplication(X0,multiplication(addition(multiplication(X1,X2),X3),X4)),multiplication(X1,multiplication(X2,X4))) ),
inference(paramodulation,[status(thm)],[f204,f291]) ).
fof(f8175,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(X0),multiplication(X0,addition(multiplication(X2,X3),X4))),multiplication(X1,X3))
| ~ leq(multiplication(X0,addition(multiplication(addition(X1,X2),X3),X4)),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f219,f291]) ).
fof(f8176,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(X0),multiplication(X0,addition(multiplication(X1,X3),X4))),multiplication(X1,X2))
| ~ leq(multiplication(X0,addition(multiplication(X1,addition(X2,X3)),X4)),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f170,f291]) ).
fof(f8177,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X2,multiplication(X3,X4)))),multiplication(X1,X4))
| ~ leq(multiplication(X0,multiplication(addition(X1,multiplication(X2,X3)),X4)),multiplication(X1,X4)) ),
inference(paramodulation,[status(thm)],[f211,f291]) ).
fof(f8178,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X3))),multiplication(X2,X3))
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),multiplication(X2,X3)) ),
inference(paramodulation,[status(thm)],[f201,f291]) ).
fof(f8179,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),multiplication(X1,X3))
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f153,f291]) ).
fof(f8180,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X2,X3))),multiplication(X1,X3))
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f43,f291]) ).
fof(f8181,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X3))),multiplication(X1,X2))
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f42,f291]) ).
fof(f8182,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,X3)),addition(X2,X1))
| ~ leq(multiplication(X0,addition(X1,addition(X2,X3))),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f103,f291]) ).
fof(f8183,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,X3)),addition(X1,X2))
| ~ leq(multiplication(X0,addition(X1,addition(X2,X3))),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f36,f291]) ).
fof(f8184,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),zero)
| ~ leq(multiplication(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f80,f291]) ).
fof(f8185,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(domain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4516,f291]) ).
fof(f8186,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(coantidomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4515,f291]) ).
fof(f8187,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(antidomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4514,f291]) ).
fof(f8188,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(c(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4513,f291]) ).
fof(f8189,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(codomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4512,f291]) ).
fof(f8190,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(divergence(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4511,f291]) ).
fof(f8191,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,domain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2497,f291]) ).
fof(f8192,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,coantidomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2496,f291]) ).
fof(f8193,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,antidomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2495,f291]) ).
fof(f8194,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,c(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2494,f291]) ).
fof(f8195,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,codomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2493,f291]) ).
fof(f8196,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,divergence(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2492,f291]) ).
fof(f8197,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(X0,multiplication(addition(X1,one),X2)),X2) ),
inference(paramodulation,[status(thm)],[f232,f291]) ).
fof(f8198,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(X0,multiplication(addition(one,X1),X2)),X2) ),
inference(paramodulation,[status(thm)],[f207,f291]) ).
fof(f8199,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X1)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,one))),X1) ),
inference(paramodulation,[status(thm)],[f192,f291]) ).
fof(f8200,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X1)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X1) ),
inference(paramodulation,[status(thm)],[f162,f291]) ).
fof(f8201,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,addition(X2,addition(X1,X2)))),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f99,f291]) ).
fof(f8202,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,addition(X1,X2))),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f105,f291]) ).
fof(f8203,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,addition(X1,X2))),X3)
| ~ leq(multiplication(X0,addition(X1,addition(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f97,f291]) ).
fof(f8204,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,addition(X3,X1))),X2)
| ~ leq(multiplication(X0,addition(X1,addition(X2,X3))),X2) ),
inference(paramodulation,[status(thm)],[f97,f291]) ).
fof(f8206,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f35,f291]) ).
fof(f8207,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f35,f291]) ).
fof(f8208,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f38,f291]) ).
fof(f8209,plain,
! [X0,X1] : leq(multiplication(star(c(addition(X0,X1))),multiplication(c(addition(X0,X1)),X1)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8145,f240]) ).
fof(f8210,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8147]) ).
fof(f8213,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,X1))),multiplication(antidomain(addition(X0,X1)),X1)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8150,f240]) ).
fof(f8215,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f41,f8152]) ).
fof(f8216,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),X1)
| ~ leq(addition(X0,multiplication(X0,X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f40,f8155]) ).
fof(f8219,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8159]) ).
fof(f8220,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_box(X1,X2))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8160]) ).
fof(f8221,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_box(X1,X2))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8161]) ).
fof(f8222,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8162]) ).
fof(f8223,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,divergence(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8163]) ).
fof(f8224,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8164]) ).
fof(f8225,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8165]) ).
fof(f8226,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8166]) ).
fof(f8227,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,coantidomain(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8167]) ).
fof(f8228,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8168]) ).
fof(f8229,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f40,f8169]) ).
fof(f8230,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f40,f8171]) ).
fof(f8231,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f40,f8173]) ).
fof(f8234,plain,
! [X0] : addition(antidomain(X0),codomain(antidomain(X0))) = codomain(antidomain(X0)),
inference(resolution,[status(thm)],[f6796,f48]) ).
fof(f8255,plain,
! [X0] : addition(domain(X0),codomain(domain(X0))) = codomain(domain(X0)),
inference(resolution,[status(thm)],[f7000,f48]) ).
fof(f8256,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(domain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f69,f7000]) ).
fof(f8261,plain,
! [X0,X1] : leq(domain(multiplication(X0,domain(X1))),codomain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f69,f7000]) ).
fof(f8266,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f69,f8256]) ).
fof(f8273,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f69,f8261]) ).
fof(f8281,plain,
! [X0] :
( leq(multiplication(star(star(X0)),one),addition(X0,one))
| ~ leq(star(X0),addition(X0,one)) ),
inference(paramodulation,[status(thm)],[f7789,f293]) ).
fof(f8282,plain,
! [X0] :
( leq(multiplication(star(addition(X0,one)),one),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f7510,f293]) ).
fof(f8283,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X2),multiplication(X0,multiplication(X1,X3))),X3)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),X3) ),
inference(paramodulation,[status(thm)],[f204,f293]) ).
fof(f8284,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X1),multiplication(X0,X3)),multiplication(X2,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),multiplication(X2,X3)) ),
inference(paramodulation,[status(thm)],[f211,f293]) ).
fof(f8287,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f43,f293]) ).
fof(f8288,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f42,f293]) ).
fof(f8289,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X2),addition(X1,X0)),X3)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f103,f293]) ).
fof(f8290,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X2),addition(X0,X1)),X3)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f36,f293]) ).
fof(f8292,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4516,f293]) ).
fof(f8293,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4515,f293]) ).
fof(f8294,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4514,f293]) ).
fof(f8295,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4513,f293]) ).
fof(f8296,plain,
! [X0,X1] :
( leq(multiplication(star(codomain(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4512,f293]) ).
fof(f8297,plain,
! [X0,X1] :
( leq(multiplication(star(divergence(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4511,f293]) ).
fof(f8298,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(paramodulation,[status(thm)],[f2497,f293]) ).
fof(f8299,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f2496,f293]) ).
fof(f8300,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f2495,f293]) ).
fof(f8301,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),c(X1))
| ~ leq(X0,c(X1)) ),
inference(paramodulation,[status(thm)],[f2494,f293]) ).
fof(f8302,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(paramodulation,[status(thm)],[f2493,f293]) ).
fof(f8303,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),divergence(X1))
| ~ leq(X0,divergence(X1)) ),
inference(paramodulation,[status(thm)],[f2492,f293]) ).
fof(f8304,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),X1)
| ~ leq(multiplication(addition(X0,one),X1),X1) ),
inference(paramodulation,[status(thm)],[f232,f293]) ).
fof(f8305,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),X1)
| ~ leq(multiplication(addition(one,X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f207,f293]) ).
fof(f8306,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),X1)
| ~ leq(multiplication(X0,addition(X1,one)),X1) ),
inference(paramodulation,[status(thm)],[f192,f293]) ).
fof(f8307,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),X1)
| ~ leq(multiplication(X0,addition(one,X1)),X1) ),
inference(paramodulation,[status(thm)],[f162,f293]) ).
fof(f8310,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f38,f293]) ).
fof(f8311,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(one,X2)),X0),X1)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X1))),X1) ),
inference(paramodulation,[status(thm)],[f207,f293]) ).
fof(f8312,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(antidomain(X2),X1)),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f224,f293]) ).
fof(f8313,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X2,one)),X0),X1)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X1))),X1) ),
inference(paramodulation,[status(thm)],[f232,f293]) ).
fof(f8314,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,antidomain(X2))),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f230,f293]) ).
fof(f8315,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,X2)),X0),coantidomain(X2))
| ~ leq(addition(X0,multiplication(X1,coantidomain(X2))),coantidomain(X2)) ),
inference(paramodulation,[status(thm)],[f233,f293]) ).
fof(f8316,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X2,X1)),X0),coantidomain(X2))
| ~ leq(addition(X0,multiplication(X1,coantidomain(X2))),coantidomain(X2)) ),
inference(paramodulation,[status(thm)],[f226,f293]) ).
fof(f8317,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),domain(X1))
| ~ leq(addition(X0,zero),domain(X1)) ),
inference(paramodulation,[status(thm)],[f197,f293]) ).
fof(f8318,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f4265,f293]) ).
fof(f8319,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(addition(X0,zero),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f195,f293]) ).
fof(f8320,plain,
! [X0,X1,X2] :
( leq(multiplication(star(domain(X1)),X0),antidomain(X2))
| ~ leq(addition(X0,domain_difference(X1,X2)),antidomain(X2)) ),
inference(paramodulation,[status(thm)],[f68,f293]) ).
fof(f8321,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4146,f293]) ).
fof(f8322,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),X0),X3)
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f39,f293]) ).
fof(f8323,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),addition(X2,X1))
| ~ leq(addition(X0,multiplication(antidomain(X1),X2)),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f186,f293]) ).
fof(f8324,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),addition(X1,X2))
| ~ leq(addition(X0,multiplication(antidomain(X1),X2)),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f177,f293]) ).
fof(f8325,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),omega(X1))
| ~ leq(addition(X0,zero),omega(X1)) ),
inference(paramodulation,[status(thm)],[f1569,f293]) ).
fof(f8326,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),multiplication(X1,X2))
| ~ leq(addition(X0,zero),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f136,f293]) ).
fof(f8327,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f59,f293]) ).
fof(f8328,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f45,f293]) ).
fof(f8329,plain,
! [X0,X1] :
( leq(multiplication(star(one),X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f41,f293]) ).
fof(f8330,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),codomain(X1))
| ~ leq(addition(X0,X1),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f2309,f293]) ).
fof(f8331,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),addition(one,X2))
| ~ leq(addition(X0,addition(X1,multiplication(X1,X2))),addition(one,X2)) ),
inference(paramodulation,[status(thm)],[f162,f293]) ).
fof(f8332,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),addition(coantidomain(X1),X2))
| ~ leq(addition(X0,multiplication(X1,X2)),addition(coantidomain(X1),X2)) ),
inference(paramodulation,[status(thm)],[f181,f293]) ).
fof(f8333,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),addition(X2,one))
| ~ leq(addition(X0,addition(X1,multiplication(X1,X2))),addition(X2,one)) ),
inference(paramodulation,[status(thm)],[f192,f293]) ).
fof(f8334,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),addition(X2,coantidomain(X1)))
| ~ leq(addition(X0,multiplication(X1,X2)),addition(X2,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f190,f293]) ).
fof(f8335,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),multiplication(coantidomain(X1),X2))
| ~ leq(addition(X0,zero),multiplication(coantidomain(X1),X2)) ),
inference(paramodulation,[status(thm)],[f151,f293]) ).
fof(f8336,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X2),X0),multiplication(X1,coantidomain(multiplication(X2,X1))))
| ~ leq(addition(X0,zero),multiplication(X1,coantidomain(multiplication(X2,X1)))) ),
inference(paramodulation,[status(thm)],[f144,f293]) ).
fof(f8337,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),omega(coantidomain(X1)))
| ~ leq(addition(X0,zero),omega(coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f1813,f293]) ).
fof(f8338,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),omega(X1))
| ~ leq(addition(X0,omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f56,f293]) ).
fof(f8339,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),coantidomain(X1))
| ~ leq(addition(X0,zero),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f63,f293]) ).
fof(f8340,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(addition(X0,zero),zero) ),
inference(paramodulation,[status(thm)],[f44,f293]) ).
fof(f8341,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f40,f293]) ).
fof(f8343,plain,
! [X0] :
( leq(star(star(X0)),addition(X0,one))
| ~ leq(star(X0),addition(X0,one)) ),
inference(forward_demodulation,[status(thm)],[f40,f8281]) ).
fof(f8344,plain,
! [X0] :
( leq(star(addition(X0,one)),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f40,f8282]) ).
fof(f8345,plain,
! [X0] : leq(star(addition(X0,one)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f8344,f239]) ).
fof(f8347,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8292,f239]) ).
fof(f8348,plain,
! [X0,X1] : leq(multiplication(star(coantidomain(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8293,f239]) ).
fof(f8349,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8294,f239]) ).
fof(f8350,plain,
! [X0,X1] : leq(multiplication(star(c(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8295,f239]) ).
fof(f8351,plain,
! [X0,X1] : leq(multiplication(star(codomain(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8296,f239]) ).
fof(f8352,plain,
! [X0,X1] : leq(multiplication(star(divergence(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8297,f239]) ).
fof(f8353,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f8317]) ).
fof(f8354,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f8318]) ).
fof(f8355,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f8319]) ).
fof(f8356,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),omega(X1))
| ~ leq(X0,omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f8325]) ).
fof(f8357,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f37,f8326]) ).
fof(f8358,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f8327]) ).
fof(f8359,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f8328]) ).
fof(f8360,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),multiplication(coantidomain(X1),X2))
| ~ leq(X0,multiplication(coantidomain(X1),X2)) ),
inference(forward_demodulation,[status(thm)],[f37,f8335]) ).
fof(f8361,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X2),X0),multiplication(X1,coantidomain(multiplication(X2,X1))))
| ~ leq(X0,multiplication(X1,coantidomain(multiplication(X2,X1)))) ),
inference(forward_demodulation,[status(thm)],[f37,f8336]) ).
fof(f8362,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),omega(coantidomain(X1)))
| ~ leq(X0,omega(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f37,f8337]) ).
fof(f8363,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f8339]) ).
fof(f8364,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f8340]) ).
fof(f8365,plain,
! [X0,X1,X2] : addition(multiplication(forward_diamond(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f7010,f48]) ).
fof(f8366,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f2309,f7010]) ).
fof(f8367,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),addition(coantidomain(forward_diamond(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f181,f7010]) ).
fof(f8368,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),addition(X2,coantidomain(forward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f190,f7010]) ).
fof(f8383,plain,
! [X0,X1,X2] : addition(X0,multiplication(forward_diamond(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f35,f8365]) ).
fof(f8388,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(resolution,[status(thm)],[f7305,f48]) ).
fof(f8392,plain,
! [X0,X1] : leq(coantidomain(multiplication(codomain(X0),X1)),coantidomain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f70,f7305]) ).
fof(f8408,plain,
! [X0,X1] : leq(one,addition(omega(X0),multiplication(star(X0),star(X1)))),
inference(resolution,[status(thm)],[f7532,f58]) ).
fof(f8409,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(X0,star(X1)),
inference(resolution,[status(thm)],[f7532,f48]) ).
fof(f8410,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f103,f7532]) ).
fof(f8411,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f36,f7532]) ).
fof(f8413,plain,
! [X0,X1] : leq(one,addition(star(X0),X1)),
inference(paramodulation,[status(thm)],[f35,f7532]) ).
fof(f8418,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f7563,f207]) ).
fof(f8425,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f7563,f162]) ).
fof(f8427,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,star(X1))),one)
| ~ leq(multiplication(X0,star(X1)),one) ),
inference(paramodulation,[status(thm)],[f7563,f291]) ).
fof(f8428,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(star(X0),X1)),X1)
| ~ leq(multiplication(star(X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f7563,f290]) ).
fof(f8429,plain,
! [X0,X1] :
( addition(X0,star(X1)) != star(X1)
| leq(addition(X0,one),star(X1)) ),
inference(paramodulation,[status(thm)],[f7563,f243]) ).
fof(f8430,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,star(X1))
| leq(multiplication(X0,one),multiplication(X0,star(X1))) ),
inference(paramodulation,[status(thm)],[f7563,f242]) ).
fof(f8431,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(star(X1),X0)
| leq(multiplication(one,X0),multiplication(star(X1),X0)) ),
inference(paramodulation,[status(thm)],[f7563,f241]) ).
fof(f8432,plain,
! [X0] : multiplication(star(X0),coantidomain(star(X0))) = multiplication(one,coantidomain(star(X0))),
inference(paramodulation,[status(thm)],[f7563,f233]) ).
fof(f8434,plain,
! [X0] : multiplication(antidomain(star(X0)),star(X0)) = multiplication(antidomain(star(X0)),one),
inference(paramodulation,[status(thm)],[f7563,f186]) ).
fof(f8441,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7563,f103]) ).
fof(f8443,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f7563,f97]) ).
fof(f8444,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(star(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f7563,f97]) ).
fof(f8445,plain,
! [X0] :
( star(X0) != one
| leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7563,f246]) ).
fof(f8447,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7563,f36]) ).
fof(f8448,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,star(X1))
| leq(X0,multiplication(X0,star(X1))) ),
inference(forward_demodulation,[status(thm)],[f40,f8430]) ).
fof(f8449,plain,
! [X0,X1] : leq(X0,multiplication(X0,star(X1))),
inference(trivial_equality_resolution,[status(thm)],[f8448]) ).
fof(f8450,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(star(X1),X0)
| leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f8431]) ).
fof(f8451,plain,
! [X0,X1] : leq(X0,multiplication(star(X1),X0)),
inference(trivial_equality_resolution,[status(thm)],[f8450]) ).
fof(f8452,plain,
! [X0] : zero = multiplication(one,coantidomain(star(X0))),
inference(forward_demodulation,[status(thm)],[f63,f8432]) ).
fof(f8453,plain,
! [X0] : zero = coantidomain(star(X0)),
inference(forward_demodulation,[status(thm)],[f41,f8452]) ).
fof(f8454,plain,
! [X0] : zero = multiplication(antidomain(star(X0)),one),
inference(forward_demodulation,[status(thm)],[f59,f8434]) ).
fof(f8455,plain,
! [X0] : zero = antidomain(star(X0)),
inference(forward_demodulation,[status(thm)],[f40,f8454]) ).
fof(f8456,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(star(X1),X0),
inference(forward_demodulation,[status(thm)],[f97,f8441]) ).
fof(f8457,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(star(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f8444]) ).
fof(f8478,plain,
! [X0] : addition(zero,codomain(star(X0))) = one,
inference(paramodulation,[status(thm)],[f8453,f683]) ).
fof(f8498,plain,
! [X0] : codomain(star(X0)) = one,
inference(forward_demodulation,[status(thm)],[f80,f8478]) ).
fof(f8522,plain,
! [X0,X1] : domain_difference(X0,star(X1)) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f8455,f68]) ).
fof(f8523,plain,
! [X0] : addition(zero,domain(star(X0))) = one,
inference(paramodulation,[status(thm)],[f8455,f558]) ).
fof(f8525,plain,
! [X0] : domain(zero) = c(star(X0)),
inference(paramodulation,[status(thm)],[f8455,f361]) ).
fof(f8542,plain,
! [X0,X1] : domain_difference(X0,star(X1)) = zero,
inference(forward_demodulation,[status(thm)],[f44,f8522]) ).
fof(f8543,plain,
! [X0] : domain(star(X0)) = one,
inference(forward_demodulation,[status(thm)],[f80,f8523]) ).
fof(f8545,plain,
! [X0] : zero = c(star(X0)),
inference(forward_demodulation,[status(thm)],[f607,f8525]) ).
fof(f8563,plain,
! [X0,X1] : backward_diamond(X0,star(X1)) = codomain(multiplication(one,X0)),
inference(paramodulation,[status(thm)],[f8498,f70]) ).
fof(f8565,plain,
! [X0,X1] : addition(coantidomain(multiplication(star(X0),X1)),coantidomain(multiplication(one,X1))) = coantidomain(multiplication(codomain(star(X0)),X1)),
inference(paramodulation,[status(thm)],[f8498,f615]) ).
fof(f8582,plain,
! [X0,X1] : backward_diamond(X0,star(X1)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f41,f8563]) ).
fof(f8584,plain,
! [X0,X1] : addition(coantidomain(multiplication(one,X0)),coantidomain(multiplication(star(X1),X0))) = coantidomain(multiplication(codomain(star(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f35,f8565]) ).
fof(f8585,plain,
! [X0,X1] : addition(coantidomain(X0),coantidomain(multiplication(star(X1),X0))) = coantidomain(multiplication(codomain(star(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f41,f8584]) ).
fof(f8586,plain,
! [X0,X1] : addition(coantidomain(X0),coantidomain(multiplication(star(X1),X0))) = coantidomain(multiplication(one,X0)),
inference(forward_demodulation,[status(thm)],[f8498,f8585]) ).
fof(f8587,plain,
! [X0,X1] : addition(coantidomain(X0),coantidomain(multiplication(star(X1),X0))) = coantidomain(X0),
inference(forward_demodulation,[status(thm)],[f41,f8586]) ).
fof(f8589,plain,
! [X0,X1,X2] : leq(multiplication(star(forward_diamond(X0,X1)),multiplication(forward_diamond(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f295,f7010]) ).
fof(f8590,plain,
! [X0,X1,X2] : leq(multiplication(star(forward_box(X0,X1)),multiplication(forward_box(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f295,f6659]) ).
fof(f8591,plain,
! [X0,X1,X2] : leq(multiplication(star(backward_box(X0,X1)),multiplication(backward_box(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f295,f6658]) ).
fof(f8592,plain,
! [X0,X1,X2] : leq(multiplication(star(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f295,f6519]) ).
fof(f8593,plain,
! [X0,X1] : leq(multiplication(star(coantidomain(X0)),multiplication(coantidomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f295,f7158]) ).
fof(f8594,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),multiplication(domain(X0),X1)),X1),
inference(resolution,[status(thm)],[f295,f6808]) ).
fof(f8595,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f295,f6667]) ).
fof(f8596,plain,
! [X0,X1] : leq(multiplication(star(c(X0)),multiplication(c(X0),X1)),X1),
inference(resolution,[status(thm)],[f295,f6526]) ).
fof(f8597,plain,
! [X0,X1] : leq(multiplication(star(codomain(X0)),multiplication(codomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f295,f6393]) ).
fof(f8598,plain,
! [X0,X1] : leq(multiplication(star(divergence(X0)),multiplication(divergence(X0),X1)),X1),
inference(resolution,[status(thm)],[f295,f5965]) ).
fof(f8599,plain,
! [X0,X1] : leq(multiplication(star(forward_diamond(X0,X1)),multiplication(forward_diamond(X0,X1),forward_diamond(X0,X1))),forward_diamond(X0,X1)),
inference(resolution,[status(thm)],[f295,f4077]) ).
fof(f8600,plain,
! [X0,X1] : leq(multiplication(star(forward_box(X0,X1)),multiplication(forward_box(X0,X1),forward_box(X0,X1))),forward_box(X0,X1)),
inference(resolution,[status(thm)],[f295,f3741]) ).
fof(f8601,plain,
! [X0,X1] : leq(multiplication(star(backward_box(X0,X1)),multiplication(backward_box(X0,X1),backward_box(X0,X1))),backward_box(X0,X1)),
inference(resolution,[status(thm)],[f295,f3740]) ).
fof(f8602,plain,
! [X0,X1] : leq(multiplication(star(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),backward_diamond(X0,X1))),backward_diamond(X0,X1)),
inference(resolution,[status(thm)],[f295,f3497]) ).
fof(f8603,plain,
! [X0] : leq(multiplication(star(coantidomain(X0)),multiplication(coantidomain(X0),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f295,f4627]) ).
fof(f8604,plain,
! [X0] : leq(multiplication(star(domain(X0)),multiplication(domain(X0),domain(X0))),domain(X0)),
inference(resolution,[status(thm)],[f295,f3841]) ).
fof(f8605,plain,
! [X0] : leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),antidomain(X0))),antidomain(X0)),
inference(resolution,[status(thm)],[f295,f3749]) ).
fof(f8606,plain,
! [X0] : leq(multiplication(star(c(X0)),multiplication(c(X0),c(X0))),c(X0)),
inference(resolution,[status(thm)],[f295,f3652]) ).
fof(f8607,plain,
! [X0] : leq(multiplication(star(codomain(X0)),multiplication(codomain(X0),codomain(X0))),codomain(X0)),
inference(resolution,[status(thm)],[f295,f3411]) ).
fof(f8608,plain,
! [X0] : leq(multiplication(star(divergence(X0)),multiplication(divergence(X0),divergence(X0))),divergence(X0)),
inference(resolution,[status(thm)],[f295,f3330]) ).
fof(f8609,plain,
! [X0,X1] :
( leq(multiplication(star(addition(one,X1)),multiplication(addition(one,X1),X0)),X0)
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(paramodulation,[status(thm)],[f207,f295]) ).
fof(f8610,plain,
! [X0,X1] :
( leq(multiplication(star(addition(antidomain(X1),X0)),multiplication(addition(antidomain(X1),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f224,f295]) ).
fof(f8611,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X1,one)),multiplication(addition(X1,one),X0)),X0)
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(paramodulation,[status(thm)],[f232,f295]) ).
fof(f8612,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X0,antidomain(X1))),multiplication(addition(X0,antidomain(X1)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f230,f295]) ).
fof(f8613,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X0,X1)),multiplication(addition(X0,X1),coantidomain(X1))),coantidomain(X1))
| ~ leq(multiplication(X0,coantidomain(X1)),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f233,f295]) ).
fof(f8614,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X1,X0)),multiplication(addition(X1,X0),coantidomain(X1))),coantidomain(X1))
| ~ leq(multiplication(X0,coantidomain(X1)),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f226,f295]) ).
fof(f8618,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X0)),multiplication(domain(X0),antidomain(X1))),antidomain(X1))
| ~ leq(domain_difference(X0,X1),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f68,f295]) ).
fof(f8619,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),multiplication(domain(X0),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4146,f295]) ).
fof(f8620,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,X1),X2)),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f39,f295]) ).
fof(f8621,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),addition(X1,X0))),addition(X1,X0))
| ~ leq(multiplication(antidomain(X0),X1),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f186,f295]) ).
fof(f8622,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),addition(X0,X1))),addition(X0,X1))
| ~ leq(multiplication(antidomain(X0),X1),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f177,f295]) ).
fof(f8627,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(one,X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f41,f295]) ).
fof(f8628,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X0))),codomain(X0))
| ~ leq(X0,codomain(X0)) ),
inference(paramodulation,[status(thm)],[f2309,f295]) ).
fof(f8629,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,addition(one,X1))),addition(one,X1))
| ~ leq(addition(X0,multiplication(X0,X1)),addition(one,X1)) ),
inference(paramodulation,[status(thm)],[f162,f295]) ).
fof(f8630,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,addition(coantidomain(X0),X1))),addition(coantidomain(X0),X1))
| ~ leq(multiplication(X0,X1),addition(coantidomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f181,f295]) ).
fof(f8631,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,addition(X1,one))),addition(X1,one))
| ~ leq(addition(X0,multiplication(X0,X1)),addition(X1,one)) ),
inference(paramodulation,[status(thm)],[f192,f295]) ).
fof(f8632,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,addition(X1,coantidomain(X0)))),addition(X1,coantidomain(X0)))
| ~ leq(multiplication(X0,X1),addition(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f190,f295]) ).
fof(f8636,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(X0,omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f56,f295]) ).
fof(f8638,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(X0,zero)),zero)
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f44,f295]) ).
fof(f8639,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(X0,one)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f40,f295]) ).
fof(f8640,plain,
! [X0,X1] :
( leq(multiplication(star(addition(antidomain(X1),X0)),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f224,f8610]) ).
fof(f8641,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X0,antidomain(X1))),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f230,f8612]) ).
fof(f8642,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X0,X1)),multiplication(X0,coantidomain(X1))),coantidomain(X1))
| ~ leq(multiplication(X0,coantidomain(X1)),coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f233,f8613]) ).
fof(f8643,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X1,X0)),multiplication(X0,coantidomain(X1))),coantidomain(X1))
| ~ leq(multiplication(X0,coantidomain(X1)),coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f226,f8614]) ).
fof(f8647,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X0)),domain_difference(X0,X1)),antidomain(X1))
| ~ leq(domain_difference(X0,X1),antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f68,f8618]) ).
fof(f8648,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),domain_difference(X0,X1)),antidomain(X1)),
inference(forward_subsumption_resolution,[status(thm)],[f8647,f6998]) ).
fof(f8649,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),X0),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f4146,f8619]) ).
fof(f8650,plain,
! [X0] : leq(multiplication(star(domain(X0)),X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8649,f239]) ).
fof(f8651,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8620]) ).
fof(f8652,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X1)),addition(X1,X0))
| ~ leq(multiplication(antidomain(X0),X1),addition(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f186,f8621]) ).
fof(f8653,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X1)),addition(X0,X1))
| ~ leq(multiplication(antidomain(X0),X1),addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f177,f8622]) ).
fof(f8658,plain,
! [X0] :
( leq(multiplication(star(one),X0),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f8627]) ).
fof(f8659,plain,
! [X0] : leq(multiplication(star(one),X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8658,f239]) ).
fof(f8660,plain,
! [X0] :
( leq(multiplication(star(X0),X0),codomain(X0))
| ~ leq(X0,codomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2309,f8628]) ).
fof(f8661,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),addition(coantidomain(X0),X1))
| ~ leq(multiplication(X0,X1),addition(coantidomain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f181,f8630]) ).
fof(f8662,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),addition(X1,coantidomain(X0)))
| ~ leq(multiplication(X0,X1),addition(X1,coantidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f190,f8632]) ).
fof(f8666,plain,
! [X0] :
( leq(multiplication(star(X0),omega(X0)),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(forward_demodulation,[status(thm)],[f56,f8636]) ).
fof(f8667,plain,
! [X0] : leq(multiplication(star(X0),omega(X0)),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f8666,f239]) ).
fof(f8669,definition,
! [X0] :
( sQ13_spl
<=> leq(multiplication(star(X0),multiplication(X0,zero)),zero) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f8672,plain,
( sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8638,f7983,f8669]) ).
fof(f8673,plain,
! [X0] :
( leq(multiplication(star(X0),X0),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f40,f8639]) ).
fof(f8681,plain,
! [X0] : leq(one,antidomain(c(star(X0)))),
inference(paramodulation,[status(thm)],[f8543,f4249]) ).
fof(f8691,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),one)) != addition(forward_diamond(X1,domain(X0)),domain(star(X2))) ),
inference(paramodulation,[status(thm)],[f8543,f75]) ).
fof(f8692,plain,
! [X0,X1,X2] :
( addition(domain(star(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(star(X0)),addition(forward_diamond(X1,one),domain(X2))) != addition(forward_diamond(X1,domain(star(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f8543,f75]) ).
fof(f8693,plain,
! [X0,X1,X2] :
( addition(domain(star(X1)),addition(divergence(X0),forward_diamond(star(X0),domain(X2)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X2)))
| addition(one,addition(forward_diamond(X0,domain(star(X1))),domain(X2))) != addition(forward_diamond(X0,domain(star(X1))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f8543,f75]) ).
fof(f8694,plain,
! [X0,X1] : forward_diamond(X0,star(X1)) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f8543,f69]) ).
fof(f8695,plain,
! [X0,X1] : domain_difference(star(X0),X1) = multiplication(one,antidomain(X1)),
inference(paramodulation,[status(thm)],[f8543,f68]) ).
fof(f8698,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,star(X1))),antidomain(multiplication(X0,one))) = antidomain(multiplication(X0,domain(star(X1)))),
inference(paramodulation,[status(thm)],[f8543,f479]) ).
fof(f8710,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(forward_diamond(X1,domain(X0)),domain(star(X2))) ),
inference(forward_demodulation,[status(thm)],[f97,f8691]) ).
fof(f8711,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(forward_diamond(X1,domain(X0)),one) ),
inference(forward_demodulation,[status(thm)],[f8543,f8710]) ).
fof(f8712,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(one,forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f8711]) ).
fof(f8713,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f1485,f8712]) ).
fof(f8714,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f8713]) ).
fof(f8715,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),domain(star(X1)))) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f777,f8714]) ).
fof(f8716,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),one)) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f8715]) ).
fof(f8717,plain,
! [X0,X1,X2] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),domain(star(X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f97,f8716]) ).
fof(f8718,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f8717]) ).
fof(f8719,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),domain(star(X1)))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f777,f8718]) ).
fof(f8720,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),one)
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f8719]) ).
fof(f8721,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(one,divergence(X1))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f35,f8720]) ).
fof(f8722,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = one
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f1488,f8721]) ).
fof(f8723,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(star(X2))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f8692]) ).
fof(f8724,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,domain(star(X2))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f8723]) ).
fof(f8725,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f8724]) ).
fof(f8726,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f8725]) ).
fof(f8727,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f8726]) ).
fof(f8728,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(star(X2))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f8693]) ).
fof(f8729,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,domain(star(X2))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f8728]) ).
fof(f8730,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f8729]) ).
fof(f8731,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f8730]) ).
fof(f8732,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f8731]) ).
fof(f8733,plain,
! [X0,X1] : forward_diamond(X0,star(X1)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f40,f8694]) ).
fof(f8734,plain,
! [X0,X1] : domain_difference(star(X0),X1) = antidomain(X1),
inference(forward_demodulation,[status(thm)],[f41,f8695]) ).
fof(f8737,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,one)),antidomain(multiplication(X0,star(X1)))) = antidomain(multiplication(X0,domain(star(X1)))),
inference(forward_demodulation,[status(thm)],[f35,f8698]) ).
fof(f8738,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,star(X1)))) = antidomain(multiplication(X0,domain(star(X1)))),
inference(forward_demodulation,[status(thm)],[f40,f8737]) ).
fof(f8739,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,star(X1)))) = antidomain(multiplication(X0,one)),
inference(forward_demodulation,[status(thm)],[f8543,f8738]) ).
fof(f8740,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,star(X1)))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f40,f8739]) ).
fof(f8765,plain,
! [X0,X1] : backward_box(X0,star(X1)) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f8545,f72]) ).
fof(f8766,plain,
! [X0,X1] : forward_box(X0,star(X1)) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f8545,f71]) ).
fof(f8787,plain,
! [X0,X1] : backward_box(X0,star(X1)) = c(zero),
inference(forward_demodulation,[status(thm)],[f809,f8765]) ).
fof(f8788,plain,
! [X0,X1] : backward_box(X0,star(X1)) = one,
inference(forward_demodulation,[status(thm)],[f597,f8787]) ).
fof(f8789,plain,
! [X0,X1] : forward_box(X0,star(X1)) = c(zero),
inference(forward_demodulation,[status(thm)],[f776,f8766]) ).
fof(f8790,plain,
! [X0,X1] : forward_box(X0,star(X1)) = one,
inference(forward_demodulation,[status(thm)],[f597,f8789]) ).
fof(f8792,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X2)),addition(multiplication(X1,multiplication(X2,X3)),X4)),X3)
| ~ leq(addition(multiplication(addition(X0,X1),multiplication(X2,X3)),X4),X3) ),
inference(paramodulation,[status(thm)],[f219,f296]) ).
fof(f8793,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),addition(multiplication(X0,X3),X4)),X2)
| ~ leq(addition(multiplication(X0,addition(multiplication(X1,X2),X3)),X4),X2) ),
inference(paramodulation,[status(thm)],[f170,f296]) ).
fof(f8794,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X3)),multiplication(X1,multiplication(X2,multiplication(X3,X4)))),X4)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),X4) ),
inference(paramodulation,[status(thm)],[f211,f296]) ).
fof(f8795,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),multiplication(X0,multiplication(X2,X3))),X3)
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),X3) ),
inference(paramodulation,[status(thm)],[f201,f296]) ).
fof(f8796,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(X0,X1)),X3)
| ~ leq(multiplication(X0,addition(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f153,f296]) ).
fof(f8797,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(X1,multiplication(X2,X3))),X3)
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),X3) ),
inference(paramodulation,[status(thm)],[f43,f296]) ).
fof(f8798,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,X3)),X2)
| ~ leq(multiplication(X0,addition(multiplication(X1,X2),X3)),X2) ),
inference(paramodulation,[status(thm)],[f42,f296]) ).
fof(f8799,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(domain(X3),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4516,f296]) ).
fof(f8800,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(coantidomain(X3),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4515,f296]) ).
fof(f8801,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(antidomain(X3),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4514,f296]) ).
fof(f8802,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(c(X3),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4513,f296]) ).
fof(f8803,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(codomain(X3),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4512,f296]) ).
fof(f8804,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(divergence(X3),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4511,f296]) ).
fof(f8805,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),domain(X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2497,f296]) ).
fof(f8806,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),coantidomain(X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2496,f296]) ).
fof(f8807,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),antidomain(X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2495,f296]) ).
fof(f8808,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),c(X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2494,f296]) ).
fof(f8809,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),codomain(X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2493,f296]) ).
fof(f8810,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),divergence(X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2492,f296]) ).
fof(f8811,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),multiplication(X0,multiplication(X1,multiplication(X2,X3)))),X3)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f232,f296]) ).
fof(f8812,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),multiplication(X0,multiplication(X1,multiplication(X2,X3)))),X3)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f207,f296]) ).
fof(f8813,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),X3)),X2)
| ~ leq(multiplication(multiplication(X0,multiplication(X1,X2)),addition(X3,one)),X2) ),
inference(paramodulation,[status(thm)],[f192,f296]) ).
fof(f8814,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),X3)),X2)
| ~ leq(multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X3)),X2) ),
inference(paramodulation,[status(thm)],[f162,f296]) ).
fof(f8815,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),addition(X3,addition(multiplication(X0,multiplication(X1,X2)),X3))),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f99,f296]) ).
fof(f8816,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),addition(multiplication(X0,multiplication(X1,X2)),X3)),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f105,f296]) ).
fof(f8817,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X2,X3)),addition(X0,X1)),X4)
| ~ leq(addition(X0,addition(X1,multiplication(X2,multiplication(X3,X4)))),X4) ),
inference(paramodulation,[status(thm)],[f97,f296]) ).
fof(f8818,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X1,X2)),addition(X4,X0)),X3)
| ~ leq(addition(X0,addition(multiplication(X1,multiplication(X2,X3)),X4)),X3) ),
inference(paramodulation,[status(thm)],[f97,f296]) ).
fof(f8820,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),X0),X3)
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f35,f296]) ).
fof(f8821,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),X0),X3)
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f35,f296]) ).
fof(f8822,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f38,f296]) ).
fof(f8823,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(addition(antidomain(multiplication(X1,X2)),X0),X1)),X3),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f224,f296]) ).
fof(f8824,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(addition(X0,antidomain(multiplication(X1,X2))),X1)),X3),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f230,f296]) ).
fof(f8825,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(c(multiplication(X2,X1)),X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f4265,f296]) ).
fof(f8826,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(domain(multiplication(X0,X1)),X0)),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f4146,f296]) ).
fof(f8827,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(multiplication(X0,X1),X2)),X4),X3)
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),X3) ),
inference(paramodulation,[status(thm)],[f39,f296]) ).
fof(f8828,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(antidomain(X2),X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f136,f296]) ).
fof(f8829,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(antidomain(multiplication(X2,X1)),X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f59,f296]) ).
fof(f8830,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(zero,X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f45,f296]) ).
fof(f8832,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,coantidomain(X2))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f151,f296]) ).
fof(f8833,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X1,X2)),X0),coantidomain(multiplication(X1,X2)))
| ~ leq(addition(zero,X0),coantidomain(multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f144,f296]) ).
fof(f8834,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(one,X2))),X3),X1)
| ~ leq(addition(multiplication(X0,addition(X1,multiplication(X2,X1))),X3),X1) ),
inference(paramodulation,[status(thm)],[f207,f296]) ).
fof(f8835,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(antidomain(X2),X1))),X3),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f224,f296]) ).
fof(f8836,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(X2,one))),X3),X1)
| ~ leq(addition(multiplication(X0,addition(X1,multiplication(X2,X1))),X3),X1) ),
inference(paramodulation,[status(thm)],[f232,f296]) ).
fof(f8837,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(X1,antidomain(X2)))),X3),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f230,f296]) ).
fof(f8838,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(X1,X2))),X3),coantidomain(X2))
| ~ leq(addition(multiplication(X0,multiplication(X1,coantidomain(X2))),X3),coantidomain(X2)) ),
inference(paramodulation,[status(thm)],[f233,f296]) ).
fof(f8839,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(X2,X1))),X3),coantidomain(X2))
| ~ leq(addition(multiplication(X0,multiplication(X1,coantidomain(X2))),X3),coantidomain(X2)) ),
inference(paramodulation,[status(thm)],[f226,f296]) ).
fof(f8840,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,c(X2))),X1),domain(X2))
| ~ leq(addition(multiplication(X0,zero),X1),domain(X2)) ),
inference(paramodulation,[status(thm)],[f197,f296]) ).
fof(f8841,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,c(X2))),X1),X2)
| ~ leq(addition(multiplication(X0,zero),X1),X2) ),
inference(paramodulation,[status(thm)],[f4265,f296]) ).
fof(f8842,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,coantidomain(X2))),X1),codomain(X2))
| ~ leq(addition(multiplication(X0,zero),X1),codomain(X2)) ),
inference(paramodulation,[status(thm)],[f195,f296]) ).
fof(f8843,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,domain(X1))),X3),antidomain(X2))
| ~ leq(addition(multiplication(X0,domain_difference(X1,X2)),X3),antidomain(X2)) ),
inference(paramodulation,[status(thm)],[f68,f296]) ).
fof(f8844,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,domain(X1))),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f4146,f296]) ).
fof(f8845,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,multiplication(X1,X2))),X4),X3)
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),X3) ),
inference(paramodulation,[status(thm)],[f39,f296]) ).
fof(f8846,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,antidomain(X1))),X3),addition(X2,X1))
| ~ leq(addition(multiplication(X0,multiplication(antidomain(X1),X2)),X3),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f186,f296]) ).
fof(f8847,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,antidomain(X1))),X3),addition(X1,X2))
| ~ leq(addition(multiplication(X0,multiplication(antidomain(X1),X2)),X3),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f177,f296]) ).
fof(f8848,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,antidomain(X2))),X1),omega(X2))
| ~ leq(addition(multiplication(X0,zero),X1),omega(X2)) ),
inference(paramodulation,[status(thm)],[f1569,f296]) ).
fof(f8849,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,antidomain(X2))),X1),multiplication(X2,X3))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X2,X3)) ),
inference(paramodulation,[status(thm)],[f136,f296]) ).
fof(f8850,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,antidomain(X2))),X1),X2)
| ~ leq(addition(multiplication(X0,zero),X1),X2) ),
inference(paramodulation,[status(thm)],[f59,f296]) ).
fof(f8851,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,zero)),X1),X2)
| ~ leq(addition(multiplication(X0,zero),X1),X2) ),
inference(paramodulation,[status(thm)],[f45,f296]) ).
fof(f8853,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),X2),codomain(X1))
| ~ leq(addition(multiplication(X0,X1),X2),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f2309,f296]) ).
fof(f8854,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),addition(one,X2))
| ~ leq(addition(multiplication(X0,addition(X1,multiplication(X1,X2))),X3),addition(one,X2)) ),
inference(paramodulation,[status(thm)],[f162,f296]) ).
fof(f8855,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),addition(coantidomain(X1),X2))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),addition(coantidomain(X1),X2)) ),
inference(paramodulation,[status(thm)],[f181,f296]) ).
fof(f8856,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),addition(X2,one))
| ~ leq(addition(multiplication(X0,addition(X1,multiplication(X1,X2))),X3),addition(X2,one)) ),
inference(paramodulation,[status(thm)],[f192,f296]) ).
fof(f8857,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),addition(X2,coantidomain(X1)))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),addition(X2,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f190,f296]) ).
fof(f8858,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),X1),multiplication(coantidomain(X2),X3))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(coantidomain(X2),X3)) ),
inference(paramodulation,[status(thm)],[f151,f296]) ).
fof(f8859,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X3)),X1),multiplication(X2,coantidomain(multiplication(X3,X2))))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X2,coantidomain(multiplication(X3,X2)))) ),
inference(paramodulation,[status(thm)],[f144,f296]) ).
fof(f8860,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X2)),X1),omega(coantidomain(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),omega(coantidomain(X2))) ),
inference(paramodulation,[status(thm)],[f1813,f296]) ).
fof(f8861,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),X2),omega(X1))
| ~ leq(addition(multiplication(X0,omega(X1)),X2),omega(X1)) ),
inference(paramodulation,[status(thm)],[f56,f296]) ).
fof(f8862,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X2)),X1),coantidomain(X2))
| ~ leq(addition(multiplication(X0,zero),X1),coantidomain(X2)) ),
inference(paramodulation,[status(thm)],[f63,f296]) ).
fof(f8863,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X2)),X1),zero)
| ~ leq(addition(multiplication(X0,zero),X1),zero) ),
inference(paramodulation,[status(thm)],[f44,f296]) ).
fof(f8864,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),X2),one)
| ~ leq(addition(multiplication(X0,X1),X2),one) ),
inference(paramodulation,[status(thm)],[f40,f296]) ).
fof(f8865,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),domain(X3)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8805]) ).
fof(f8866,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,domain(X3))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8865]) ).
fof(f8867,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),coantidomain(X3)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8806]) ).
fof(f8868,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(X3))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8867]) ).
fof(f8869,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),antidomain(X3)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8807]) ).
fof(f8870,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,antidomain(X3))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8869]) ).
fof(f8871,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),c(X3)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8808]) ).
fof(f8872,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,c(X3))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8871]) ).
fof(f8873,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),codomain(X3)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8809]) ).
fof(f8874,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,codomain(X3))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8873]) ).
fof(f8875,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),divergence(X3)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8810]) ).
fof(f8876,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,divergence(X3))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8875]) ).
fof(f8877,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),X3)),X2)
| ~ leq(multiplication(X0,multiplication(multiplication(X1,X2),addition(X3,one))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8813]) ).
fof(f8878,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),X3)),X2)
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(X3,one)))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8877]) ).
fof(f8879,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(X3,one)))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8878]) ).
fof(f8880,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,X3)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(X3,one)))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8879]) ).
fof(f8881,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),X3)),X2)
| ~ leq(multiplication(X0,multiplication(multiplication(X1,X2),addition(one,X3))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8814]) ).
fof(f8882,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),X3)),X2)
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X3)))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8881]) ).
fof(f8883,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),X3))),X2)
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X3)))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8882]) ).
fof(f8884,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,X3)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X3)))),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f8883]) ).
fof(f8886,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(c(multiplication(X2,X1)),X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f8825]) ).
fof(f8887,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,multiplication(X1,X2))),X4),X3)
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),X3) ),
inference(forward_demodulation,[status(thm)],[f39,f8827]) ).
fof(f8888,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(antidomain(X2),X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f8828]) ).
fof(f8889,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f59,f8888]) ).
fof(f8890,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(antidomain(multiplication(X2,X1)),X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f8829]) ).
fof(f8891,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(zero,X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f8830]) ).
fof(f8892,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f45,f8891]) ).
fof(f8894,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,coantidomain(X2))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f8832]) ).
fof(f8895,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f63,f8894]) ).
fof(f8896,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X1,X2)),X0),coantidomain(multiplication(X1,X2)))
| ~ leq(X0,coantidomain(multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f8833]) ).
fof(f8897,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,c(X1))),X0),domain(X1))
| ~ leq(addition(zero,X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f8840]) ).
fof(f8898,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,c(X1))),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f8897]) ).
fof(f8899,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,c(X1))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f44,f8841]) ).
fof(f8900,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,c(X1))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f8899]) ).
fof(f8901,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,coantidomain(X1))),X0),codomain(X1))
| ~ leq(addition(zero,X0),codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f8842]) ).
fof(f8902,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,coantidomain(X1))),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f8901]) ).
fof(f8903,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),omega(X1))
| ~ leq(addition(zero,X0),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f8848]) ).
fof(f8904,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),omega(X1))
| ~ leq(X0,omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f8903]) ).
fof(f8905,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X3,antidomain(X1))),X0),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f8849]) ).
fof(f8906,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X3,antidomain(X1))),X0),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f8905]) ).
fof(f8907,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f44,f8850]) ).
fof(f8908,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f8907]) ).
fof(f8909,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,zero)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f44,f8851]) ).
fof(f8910,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,zero)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f8909]) ).
fof(f8911,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f44,f8910]) ).
fof(f8913,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X3,X1)),X0),multiplication(coantidomain(X1),X2))
| ~ leq(addition(zero,X0),multiplication(coantidomain(X1),X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f8858]) ).
fof(f8914,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X3,X1)),X0),multiplication(coantidomain(X1),X2))
| ~ leq(X0,multiplication(coantidomain(X1),X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f8913]) ).
fof(f8915,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X3,X2)),X0),multiplication(X1,coantidomain(multiplication(X2,X1))))
| ~ leq(addition(zero,X0),multiplication(X1,coantidomain(multiplication(X2,X1)))) ),
inference(forward_demodulation,[status(thm)],[f44,f8859]) ).
fof(f8916,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X3,X2)),X0),multiplication(X1,coantidomain(multiplication(X2,X1))))
| ~ leq(X0,multiplication(X1,coantidomain(multiplication(X2,X1)))) ),
inference(forward_demodulation,[status(thm)],[f80,f8915]) ).
fof(f8917,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),omega(coantidomain(X1)))
| ~ leq(addition(zero,X0),omega(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f44,f8860]) ).
fof(f8918,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),omega(coantidomain(X1)))
| ~ leq(X0,omega(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f80,f8917]) ).
fof(f8919,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),coantidomain(X1))
| ~ leq(addition(zero,X0),coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f8862]) ).
fof(f8920,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f8919]) ).
fof(f8921,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X1,X2)),X0),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f8863]) ).
fof(f8922,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X1,X2)),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f8921]) ).
fof(f8956,plain,
! [X0,X1] : leq(multiplication(star(antidomain(antidomain(X0))),domain_difference(X1,X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f304,f6998]) ).
fof(f8957,plain,
! [X0,X1] : leq(multiplication(star(antidomain(domain(X0))),domain_difference(X0,X1)),domain(X0)),
inference(resolution,[status(thm)],[f304,f3834]) ).
fof(f8958,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(forward_diamond(X1,X2),X0)),X0),
inference(resolution,[status(thm)],[f304,f7010]) ).
fof(f8959,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(forward_box(X1,X2),X0)),X0),
inference(resolution,[status(thm)],[f304,f6659]) ).
fof(f8960,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(backward_box(X1,X2),X0)),X0),
inference(resolution,[status(thm)],[f304,f6658]) ).
fof(f8961,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(backward_diamond(X1,X2),X0)),X0),
inference(resolution,[status(thm)],[f304,f6519]) ).
fof(f8962,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(coantidomain(X1),X0)),X0),
inference(resolution,[status(thm)],[f304,f7158]) ).
fof(f8963,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(domain(X1),X0)),X0),
inference(resolution,[status(thm)],[f304,f6808]) ).
fof(f8964,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X1),X0)),X0),
inference(resolution,[status(thm)],[f304,f6667]) ).
fof(f8965,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(c(X1),X0)),X0),
inference(resolution,[status(thm)],[f304,f6526]) ).
fof(f8966,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(codomain(X1),X0)),X0),
inference(resolution,[status(thm)],[f304,f6393]) ).
fof(f8967,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(divergence(X1),X0)),X0),
inference(resolution,[status(thm)],[f304,f5965]) ).
fof(f8968,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(X0,forward_diamond(X1,X2))),X0),
inference(resolution,[status(thm)],[f304,f4077]) ).
fof(f8969,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(X0,forward_box(X1,X2))),X0),
inference(resolution,[status(thm)],[f304,f3741]) ).
fof(f8970,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(X0,backward_box(X1,X2))),X0),
inference(resolution,[status(thm)],[f304,f3740]) ).
fof(f8971,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(X0,backward_diamond(X1,X2))),X0),
inference(resolution,[status(thm)],[f304,f3497]) ).
fof(f8972,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,coantidomain(X1))),X0),
inference(resolution,[status(thm)],[f304,f4627]) ).
fof(f8973,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,domain(X1))),X0),
inference(resolution,[status(thm)],[f304,f3841]) ).
fof(f8974,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,antidomain(X1))),X0),
inference(resolution,[status(thm)],[f304,f3749]) ).
fof(f8975,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,c(X1))),X0),
inference(resolution,[status(thm)],[f304,f3652]) ).
fof(f8976,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,codomain(X1))),X0),
inference(resolution,[status(thm)],[f304,f3411]) ).
fof(f8977,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,divergence(X1))),X0),
inference(resolution,[status(thm)],[f304,f3330]) ).
fof(f8978,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(star(X0))),backward_diamond(X1,X2)),star(X0)),
inference(resolution,[status(thm)],[f304,f7768]) ).
fof(f8979,plain,
! [X0,X1] : leq(multiplication(star(antidomain(one)),backward_diamond(X0,X1)),one),
inference(resolution,[status(thm)],[f304,f1473]) ).
fof(f8980,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(star(X0))),forward_box(X1,X2)),star(X0)),
inference(resolution,[status(thm)],[f304,f7762]) ).
fof(f8981,plain,
! [X0,X1] : leq(multiplication(star(antidomain(one)),forward_box(X0,X1)),one),
inference(resolution,[status(thm)],[f304,f1466]) ).
fof(f8982,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(star(X0))),backward_box(X1,X2)),star(X0)),
inference(resolution,[status(thm)],[f304,f7761]) ).
fof(f8983,plain,
! [X0,X1] : leq(multiplication(star(antidomain(one)),backward_box(X0,X1)),one),
inference(resolution,[status(thm)],[f304,f1465]) ).
fof(f8984,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(divergence(X0)))),divergence(X0)),codomain(divergence(X0))),
inference(resolution,[status(thm)],[f304,f6073]) ).
fof(f8985,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),divergence(X1)),star(X0)),
inference(resolution,[status(thm)],[f304,f7523]) ).
fof(f8986,plain,
! [X0] : leq(multiplication(star(antidomain(domain(divergence(X0)))),divergence(X0)),domain(divergence(X0))),
inference(resolution,[status(thm)],[f304,f4208]) ).
fof(f8987,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),divergence(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f304,f2232]) ).
fof(f8988,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),divergence(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f304,f1779]) ).
fof(f8989,plain,
! [X0] : leq(multiplication(star(antidomain(one)),divergence(X0)),one),
inference(resolution,[status(thm)],[f304,f1484]) ).
fof(f8990,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(star(X0))),forward_diamond(X1,X2)),star(X0)),
inference(resolution,[status(thm)],[f304,f7572]) ).
fof(f8991,plain,
! [X0,X1] : leq(multiplication(star(antidomain(one)),forward_diamond(X0,X1)),one),
inference(resolution,[status(thm)],[f304,f1427]) ).
fof(f8992,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(codomain(X0)))),codomain(X0)),codomain(codomain(X0))),
inference(resolution,[status(thm)],[f304,f6509]) ).
fof(f8993,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),codomain(X1)),star(X0)),
inference(resolution,[status(thm)],[f304,f7522]) ).
fof(f8994,plain,
! [X0] : leq(multiplication(star(antidomain(domain(codomain(X0)))),codomain(X0)),domain(codomain(X0))),
inference(resolution,[status(thm)],[f304,f4210]) ).
fof(f8995,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),codomain(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f304,f2247]) ).
fof(f8996,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),codomain(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f304,f1780]) ).
fof(f8997,plain,
! [X0] : leq(multiplication(star(antidomain(one)),codomain(X0)),one),
inference(resolution,[status(thm)],[f304,f1435]) ).
fof(f8998,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(c(X0)))),c(X0)),codomain(c(X0))),
inference(resolution,[status(thm)],[f304,f6648]) ).
fof(f8999,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),c(X1)),star(X0)),
inference(resolution,[status(thm)],[f304,f7521]) ).
fof(f9000,plain,
! [X0] : leq(multiplication(star(antidomain(domain(c(X0)))),c(X0)),domain(c(X0))),
inference(resolution,[status(thm)],[f304,f4206]) ).
fof(f9001,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),c(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f304,f2264]) ).
fof(f9002,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),c(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f304,f1781]) ).
fof(f9003,plain,
! [X0] : leq(multiplication(star(antidomain(one)),c(X0)),one),
inference(resolution,[status(thm)],[f304,f1430]) ).
fof(f9004,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(antidomain(X0)))),antidomain(X0)),codomain(antidomain(X0))),
inference(resolution,[status(thm)],[f304,f6796]) ).
fof(f9005,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),antidomain(X1)),star(X0)),
inference(resolution,[status(thm)],[f304,f7520]) ).
fof(f9006,plain,
! [X0] : leq(multiplication(star(antidomain(c(X0))),antidomain(X0)),c(X0)),
inference(resolution,[status(thm)],[f304,f4241]) ).
fof(f9007,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),antidomain(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f304,f2373]) ).
fof(f9008,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),antidomain(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f304,f1782]) ).
fof(f9009,plain,
! [X0] : leq(multiplication(star(antidomain(one)),antidomain(X0)),one),
inference(resolution,[status(thm)],[f304,f1412]) ).
fof(f9010,plain,
! [X0] : leq(multiplication(star(antidomain(coantidomain(codomain(X0)))),coantidomain(X0)),coantidomain(codomain(X0))),
inference(resolution,[status(thm)],[f304,f7305]) ).
fof(f9011,plain,
! [X0] : leq(multiplication(star(antidomain(domain(coantidomain(X0)))),coantidomain(X0)),domain(coantidomain(X0))),
inference(resolution,[status(thm)],[f304,f4735]) ).
fof(f9012,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),coantidomain(X1)),star(X0)),
inference(resolution,[status(thm)],[f304,f7519]) ).
fof(f9013,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),coantidomain(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f304,f2387]) ).
fof(f9014,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),coantidomain(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f304,f1783]) ).
fof(f9015,plain,
! [X0] : leq(multiplication(star(antidomain(one)),coantidomain(X0)),one),
inference(resolution,[status(thm)],[f304,f1410]) ).
fof(f9016,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(domain(X0)))),domain(X0)),codomain(domain(X0))),
inference(resolution,[status(thm)],[f304,f7000]) ).
fof(f9017,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),domain(X1)),star(X0)),
inference(resolution,[status(thm)],[f304,f7518]) ).
fof(f9018,plain,
! [X0] : leq(multiplication(star(antidomain(antidomain(c(X0)))),domain(X0)),antidomain(c(X0))),
inference(resolution,[status(thm)],[f304,f4249]) ).
fof(f9019,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),domain(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f304,f2403]) ).
fof(f9020,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),domain(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f304,f1784]) ).
fof(f9021,plain,
! [X0] : leq(multiplication(star(antidomain(one)),domain(X0)),one),
inference(resolution,[status(thm)],[f304,f1408]) ).
fof(f9022,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,star(X1)))),one),addition(X0,star(X1))),
inference(resolution,[status(thm)],[f304,f7532]) ).
fof(f9023,plain,
! [X0] : leq(multiplication(star(antidomain(star(X0))),one),star(X0)),
inference(resolution,[status(thm)],[f304,f7535]) ).
fof(f9025,plain,
! [X0] : leq(multiplication(star(antidomain(star(X0))),addition(one,multiplication(star(X0),X0))),star(X0)),
inference(resolution,[status(thm)],[f304,f51]) ).
fof(f9026,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(multiplication(X0,X1)))),addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))))),star(multiplication(X0,X1))),
inference(resolution,[status(thm)],[f304,f252]) ).
fof(f9027,plain,
! [X0] : leq(multiplication(star(antidomain(star(X0))),addition(one,multiplication(X0,star(X0)))),star(X0)),
inference(resolution,[status(thm)],[f304,f50]) ).
fof(f9028,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,addition(X1,X2)))),X1),addition(X0,addition(X1,X2))),
inference(resolution,[status(thm)],[f304,f1421]) ).
fof(f9029,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,addition(X1,X2)))),X2),addition(X0,addition(X1,X2))),
inference(resolution,[status(thm)],[f304,f1420]) ).
fof(f9030,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,X1))),X1),addition(X0,X1)),
inference(resolution,[status(thm)],[f304,f1423]) ).
fof(f9031,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,X1))),X0),addition(X0,X1)),
inference(resolution,[status(thm)],[f304,f1324]) ).
fof(f9032,plain,
! [X0] : leq(multiplication(star(antidomain(X0)),X0),X0),
inference(resolution,[status(thm)],[f304,f239]) ).
fof(f9033,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),domain_difference(X1,X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f8956]) ).
fof(f9034,plain,
! [X0,X1] : leq(multiplication(star(c(X0)),domain_difference(X0,X1)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f67,f8957]) ).
fof(f9035,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),backward_diamond(X0,X1)),star(X2)),
inference(forward_demodulation,[status(thm)],[f8455,f8978]) ).
fof(f9036,plain,
! [X0,X1] : leq(multiplication(star(zero),backward_diamond(X0,X1)),one),
inference(forward_demodulation,[status(thm)],[f119,f8979]) ).
fof(f9037,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),forward_box(X0,X1)),star(X2)),
inference(forward_demodulation,[status(thm)],[f8455,f8980]) ).
fof(f9038,plain,
! [X0,X1] : leq(multiplication(star(zero),forward_box(X0,X1)),one),
inference(forward_demodulation,[status(thm)],[f119,f8981]) ).
fof(f9039,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),backward_box(X0,X1)),star(X2)),
inference(forward_demodulation,[status(thm)],[f8455,f8982]) ).
fof(f9040,plain,
! [X0,X1] : leq(multiplication(star(zero),backward_box(X0,X1)),one),
inference(forward_demodulation,[status(thm)],[f119,f8983]) ).
fof(f9041,plain,
! [X0,X1] : leq(multiplication(star(zero),divergence(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8455,f8985]) ).
fof(f9042,plain,
! [X0] : leq(multiplication(star(c(divergence(X0))),divergence(X0)),domain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f67,f8986]) ).
fof(f9043,plain,
! [X0] : leq(multiplication(star(zero),divergence(X0)),one),
inference(forward_demodulation,[status(thm)],[f119,f8989]) ).
fof(f9044,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),forward_diamond(X0,X1)),star(X2)),
inference(forward_demodulation,[status(thm)],[f8455,f8990]) ).
fof(f9045,plain,
! [X0,X1] : leq(multiplication(star(zero),forward_diamond(X0,X1)),one),
inference(forward_demodulation,[status(thm)],[f119,f8991]) ).
fof(f9046,plain,
! [X0,X1] : leq(multiplication(star(zero),codomain(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8455,f8993]) ).
fof(f9047,plain,
! [X0] : leq(multiplication(star(c(codomain(X0))),codomain(X0)),domain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f67,f8994]) ).
fof(f9048,plain,
! [X0] : leq(multiplication(star(zero),codomain(X0)),one),
inference(forward_demodulation,[status(thm)],[f119,f8997]) ).
fof(f9049,plain,
! [X0,X1] : leq(multiplication(star(zero),c(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8455,f8999]) ).
fof(f9050,plain,
! [X0] : leq(multiplication(star(c(c(X0))),c(X0)),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f67,f9000]) ).
fof(f9051,plain,
! [X0] : leq(multiplication(star(zero),c(X0)),one),
inference(forward_demodulation,[status(thm)],[f119,f9003]) ).
fof(f9052,plain,
! [X0,X1] : leq(multiplication(star(zero),antidomain(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8455,f9005]) ).
fof(f9053,plain,
! [X0] : leq(multiplication(star(zero),antidomain(X0)),one),
inference(forward_demodulation,[status(thm)],[f119,f9009]) ).
fof(f9054,plain,
! [X0] : leq(multiplication(star(c(coantidomain(X0))),coantidomain(X0)),domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f67,f9011]) ).
fof(f9055,plain,
! [X0,X1] : leq(multiplication(star(zero),coantidomain(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8455,f9012]) ).
fof(f9056,plain,
! [X0] : leq(multiplication(star(zero),coantidomain(X0)),one),
inference(forward_demodulation,[status(thm)],[f119,f9015]) ).
fof(f9057,plain,
! [X0,X1] : leq(multiplication(star(zero),domain(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8455,f9017]) ).
fof(f9058,plain,
! [X0] : leq(multiplication(star(domain(c(X0))),domain(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f62,f9018]) ).
fof(f9059,plain,
! [X0] : leq(multiplication(star(zero),domain(X0)),one),
inference(forward_demodulation,[status(thm)],[f119,f9021]) ).
fof(f9060,plain,
! [X0,X1] : leq(star(antidomain(addition(X0,star(X1)))),addition(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f9022]) ).
fof(f9061,plain,
! [X0] : leq(star(antidomain(star(X0))),star(X0)),
inference(forward_demodulation,[status(thm)],[f40,f9023]) ).
fof(f9062,plain,
! [X0] : leq(star(zero),star(X0)),
inference(forward_demodulation,[status(thm)],[f8455,f9061]) ).
fof(f9064,plain,
! [X0] : leq(multiplication(star(zero),addition(one,multiplication(star(X0),X0))),star(X0)),
inference(forward_demodulation,[status(thm)],[f8455,f9025]) ).
fof(f9065,plain,
! [X0,X1] : leq(multiplication(star(zero),addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))))),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f8455,f9026]) ).
fof(f9066,plain,
! [X0] : leq(multiplication(star(zero),addition(one,multiplication(X0,star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f8455,f9027]) ).
fof(f9067,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(X0,star(X1)))),X0),multiplication(X0,star(X1))),
inference(resolution,[status(thm)],[f8449,f304]) ).
fof(f9068,plain,
! [X0,X1] : addition(X0,multiplication(X0,star(X1))) = multiplication(X0,star(X1)),
inference(resolution,[status(thm)],[f8449,f48]) ).
fof(f9073,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f39,f8449]) ).
fof(f9084,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(star(X0),X1))),X1),multiplication(star(X0),X1)),
inference(resolution,[status(thm)],[f8451,f304]) ).
fof(f9085,plain,
! [X0,X1] : addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(resolution,[status(thm)],[f8451,f48]) ).
fof(f9090,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(multiplication(star(X1),X0))),zero),
inference(paramodulation,[status(thm)],[f144,f8451]) ).
fof(f9108,plain,
! [X0,X1] : leq(multiplication(star(zero),domain_difference(X0,X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f305,f6998]) ).
fof(f9109,plain,
! [X0,X1] : leq(multiplication(star(zero),domain_difference(X0,X1)),domain(X0)),
inference(resolution,[status(thm)],[f305,f3834]) ).
fof(f9110,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(forward_diamond(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f305,f7010]) ).
fof(f9111,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(forward_box(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f305,f6659]) ).
fof(f9112,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(backward_box(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f305,f6658]) ).
fof(f9113,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(backward_diamond(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f305,f6519]) ).
fof(f9114,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(coantidomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f305,f7158]) ).
fof(f9115,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(domain(X0),X1)),X1),
inference(resolution,[status(thm)],[f305,f6808]) ).
fof(f9116,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(antidomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f305,f6667]) ).
fof(f9117,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(c(X0),X1)),X1),
inference(resolution,[status(thm)],[f305,f6526]) ).
fof(f9118,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(codomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f305,f6393]) ).
fof(f9119,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(divergence(X0),X1)),X1),
inference(resolution,[status(thm)],[f305,f5965]) ).
fof(f9120,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(X0,forward_diamond(X1,X2))),X0),
inference(resolution,[status(thm)],[f305,f4077]) ).
fof(f9121,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(X0,forward_box(X1,X2))),X0),
inference(resolution,[status(thm)],[f305,f3741]) ).
fof(f9122,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(X0,backward_box(X1,X2))),X0),
inference(resolution,[status(thm)],[f305,f3740]) ).
fof(f9123,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(X0,backward_diamond(X1,X2))),X0),
inference(resolution,[status(thm)],[f305,f3497]) ).
fof(f9124,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,coantidomain(X1))),X0),
inference(resolution,[status(thm)],[f305,f4627]) ).
fof(f9125,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,domain(X1))),X0),
inference(resolution,[status(thm)],[f305,f3841]) ).
fof(f9126,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,antidomain(X1))),X0),
inference(resolution,[status(thm)],[f305,f3749]) ).
fof(f9127,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,c(X1))),X0),
inference(resolution,[status(thm)],[f305,f3652]) ).
fof(f9128,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,codomain(X1))),X0),
inference(resolution,[status(thm)],[f305,f3411]) ).
fof(f9129,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,divergence(X1))),X0),
inference(resolution,[status(thm)],[f305,f3330]) ).
fof(f9130,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),backward_diamond(X0,X1)),star(X2)),
inference(resolution,[status(thm)],[f305,f7768]) ).
fof(f9131,plain,
! [X0,X1] : leq(multiplication(star(zero),backward_diamond(X0,X1)),one),
inference(resolution,[status(thm)],[f305,f1473]) ).
fof(f9132,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),forward_box(X0,X1)),star(X2)),
inference(resolution,[status(thm)],[f305,f7762]) ).
fof(f9133,plain,
! [X0,X1] : leq(multiplication(star(zero),forward_box(X0,X1)),one),
inference(resolution,[status(thm)],[f305,f1466]) ).
fof(f9134,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),backward_box(X0,X1)),star(X2)),
inference(resolution,[status(thm)],[f305,f7761]) ).
fof(f9135,plain,
! [X0,X1] : leq(multiplication(star(zero),backward_box(X0,X1)),one),
inference(resolution,[status(thm)],[f305,f1465]) ).
fof(f9136,plain,
! [X0] : leq(multiplication(star(zero),divergence(X0)),codomain(divergence(X0))),
inference(resolution,[status(thm)],[f305,f6073]) ).
fof(f9137,plain,
! [X0,X1] : leq(multiplication(star(zero),divergence(X0)),star(X1)),
inference(resolution,[status(thm)],[f305,f7523]) ).
fof(f9138,plain,
! [X0] : leq(multiplication(star(zero),divergence(X0)),domain(divergence(X0))),
inference(resolution,[status(thm)],[f305,f4208]) ).
fof(f9139,plain,
! [X0,X1] : leq(multiplication(star(zero),divergence(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f305,f2232]) ).
fof(f9140,plain,
! [X0,X1] : leq(multiplication(star(zero),divergence(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f305,f1779]) ).
fof(f9141,plain,
! [X0] : leq(multiplication(star(zero),divergence(X0)),one),
inference(resolution,[status(thm)],[f305,f1484]) ).
fof(f9142,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),forward_diamond(X0,X1)),star(X2)),
inference(resolution,[status(thm)],[f305,f7572]) ).
fof(f9143,plain,
! [X0,X1] : leq(multiplication(star(zero),forward_diamond(X0,X1)),one),
inference(resolution,[status(thm)],[f305,f1427]) ).
fof(f9144,plain,
! [X0] : leq(multiplication(star(zero),codomain(X0)),codomain(codomain(X0))),
inference(resolution,[status(thm)],[f305,f6509]) ).
fof(f9145,plain,
! [X0,X1] : leq(multiplication(star(zero),codomain(X0)),star(X1)),
inference(resolution,[status(thm)],[f305,f7522]) ).
fof(f9146,plain,
! [X0] : leq(multiplication(star(zero),codomain(X0)),domain(codomain(X0))),
inference(resolution,[status(thm)],[f305,f4210]) ).
fof(f9147,plain,
! [X0,X1] : leq(multiplication(star(zero),codomain(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f305,f2247]) ).
fof(f9148,plain,
! [X0,X1] : leq(multiplication(star(zero),codomain(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f305,f1780]) ).
fof(f9149,plain,
! [X0] : leq(multiplication(star(zero),codomain(X0)),one),
inference(resolution,[status(thm)],[f305,f1435]) ).
fof(f9150,plain,
! [X0] : leq(multiplication(star(zero),c(X0)),codomain(c(X0))),
inference(resolution,[status(thm)],[f305,f6648]) ).
fof(f9151,plain,
! [X0,X1] : leq(multiplication(star(zero),c(X0)),star(X1)),
inference(resolution,[status(thm)],[f305,f7521]) ).
fof(f9152,plain,
! [X0] : leq(multiplication(star(zero),c(X0)),domain(c(X0))),
inference(resolution,[status(thm)],[f305,f4206]) ).
fof(f9153,plain,
! [X0,X1] : leq(multiplication(star(zero),c(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f305,f2264]) ).
fof(f9154,plain,
! [X0,X1] : leq(multiplication(star(zero),c(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f305,f1781]) ).
fof(f9155,plain,
! [X0] : leq(multiplication(star(zero),c(X0)),one),
inference(resolution,[status(thm)],[f305,f1430]) ).
fof(f9156,plain,
! [X0] : leq(multiplication(star(zero),antidomain(X0)),codomain(antidomain(X0))),
inference(resolution,[status(thm)],[f305,f6796]) ).
fof(f9157,plain,
! [X0,X1] : leq(multiplication(star(zero),antidomain(X0)),star(X1)),
inference(resolution,[status(thm)],[f305,f7520]) ).
fof(f9158,plain,
! [X0] : leq(multiplication(star(zero),antidomain(X0)),c(X0)),
inference(resolution,[status(thm)],[f305,f4241]) ).
fof(f9159,plain,
! [X0,X1] : leq(multiplication(star(zero),antidomain(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f305,f2373]) ).
fof(f9160,plain,
! [X0,X1] : leq(multiplication(star(zero),antidomain(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f305,f1782]) ).
fof(f9161,plain,
! [X0] : leq(multiplication(star(zero),antidomain(X0)),one),
inference(resolution,[status(thm)],[f305,f1412]) ).
fof(f9162,plain,
! [X0] : leq(multiplication(star(zero),coantidomain(X0)),coantidomain(codomain(X0))),
inference(resolution,[status(thm)],[f305,f7305]) ).
fof(f9163,plain,
! [X0] : leq(multiplication(star(zero),coantidomain(X0)),domain(coantidomain(X0))),
inference(resolution,[status(thm)],[f305,f4735]) ).
fof(f9164,plain,
! [X0,X1] : leq(multiplication(star(zero),coantidomain(X0)),star(X1)),
inference(resolution,[status(thm)],[f305,f7519]) ).
fof(f9165,plain,
! [X0,X1] : leq(multiplication(star(zero),coantidomain(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f305,f2387]) ).
fof(f9166,plain,
! [X0,X1] : leq(multiplication(star(zero),coantidomain(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f305,f1783]) ).
fof(f9167,plain,
! [X0] : leq(multiplication(star(zero),coantidomain(X0)),one),
inference(resolution,[status(thm)],[f305,f1410]) ).
fof(f9168,plain,
! [X0] : leq(multiplication(star(zero),domain(X0)),codomain(domain(X0))),
inference(resolution,[status(thm)],[f305,f7000]) ).
fof(f9169,plain,
! [X0,X1] : leq(multiplication(star(zero),domain(X0)),star(X1)),
inference(resolution,[status(thm)],[f305,f7518]) ).
fof(f9170,plain,
! [X0] : leq(multiplication(star(zero),domain(X0)),antidomain(c(X0))),
inference(resolution,[status(thm)],[f305,f4249]) ).
fof(f9171,plain,
! [X0,X1] : leq(multiplication(star(zero),domain(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f305,f2403]) ).
fof(f9172,plain,
! [X0,X1] : leq(multiplication(star(zero),domain(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f305,f1784]) ).
fof(f9173,plain,
! [X0] : leq(multiplication(star(zero),domain(X0)),one),
inference(resolution,[status(thm)],[f305,f1408]) ).
fof(f9174,plain,
! [X0,X1] : leq(multiplication(star(zero),one),addition(X0,star(X1))),
inference(resolution,[status(thm)],[f305,f7532]) ).
fof(f9177,plain,
! [X0] : leq(multiplication(star(zero),addition(one,multiplication(star(X0),X0))),star(X0)),
inference(resolution,[status(thm)],[f305,f51]) ).
fof(f9178,plain,
! [X0,X1] : leq(multiplication(star(zero),addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))))),star(multiplication(X0,X1))),
inference(resolution,[status(thm)],[f305,f252]) ).
fof(f9179,plain,
! [X0] : leq(multiplication(star(zero),addition(one,multiplication(X0,star(X0)))),star(X0)),
inference(resolution,[status(thm)],[f305,f50]) ).
fof(f9180,plain,
! [X0,X1] : leq(multiplication(star(zero),X0),multiplication(star(X1),X0)),
inference(resolution,[status(thm)],[f305,f8451]) ).
fof(f9181,plain,
! [X0,X1] : leq(multiplication(star(zero),X0),multiplication(X0,star(X1))),
inference(resolution,[status(thm)],[f305,f8449]) ).
fof(f9182,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),X0),addition(X1,addition(X0,X2))),
inference(resolution,[status(thm)],[f305,f1421]) ).
fof(f9183,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),X0),addition(X1,addition(X2,X0))),
inference(resolution,[status(thm)],[f305,f1420]) ).
fof(f9184,plain,
! [X0,X1] : leq(multiplication(star(zero),X0),addition(X1,X0)),
inference(resolution,[status(thm)],[f305,f1423]) ).
fof(f9185,plain,
! [X0,X1] : leq(multiplication(star(zero),X0),addition(X0,X1)),
inference(resolution,[status(thm)],[f305,f1324]) ).
fof(f9187,plain,
! [X0,X1] : leq(star(zero),addition(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f9174]) ).
fof(f9248,plain,
! [X0] :
( leq(multiplication(star(one),star(X0)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7563,f299]) ).
fof(f9249,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(star(X0),addition(X0,one))),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7789,f299]) ).
fof(f9250,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(addition(X0,one),star(X0))),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7510,f299]) ).
fof(f9251,plain,
! [X0,X1] :
( leq(multiplication(star(one),backward_diamond(X0,X1)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1504,f299]) ).
fof(f9252,plain,
! [X0,X1] :
( leq(multiplication(star(one),forward_box(X0,X1)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1497,f299]) ).
fof(f9253,plain,
! [X0,X1] :
( leq(multiplication(star(one),backward_box(X0,X1)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1492,f299]) ).
fof(f9254,plain,
! [X0,X1] :
( leq(multiplication(star(one),forward_diamond(X0,X1)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1485,f299]) ).
fof(f9255,plain,
! [X0] :
( leq(multiplication(star(one),divergence(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1488,f299]) ).
fof(f9256,plain,
! [X0] :
( leq(multiplication(star(one),codomain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1477,f299]) ).
fof(f9257,plain,
! [X0] :
( leq(multiplication(star(one),c(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1471,f299]) ).
fof(f9258,plain,
! [X0] :
( leq(multiplication(star(one),antidomain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1379,f299]) ).
fof(f9259,plain,
! [X0] :
( leq(multiplication(star(one),coantidomain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1377,f299]) ).
fof(f9260,plain,
! [X0] :
( leq(multiplication(star(one),domain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1375,f299]) ).
fof(f9261,plain,
! [X0] :
( leq(multiplication(star(one),c(X0)),domain(X0))
| ~ leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f569,f299]) ).
fof(f9262,plain,
! [X0,X1] :
( leq(multiplication(star(one),coantidomain(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,X1)))
| ~ leq(coantidomain(multiplication(codomain(X0),X1)),coantidomain(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f615,f299]) ).
fof(f9263,plain,
! [X0] :
( leq(multiplication(star(one),codomain(X0)),coantidomain(X0))
| ~ leq(one,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f683,f299]) ).
fof(f9264,plain,
! [X0,X1] :
( leq(multiplication(star(one),antidomain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,X1)))
| ~ leq(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f479,f299]) ).
fof(f9265,plain,
! [X0] :
( leq(multiplication(star(one),domain(X0)),antidomain(X0))
| ~ leq(one,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f558,f299]) ).
fof(f9266,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(one),multiplication(X2,X3)),multiplication(X0,multiplication(X1,X3)))
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(X0,multiplication(X1,X3))) ),
inference(paramodulation,[status(thm)],[f204,f299]) ).
fof(f9267,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(one),addition(multiplication(X1,X2),X3)),multiplication(X0,X2))
| ~ leq(addition(multiplication(addition(X0,X1),X2),X3),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f219,f299]) ).
fof(f9268,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(one),addition(multiplication(X0,X2),X3)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,addition(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f170,f299]) ).
fof(f9269,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(one),multiplication(X1,multiplication(X2,X3))),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f211,f299]) ).
fof(f9270,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(X0,X2)),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f201,f299]) ).
fof(f9271,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(X0,X1)),multiplication(X0,X2))
| ~ leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f153,f299]) ).
fof(f9272,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(X1,X2)),multiplication(X0,X2))
| ~ leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f43,f299]) ).
fof(f9273,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(X0,X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f42,f299]) ).
fof(f9274,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),X2),addition(X1,X0))
| ~ leq(addition(X0,addition(X1,X2)),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f103,f299]) ).
fof(f9275,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),X2),addition(X0,X1))
| ~ leq(addition(X0,addition(X1,X2)),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f36,f299]) ).
fof(f9276,plain,
! [X0] :
( leq(multiplication(star(one),X0),zero)
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f80,f299]) ).
fof(f9277,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(domain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4516,f299]) ).
fof(f9278,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(coantidomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4515,f299]) ).
fof(f9279,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(antidomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4514,f299]) ).
fof(f9280,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(c(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4513,f299]) ).
fof(f9281,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(codomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4512,f299]) ).
fof(f9282,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(divergence(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4511,f299]) ).
fof(f9283,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,domain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2497,f299]) ).
fof(f9284,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,coantidomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2496,f299]) ).
fof(f9285,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,antidomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2495,f299]) ).
fof(f9286,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,c(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2494,f299]) ).
fof(f9287,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,codomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2493,f299]) ).
fof(f9288,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,divergence(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2492,f299]) ).
fof(f9289,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,X1)),X1)
| ~ leq(multiplication(addition(X0,one),X1),X1) ),
inference(paramodulation,[status(thm)],[f232,f299]) ).
fof(f9291,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,X1)),X0)
| ~ leq(multiplication(X0,addition(X1,one)),X0) ),
inference(paramodulation,[status(thm)],[f192,f299]) ).
fof(f9292,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,X1)),X0)
| ~ leq(multiplication(X0,addition(one,X1)),X0) ),
inference(paramodulation,[status(thm)],[f162,f299]) ).
fof(f9293,plain,
! [X0,X1] :
( leq(multiplication(star(one),addition(X1,addition(X0,X1))),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f99,f299]) ).
fof(f9294,plain,
! [X0,X1] :
( leq(multiplication(star(one),addition(X0,X1)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f105,f299]) ).
fof(f9295,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),addition(X0,X1)),X2)
| ~ leq(addition(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f97,f299]) ).
fof(f9296,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),addition(X2,X0)),X1)
| ~ leq(addition(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f97,f299]) ).
fof(f9298,plain,
! [X0,X1] :
( leq(multiplication(star(one),X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f35,f299]) ).
fof(f9299,plain,
! [X0,X1] :
( leq(multiplication(star(one),X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f35,f299]) ).
fof(f9301,definition,
( sQ14_spl
<=> leq(one,one) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f9303,plain,
( sQ14_spl
| ~ leq(one,one) ),
inference(component_clause,[status(thm)],[f9301]) ).
fof(f9304,definition,
! [X0,X1] :
( sQ15_spl
<=> leq(multiplication(star(one),backward_diamond(X0,X1)),one) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f9305,plain,
! [X0,X1] :
( ~ sQ15_spl
| leq(multiplication(star(one),backward_diamond(X0,X1)),one) ),
inference(component_clause,[status(thm)],[f9304]) ).
fof(f9307,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9251,f9301,f9304]) ).
fof(f9308,definition,
! [X0,X1] :
( sQ16_spl
<=> leq(multiplication(star(one),forward_box(X0,X1)),one) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f9309,plain,
! [X0,X1] :
( ~ sQ16_spl
| leq(multiplication(star(one),forward_box(X0,X1)),one) ),
inference(component_clause,[status(thm)],[f9308]) ).
fof(f9311,plain,
( sQ16_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9252,f9301,f9308]) ).
fof(f9312,definition,
! [X0,X1] :
( sQ17_spl
<=> leq(multiplication(star(one),backward_box(X0,X1)),one) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f9313,plain,
! [X0,X1] :
( ~ sQ17_spl
| leq(multiplication(star(one),backward_box(X0,X1)),one) ),
inference(component_clause,[status(thm)],[f9312]) ).
fof(f9315,plain,
( sQ17_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9253,f9301,f9312]) ).
fof(f9316,definition,
! [X0,X1] :
( sQ18_spl
<=> leq(multiplication(star(one),forward_diamond(X0,X1)),one) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f9317,plain,
! [X0,X1] :
( ~ sQ18_spl
| leq(multiplication(star(one),forward_diamond(X0,X1)),one) ),
inference(component_clause,[status(thm)],[f9316]) ).
fof(f9319,plain,
( sQ18_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9254,f9301,f9316]) ).
fof(f9320,definition,
! [X0] :
( sQ19_spl
<=> leq(multiplication(star(one),divergence(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f9321,plain,
! [X0] :
( ~ sQ19_spl
| leq(multiplication(star(one),divergence(X0)),one) ),
inference(component_clause,[status(thm)],[f9320]) ).
fof(f9323,plain,
( sQ19_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9255,f9301,f9320]) ).
fof(f9324,definition,
! [X0] :
( sQ20_spl
<=> leq(multiplication(star(one),codomain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f9325,plain,
! [X0] :
( ~ sQ20_spl
| leq(multiplication(star(one),codomain(X0)),one) ),
inference(component_clause,[status(thm)],[f9324]) ).
fof(f9327,plain,
( sQ20_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9256,f9301,f9324]) ).
fof(f9328,definition,
! [X0] :
( sQ21_spl
<=> leq(multiplication(star(one),c(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f9329,plain,
! [X0] :
( ~ sQ21_spl
| leq(multiplication(star(one),c(X0)),one) ),
inference(component_clause,[status(thm)],[f9328]) ).
fof(f9331,plain,
( sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9257,f9301,f9328]) ).
fof(f9332,definition,
! [X0] :
( sQ22_spl
<=> leq(multiplication(star(one),antidomain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f9333,plain,
! [X0] :
( ~ sQ22_spl
| leq(multiplication(star(one),antidomain(X0)),one) ),
inference(component_clause,[status(thm)],[f9332]) ).
fof(f9335,plain,
( sQ22_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9258,f9301,f9332]) ).
fof(f9336,definition,
! [X0] :
( sQ23_spl
<=> leq(multiplication(star(one),coantidomain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f9337,plain,
! [X0] :
( ~ sQ23_spl
| leq(multiplication(star(one),coantidomain(X0)),one) ),
inference(component_clause,[status(thm)],[f9336]) ).
fof(f9339,plain,
( sQ23_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9259,f9301,f9336]) ).
fof(f9340,definition,
! [X0] :
( sQ24_spl
<=> leq(multiplication(star(one),domain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f9341,plain,
! [X0] :
( ~ sQ24_spl
| leq(multiplication(star(one),domain(X0)),one) ),
inference(component_clause,[status(thm)],[f9340]) ).
fof(f9343,plain,
( sQ24_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9260,f9301,f9340]) ).
fof(f9344,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(domain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9277,f239]) ).
fof(f9345,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(coantidomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9278,f239]) ).
fof(f9346,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(antidomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9279,f239]) ).
fof(f9347,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(c(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9280,f239]) ).
fof(f9348,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(codomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9281,f239]) ).
fof(f9349,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(divergence(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9282,f239]) ).
fof(f9350,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,domain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9283,f239]) ).
fof(f9351,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,coantidomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9284,f239]) ).
fof(f9352,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,antidomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9285,f239]) ).
fof(f9353,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,c(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9286,f239]) ).
fof(f9354,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,codomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9287,f239]) ).
fof(f9355,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,divergence(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9288,f239]) ).
fof(f9358,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9303,f239]) ).
fof(f9359,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f9358]) ).
fof(f9361,plain,
! [X0] : leq(multiplication(star(zero),star(zero)),star(X0)),
inference(resolution,[status(thm)],[f9062,f305]) ).
fof(f9362,plain,
! [X0] : leq(multiplication(star(antidomain(star(X0))),star(zero)),star(X0)),
inference(resolution,[status(thm)],[f9062,f304]) ).
fof(f9363,plain,
! [X0] : addition(star(zero),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f9062,f48]) ).
fof(f9364,plain,
! [X0] : leq(multiplication(star(zero),star(zero)),star(X0)),
inference(forward_demodulation,[status(thm)],[f8455,f9362]) ).
fof(f9365,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(forward_diamond(X1,X2),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f7010]) ).
fof(f9366,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(forward_box(X1,X2),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f6659]) ).
fof(f9367,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(backward_box(X1,X2),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f6658]) ).
fof(f9368,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(backward_diamond(X1,X2),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f6519]) ).
fof(f9369,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f7158]) ).
fof(f9370,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(domain(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f6808]) ).
fof(f9371,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(antidomain(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f6667]) ).
fof(f9372,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(c(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f6526]) ).
fof(f9373,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(codomain(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f6393]) ).
fof(f9374,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(divergence(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f5965]) ).
fof(f9375,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(coantidomain(X0),forward_diamond(X1,X2))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f4077]) ).
fof(f9376,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(coantidomain(X0),forward_box(X1,X2))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f3741]) ).
fof(f9377,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(coantidomain(X0),backward_box(X1,X2))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f3740]) ).
fof(f9378,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(coantidomain(X0),backward_diamond(X1,X2))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f3497]) ).
fof(f9379,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),coantidomain(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f4627]) ).
fof(f9380,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),domain(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f3841]) ).
fof(f9381,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),antidomain(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f3749]) ).
fof(f9382,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),c(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f3652]) ).
fof(f9383,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),codomain(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f3411]) ).
fof(f9384,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),divergence(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f3330]) ).
fof(f9385,plain,
! [X0] : leq(multiplication(star(codomain(X0)),coantidomain(X0)),coantidomain(codomain(X0))),
inference(resolution,[status(thm)],[f306,f7305]) ).
fof(f9387,plain,
! [X0] : leq(multiplication(star(X0),coantidomain(X0)),coantidomain(X0)),
inference(resolution,[status(thm)],[f306,f239]) ).
fof(f9388,plain,
! [X0,X1] :
( leq(multiplication(star(star(X1)),X0),coantidomain(star(X1)))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f8453,f306]) ).
fof(f9390,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),coantidomain(coantidomain(X1)))
| ~ leq(X0,codomain(X1)) ),
inference(paramodulation,[status(thm)],[f66,f306]) ).
fof(f9391,plain,
! [X0] :
( leq(multiplication(star(one),X0),coantidomain(one))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f146,f306]) ).
fof(f9393,plain,
! [X0,X1] :
( leq(multiplication(star(star(X1)),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f8453,f9388]) ).
fof(f9395,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f66,f9390]) ).
fof(f9396,plain,
! [X0] :
( leq(multiplication(star(one),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f146,f9391]) ).
fof(f9461,plain,
! [X0,X1] : leq(multiplication(star(zero),one),addition(star(X0),X1)),
inference(resolution,[status(thm)],[f8413,f305]) ).
fof(f9462,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(star(X0),X1))),one),addition(star(X0),X1)),
inference(resolution,[status(thm)],[f8413,f304]) ).
fof(f9463,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(resolution,[status(thm)],[f8413,f48]) ).
fof(f9476,plain,
! [X0,X1] : leq(one,multiplication(addition(X0,one),star(X1))),
inference(paramodulation,[status(thm)],[f232,f8413]) ).
fof(f9477,plain,
! [X0,X1] : leq(one,multiplication(addition(one,X0),star(X1))),
inference(paramodulation,[status(thm)],[f207,f8413]) ).
fof(f9478,plain,
! [X0,X1] : leq(one,multiplication(star(X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f192,f8413]) ).
fof(f9479,plain,
! [X0,X1] : leq(one,multiplication(star(X0),addition(one,X1))),
inference(paramodulation,[status(thm)],[f162,f8413]) ).
fof(f9482,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f97,f8413]) ).
fof(f9483,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(star(X1),X2))),
inference(paramodulation,[status(thm)],[f97,f8413]) ).
fof(f9488,plain,
! [X0,X1] : leq(star(zero),addition(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f40,f9461]) ).
fof(f9489,plain,
! [X0,X1] : leq(star(antidomain(addition(star(X0),X1))),addition(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f40,f9462]) ).
fof(f9490,plain,
! [X0] :
( leq(multiplication(star(one),star(X0)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7563,f302]) ).
fof(f9491,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(star(X0),addition(X0,one))),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7789,f302]) ).
fof(f9492,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(addition(X0,one),star(X0))),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7510,f302]) ).
fof(f9503,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),c(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f569,f302]) ).
fof(f9504,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),X1))),one)
| ~ leq(coantidomain(multiplication(codomain(X0),X1)),one) ),
inference(paramodulation,[status(thm)],[f615,f302]) ).
fof(f9505,plain,
! [X0] :
( leq(multiplication(star(coantidomain(X0)),codomain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f683,f302]) ).
fof(f9506,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))),one)
| ~ leq(antidomain(multiplication(X0,domain(X1))),one) ),
inference(paramodulation,[status(thm)],[f479,f302]) ).
fof(f9507,plain,
! [X0] :
( leq(multiplication(star(antidomain(X0)),domain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f558,f302]) ).
fof(f9508,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,multiplication(X1,X3))),multiplication(X2,X3)),one)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),one) ),
inference(paramodulation,[status(thm)],[f204,f302]) ).
fof(f9509,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X2)),addition(multiplication(X1,X2),X3)),one)
| ~ leq(addition(multiplication(addition(X0,X1),X2),X3),one) ),
inference(paramodulation,[status(thm)],[f219,f302]) ).
fof(f9510,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),addition(multiplication(X0,X2),X3)),one)
| ~ leq(addition(multiplication(X0,addition(X1,X2)),X3),one) ),
inference(paramodulation,[status(thm)],[f170,f302]) ).
fof(f9511,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X3)),multiplication(X1,multiplication(X2,X3))),one)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),one) ),
inference(paramodulation,[status(thm)],[f211,f302]) ).
fof(f9512,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X1,X2)),multiplication(X0,X2)),one)
| ~ leq(multiplication(addition(X0,X1),X2),one) ),
inference(paramodulation,[status(thm)],[f201,f302]) ).
fof(f9513,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(X0,X1)),one)
| ~ leq(multiplication(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f153,f302]) ).
fof(f9514,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X2)),multiplication(X1,X2)),one)
| ~ leq(multiplication(addition(X0,X1),X2),one) ),
inference(paramodulation,[status(thm)],[f43,f302]) ).
fof(f9515,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,X2)),one)
| ~ leq(multiplication(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f42,f302]) ).
fof(f9516,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,X0)),X2),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f103,f302]) ).
fof(f9517,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,X1)),X2),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f36,f302]) ).
fof(f9519,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(domain(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4516,f302]) ).
fof(f9520,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(coantidomain(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4515,f302]) ).
fof(f9521,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(antidomain(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4514,f302]) ).
fof(f9522,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(c(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4513,f302]) ).
fof(f9523,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(codomain(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4512,f302]) ).
fof(f9524,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(divergence(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4511,f302]) ).
fof(f9525,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2497,f302]) ).
fof(f9526,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,coantidomain(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2496,f302]) ).
fof(f9527,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2495,f302]) ).
fof(f9528,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2494,f302]) ).
fof(f9529,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2493,f302]) ).
fof(f9530,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,divergence(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2492,f302]) ).
fof(f9531,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,X1)),one)
| ~ leq(multiplication(addition(X0,one),X1),one) ),
inference(paramodulation,[status(thm)],[f232,f302]) ).
fof(f9532,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,X1)),one)
| ~ leq(multiplication(addition(one,X0),X1),one) ),
inference(paramodulation,[status(thm)],[f207,f302]) ).
fof(f9533,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),one)
| ~ leq(multiplication(X0,addition(X1,one)),one) ),
inference(paramodulation,[status(thm)],[f192,f302]) ).
fof(f9535,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(X1,addition(X0,X1))),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f99,f302]) ).
fof(f9536,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(X0,X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f105,f302]) ).
fof(f9537,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X2),addition(X0,X1)),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f97,f302]) ).
fof(f9538,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(X2,X0)),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f97,f302]) ).
fof(f9540,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f35,f302]) ).
fof(f9541,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f35,f302]) ).
fof(f9542,plain,
! [X0] :
( leq(multiplication(star(X0),X0),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f38,f302]) ).
fof(f9553,definition,
! [X0] :
( sQ25_spl
<=> leq(multiplication(star(domain(X0)),c(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f9554,plain,
! [X0] :
( ~ sQ25_spl
| leq(multiplication(star(domain(X0)),c(X0)),one) ),
inference(component_clause,[status(thm)],[f9553]) ).
fof(f9556,plain,
( sQ25_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9503,f9301,f9553]) ).
fof(f9557,plain,
! [X0,X1] : leq(multiplication(star(coantidomain(multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),X1))),one),
inference(forward_subsumption_resolution,[status(thm)],[f9504,f1410]) ).
fof(f9558,definition,
! [X0] :
( sQ26_spl
<=> leq(multiplication(star(coantidomain(X0)),codomain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f9559,plain,
! [X0] :
( ~ sQ26_spl
| leq(multiplication(star(coantidomain(X0)),codomain(X0)),one) ),
inference(component_clause,[status(thm)],[f9558]) ).
fof(f9561,plain,
( sQ26_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9505,f9301,f9558]) ).
fof(f9562,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))),one),
inference(forward_subsumption_resolution,[status(thm)],[f9506,f1412]) ).
fof(f9563,definition,
! [X0] :
( sQ27_spl
<=> leq(multiplication(star(antidomain(X0)),domain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f9564,plain,
! [X0] :
( ~ sQ27_spl
| leq(multiplication(star(antidomain(X0)),domain(X0)),one) ),
inference(component_clause,[status(thm)],[f9563]) ).
fof(f9566,plain,
( sQ27_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9507,f9301,f9563]) ).
fof(f9569,plain,
! [X0] : leq(multiplication(star(star(one)),multiplication(star(one),X0)),X0),
inference(resolution,[status(thm)],[f8659,f295]) ).
fof(f9571,plain,
! [X0] : leq(multiplication(star(X0),multiplication(star(one),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f8659,f306]) ).
fof(f9572,plain,
! [X0] : leq(multiplication(star(zero),multiplication(star(one),X0)),X0),
inference(resolution,[status(thm)],[f8659,f305]) ).
fof(f9573,plain,
! [X0] : leq(multiplication(star(antidomain(X0)),multiplication(star(one),X0)),X0),
inference(resolution,[status(thm)],[f8659,f304]) ).
fof(f9574,plain,
! [X0] : addition(multiplication(star(one),X0),X0) = X0,
inference(resolution,[status(thm)],[f8659,f48]) ).
fof(f9575,plain,
leq(star(one),codomain(star(one))),
inference(paramodulation,[status(thm)],[f2309,f8659]) ).
fof(f9587,plain,
! [X0] : addition(X0,multiplication(star(one),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f35,f9574]) ).
fof(f9588,plain,
leq(star(one),one),
inference(forward_demodulation,[status(thm)],[f8498,f9575]) ).
fof(f9598,plain,
leq(multiplication(star(zero),star(one)),one),
inference(resolution,[status(thm)],[f9588,f305]) ).
fof(f9599,plain,
leq(multiplication(star(antidomain(one)),star(one)),one),
inference(resolution,[status(thm)],[f9588,f304]) ).
fof(f9600,plain,
addition(star(one),one) = one,
inference(resolution,[status(thm)],[f9588,f48]) ).
fof(f9601,plain,
leq(multiplication(star(zero),star(one)),one),
inference(forward_demodulation,[status(thm)],[f119,f9599]) ).
fof(f9602,plain,
addition(one,star(one)) = one,
inference(forward_demodulation,[status(thm)],[f35,f9600]) ).
fof(f9603,plain,
star(one) = one,
inference(forward_demodulation,[status(thm)],[f7563,f9602]) ).
fof(f9606,plain,
! [X0,X1] :
( leq(multiplication(one,X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(backward_demodulation,[status(thm)],[f9603,f299]) ).
fof(f9608,plain,
leq(star(zero),one),
inference(paramodulation,[status(thm)],[f9603,f9062]) ).
fof(f9642,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f41,f9606]) ).
fof(f9665,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(multiplication(X0,X1),X2))))) = omega(multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f39,f308]) ).
fof(f9670,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(X0,multiplication(X1,X2)))))) = omega(multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f39,f308]) ).
fof(f9673,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,omega(addition(X1,multiplication(X0,X1))))) = omega(multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f207,f308]) ).
fof(f9674,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),multiplication(X0,omega(multiplication(X1,X0)))) = omega(multiplication(addition(antidomain(X0),X1),X0)),
inference(paramodulation,[status(thm)],[f224,f308]) ).
fof(f9675,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,omega(addition(X1,multiplication(X0,X1))))) = omega(multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f232,f308]) ).
fof(f9676,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,omega(multiplication(X0,X1)))) = omega(multiplication(addition(X0,antidomain(X1)),X1)),
inference(paramodulation,[status(thm)],[f230,f308]) ).
fof(f9677,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),omega(multiplication(X0,coantidomain(X1))))) = omega(multiplication(addition(X0,X1),coantidomain(X1))),
inference(paramodulation,[status(thm)],[f233,f308]) ).
fof(f9678,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),omega(multiplication(X1,coantidomain(X0))))) = omega(multiplication(addition(X0,X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f226,f308]) ).
fof(f9682,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),omega(domain_difference(X0,X1)))) = omega(multiplication(domain(X0),antidomain(X1))),
inference(paramodulation,[status(thm)],[f68,f308]) ).
fof(f9683,plain,
! [X0] : multiplication(domain(X0),multiplication(X0,omega(X0))) = omega(multiplication(domain(X0),X0)),
inference(paramodulation,[status(thm)],[f4146,f308]) ).
fof(f9684,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),multiplication(X2,omega(multiplication(X0,multiplication(X1,X2))))) = omega(multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f39,f308]) ).
fof(f9685,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,X0),omega(multiplication(antidomain(X0),X1)))) = omega(multiplication(antidomain(X0),addition(X1,X0))),
inference(paramodulation,[status(thm)],[f186,f308]) ).
fof(f9686,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X0,X1),omega(multiplication(antidomain(X0),X1)))) = omega(multiplication(antidomain(X0),addition(X0,X1))),
inference(paramodulation,[status(thm)],[f177,f308]) ).
fof(f9692,plain,
! [X0] : multiplication(X0,multiplication(codomain(X0),omega(X0))) = omega(multiplication(X0,codomain(X0))),
inference(paramodulation,[status(thm)],[f2309,f308]) ).
fof(f9693,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),omega(addition(X0,multiplication(X0,X1))))) = omega(multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f162,f308]) ).
fof(f9694,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),omega(multiplication(X0,X1)))) = omega(multiplication(X0,addition(coantidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f181,f308]) ).
fof(f9695,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),omega(addition(X0,multiplication(X0,X1))))) = omega(multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f192,f308]) ).
fof(f9696,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),omega(multiplication(X0,X1)))) = omega(multiplication(X0,addition(X1,coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f190,f308]) ).
fof(f9698,plain,
! [X0,X1] : multiplication(X0,multiplication(multiplication(X1,omega(multiplication(X0,X1))),omega(omega(multiplication(X0,X1))))) = omega(multiplication(X0,multiplication(X1,omega(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f308,f308]) ).
fof(f9701,plain,
! [X0] : multiplication(X0,multiplication(omega(X0),omega(omega(X0)))) = omega(multiplication(X0,omega(X0))),
inference(paramodulation,[status(thm)],[f56,f308]) ).
fof(f9705,plain,
! [X0,X1,X2] : leq(omega(multiplication(forward_diamond(X0,X1),X2)),multiplication(X2,omega(multiplication(forward_diamond(X0,X1),X2)))),
inference(paramodulation,[status(thm)],[f308,f7010]) ).
fof(f9706,plain,
! [X0,X1,X2] : leq(omega(multiplication(forward_box(X0,X1),X2)),multiplication(X2,omega(multiplication(forward_box(X0,X1),X2)))),
inference(paramodulation,[status(thm)],[f308,f6659]) ).
fof(f9707,plain,
! [X0,X1,X2] : leq(omega(multiplication(backward_box(X0,X1),X2)),multiplication(X2,omega(multiplication(backward_box(X0,X1),X2)))),
inference(paramodulation,[status(thm)],[f308,f6658]) ).
fof(f9708,plain,
! [X0,X1,X2] : leq(omega(multiplication(backward_diamond(X0,X1),X2)),multiplication(X2,omega(multiplication(backward_diamond(X0,X1),X2)))),
inference(paramodulation,[status(thm)],[f308,f6519]) ).
fof(f9709,plain,
! [X0,X1] : leq(omega(multiplication(divergence(X0),X1)),multiplication(X1,omega(multiplication(divergence(X0),X1)))),
inference(paramodulation,[status(thm)],[f308,f5965]) ).
fof(f9710,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(divergence(X1),X0))) = addition(multiplication(X0,omega(multiplication(divergence(X1),X0))),omega(multiplication(divergence(X1),X0))),
inference(paramodulation,[status(thm)],[f308,f4511]) ).
fof(f9711,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,multiplication(X2,omega(multiplication(addition(X0,X1),X2))))),multiplication(X2,omega(multiplication(addition(X0,X1),X2))))
| ~ leq(omega(multiplication(addition(X0,X1),X2)),multiplication(X2,omega(multiplication(addition(X0,X1),X2)))) ),
inference(paramodulation,[status(thm)],[f308,f290]) ).
fof(f9712,plain,
! [X0,X1,X2] :
( omega(multiplication(addition(X0,X2),X1)) != multiplication(X2,multiplication(X1,omega(multiplication(addition(X0,X2),X1))))
| leq(multiplication(X0,multiplication(X1,omega(multiplication(addition(X0,X2),X1)))),multiplication(X2,multiplication(X1,omega(multiplication(addition(X0,X2),X1))))) ),
inference(paramodulation,[status(thm)],[f308,f241]) ).
fof(f9713,plain,
! [X0,X1] : leq(omega(multiplication(codomain(X0),X1)),multiplication(X1,omega(multiplication(codomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f308,f6393]) ).
fof(f9714,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(codomain(X1),X0))) = addition(multiplication(X0,omega(multiplication(codomain(X1),X0))),omega(multiplication(codomain(X1),X0))),
inference(paramodulation,[status(thm)],[f308,f4512]) ).
fof(f9715,plain,
! [X0,X1] : backward_diamond(multiplication(X0,omega(multiplication(codomain(X1),X0))),X1) = codomain(omega(multiplication(codomain(X1),X0))),
inference(paramodulation,[status(thm)],[f308,f70]) ).
fof(f9716,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,multiplication(X1,omega(multiplication(codomain(X0),X1))))),coantidomain(omega(multiplication(codomain(X0),X1)))) = coantidomain(multiplication(codomain(X0),multiplication(X1,omega(multiplication(codomain(X0),X1))))),
inference(paramodulation,[status(thm)],[f308,f615]) ).
fof(f9717,plain,
! [X0,X1] : leq(omega(multiplication(c(X0),X1)),multiplication(X1,omega(multiplication(c(X0),X1)))),
inference(paramodulation,[status(thm)],[f308,f6526]) ).
fof(f9718,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(c(X1),X0))) = addition(multiplication(X0,omega(multiplication(c(X1),X0))),omega(multiplication(c(X1),X0))),
inference(paramodulation,[status(thm)],[f308,f4513]) ).
fof(f9719,plain,
! [X0,X1] : leq(omega(multiplication(coantidomain(X0),X1)),multiplication(X1,omega(multiplication(coantidomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f308,f7158]) ).
fof(f9720,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(coantidomain(X1),X0))) = addition(multiplication(X0,omega(multiplication(coantidomain(X1),X0))),omega(multiplication(coantidomain(X1),X0))),
inference(paramodulation,[status(thm)],[f308,f4515]) ).
fof(f9721,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(coantidomain(X0),X1))) = zero,
inference(paramodulation,[status(thm)],[f308,f151]) ).
fof(f9722,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(domain(X1),X0))) = addition(multiplication(X0,omega(multiplication(domain(X1),X0))),omega(multiplication(domain(X1),X0))),
inference(paramodulation,[status(thm)],[f308,f4516]) ).
fof(f9723,plain,
! [X0,X1] : leq(omega(multiplication(domain(X0),X1)),multiplication(X1,omega(multiplication(domain(X0),X1)))),
inference(paramodulation,[status(thm)],[f308,f6808]) ).
fof(f9724,plain,
! [X0,X1] : leq(multiplication(X0,omega(multiplication(star(X1),X0))),omega(multiplication(star(X1),X0))),
inference(paramodulation,[status(thm)],[f308,f8451]) ).
fof(f9725,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(multiplication(X0,X1),X2))))) = omega(multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f308,f39]) ).
fof(f9727,plain,
! [X0,X1] : leq(omega(multiplication(antidomain(X0),X1)),multiplication(X1,omega(multiplication(antidomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f308,f6667]) ).
fof(f9728,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(antidomain(X1),X0))) = addition(multiplication(X0,omega(multiplication(antidomain(X1),X0))),omega(multiplication(antidomain(X1),X0))),
inference(paramodulation,[status(thm)],[f308,f4514]) ).
fof(f9732,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),X2),omega(multiplication(X0,X1)))
| ~ leq(addition(omega(multiplication(X0,X1)),X2),omega(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f308,f296]) ).
fof(f9733,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(multiplication(X1,X2))) = addition(multiplication(X0,omega(multiplication(X1,X2))),omega(multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f308,f211]) ).
fof(f9734,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(multiplication(X0,X1))) = addition(omega(multiplication(X0,X1)),multiplication(X2,omega(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f308,f204]) ).
fof(f9735,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),multiplication(X2,omega(multiplication(X1,X2))))
| ~ leq(addition(multiplication(X0,omega(multiplication(X1,X2))),X3),multiplication(X2,omega(multiplication(X1,X2)))) ),
inference(paramodulation,[status(thm)],[f308,f296]) ).
fof(f9736,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,omega(multiplication(X0,X1))))),multiplication(X1,omega(multiplication(X0,X1))))
| ~ leq(omega(multiplication(X0,X1)),multiplication(X1,omega(multiplication(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f308,f295]) ).
fof(f9737,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),multiplication(X2,omega(multiplication(X1,X2))))
| ~ leq(addition(X0,omega(multiplication(X1,X2))),multiplication(X2,omega(multiplication(X1,X2)))) ),
inference(paramodulation,[status(thm)],[f308,f293]) ).
fof(f9738,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(multiplication(X1,omega(multiplication(X0,X1))),star(multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))))))),star(omega(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f308,f252]) ).
fof(f9739,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(multiplication(X1,omega(multiplication(X0,X1))),star(omega(multiplication(X0,X1)))))),star(multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f308,f252]) ).
fof(f9740,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,omega(multiplication(X2,X1)))),addition(omega(multiplication(X2,X1)),X3)) = addition(multiplication(addition(X0,X2),multiplication(X1,omega(multiplication(X2,X1)))),X3),
inference(paramodulation,[status(thm)],[f308,f219]) ).
fof(f9741,plain,
! [X0,X1,X2,X3] : addition(omega(multiplication(X0,X1)),addition(multiplication(X2,multiplication(X1,omega(multiplication(X0,X1)))),X3)) = addition(multiplication(addition(X0,X2),multiplication(X1,omega(multiplication(X0,X1)))),X3),
inference(paramodulation,[status(thm)],[f308,f219]) ).
fof(f9742,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,omega(multiplication(X0,X1)))) = addition(multiplication(X1,omega(multiplication(X0,X1))),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f308,f232]) ).
fof(f9743,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,omega(multiplication(X2,X3)))) = addition(multiplication(X0,multiplication(X3,omega(multiplication(X2,X3)))),multiplication(X1,omega(multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f308,f211]) ).
fof(f9744,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,omega(multiplication(X0,X3)))) = addition(omega(multiplication(X0,X3)),multiplication(X1,multiplication(X2,multiplication(X3,omega(multiplication(X0,X3)))))),
inference(paramodulation,[status(thm)],[f308,f211]) ).
fof(f9745,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,omega(multiplication(X0,X1)))) = addition(multiplication(X1,omega(multiplication(X0,X1))),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f308,f207]) ).
fof(f9746,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,omega(multiplication(X2,X3)))) = addition(multiplication(X0,multiplication(X1,multiplication(X3,omega(multiplication(X2,X3))))),omega(multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f308,f204]) ).
fof(f9747,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,omega(multiplication(X1,X3)))) = addition(multiplication(X0,omega(multiplication(X1,X3))),multiplication(X2,multiplication(X3,omega(multiplication(X1,X3))))),
inference(paramodulation,[status(thm)],[f308,f204]) ).
fof(f9748,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X0,X2)))) = addition(multiplication(X1,multiplication(X2,omega(multiplication(X0,X2)))),omega(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f308,f201]) ).
fof(f9749,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X1,X2)))) = addition(omega(multiplication(X1,X2)),multiplication(X0,multiplication(X2,omega(multiplication(X1,X2))))),
inference(paramodulation,[status(thm)],[f308,f201]) ).
fof(f9750,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(omega(multiplication(X0,X2)),X3)) = addition(multiplication(X0,addition(X1,multiplication(X2,omega(multiplication(X0,X2))))),X3),
inference(paramodulation,[status(thm)],[f308,f170]) ).
fof(f9751,plain,
! [X0,X1,X2,X3] : addition(omega(multiplication(X0,X1)),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(multiplication(X1,omega(multiplication(X0,X1))),X2)),X3),
inference(paramodulation,[status(thm)],[f308,f170]) ).
fof(f9752,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X1,omega(multiplication(X0,X1))),one)) = addition(X0,omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f308,f192]) ).
fof(f9753,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,omega(multiplication(X0,X1))))) = addition(X0,omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f308,f162]) ).
fof(f9754,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,omega(multiplication(X0,X1))),X2)) = addition(multiplication(X0,X2),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f308,f153]) ).
fof(f9755,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,omega(multiplication(X0,X2))))) = addition(omega(multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f308,f153]) ).
fof(f9757,plain,
! [X0,X1] : multiplication(antidomain(X0),omega(multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f308,f136]) ).
fof(f9758,plain,
! [X0,X1] : addition(coantidomain(omega(multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),multiplication(X1,omega(multiplication(X0,X1)))))) = coantidomain(multiplication(codomain(X0),multiplication(X1,omega(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f308,f615]) ).
fof(f9759,plain,
! [X0,X1] : addition(antidomain(omega(multiplication(X0,X1))),antidomain(multiplication(X0,domain(multiplication(X1,omega(multiplication(X0,X1))))))) = antidomain(multiplication(X0,domain(multiplication(X1,omega(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f308,f479]) ).
fof(f9760,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,omega(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(multiplication(X0,omega(multiplication(X1,X0))),addition(omega(multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f308,f58]) ).
fof(f9761,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(multiplication(X1,omega(multiplication(X0,X1))))),X0)
| ~ leq(addition(omega(multiplication(X0,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f308,f55]) ).
fof(f9762,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),multiplication(X1,omega(multiplication(X0,X1))))
| ~ leq(addition(omega(multiplication(X0,X1)),X2),multiplication(X1,omega(multiplication(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f308,f53]) ).
fof(f9763,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X1,X2)))) = addition(multiplication(X0,multiplication(X2,omega(multiplication(X1,X2)))),omega(multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f308,f43]) ).
fof(f9764,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X0,X2)))) = addition(omega(multiplication(X0,X2)),multiplication(X1,multiplication(X2,omega(multiplication(X0,X2))))),
inference(paramodulation,[status(thm)],[f308,f43]) ).
fof(f9765,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,omega(multiplication(X0,X2))))) = addition(multiplication(X0,X1),omega(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f308,f42]) ).
fof(f9766,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,omega(multiplication(X0,X1))),X2)) = addition(omega(multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f308,f42]) ).
fof(f9767,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(multiplication(X1,omega(multiplication(X0,X1))),X2)) = multiplication(omega(multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f308,f39]) ).
fof(f9768,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(X0,multiplication(X1,X2)))))) = omega(multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f9665]) ).
fof(f9769,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(X0,multiplication(X1,X2)))))) = omega(multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f9768]) ).
fof(f9779,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),multiplication(X0,omega(multiplication(X1,X0)))) = omega(multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f224,f9674]) ).
fof(f9780,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,omega(multiplication(X0,X1)))) = omega(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f230,f9676]) ).
fof(f9781,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),omega(multiplication(X0,coantidomain(X1))))) = omega(multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f233,f9677]) ).
fof(f9782,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),omega(multiplication(X1,coantidomain(X0))))) = omega(multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f226,f9678]) ).
fof(f9795,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),omega(domain_difference(X0,X1)))) = omega(domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f68,f9682]) ).
fof(f9796,plain,
! [X0] : multiplication(domain(X0),omega(X0)) = omega(multiplication(domain(X0),X0)),
inference(forward_demodulation,[status(thm)],[f56,f9683]) ).
fof(f9797,plain,
! [X0] : multiplication(domain(X0),omega(X0)) = omega(X0),
inference(forward_demodulation,[status(thm)],[f4146,f9796]) ).
fof(f9798,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(X0,multiplication(X1,X2)))))) = omega(multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f9684]) ).
fof(f9799,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(X0,multiplication(X1,X2)))))) = omega(multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f9798]) ).
fof(f9800,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,X0),omega(multiplication(antidomain(X0),X1)))) = omega(multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f186,f9685]) ).
fof(f9801,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X0,X1),omega(multiplication(antidomain(X0),X1)))) = omega(multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f177,f9686]) ).
fof(f9815,plain,
! [X0] : multiplication(X0,multiplication(codomain(X0),omega(X0))) = omega(X0),
inference(forward_demodulation,[status(thm)],[f2309,f9692]) ).
fof(f9816,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),omega(multiplication(X0,X1)))) = omega(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f181,f9694]) ).
fof(f9817,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),omega(multiplication(X0,X1)))) = omega(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f190,f9696]) ).
fof(f9821,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),omega(omega(multiplication(X0,X1)))))) = omega(multiplication(X0,multiplication(X1,omega(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f39,f9698]) ).
fof(f9822,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,omega(omega(multiplication(X0,X1))))) = omega(multiplication(X0,multiplication(X1,omega(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f56,f9821]) ).
fof(f9823,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,omega(omega(multiplication(X0,X1))))) = omega(omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f308,f9822]) ).
fof(f9834,plain,
! [X0] : multiplication(X0,omega(omega(X0))) = omega(multiplication(X0,omega(X0))),
inference(forward_demodulation,[status(thm)],[f56,f9701]) ).
fof(f9835,plain,
! [X0] : multiplication(X0,omega(omega(X0))) = omega(omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f9834]) ).
fof(f9843,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(divergence(X1),X0))) = addition(omega(multiplication(divergence(X1),X0)),multiplication(X0,omega(multiplication(divergence(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f9710]) ).
fof(f9844,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(divergence(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(divergence(X1),X0))),
inference(forward_demodulation,[status(thm)],[f232,f9843]) ).
fof(f9845,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(codomain(X1),X0))) = addition(omega(multiplication(codomain(X1),X0)),multiplication(X0,omega(multiplication(codomain(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f9714]) ).
fof(f9846,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(codomain(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(codomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f232,f9845]) ).
fof(f9847,plain,
! [X0,X1] : addition(coantidomain(omega(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,multiplication(X1,omega(multiplication(codomain(X0),X1)))))) = coantidomain(multiplication(codomain(X0),multiplication(X1,omega(multiplication(codomain(X0),X1))))),
inference(forward_demodulation,[status(thm)],[f35,f9716]) ).
fof(f9848,plain,
! [X0,X1] : addition(coantidomain(omega(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,multiplication(X1,omega(multiplication(codomain(X0),X1)))))) = coantidomain(omega(multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f308,f9847]) ).
fof(f9849,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(c(X1),X0))) = addition(omega(multiplication(c(X1),X0)),multiplication(X0,omega(multiplication(c(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f9718]) ).
fof(f9850,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(c(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(c(X1),X0))),
inference(forward_demodulation,[status(thm)],[f232,f9849]) ).
fof(f9851,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(coantidomain(X1),X0))) = addition(omega(multiplication(coantidomain(X1),X0)),multiplication(X0,omega(multiplication(coantidomain(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f9720]) ).
fof(f9852,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(coantidomain(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(coantidomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f232,f9851]) ).
fof(f9853,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(domain(X1),X0))) = addition(omega(multiplication(domain(X1),X0)),multiplication(X0,omega(multiplication(domain(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f9722]) ).
fof(f9854,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(domain(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(domain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f232,f9853]) ).
fof(f9855,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(X0,multiplication(X1,X2)))))) = omega(multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f9725]) ).
fof(f9856,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,omega(multiplication(X0,multiplication(X1,X2)))))) = omega(multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f9855]) ).
fof(f9858,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(antidomain(X1),X0))) = addition(omega(multiplication(antidomain(X1),X0)),multiplication(X0,omega(multiplication(antidomain(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f9728]) ).
fof(f9859,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(antidomain(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f232,f9858]) ).
fof(f9864,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(multiplication(X1,X2))) = addition(omega(multiplication(X1,X2)),multiplication(X0,omega(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f35,f9733]) ).
fof(f9865,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),omega(multiplication(X1,X2))) = multiplication(addition(X0,one),omega(multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f232,f9864]) ).
fof(f9866,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),omega(multiplication(X0,X1))) = multiplication(addition(X2,one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f232,f9734]) ).
fof(f9867,plain,
! [X0,X1] :
( leq(multiplication(star(X0),omega(multiplication(X0,X1))),multiplication(X1,omega(multiplication(X0,X1))))
| ~ leq(omega(multiplication(X0,X1)),multiplication(X1,omega(multiplication(X0,X1)))) ),
inference(forward_demodulation,[status(thm)],[f308,f9736]) ).
fof(f9868,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),star(multiplication(X0,multiplication(X1,omega(multiplication(X0,X1))))))))),star(omega(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f39,f9738]) ).
fof(f9869,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),star(omega(multiplication(X0,X1))))))),star(omega(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f308,f9868]) ).
fof(f9870,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),star(omega(multiplication(X0,X1))))))),star(multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f39,f9739]) ).
fof(f9871,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),star(omega(multiplication(X0,X1))))))),star(omega(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f308,f9870]) ).
fof(f9872,plain,
! [X0,X1,X2,X3] : addition(omega(multiplication(X0,X1)),addition(X2,multiplication(X3,multiplication(X1,omega(multiplication(X0,X1)))))) = addition(multiplication(addition(X3,X0),multiplication(X1,omega(multiplication(X0,X1)))),X2),
inference(forward_demodulation,[status(thm)],[f97,f9740]) ).
fof(f9873,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,omega(multiplication(X0,X1)))) = addition(omega(multiplication(X0,X1)),multiplication(X1,omega(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f35,f9742]) ).
fof(f9874,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,omega(multiplication(X0,X1)))) = multiplication(addition(X1,one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f232,f9873]) ).
fof(f9875,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,omega(multiplication(X2,X3)))) = multiplication(addition(multiplication(X0,X3),X1),omega(multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f204,f9743]) ).
fof(f9876,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,omega(multiplication(X0,X1)))) = addition(omega(multiplication(X0,X1)),multiplication(X1,omega(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f35,f9745]) ).
fof(f9877,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,omega(multiplication(X0,X1)))) = multiplication(addition(X1,one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f232,f9876]) ).
fof(f9878,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,omega(multiplication(X2,X3)))) = addition(omega(multiplication(X2,X3)),multiplication(X0,multiplication(X1,multiplication(X3,omega(multiplication(X2,X3)))))),
inference(forward_demodulation,[status(thm)],[f35,f9746]) ).
fof(f9879,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,omega(multiplication(X1,X3)))) = multiplication(addition(X0,multiplication(X2,X3)),omega(multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f211,f9747]) ).
fof(f9880,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X0,X2)))) = addition(omega(multiplication(X0,X2)),multiplication(X1,multiplication(X2,omega(multiplication(X0,X2))))),
inference(forward_demodulation,[status(thm)],[f35,f9748]) ).
fof(f9881,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,omega(multiplication(X0,X1))))) = addition(X0,omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f9752]) ).
fof(f9885,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X1,X2)))) = addition(omega(multiplication(X1,X2)),multiplication(X0,multiplication(X2,omega(multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f35,f9763]) ).
fof(f9886,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),X2))) = multiplication(omega(multiplication(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f39,f9767]) ).
fof(f9888,plain,
leq(multiplication(star(zero),star(zero)),one),
inference(resolution,[status(thm)],[f9608,f305]) ).
fof(f9889,plain,
leq(multiplication(star(antidomain(one)),star(zero)),one),
inference(resolution,[status(thm)],[f9608,f304]) ).
fof(f9890,plain,
addition(star(zero),one) = one,
inference(resolution,[status(thm)],[f9608,f48]) ).
fof(f9891,plain,
leq(multiplication(star(zero),star(zero)),one),
inference(forward_demodulation,[status(thm)],[f119,f9889]) ).
fof(f9892,plain,
addition(one,star(zero)) = one,
inference(forward_demodulation,[status(thm)],[f35,f9890]) ).
fof(f9893,plain,
star(zero) = one,
inference(forward_demodulation,[status(thm)],[f7563,f9892]) ).
fof(f9959,plain,
! [X0] : addition(c(X0),c(domain(X0))) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f67,f514]) ).
fof(f9960,plain,
! [X0] : addition(domain(X0),c(antidomain(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f62,f514]) ).
fof(f9963,plain,
! [X0,X1] : addition(antidomain(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f72,f514]) ).
fof(f9964,plain,
! [X0,X1] : addition(antidomain(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f71,f514]) ).
fof(f9966,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(c(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f547,f514]) ).
fof(f9967,plain,
! [X0] : addition(antidomain(domain(X0)),domain(c(X0))) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f362,f514]) ).
fof(f9970,plain,
! [X0] :
( leq(multiplication(star(antidomain(X0)),c(X0)),one)
| ~ leq(c(X0),one) ),
inference(paramodulation,[status(thm)],[f514,f302]) ).
fof(f9971,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),antidomain(X1))
| ~ leq(multiplication(X0,c(X1)),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f514,f291]) ).
fof(f9972,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X0)),multiplication(c(X0),X1)),X1)
| ~ leq(multiplication(c(X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f514,f290]) ).
fof(f9973,plain,
! [X0,X1] :
( addition(X0,c(X1)) != c(X1)
| leq(addition(X0,antidomain(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f514,f243]) ).
fof(f9974,plain,
! [X0,X1] :
( multiplication(X0,c(X1)) != multiplication(X0,c(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f514,f242]) ).
fof(f9975,plain,
! [X0,X1] :
( multiplication(c(X0),X1) != multiplication(c(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(c(X0),X1)) ),
inference(paramodulation,[status(thm)],[f514,f241]) ).
fof(f9976,plain,
! [X0] : multiplication(c(X0),coantidomain(c(X0))) = multiplication(antidomain(X0),coantidomain(c(X0))),
inference(paramodulation,[status(thm)],[f514,f233]) ).
fof(f9978,plain,
! [X0] : multiplication(antidomain(c(X0)),c(X0)) = multiplication(antidomain(c(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f514,f186]) ).
fof(f9980,plain,
! [X0,X1] : leq(antidomain(X0),addition(X1,c(X0))),
inference(paramodulation,[status(thm)],[f514,f1421]) ).
fof(f9985,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(X0),X1)) = addition(c(X0),X1),
inference(paramodulation,[status(thm)],[f514,f103]) ).
fof(f9987,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(X1,c(X0)),
inference(paramodulation,[status(thm)],[f514,f97]) ).
fof(f9988,plain,
! [X0,X1] : addition(X0,c(X1)) = addition(c(X1),addition(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f514,f97]) ).
fof(f9989,plain,
! [X0] :
( c(X0) != antidomain(X0)
| leq(c(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f514,f246]) ).
fof(f9991,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(paramodulation,[status(thm)],[f514,f36]) ).
fof(f9993,plain,
! [X0] : addition(c(X0),domain(c(X0))) = c(domain(X0)),
inference(forward_demodulation,[status(thm)],[f362,f9959]) ).
fof(f9994,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(forward_demodulation,[status(thm)],[f362,f9993]) ).
fof(f9995,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f547,f9960]) ).
fof(f9996,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f547,f9995]) ).
fof(f9999,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))) = c(backward_diamond(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f35,f9963]) ).
fof(f10000,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f72,f9999]) ).
fof(f10001,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))) = c(forward_diamond(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f35,f9964]) ).
fof(f10002,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f71,f10001]) ).
fof(f10005,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f9966]) ).
fof(f10006,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f547,f10005]) ).
fof(f10007,plain,
! [X0] : addition(c(X0),domain(c(X0))) = c(domain(X0)),
inference(forward_demodulation,[status(thm)],[f67,f9967]) ).
fof(f10008,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(forward_demodulation,[status(thm)],[f362,f10007]) ).
fof(f10011,plain,
! [X0] : leq(multiplication(star(antidomain(X0)),c(X0)),one),
inference(forward_subsumption_resolution,[status(thm)],[f9970,f1430]) ).
fof(f10012,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(c(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9972,f6526]) ).
fof(f10013,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),multiplication(X0,c(X1))),
inference(trivial_equality_resolution,[status(thm)],[f9974]) ).
fof(f10014,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),multiplication(c(X0),X1)),
inference(trivial_equality_resolution,[status(thm)],[f9975]) ).
fof(f10015,plain,
! [X0] : zero = multiplication(antidomain(X0),coantidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f63,f9976]) ).
fof(f10016,plain,
! [X0] : zero = multiplication(antidomain(c(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f59,f9978]) ).
fof(f10017,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,c(X0))) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f97,f9985]) ).
fof(f10018,plain,
! [X0,X1] : addition(X0,c(X1)) = addition(antidomain(X1),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f9988]) ).
fof(f10020,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(domain(X1),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4516,f314]) ).
fof(f10021,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(coantidomain(X1),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4515,f314]) ).
fof(f10022,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(antidomain(X1),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4514,f314]) ).
fof(f10023,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(c(X1),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4513,f314]) ).
fof(f10024,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(codomain(X1),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4512,f314]) ).
fof(f10025,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(divergence(X1),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4511,f314]) ).
fof(f10026,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),domain(X1))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2497,f314]) ).
fof(f10027,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),coantidomain(X1))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2496,f314]) ).
fof(f10028,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),antidomain(X1))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2495,f314]) ).
fof(f10029,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),c(X1))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2494,f314]) ).
fof(f10030,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),codomain(X1))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2493,f314]) ).
fof(f10031,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),divergence(X1))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2492,f314]) ).
fof(f10032,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,omega(X1))),omega(X1))
| ~ leq(multiplication(addition(X0,one),omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f232,f314]) ).
fof(f10033,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,omega(X1))),omega(X1))
| ~ leq(multiplication(addition(one,X0),omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f207,f314]) ).
fof(f10034,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),X1)),omega(X0))
| ~ leq(multiplication(omega(X0),addition(X1,one)),omega(X0)) ),
inference(paramodulation,[status(thm)],[f192,f314]) ).
fof(f10035,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),X1)),omega(X0))
| ~ leq(multiplication(omega(X0),addition(one,X1)),omega(X0)) ),
inference(paramodulation,[status(thm)],[f162,f314]) ).
fof(f10036,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(X1,addition(omega(X0),X1))),omega(X0))
| ~ leq(addition(omega(X0),X1),omega(X0)) ),
inference(paramodulation,[status(thm)],[f99,f314]) ).
fof(f10037,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(omega(X0),X1)),omega(X0))
| ~ leq(addition(omega(X0),X1),omega(X0)) ),
inference(paramodulation,[status(thm)],[f105,f314]) ).
fof(f10038,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X2),addition(X0,X1)),omega(X2))
| ~ leq(addition(X0,addition(X1,omega(X2))),omega(X2)) ),
inference(paramodulation,[status(thm)],[f97,f314]) ).
fof(f10039,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(X2,X0)),omega(X1))
| ~ leq(addition(X0,addition(omega(X1),X2)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f97,f314]) ).
fof(f10041,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),omega(X1))
| ~ leq(addition(X0,omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f35,f314]) ).
fof(f10042,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),omega(X1))
| ~ leq(addition(X0,omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f35,f314]) ).
fof(f10043,plain,
! [X0] :
( leq(multiplication(star(X0),omega(X0)),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f38,f314]) ).
fof(f10046,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(domain(X1),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10020,f239]) ).
fof(f10047,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X1),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10021,f239]) ).
fof(f10048,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(antidomain(X1),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10022,f239]) ).
fof(f10049,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(c(X1),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10023,f239]) ).
fof(f10050,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(codomain(X1),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10024,f239]) ).
fof(f10051,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(divergence(X1),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10025,f239]) ).
fof(f10052,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(omega(X0),domain(X1))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10026,f239]) ).
fof(f10053,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(omega(X0),coantidomain(X1))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10027,f239]) ).
fof(f10054,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(omega(X0),antidomain(X1))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10028,f239]) ).
fof(f10055,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(omega(X0),c(X1))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10029,f239]) ).
fof(f10056,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(omega(X0),codomain(X1))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10030,f239]) ).
fof(f10057,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(omega(X0),divergence(X1))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10031,f239]) ).
fof(f10059,plain,
! [X0] : leq(multiplication(star(X0),omega(X0)),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10043,f239]) ).
fof(f10069,plain,
! [X0,X1] : addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X0)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X0))),
inference(resolution,[status(thm)],[f1005,f75]) ).
fof(f10073,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f103,f1005]) ).
fof(f10074,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f36,f1005]) ).
fof(f10078,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f97,f1005]) ).
fof(f10080,plain,
! [X0] : addition(one,multiplication(star(X0),addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),star(X0)),
inference(paramodulation,[status(thm)],[f7789,f1005]) ).
fof(f10081,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = addition(multiplication(addition(X0,one),star(X0)),star(X0)),
inference(paramodulation,[status(thm)],[f7510,f1005]) ).
fof(f10102,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(X2,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f201,f1005]) ).
fof(f10103,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,X2),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f153,f1005]) ).
fof(f10104,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(X2,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f43,f1005]) ).
fof(f10105,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,X2),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f42,f1005]) ).
fof(f10106,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X2,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f103,f1005]) ).
fof(f10107,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X2,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f1005]) ).
fof(f10127,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f97,f1005]) ).
fof(f10128,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f97,f1005]) ).
fof(f10130,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f35,f1005]) ).
fof(f10131,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f35,f1005]) ).
fof(f10133,plain,
! [X0,X1] :
( leq(multiplication(star(X1),addition(X0,omega(X1))),omega(X1))
| ~ leq(addition(X0,omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f1005,f314]) ).
fof(f10135,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(forward_diamond(X0,domain(X1)),domain(X1)) != addition(forward_diamond(X0,domain(X1)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f1005,f75]) ).
fof(f10138,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f1005,f207]) ).
fof(f10145,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f1005,f162]) ).
fof(f10146,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),addition(X0,multiplication(X1,multiplication(X2,X3)))),X3)
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f1005,f296]) ).
fof(f10149,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),addition(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f1005,f219]) ).
fof(f10150,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),addition(X2,multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f1005,f170]) ).
fof(f10151,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),addition(X1,multiplication(X2,X0)))))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f1005,f58]) ).
fof(f10152,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,multiplication(X1,X2)),star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f1005,f55]) ).
fof(f10153,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(X0,multiplication(X1,X2))),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f1005,f53]) ).
fof(f10154,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1005,f103]) ).
fof(f10155,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1005,f36]) ).
fof(f10157,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f1005,f243]) ).
fof(f10162,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1005,f97]) ).
fof(f10163,plain,
! [X0,X1] :
( leq(multiplication(star(X1),addition(X0,X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1005,f302]) ).
fof(f10164,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,addition(X1,X2))),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f1005,f291]) ).
fof(f10165,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(addition(X0,X1),X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f1005,f290]) ).
fof(f10166,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != addition(X2,X1)
| leq(addition(X0,X1),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f1005,f243]) ).
fof(f10167,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,addition(X2,X1))
| leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))) ),
inference(paramodulation,[status(thm)],[f1005,f242]) ).
fof(f10168,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(addition(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)) ),
inference(paramodulation,[status(thm)],[f1005,f241]) ).
fof(f10169,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X0,X1))) = multiplication(X1,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f1005,f233]) ).
fof(f10171,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,X1)) = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f1005,f186]) ).
fof(f10178,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f1005,f103]) ).
fof(f10179,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1005,f97]) ).
fof(f10180,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f1005,f97]) ).
fof(f10181,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f1005,f246]) ).
fof(f10189,plain,
! [X0] : star(X0) = addition(multiplication(star(X0),addition(X0,one)),star(X0)),
inference(forward_demodulation,[status(thm)],[f7789,f10080]) ).
fof(f10190,plain,
! [X0] : star(X0) = addition(star(X0),multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f35,f10189]) ).
fof(f10191,plain,
! [X0] : star(X0) = multiplication(star(X0),addition(addition(X0,one),one)),
inference(forward_demodulation,[status(thm)],[f192,f10190]) ).
fof(f10192,plain,
! [X0] : star(X0) = multiplication(star(X0),addition(one,addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f103,f10191]) ).
fof(f10193,plain,
! [X0] : star(X0) = multiplication(star(X0),addition(X0,one)),
inference(forward_demodulation,[status(thm)],[f1005,f10192]) ).
fof(f10194,plain,
! [X0] : star(X0) = addition(multiplication(addition(X0,one),star(X0)),star(X0)),
inference(forward_demodulation,[status(thm)],[f7510,f10081]) ).
fof(f10195,plain,
! [X0] : star(X0) = addition(star(X0),multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f35,f10194]) ).
fof(f10196,plain,
! [X0] : star(X0) = multiplication(addition(addition(X0,one),one),star(X0)),
inference(forward_demodulation,[status(thm)],[f232,f10195]) ).
fof(f10197,plain,
! [X0] : star(X0) = multiplication(addition(one,addition(X0,one)),star(X0)),
inference(forward_demodulation,[status(thm)],[f103,f10196]) ).
fof(f10198,plain,
! [X0] : star(X0) = multiplication(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f1005,f10197]) ).
fof(f10241,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f201,f10102]) ).
fof(f10242,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X0,X1),X0),X2),
inference(forward_demodulation,[status(thm)],[f201,f10241]) ).
fof(f10243,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,addition(X0,X0)),X2),
inference(forward_demodulation,[status(thm)],[f103,f10242]) ).
fof(f10244,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f38,f10243]) ).
fof(f10245,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f153,f10103]) ).
fof(f10246,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(addition(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f153,f10245]) ).
fof(f10247,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,addition(X1,X1))),
inference(forward_demodulation,[status(thm)],[f103,f10246]) ).
fof(f10248,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f38,f10247]) ).
fof(f10249,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f10104]) ).
fof(f10250,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),X0),X2),
inference(forward_demodulation,[status(thm)],[f201,f10249]) ).
fof(f10251,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f103,f10250]) ).
fof(f10252,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f1005,f10251]) ).
fof(f10253,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f10105]) ).
fof(f10254,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(addition(X2,X1),X1)),
inference(forward_demodulation,[status(thm)],[f153,f10253]) ).
fof(f10255,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f103,f10254]) ).
fof(f10256,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f1005,f10255]) ).
fof(f10257,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f103,f10106]) ).
fof(f10258,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f10107]) ).
fof(f10302,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X1,addition(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f103,f10127]) ).
fof(f10303,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f105,f10302]) ).
fof(f10304,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,addition(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f10128]) ).
fof(f10306,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X0)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X0)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != addition(forward_diamond(X1,domain(X0)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f10135]) ).
fof(f10307,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X0)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X0)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != addition(domain(X0),forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f10306]) ).
fof(f10308,plain,
! [X0,X1] : addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X0)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X0))),
inference(trivial_equality_resolution,[status(thm)],[f10307]) ).
fof(f10313,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(X3,X1),addition(multiplication(addition(X0,X3),X1),X2)),
inference(forward_demodulation,[status(thm)],[f97,f10149]) ).
fof(f10314,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X3,addition(X0,X3)),X1),X2),
inference(forward_demodulation,[status(thm)],[f219,f10313]) ).
fof(f10315,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),X2),
inference(forward_demodulation,[status(thm)],[f1005,f10314]) ).
fof(f10316,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,X3),addition(multiplication(X0,addition(X1,X3)),X2)),
inference(forward_demodulation,[status(thm)],[f97,f10150]) ).
fof(f10317,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X3,addition(X1,X3))),X2),
inference(forward_demodulation,[status(thm)],[f170,f10316]) ).
fof(f10318,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),X2),
inference(forward_demodulation,[status(thm)],[f1005,f10317]) ).
fof(f10319,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(trivial_equality_resolution,[status(thm)],[f10167]) ).
fof(f10320,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(trivial_equality_resolution,[status(thm)],[f10168]) ).
fof(f10321,plain,
! [X0,X1] : zero = multiplication(X0,coantidomain(addition(X1,X0))),
inference(forward_demodulation,[status(thm)],[f63,f10169]) ).
fof(f10322,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f59,f10171]) ).
fof(f10323,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f10178]) ).
fof(f10324,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f10323]) ).
fof(f10325,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10179]) ).
fof(f10326,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f105,f10325]) ).
fof(f10327,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f10180]) ).
fof(f10334,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f103,f1026]) ).
fof(f10335,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f36,f1026]) ).
fof(f10360,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X1),X3),X2)) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f204,f1026]) ).
fof(f10361,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X1),X3)) = addition(addition(multiplication(X2,X1),X3),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f219,f1026]) ).
fof(f10362,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,addition(X1,X2)),X3)) = addition(addition(multiplication(X0,X2),X3),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f170,f1026]) ).
fof(f10368,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f103,f1026]) ).
fof(f10369,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f36,f1026]) ).
fof(f10383,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f232,f1026]) ).
fof(f10384,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f207,f1026]) ).
fof(f10385,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f192,f1026]) ).
fof(f10386,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f162,f1026]) ).
fof(f10390,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f97,f1026]) ).
fof(f10391,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X2,X1),X0),
inference(paramodulation,[status(thm)],[f97,f1026]) ).
fof(f10396,plain,
! [X0,X1] :
( leq(multiplication(star(X1),addition(omega(X1),X0)),omega(X1))
| ~ leq(addition(X0,omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f1026,f314]) ).
fof(f10400,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f1026,f207]) ).
fof(f10407,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f1026,f162]) ).
fof(f10408,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X1,X2)),addition(multiplication(X1,multiplication(X2,X3)),X0)),X3)
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f1026,f296]) ).
fof(f10411,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),addition(multiplication(X3,X1),X2)),
inference(paramodulation,[status(thm)],[f1026,f219]) ).
fof(f10412,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),addition(multiplication(X0,X3),X2)),
inference(paramodulation,[status(thm)],[f1026,f170]) ).
fof(f10413,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),addition(multiplication(X2,X0),X1))))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f1026,f58]) ).
fof(f10414,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(multiplication(X1,X2),X0),star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f1026,f55]) ).
fof(f10415,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(multiplication(X1,X2),X0)),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f1026,f53]) ).
fof(f10416,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1026,f103]) ).
fof(f10417,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1026,f36]) ).
fof(f10427,plain,
! [X0,X1] :
( leq(multiplication(star(X1),addition(X1,X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1026,f302]) ).
fof(f10428,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,addition(X2,X1))),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f1026,f291]) ).
fof(f10429,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(addition(X1,X0),X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f1026,f290]) ).
fof(f10430,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != addition(X1,X2)
| leq(addition(X0,X1),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1026,f243]) ).
fof(f10431,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,addition(X1,X2))
| leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1026,f242]) ).
fof(f10432,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)) ),
inference(paramodulation,[status(thm)],[f1026,f241]) ).
fof(f10433,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X1,X0))) = multiplication(X1,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1026,f233]) ).
fof(f10435,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X1,X0)) = multiplication(antidomain(addition(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f1026,f186]) ).
fof(f10438,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1026,f1420]) ).
fof(f10439,plain,
! [X0,X1] : leq(addition(X0,X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1026,f1423]) ).
fof(f10442,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1026,f103]) ).
fof(f10443,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1026,f97]) ).
fof(f10444,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f1026,f97]) ).
fof(f10445,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f1026,f246]) ).
fof(f10447,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1026,f36]) ).
fof(f10451,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10334]) ).
fof(f10452,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f10335]) ).
fof(f10453,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f1026,f10452]) ).
fof(f10454,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f10453]) ).
fof(f10497,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(multiplication(X0,X1),X2)),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f204,f10360]) ).
fof(f10498,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X0),X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f219,f10497]) ).
fof(f10499,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f38,f10498]) ).
fof(f10500,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X0,X1)),X2),X3) = addition(addition(multiplication(X1,X2),X3),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f219,f10361]) ).
fof(f10501,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(addition(multiplication(X0,X2),X3),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f1026,f10500]) ).
fof(f10502,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f103,f10501]) ).
fof(f10503,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f10502]) ).
fof(f10504,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,addition(X1,X2))),X3) = addition(addition(multiplication(X0,X2),X3),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f170,f10362]) ).
fof(f10505,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(addition(multiplication(X0,X1),X3),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f1026,f10504]) ).
fof(f10506,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f10505]) ).
fof(f10507,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f10506]) ).
fof(f10523,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10368]) ).
fof(f10524,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10369]) ).
fof(f10525,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f1026,f10524]) ).
fof(f10526,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10525]) ).
fof(f10552,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f10383]) ).
fof(f10553,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f10384]) ).
fof(f10554,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f10385]) ).
fof(f10555,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f10386]) ).
fof(f10562,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10390]) ).
fof(f10563,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10391]) ).
fof(f10569,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(addition(X0,X3),X3),X1),X2),
inference(forward_demodulation,[status(thm)],[f219,f10411]) ).
fof(f10570,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X3,addition(X0,X3)),X1),X2),
inference(forward_demodulation,[status(thm)],[f103,f10569]) ).
fof(f10571,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),X2),
inference(forward_demodulation,[status(thm)],[f1005,f10570]) ).
fof(f10572,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(addition(X1,X3),X3)),X2),
inference(forward_demodulation,[status(thm)],[f170,f10412]) ).
fof(f10573,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X3,addition(X1,X3))),X2),
inference(forward_demodulation,[status(thm)],[f103,f10572]) ).
fof(f10574,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),X2),
inference(forward_demodulation,[status(thm)],[f1005,f10573]) ).
fof(f10575,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10416]) ).
fof(f10576,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f10417]) ).
fof(f10577,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f1026,f10576]) ).
fof(f10578,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f10577]) ).
fof(f10587,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f103,f10442]) ).
fof(f10588,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f1026,f10587]) ).
fof(f10589,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f103,f10443]) ).
fof(f10590,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f10444]) ).
fof(f10591,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f1005,f10590]) ).
fof(f10592,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f10447]) ).
fof(f10593,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f10592]) ).
fof(f10594,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,X1))),addition(X1,X0)),addition(X0,X1)),
inference(resolution,[status(thm)],[f10439,f304]) ).
fof(f10615,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3)))),
inference(paramodulation,[status(thm)],[f204,f10439]) ).
fof(f10618,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f211,f10439]) ).
fof(f10619,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f201,f10439]) ).
fof(f10620,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f153,f10439]) ).
fof(f10623,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f103,f10439]) ).
fof(f10624,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f10439]) ).
fof(f10638,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),X1),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f232,f10439]) ).
fof(f10639,plain,
! [X0,X1] : leq(multiplication(addition(one,X0),X1),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f207,f10439]) ).
fof(f10640,plain,
! [X0,X1] : leq(multiplication(X0,addition(X1,one)),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f192,f10439]) ).
fof(f10641,plain,
! [X0,X1] : leq(multiplication(X0,addition(one,X1)),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f162,f10439]) ).
fof(f10645,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f97,f10439]) ).
fof(f10646,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f97,f10439]) ).
fof(f10670,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),multiplication(addition(multiplication(X2,X3),X0),X1)),
inference(paramodulation,[status(thm)],[f204,f10439]) ).
fof(f10673,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f211,f10439]) ).
fof(f10674,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f201,f10439]) ).
fof(f10675,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f153,f10439]) ).
fof(f10678,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f103,f10439]) ).
fof(f10679,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f36,f10439]) ).
fof(f10693,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f232,f10439]) ).
fof(f10694,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f207,f10439]) ).
fof(f10695,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f192,f10439]) ).
fof(f10696,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f162,f10439]) ).
fof(f10700,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f97,f10439]) ).
fof(f10701,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f97,f10439]) ).
fof(f10746,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(addition(X2,multiplication(X0,X1)),X3)),
inference(forward_demodulation,[status(thm)],[f211,f10615]) ).
fof(f10751,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),multiplication(addition(multiplication(X1,X2),X0),X3)),
inference(forward_demodulation,[status(thm)],[f204,f10618]) ).
fof(f10752,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f10619]) ).
fof(f10753,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f10620]) ).
fof(f10781,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),X1),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f10638]) ).
fof(f10782,plain,
! [X0,X1] : leq(multiplication(addition(one,X0),X1),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f10639]) ).
fof(f10783,plain,
! [X0,X1] : leq(multiplication(X0,addition(X1,one)),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f10640]) ).
fof(f10784,plain,
! [X0,X1] : leq(multiplication(X0,addition(one,X1)),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f10641]) ).
fof(f10791,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f10645]) ).
fof(f10792,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f103,f10646]) ).
fof(f10833,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),multiplication(addition(multiplication(X1,X2),X0),X3)),
inference(forward_demodulation,[status(thm)],[f211,f10670]) ).
fof(f10838,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(addition(X2,multiplication(X0,X1)),X3)),
inference(forward_demodulation,[status(thm)],[f204,f10673]) ).
fof(f10839,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f201,f10674]) ).
fof(f10840,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f10675]) ).
fof(f10868,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(X1,one),X0)),
inference(forward_demodulation,[status(thm)],[f35,f10693]) ).
fof(f10869,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(one,X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f10694]) ).
fof(f10870,plain,
! [X0,X1] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f35,f10695]) ).
fof(f10871,plain,
! [X0,X1] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f35,f10696]) ).
fof(f10878,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f10700]) ).
fof(f10879,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f103,f10701]) ).
fof(f10882,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = multiplication(addition(X0,one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f232,f320]) ).
fof(f10883,plain,
! [X0] : leq(multiplication(X0,omega(addition(X0,one))),multiplication(addition(X0,one),omega(addition(X0,one)))),
inference(resolution,[status(thm)],[f10882,f241]) ).
fof(f10887,plain,
! [X0] : multiplication(star(X0),omega(multiplication(star(X0),addition(X0,one)))) = multiplication(addition(one,one),omega(multiplication(star(X0),addition(X0,one)))),
inference(paramodulation,[status(thm)],[f7789,f10882]) ).
fof(f10888,plain,
! [X0] : multiplication(star(X0),omega(multiplication(addition(X0,one),star(X0)))) = multiplication(addition(one,one),omega(multiplication(addition(X0,one),star(X0)))),
inference(paramodulation,[status(thm)],[f7510,f10882]) ).
fof(f10905,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(addition(multiplication(X0,X1),X2),X3),omega(multiplication(X2,X3))) = multiplication(addition(multiplication(X0,multiplication(X1,X3)),one),omega(multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f204,f10882]) ).
fof(f10906,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X1),X2),X3),omega(addition(multiplication(X1,X2),X3))) = multiplication(addition(multiplication(X0,X2),one),omega(addition(multiplication(X1,X2),X3))),
inference(paramodulation,[status(thm)],[f219,f10882]) ).
fof(f10907,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(addition(multiplication(X0,X2),X3))) = multiplication(addition(multiplication(X0,X1),one),omega(addition(multiplication(X0,X2),X3))),
inference(paramodulation,[status(thm)],[f170,f10882]) ).
fof(f10908,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(addition(X0,multiplication(X1,X2)),X3),omega(multiplication(X1,multiplication(X2,X3)))) = multiplication(addition(multiplication(X0,X3),one),omega(multiplication(X1,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f211,f10882]) ).
fof(f10909,plain,
! [X0,X1,X2] : multiplication(multiplication(addition(X0,X1),X2),omega(multiplication(X0,X2))) = multiplication(addition(multiplication(X1,X2),one),omega(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f201,f10882]) ).
fof(f10910,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,X2)),omega(multiplication(X0,X1))) = multiplication(addition(multiplication(X0,X2),one),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f153,f10882]) ).
fof(f10911,plain,
! [X0,X1,X2] : multiplication(multiplication(addition(X0,X1),X2),omega(multiplication(X1,X2))) = multiplication(addition(multiplication(X0,X2),one),omega(multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f43,f10882]) ).
fof(f10912,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,X2)),omega(multiplication(X0,X2))) = multiplication(addition(multiplication(X0,X1),one),omega(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f42,f10882]) ).
fof(f10913,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(addition(X1,X0),one),omega(X2)),
inference(paramodulation,[status(thm)],[f103,f10882]) ).
fof(f10914,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(addition(X0,X1),one),omega(X2)),
inference(paramodulation,[status(thm)],[f36,f10882]) ).
fof(f10916,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(domain(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(domain(X1),X0))),
inference(paramodulation,[status(thm)],[f4516,f10882]) ).
fof(f10917,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(coantidomain(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(coantidomain(X1),X0))),
inference(paramodulation,[status(thm)],[f4515,f10882]) ).
fof(f10918,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(antidomain(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(antidomain(X1),X0))),
inference(paramodulation,[status(thm)],[f4514,f10882]) ).
fof(f10919,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(c(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(c(X1),X0))),
inference(paramodulation,[status(thm)],[f4513,f10882]) ).
fof(f10920,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(codomain(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(codomain(X1),X0))),
inference(paramodulation,[status(thm)],[f4512,f10882]) ).
fof(f10921,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(divergence(X1),X0))) = multiplication(addition(X0,one),omega(multiplication(divergence(X1),X0))),
inference(paramodulation,[status(thm)],[f4511,f10882]) ).
fof(f10922,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(X0,domain(X1)))) = multiplication(addition(X0,one),omega(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f2497,f10882]) ).
fof(f10923,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(X0,coantidomain(X1)))) = multiplication(addition(X0,one),omega(multiplication(X0,coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f2496,f10882]) ).
fof(f10924,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(X0,antidomain(X1)))) = multiplication(addition(X0,one),omega(multiplication(X0,antidomain(X1)))),
inference(paramodulation,[status(thm)],[f2495,f10882]) ).
fof(f10925,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(X0,c(X1)))) = multiplication(addition(X0,one),omega(multiplication(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f2494,f10882]) ).
fof(f10926,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(X0,codomain(X1)))) = multiplication(addition(X0,one),omega(multiplication(X0,codomain(X1)))),
inference(paramodulation,[status(thm)],[f2493,f10882]) ).
fof(f10927,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(X0,divergence(X1)))) = multiplication(addition(X0,one),omega(multiplication(X0,divergence(X1)))),
inference(paramodulation,[status(thm)],[f2492,f10882]) ).
fof(f10928,plain,
! [X0,X1] : multiplication(multiplication(addition(X0,one),X1),omega(multiplication(X0,X1))) = multiplication(addition(X1,one),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f232,f10882]) ).
fof(f10929,plain,
! [X0,X1] : multiplication(multiplication(addition(one,X0),X1),omega(multiplication(X0,X1))) = multiplication(addition(X1,one),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f207,f10882]) ).
fof(f10930,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(X1,one)),omega(multiplication(X0,X1))) = multiplication(addition(X0,one),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f10882]) ).
fof(f10931,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(one,X1)),omega(multiplication(X0,X1))) = multiplication(addition(X0,one),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f162,f10882]) ).
fof(f10932,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(addition(X1,X0))) = multiplication(addition(X1,one),omega(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1026,f10882]) ).
fof(f10933,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(addition(X0,X1))) = multiplication(addition(X1,one),omega(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f1005,f10882]) ).
fof(f10934,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(addition(X0,X1))) = multiplication(addition(X0,one),omega(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f105,f10882]) ).
fof(f10935,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(addition(X0,X1))) = multiplication(addition(X2,one),omega(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f97,f10882]) ).
fof(f10936,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(addition(X2,X0))) = multiplication(addition(X1,one),omega(addition(X2,X0))),
inference(paramodulation,[status(thm)],[f97,f10882]) ).
fof(f10937,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(X1,one),omega(X0)),
inference(paramodulation,[status(thm)],[f35,f10882]) ).
fof(f10938,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(X1,one),omega(X0)),
inference(paramodulation,[status(thm)],[f35,f10882]) ).
fof(f10939,plain,
! [X0] : multiplication(X0,omega(X0)) = multiplication(addition(X0,one),omega(X0)),
inference(paramodulation,[status(thm)],[f38,f10882]) ).
fof(f10942,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),omega(X2)) = multiplication(addition(X1,addition(X0,one)),omega(X2)),
inference(paramodulation,[status(thm)],[f103,f10882]) ).
fof(f10943,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),omega(X2)) = multiplication(addition(X0,addition(X1,one)),omega(X2)),
inference(paramodulation,[status(thm)],[f36,f10882]) ).
fof(f10945,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = multiplication(addition(one,X0),omega(X1)),
inference(paramodulation,[status(thm)],[f35,f10882]) ).
fof(f10946,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = multiplication(addition(one,X0),omega(X1)),
inference(paramodulation,[status(thm)],[f35,f10882]) ).
fof(f10947,plain,
! [X0] : multiplication(addition(one,X0),omega(X0)) = multiplication(one,omega(X0)),
inference(paramodulation,[status(thm)],[f38,f10882]) ).
fof(f10950,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,omega(X1))),omega(X1))
| ~ leq(multiplication(addition(X0,one),omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f10882,f290]) ).
fof(f10951,plain,
! [X0,X1] :
( multiplication(addition(X0,one),omega(X1)) != multiplication(X1,omega(X1))
| leq(multiplication(X0,omega(X1)),multiplication(X1,omega(X1))) ),
inference(paramodulation,[status(thm)],[f10882,f241]) ).
fof(f10952,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(omega(X1),omega(multiplication(addition(X0,one),omega(X1))))) = omega(multiplication(addition(X0,X1),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f308]) ).
fof(f10953,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(X1,X2))),X3),omega(X2))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,one),omega(X2))),X3),omega(X2)) ),
inference(paramodulation,[status(thm)],[f10882,f296]) ).
fof(f10954,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X0,X1)),multiplication(addition(X0,X1),omega(X1))),omega(X1))
| ~ leq(multiplication(addition(X0,one),omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f10882,f295]) ).
fof(f10955,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,X2)),X0),omega(X2))
| ~ leq(addition(X0,multiplication(addition(X1,one),omega(X2))),omega(X2)) ),
inference(paramodulation,[status(thm)],[f10882,f293]) ).
fof(f10956,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(omega(X1),star(multiplication(addition(X0,X1),omega(X1)))))),star(multiplication(addition(X0,one),omega(X1)))),
inference(paramodulation,[status(thm)],[f10882,f252]) ).
fof(f10957,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(omega(X1),star(multiplication(addition(X0,one),omega(X1)))))),star(multiplication(addition(X0,X1),omega(X1)))),
inference(paramodulation,[status(thm)],[f10882,f252]) ).
fof(f10958,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,omega(X1)),addition(multiplication(addition(X2,one),omega(X1)),X3)) = addition(multiplication(addition(X0,addition(X2,X1)),omega(X1)),X3),
inference(paramodulation,[status(thm)],[f10882,f219]) ).
fof(f10959,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),omega(X1)),addition(multiplication(X2,omega(X1)),X3)) = addition(multiplication(addition(addition(X0,X1),X2),omega(X1)),X3),
inference(paramodulation,[status(thm)],[f10882,f219]) ).
fof(f10960,plain,
! [X0,X1] : multiplication(addition(addition(X0,X1),one),omega(X1)) = addition(omega(X1),multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f232]) ).
fof(f10961,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,X3))),omega(X3)) = addition(multiplication(X0,omega(X3)),multiplication(X1,multiplication(addition(X2,one),omega(X3)))),
inference(paramodulation,[status(thm)],[f10882,f211]) ).
fof(f10962,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,X1),multiplication(X2,X3)),omega(X1)) = addition(multiplication(addition(X0,one),omega(X1)),multiplication(X2,multiplication(X3,omega(X1)))),
inference(paramodulation,[status(thm)],[f10882,f211]) ).
fof(f10963,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),omega(X1)) = addition(omega(X1),multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f207]) ).
fof(f10964,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),omega(X3)) = addition(multiplication(X0,multiplication(X1,omega(X3))),multiplication(addition(X2,one),omega(X3))),
inference(paramodulation,[status(thm)],[f10882,f204]) ).
fof(f10965,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(X2)) = addition(multiplication(X0,multiplication(addition(X1,one),omega(X2))),multiplication(X3,omega(X2))),
inference(paramodulation,[status(thm)],[f10882,f204]) ).
fof(f10966,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),omega(X1)) = addition(multiplication(X2,omega(X1)),multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f201]) ).
fof(f10967,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = addition(multiplication(addition(X1,one),omega(X2)),multiplication(X0,omega(X2))),
inference(paramodulation,[status(thm)],[f10882,f201]) ).
fof(f10968,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),addition(multiplication(addition(X0,one),omega(X1)),X3)) = addition(multiplication(addition(X0,X1),addition(X2,omega(X1))),X3),
inference(paramodulation,[status(thm)],[f10882,f170]) ).
fof(f10969,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),omega(X1)),addition(multiplication(addition(X0,X1),X2),X3)) = addition(multiplication(addition(X0,X1),addition(omega(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f10882,f170]) ).
fof(f10970,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(omega(X1),one)) = addition(addition(X0,X1),multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f192]) ).
fof(f10971,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,omega(X1))) = addition(addition(X0,X1),multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f162]) ).
fof(f10972,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X1),X2)) = addition(multiplication(addition(X0,X1),X2),multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f153]) ).
fof(f10973,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X1))) = addition(multiplication(addition(X0,one),omega(X1)),multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f10882,f153]) ).
fof(f10974,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(omega(X1),coantidomain(multiplication(addition(X0,one),omega(X1))))) = zero,
inference(paramodulation,[status(thm)],[f10882,f144]) ).
fof(f10975,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),multiplication(addition(X0,one),omega(X1))) = zero,
inference(paramodulation,[status(thm)],[f10882,f136]) ).
fof(f10976,plain,
! [X0,X1] : addition(coantidomain(multiplication(addition(X0,one),omega(X1))),coantidomain(multiplication(codomain(addition(X0,X1)),omega(X1)))) = coantidomain(multiplication(codomain(addition(X0,X1)),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f615]) ).
fof(f10977,plain,
! [X0,X1] : addition(antidomain(multiplication(addition(X0,one),omega(X1))),antidomain(multiplication(addition(X0,X1),domain(omega(X1))))) = antidomain(multiplication(addition(X0,X1),domain(omega(X1)))),
inference(paramodulation,[status(thm)],[f10882,f479]) ).
fof(f10978,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(addition(X1,X0)),multiplication(star(addition(X1,X0)),X2)))
| ~ leq(omega(X0),addition(multiplication(addition(X1,one),omega(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f10882,f58]) ).
fof(f10979,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(omega(X1))),addition(X0,X1))
| ~ leq(addition(multiplication(addition(X0,one),omega(X1)),X2),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f10882,f55]) ).
fof(f10980,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,X1)),X2),omega(X1))
| ~ leq(addition(multiplication(addition(X0,one),omega(X1)),X2),omega(X1)) ),
inference(paramodulation,[status(thm)],[f10882,f53]) ).
fof(f10981,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = addition(multiplication(X0,omega(X2)),multiplication(addition(X1,one),omega(X2))),
inference(paramodulation,[status(thm)],[f10882,f43]) ).
fof(f10982,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),omega(X1)) = addition(multiplication(addition(X0,one),omega(X1)),multiplication(X2,omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f43]) ).
fof(f10983,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X1))) = addition(multiplication(addition(X0,X1),X2),multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f42]) ).
fof(f10984,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X1),X2)) = addition(multiplication(addition(X0,one),omega(X1)),multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f10882,f42]) ).
fof(f10985,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(multiplication(addition(X0,one),omega(X1)),X2),
inference(paramodulation,[status(thm)],[f10882,f39]) ).
fof(f10987,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(one,omega(X1))),omega(X1))
| ~ leq(multiplication(addition(X0,X1),omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f10882,f290]) ).
fof(f10988,plain,
! [X0,X1] :
( multiplication(addition(X0,X1),omega(X1)) != multiplication(one,omega(X1))
| leq(multiplication(X0,omega(X1)),multiplication(one,omega(X1))) ),
inference(paramodulation,[status(thm)],[f10882,f241]) ).
fof(f10989,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(omega(X1),omega(multiplication(addition(X0,X1),omega(X1))))) = omega(multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f308]) ).
fof(f10990,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(X1,one))),X3),omega(X2))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,X2),omega(X2))),X3),omega(X2)) ),
inference(paramodulation,[status(thm)],[f10882,f296]) ).
fof(f10991,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X0,one)),multiplication(addition(X0,one),omega(X1))),omega(X1))
| ~ leq(multiplication(addition(X0,X1),omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f10882,f295]) ).
fof(f10992,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,one)),X0),omega(X2))
| ~ leq(addition(X0,multiplication(addition(X1,X2),omega(X2))),omega(X2)) ),
inference(paramodulation,[status(thm)],[f10882,f293]) ).
fof(f10993,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,one),multiplication(omega(X1),star(multiplication(addition(X0,one),omega(X1)))))),star(multiplication(addition(X0,X1),omega(X1)))),
inference(paramodulation,[status(thm)],[f10882,f252]) ).
fof(f10994,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,one),multiplication(omega(X1),star(multiplication(addition(X0,X1),omega(X1)))))),star(multiplication(addition(X0,one),omega(X1)))),
inference(paramodulation,[status(thm)],[f10882,f252]) ).
fof(f10995,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,omega(X1)),addition(multiplication(addition(X2,X1),omega(X1)),X3)) = addition(multiplication(addition(X0,addition(X2,one)),omega(X1)),X3),
inference(paramodulation,[status(thm)],[f10882,f219]) ).
fof(f10996,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),omega(X1)),addition(multiplication(X2,omega(X1)),X3)) = addition(multiplication(addition(addition(X0,one),X2),omega(X1)),X3),
inference(paramodulation,[status(thm)],[f10882,f219]) ).
fof(f10997,plain,
! [X0,X1] : multiplication(addition(addition(X0,one),one),omega(X1)) = addition(omega(X1),multiplication(addition(X0,X1),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f232]) ).
fof(f10998,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,one))),omega(X3)) = addition(multiplication(X0,omega(X3)),multiplication(X1,multiplication(addition(X2,X3),omega(X3)))),
inference(paramodulation,[status(thm)],[f10882,f211]) ).
fof(f10999,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,one),multiplication(X1,X2)),omega(X3)) = addition(multiplication(addition(X0,X3),omega(X3)),multiplication(X1,multiplication(X2,omega(X3)))),
inference(paramodulation,[status(thm)],[f10882,f211]) ).
fof(f11000,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),omega(X1)) = addition(omega(X1),multiplication(addition(X0,X1),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f207]) ).
fof(f11001,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,one)),omega(X3)) = addition(multiplication(X0,multiplication(X1,omega(X3))),multiplication(addition(X2,X3),omega(X3))),
inference(paramodulation,[status(thm)],[f10882,f204]) ).
fof(f11002,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,one)),X2),omega(X3)) = addition(multiplication(X0,multiplication(addition(X1,X3),omega(X3))),multiplication(X2,omega(X3))),
inference(paramodulation,[status(thm)],[f10882,f204]) ).
fof(f11003,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),omega(X2)) = addition(multiplication(X1,omega(X2)),multiplication(addition(X0,X2),omega(X2))),
inference(paramodulation,[status(thm)],[f10882,f201]) ).
fof(f11004,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = addition(multiplication(addition(X1,X2),omega(X2)),multiplication(X0,omega(X2))),
inference(paramodulation,[status(thm)],[f10882,f201]) ).
fof(f11005,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),X1),addition(multiplication(addition(X0,X2),omega(X2)),X3)) = addition(multiplication(addition(X0,one),addition(X1,omega(X2))),X3),
inference(paramodulation,[status(thm)],[f10882,f170]) ).
fof(f11006,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),omega(X1)),addition(multiplication(addition(X0,one),X2),X3)) = addition(multiplication(addition(X0,one),addition(omega(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f10882,f170]) ).
fof(f11007,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(omega(X1),one)) = addition(addition(X0,one),multiplication(addition(X0,X1),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f192]) ).
fof(f11008,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,omega(X1))) = addition(addition(X0,one),multiplication(addition(X0,X1),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f162]) ).
fof(f11009,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(omega(X1),X2)) = addition(multiplication(addition(X0,one),X2),multiplication(addition(X0,X1),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f153]) ).
fof(f11010,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,omega(X2))) = addition(multiplication(addition(X0,X2),omega(X2)),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f10882,f153]) ).
fof(f11011,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(omega(X1),coantidomain(multiplication(addition(X0,X1),omega(X1))))) = zero,
inference(paramodulation,[status(thm)],[f10882,f144]) ).
fof(f11012,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,one)),multiplication(addition(X0,X1),omega(X1))) = zero,
inference(paramodulation,[status(thm)],[f10882,f136]) ).
fof(f11013,plain,
! [X0,X1] : addition(coantidomain(multiplication(addition(X0,X1),omega(X1))),coantidomain(multiplication(codomain(addition(X0,one)),omega(X1)))) = coantidomain(multiplication(codomain(addition(X0,one)),omega(X1))),
inference(paramodulation,[status(thm)],[f10882,f615]) ).
fof(f11014,plain,
! [X0,X1] : addition(antidomain(multiplication(addition(X0,X1),omega(X1))),antidomain(multiplication(addition(X0,one),domain(omega(X1))))) = antidomain(multiplication(addition(X0,one),domain(omega(X1)))),
inference(paramodulation,[status(thm)],[f10882,f479]) ).
fof(f11015,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),X2)))
| ~ leq(omega(X0),addition(multiplication(addition(X1,X0),omega(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f10882,f58]) ).
fof(f11016,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(omega(X1))),addition(X0,one))
| ~ leq(addition(multiplication(addition(X0,X1),omega(X1)),X2),addition(X0,one)) ),
inference(paramodulation,[status(thm)],[f10882,f55]) ).
fof(f11017,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,one)),X2),omega(X1))
| ~ leq(addition(multiplication(addition(X0,X1),omega(X1)),X2),omega(X1)) ),
inference(paramodulation,[status(thm)],[f10882,f53]) ).
fof(f11018,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = addition(multiplication(X0,omega(X2)),multiplication(addition(X1,X2),omega(X2))),
inference(paramodulation,[status(thm)],[f10882,f43]) ).
fof(f11019,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),omega(X2)) = addition(multiplication(addition(X0,X2),omega(X2)),multiplication(X1,omega(X2))),
inference(paramodulation,[status(thm)],[f10882,f43]) ).
fof(f11020,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,omega(X2))) = addition(multiplication(addition(X0,one),X1),multiplication(addition(X0,X2),omega(X2))),
inference(paramodulation,[status(thm)],[f10882,f42]) ).
fof(f11021,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(omega(X1),X2)) = addition(multiplication(addition(X0,X1),omega(X1)),multiplication(addition(X0,one),X2)),
inference(paramodulation,[status(thm)],[f10882,f42]) ).
fof(f11022,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(omega(X1),X2)) = multiplication(multiplication(addition(X0,X1),omega(X1)),X2),
inference(paramodulation,[status(thm)],[f10882,f39]) ).
fof(f11023,plain,
! [X0] : leq(multiplication(X0,omega(addition(X0,one))),omega(addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f56,f10883]) ).
fof(f11028,plain,
! [X0] : multiplication(star(X0),omega(multiplication(star(X0),addition(X0,one)))) = multiplication(one,omega(multiplication(star(X0),addition(X0,one)))),
inference(forward_demodulation,[status(thm)],[f38,f10887]) ).
fof(f11029,plain,
! [X0] : multiplication(star(X0),omega(multiplication(star(X0),addition(X0,one)))) = omega(multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f41,f11028]) ).
fof(f11030,plain,
! [X0] : multiplication(star(X0),omega(multiplication(addition(X0,one),star(X0)))) = multiplication(one,omega(multiplication(addition(X0,one),star(X0)))),
inference(forward_demodulation,[status(thm)],[f38,f10888]) ).
fof(f11031,plain,
! [X0] : multiplication(star(X0),omega(multiplication(addition(X0,one),star(X0)))) = omega(multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f41,f11030]) ).
fof(f11070,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,omega(multiplication(X2,X3)))) = multiplication(addition(multiplication(X0,multiplication(X1,X3)),one),omega(multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f39,f10905]) ).
fof(f11071,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,omega(multiplication(X2,X3)))) = multiplication(addition(one,multiplication(X0,multiplication(X1,X3))),omega(multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f35,f11070]) ).
fof(f11072,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X1),X2),X3),omega(addition(multiplication(X1,X2),X3))) = multiplication(addition(one,multiplication(X0,X2)),omega(addition(multiplication(X1,X2),X3))),
inference(forward_demodulation,[status(thm)],[f35,f10906]) ).
fof(f11073,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(addition(multiplication(X0,X2),X3))) = multiplication(addition(one,multiplication(X0,X1)),omega(addition(multiplication(X0,X2),X3))),
inference(forward_demodulation,[status(thm)],[f35,f10907]) ).
fof(f11074,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,omega(multiplication(X1,multiplication(X2,X3))))) = multiplication(addition(multiplication(X0,X3),one),omega(multiplication(X1,multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f39,f10908]) ).
fof(f11075,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,omega(multiplication(X1,multiplication(X2,X3))))) = multiplication(addition(one,multiplication(X0,X3)),omega(multiplication(X1,multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f35,f11074]) ).
fof(f11076,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X0,X2)))) = multiplication(addition(multiplication(X1,X2),one),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f10909]) ).
fof(f11077,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X0,X2)))) = multiplication(addition(one,multiplication(X1,X2)),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f35,f11076]) ).
fof(f11078,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),omega(multiplication(X0,X1)))) = multiplication(addition(multiplication(X0,X2),one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f10910]) ).
fof(f11079,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),omega(multiplication(X0,X1)))) = multiplication(addition(one,multiplication(X0,X2)),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f11078]) ).
fof(f11080,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X1,X2)))) = multiplication(addition(multiplication(X0,X2),one),omega(multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f10911]) ).
fof(f11081,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X1,X2)))) = multiplication(addition(one,multiplication(X0,X2)),omega(multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f11080]) ).
fof(f11082,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),omega(multiplication(X0,X2)))) = multiplication(addition(multiplication(X0,X1),one),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f10912]) ).
fof(f11083,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),omega(multiplication(X0,X2)))) = multiplication(addition(one,multiplication(X0,X1)),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f35,f11082]) ).
fof(f11084,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(X0,addition(X1,one)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f10913]) ).
fof(f11085,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(X1,addition(X0,one)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f10914]) ).
fof(f11088,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,omega(multiplication(X0,X1)))) = multiplication(addition(X1,one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f10928]) ).
fof(f11089,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,omega(multiplication(X0,X1)))) = multiplication(addition(X1,one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f10929]) ).
fof(f11090,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),omega(multiplication(X0,X1)))) = multiplication(addition(X0,one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f10930]) ).
fof(f11091,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),omega(multiplication(X0,X1)))) = multiplication(addition(X0,one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f10931]) ).
fof(f11092,plain,
! [X0,X1] : omega(addition(X0,X1)) = multiplication(addition(X1,one),omega(addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f56,f10933]) ).
fof(f11093,plain,
! [X0,X1] : omega(addition(X0,X1)) = multiplication(addition(X0,one),omega(addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f56,f10934]) ).
fof(f11094,plain,
! [X0] : omega(X0) = multiplication(addition(X0,one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f10939]) ).
fof(f11097,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(X0,addition(X1,one)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f10942]) ).
fof(f11098,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(X1,addition(X0,one)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f10943]) ).
fof(f11101,plain,
! [X0] : multiplication(addition(one,X0),omega(X0)) = omega(X0),
inference(forward_demodulation,[status(thm)],[f41,f10947]) ).
fof(f11109,plain,
! [X0,X1] :
( leq(multiplication(star(X0),omega(X1)),omega(X1))
| ~ leq(multiplication(addition(X0,one),omega(X1)),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f56,f10950]) ).
fof(f11110,plain,
! [X0,X1] :
( multiplication(addition(X0,one),omega(X1)) != multiplication(X1,omega(X1))
| leq(multiplication(X0,omega(X1)),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f56,f10951]) ).
fof(f11111,plain,
! [X0,X1] :
( multiplication(addition(X0,one),omega(X1)) != omega(X1)
| leq(multiplication(X0,omega(X1)),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f56,f11110]) ).
fof(f11112,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X1,one)),omega(X2)),X3) = addition(multiplication(addition(X0,addition(X1,X2)),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f219,f10958]) ).
fof(f11113,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(addition(X0,one),X1),omega(X2)),X3) = addition(multiplication(addition(addition(X0,X2),X1),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f219,f10959]) ).
fof(f11114,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,addition(X0,X1)),omega(X2)),X3) = addition(multiplication(addition(addition(X0,X2),X1),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11113]) ).
fof(f11115,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,addition(X0,X1)),omega(X2)),X3) = addition(multiplication(addition(X2,addition(X0,X1)),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11114]) ).
fof(f11116,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),omega(X0)) = addition(omega(X0),multiplication(addition(X1,one),omega(X0))),
inference(forward_demodulation,[status(thm)],[f103,f10960]) ).
fof(f11117,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),omega(X0)) = multiplication(addition(addition(X1,one),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f232,f11116]) ).
fof(f11118,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),omega(X0)) = multiplication(addition(one,addition(X1,one)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f103,f11117]) ).
fof(f11119,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),omega(X0)) = multiplication(addition(X1,one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f1005,f11118]) ).
fof(f11120,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,X3))),omega(X3)) = multiplication(addition(X0,multiplication(X1,addition(X2,one))),omega(X3)),
inference(forward_demodulation,[status(thm)],[f211,f10961]) ).
fof(f11121,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,multiplication(X2,X3))),omega(X0)) = addition(multiplication(addition(X1,one),omega(X0)),multiplication(X2,multiplication(X3,omega(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f10962]) ).
fof(f11122,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,multiplication(X2,X3))),omega(X0)) = multiplication(addition(addition(X1,one),multiplication(X2,X3)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f211,f11121]) ).
fof(f11123,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,multiplication(X2,X3))),omega(X0)) = multiplication(addition(one,addition(X1,multiplication(X2,X3))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f103,f11122]) ).
fof(f11124,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),omega(X1)) = multiplication(addition(addition(X0,one),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f232,f10963]) ).
fof(f11125,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),omega(X1)) = multiplication(addition(one,addition(X0,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11124]) ).
fof(f11126,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),omega(X1)) = multiplication(addition(X0,one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f1005,f11125]) ).
fof(f11127,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),omega(X3)) = multiplication(addition(multiplication(X0,X1),addition(X2,one)),omega(X3)),
inference(forward_demodulation,[status(thm)],[f204,f10964]) ).
fof(f11128,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),omega(X3)) = multiplication(addition(one,addition(multiplication(X0,X1),X2)),omega(X3)),
inference(forward_demodulation,[status(thm)],[f97,f11127]) ).
fof(f11129,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(X2)) = multiplication(addition(multiplication(X0,addition(X1,one)),X3),omega(X2)),
inference(forward_demodulation,[status(thm)],[f204,f10965]) ).
fof(f11130,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X0)) = addition(multiplication(X2,omega(X0)),multiplication(addition(X1,one),omega(X0))),
inference(forward_demodulation,[status(thm)],[f103,f10966]) ).
fof(f11131,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X0)) = multiplication(addition(addition(X1,one),X2),omega(X0)),
inference(forward_demodulation,[status(thm)],[f201,f11130]) ).
fof(f11132,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X0)) = multiplication(addition(one,addition(X1,X2)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f103,f11131]) ).
fof(f11133,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(X0,addition(X1,one)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f10967]) ).
fof(f11134,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,omega(X1))) = addition(addition(X0,X1),multiplication(addition(X0,one),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f10970]) ).
fof(f11135,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,omega(X1))) = addition(X1,addition(X0,multiplication(addition(X0,one),omega(X1)))),
inference(forward_demodulation,[status(thm)],[f103,f11134]) ).
fof(f11136,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,omega(X1))) = addition(X1,addition(X0,multiplication(addition(X0,one),omega(X1)))),
inference(forward_demodulation,[status(thm)],[f103,f10971]) ).
fof(f11137,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(addition(X1,one),X0),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f10981]) ).
fof(f11138,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(one,addition(X1,X0)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f11137]) ).
fof(f11139,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X0)) = addition(multiplication(addition(X1,one),omega(X0)),multiplication(X2,omega(X0))),
inference(forward_demodulation,[status(thm)],[f103,f10982]) ).
fof(f11140,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X0)) = multiplication(addition(X2,addition(X1,one)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f201,f11139]) ).
fof(f11141,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(addition(X0,one),multiplication(omega(X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f10985]) ).
fof(f11144,plain,
! [X0,X1] :
( leq(multiplication(star(X0),omega(X1)),omega(X1))
| ~ leq(multiplication(addition(X0,X1),omega(X1)),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f10987]) ).
fof(f11145,plain,
! [X0,X1] :
( multiplication(addition(X0,X1),omega(X1)) != multiplication(one,omega(X1))
| leq(multiplication(X0,omega(X1)),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f10988]) ).
fof(f11146,plain,
! [X0,X1] :
( multiplication(addition(X0,X1),omega(X1)) != omega(X1)
| leq(multiplication(X0,omega(X1)),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f11145]) ).
fof(f11147,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X1,X2)),omega(X2)),X3) = addition(multiplication(addition(X0,addition(X1,one)),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f219,f10995]) ).
fof(f11148,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(addition(X0,X1),X2),omega(X1)),X3) = addition(multiplication(addition(addition(X0,one),X2),omega(X1)),X3),
inference(forward_demodulation,[status(thm)],[f219,f10996]) ).
fof(f11149,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X1,X2)),omega(X0)),X3) = addition(multiplication(addition(addition(X1,one),X2),omega(X0)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11148]) ).
fof(f11150,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X1,X2)),omega(X0)),X3) = addition(multiplication(addition(one,addition(X1,X2)),omega(X0)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11149]) ).
fof(f11151,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),omega(X1)) = addition(omega(X1),multiplication(addition(X0,X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f103,f10997]) ).
fof(f11152,plain,
! [X0,X1] : multiplication(addition(X0,one),omega(X1)) = addition(omega(X1),multiplication(addition(X0,X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f1005,f11151]) ).
fof(f11153,plain,
! [X0,X1] : multiplication(addition(X0,one),omega(X1)) = multiplication(addition(addition(X0,X1),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f232,f11152]) ).
fof(f11154,plain,
! [X0,X1] : multiplication(addition(X0,one),omega(X1)) = multiplication(addition(X1,addition(X0,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11153]) ).
fof(f11155,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,one))),omega(X3)) = multiplication(addition(X0,multiplication(X1,addition(X2,X3))),omega(X3)),
inference(forward_demodulation,[status(thm)],[f211,f10998]) ).
fof(f11156,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),omega(X3)) = addition(multiplication(addition(X0,X3),omega(X3)),multiplication(X1,multiplication(X2,omega(X3)))),
inference(forward_demodulation,[status(thm)],[f103,f10999]) ).
fof(f11157,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),omega(X3)) = multiplication(addition(addition(X0,X3),multiplication(X1,X2)),omega(X3)),
inference(forward_demodulation,[status(thm)],[f211,f11156]) ).
fof(f11158,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),omega(X3)) = multiplication(addition(X3,addition(X0,multiplication(X1,X2))),omega(X3)),
inference(forward_demodulation,[status(thm)],[f103,f11157]) ).
fof(f11159,plain,
! [X0,X1] : multiplication(addition(X0,one),omega(X1)) = addition(omega(X1),multiplication(addition(X0,X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f1005,f11000]) ).
fof(f11160,plain,
! [X0,X1] : multiplication(addition(X0,one),omega(X1)) = multiplication(addition(addition(X0,X1),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f232,f11159]) ).
fof(f11161,plain,
! [X0,X1] : multiplication(addition(X0,one),omega(X1)) = multiplication(addition(X1,addition(X0,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11160]) ).
fof(f11162,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(multiplication(X0,X1),X2)),omega(X3)) = addition(multiplication(X0,multiplication(X1,omega(X3))),multiplication(addition(X2,X3),omega(X3))),
inference(forward_demodulation,[status(thm)],[f97,f11001]) ).
fof(f11163,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(multiplication(X0,X1),X2)),omega(X3)) = multiplication(addition(multiplication(X0,X1),addition(X2,X3)),omega(X3)),
inference(forward_demodulation,[status(thm)],[f204,f11162]) ).
fof(f11164,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,one)),X2),omega(X3)) = multiplication(addition(multiplication(X0,addition(X1,X3)),X2),omega(X3)),
inference(forward_demodulation,[status(thm)],[f204,f11002]) ).
fof(f11165,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = addition(multiplication(X1,omega(X2)),multiplication(addition(X0,X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f103,f11003]) ).
fof(f11166,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = multiplication(addition(addition(X0,X2),X1),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f11165]) ).
fof(f11167,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = multiplication(addition(X2,addition(X0,X1)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f11166]) ).
fof(f11168,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = multiplication(addition(X0,addition(X1,X2)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f11004]) ).
fof(f11169,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,omega(X1))) = addition(addition(X0,one),multiplication(addition(X0,X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f11007]) ).
fof(f11170,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,omega(X1))) = addition(one,addition(X0,multiplication(addition(X0,X1),omega(X1)))),
inference(forward_demodulation,[status(thm)],[f103,f11169]) ).
fof(f11171,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,omega(X1))) = addition(one,addition(X0,multiplication(addition(X0,X1),omega(X1)))),
inference(forward_demodulation,[status(thm)],[f103,f11008]) ).
fof(f11172,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = multiplication(addition(addition(X1,X2),X0),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f11018]) ).
fof(f11173,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = multiplication(addition(X2,addition(X1,X0)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f11172]) ).
fof(f11174,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = addition(multiplication(addition(X0,X2),omega(X2)),multiplication(X1,omega(X2))),
inference(forward_demodulation,[status(thm)],[f103,f11019]) ).
fof(f11175,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = multiplication(addition(X1,addition(X0,X2)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f11174]) ).
fof(f11176,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(omega(X1),X2)) = multiplication(addition(X0,X1),multiplication(omega(X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f11022]) ).
fof(f11180,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f103,f1329]) ).
fof(f11181,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f36,f1329]) ).
fof(f11189,plain,
! [X0] : addition(multiplication(star(X0),addition(X0,one)),star(X0)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(paramodulation,[status(thm)],[f7789,f1329]) ).
fof(f11190,plain,
! [X0] : addition(multiplication(addition(X0,one),star(X0)),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(paramodulation,[status(thm)],[f7510,f1329]) ).
fof(f11208,plain,
! [X0,X1,X2,X3] : addition(addition(multiplication(X0,X1),X2),addition(multiplication(addition(X3,X0),X1),X2)) = addition(addition(multiplication(X0,X1),X2),multiplication(X3,X1)),
inference(paramodulation,[status(thm)],[f219,f1329]) ).
fof(f11209,plain,
! [X0,X1,X2,X3] : addition(addition(multiplication(X0,X1),X2),addition(multiplication(X0,addition(X3,X1)),X2)) = addition(addition(multiplication(X0,X1),X2),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f170,f1329]) ).
fof(f11215,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f103,f1329]) ).
fof(f11216,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f36,f1329]) ).
fof(f11238,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f97,f1329]) ).
fof(f11239,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X2,X0))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f97,f1329]) ).
fof(f11244,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(X1,omega(X0))),omega(X0))
| ~ leq(addition(omega(X0),X1),omega(X0)) ),
inference(paramodulation,[status(thm)],[f1329,f314]) ).
fof(f11246,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X0)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X0)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != addition(forward_diamond(X1,domain(X0)),domain(X0)) ),
inference(paramodulation,[status(thm)],[f1329,f75]) ).
fof(f11249,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f1329,f207]) ).
fof(f11256,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f1329,f162]) ).
fof(f11257,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),addition(X3,multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f1329,f296]) ).
fof(f11260,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),addition(X3,multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f1329,f219]) ).
fof(f11261,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),addition(X3,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f1329,f170]) ).
fof(f11262,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),addition(X2,multiplication(X1,X0)))))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f1329,f58]) ).
fof(f11263,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X2,multiplication(X0,X1)),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f1329,f55]) ).
fof(f11264,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(X2,multiplication(X0,X1))),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f1329,f53]) ).
fof(f11265,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1329,f103]) ).
fof(f11266,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f1329,f36]) ).
fof(f11270,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f1329,f243]) ).
fof(f11276,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(addition(X1,X0))) = multiplication(addition(X0,one),omega(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1329,f10882]) ).
fof(f11281,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(X1,X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1329,f302]) ).
fof(f11282,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,addition(X2,X1))),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f1329,f291]) ).
fof(f11283,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(addition(X1,X0),X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f1329,f290]) ).
fof(f11284,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X2,X1)
| leq(addition(X0,X1),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f1329,f243]) ).
fof(f11285,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,addition(X2,X1))
| leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))) ),
inference(paramodulation,[status(thm)],[f1329,f242]) ).
fof(f11286,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(addition(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)) ),
inference(paramodulation,[status(thm)],[f1329,f241]) ).
fof(f11287,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X1,X0))) = multiplication(X0,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1329,f233]) ).
fof(f11289,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X1,X0)) = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f1329,f186]) ).
fof(f11292,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1329,f1420]) ).
fof(f11296,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1329,f103]) ).
fof(f11297,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1329,f97]) ).
fof(f11298,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1329,f97]) ).
fof(f11299,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f1329,f246]) ).
fof(f11301,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f1329,f36]) ).
fof(f11307,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f11180]) ).
fof(f11308,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f11181]) ).
fof(f11313,plain,
! [X0] : addition(star(X0),multiplication(star(X0),addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f35,f11189]) ).
fof(f11314,plain,
! [X0] : multiplication(star(X0),addition(addition(X0,one),one)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f192,f11313]) ).
fof(f11315,plain,
! [X0] : multiplication(star(X0),addition(one,addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f103,f11314]) ).
fof(f11316,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f1329,f11315]) ).
fof(f11317,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f35,f11316]) ).
fof(f11318,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f7789,f11317]) ).
fof(f11319,plain,
! [X0] : addition(star(X0),multiplication(addition(X0,one),star(X0))) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f35,f11190]) ).
fof(f11320,plain,
! [X0] : multiplication(addition(addition(X0,one),one),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f232,f11319]) ).
fof(f11321,plain,
! [X0] : multiplication(addition(one,addition(X0,one)),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f103,f11320]) ).
fof(f11322,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f1329,f11321]) ).
fof(f11323,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f35,f11322]) ).
fof(f11324,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f7510,f11323]) ).
fof(f11343,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,X2),addition(multiplication(addition(X3,X1),X2),X0))) = addition(addition(multiplication(X1,X2),X0),multiplication(X3,X2)),
inference(forward_demodulation,[status(thm)],[f103,f11208]) ).
fof(f11344,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(addition(X1,addition(X2,X1)),X3),X0)) = addition(addition(multiplication(X1,X3),X0),multiplication(X2,X3)),
inference(forward_demodulation,[status(thm)],[f219,f11343]) ).
fof(f11345,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,addition(X2,X1)),X3)) = addition(addition(multiplication(X1,X3),X0),multiplication(X2,X3)),
inference(forward_demodulation,[status(thm)],[f1329,f11344]) ).
fof(f11346,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(addition(multiplication(X1,X3),X0),multiplication(X2,X3)),
inference(forward_demodulation,[status(thm)],[f1329,f11345]) ).
fof(f11347,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(X0,addition(multiplication(X1,X3),multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f103,f11346]) ).
fof(f11348,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(X0,multiplication(addition(X2,X1),X3)),
inference(forward_demodulation,[status(thm)],[f201,f11347]) ).
fof(f11349,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,X2),addition(multiplication(X1,addition(X3,X2)),X0))) = addition(addition(multiplication(X1,X2),X0),multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f103,f11209]) ).
fof(f11350,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,addition(X2,addition(X3,X2))),X0)) = addition(addition(multiplication(X1,X2),X0),multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f170,f11349]) ).
fof(f11351,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,addition(X3,X2)))) = addition(addition(multiplication(X1,X2),X0),multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f1329,f11350]) ).
fof(f11352,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(addition(multiplication(X1,X2),X0),multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f1329,f11351]) ).
fof(f11353,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f103,f11352]) ).
fof(f11354,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f153,f11353]) ).
fof(f11403,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f11238]) ).
fof(f11404,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f1026,f11403]) ).
fof(f11405,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f103,f11404]) ).
fof(f11406,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f103,f11405]) ).
fof(f11407,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X2,X1)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f103,f11239]) ).
fof(f11408,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X2,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f11407]) ).
fof(f11409,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X0)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X0)))
| addition(domain(X0),forward_diamond(X1,domain(X0))) != addition(domain(X0),forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f11246]) ).
fof(f11410,plain,
! [X0,X1] : addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X0)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X0))),
inference(trivial_equality_resolution,[status(thm)],[f11409]) ).
fof(f11417,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X0,X1),X2),addition(X3,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f219,f11260]) ).
fof(f11418,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(X1,X2),addition(multiplication(addition(X0,X1),X2),X3)),
inference(forward_demodulation,[status(thm)],[f97,f11417]) ).
fof(f11419,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X1,addition(X0,X1)),X2),X3),
inference(forward_demodulation,[status(thm)],[f219,f11418]) ).
fof(f11420,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X1,X0),X2),X3),
inference(forward_demodulation,[status(thm)],[f1329,f11419]) ).
fof(f11421,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X1,X2)),addition(X3,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f170,f11261]) ).
fof(f11422,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,X2),addition(multiplication(X0,addition(X1,X2)),X3)),
inference(forward_demodulation,[status(thm)],[f97,f11421]) ).
fof(f11423,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X2,addition(X1,X2))),X3),
inference(forward_demodulation,[status(thm)],[f170,f11422]) ).
fof(f11424,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f1329,f11423]) ).
fof(f11425,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f103,f11265]) ).
fof(f11426,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f11266]) ).
fof(f11441,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f103,f11296]) ).
fof(f11442,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f11441]) ).
fof(f11443,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f103,f11297]) ).
fof(f11444,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f1026,f11443]) ).
fof(f11445,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f11298]) ).
fof(f11446,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f103,f11301]) ).
fof(f11447,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f1026,f11446]) ).
fof(f11448,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f36,f11447]) ).
fof(f11449,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(X1,one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f232,f316]) ).
fof(f11456,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(codomain(X0),X1)),omega(coantidomain(multiplication(X0,X1)))) = multiplication(addition(coantidomain(multiplication(codomain(X0),X1)),one),omega(coantidomain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f615,f11449]) ).
fof(f11458,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),omega(antidomain(multiplication(X0,X1)))) = multiplication(addition(antidomain(multiplication(X0,domain(X1))),one),omega(antidomain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f479,f11449]) ).
fof(f11459,plain,
! [X0] : multiplication(c(X0),omega(antidomain(X0))) = multiplication(addition(c(X0),one),omega(antidomain(X0))),
inference(paramodulation,[status(thm)],[f514,f11449]) ).
fof(f11461,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(addition(multiplication(X0,X1),X2),X3),omega(multiplication(X0,multiplication(X1,X3)))) = multiplication(addition(multiplication(X2,X3),one),omega(multiplication(X0,multiplication(X1,X3)))),
inference(paramodulation,[status(thm)],[f204,f11449]) ).
fof(f11462,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X1),X2),X3),omega(multiplication(X0,X2))) = multiplication(addition(addition(multiplication(X1,X2),X3),one),omega(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f219,f11449]) ).
fof(f11463,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(multiplication(X0,X1))) = multiplication(addition(addition(multiplication(X0,X2),X3),one),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f170,f11449]) ).
fof(f11464,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(addition(X0,multiplication(X1,X2)),X3),omega(multiplication(X0,X3))) = multiplication(addition(multiplication(X1,multiplication(X2,X3)),one),omega(multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f211,f11449]) ).
fof(f11465,plain,
! [X0,X1,X2] : multiplication(multiplication(addition(X0,X1),X2),omega(multiplication(X1,X2))) = multiplication(addition(multiplication(X0,X2),one),omega(multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f201,f11449]) ).
fof(f11466,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,X2)),omega(multiplication(X0,X2))) = multiplication(addition(multiplication(X0,X1),one),omega(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f153,f11449]) ).
fof(f11467,plain,
! [X0,X1,X2] : multiplication(multiplication(addition(X0,X1),X2),omega(multiplication(X0,X2))) = multiplication(addition(multiplication(X1,X2),one),omega(multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f43,f11449]) ).
fof(f11468,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,X2)),omega(multiplication(X0,X1))) = multiplication(addition(multiplication(X0,X2),one),omega(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f42,f11449]) ).
fof(f11469,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(addition(X1,X0))) = multiplication(addition(X2,one),omega(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f103,f11449]) ).
fof(f11470,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(addition(X0,X1))) = multiplication(addition(X2,one),omega(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f11449]) ).
fof(f11472,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(domain(X1),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4516,f11449]) ).
fof(f11473,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(coantidomain(X1),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4515,f11449]) ).
fof(f11474,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(antidomain(X1),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4514,f11449]) ).
fof(f11475,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(c(X1),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4513,f11449]) ).
fof(f11476,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(codomain(X1),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4512,f11449]) ).
fof(f11477,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(divergence(X1),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4511,f11449]) ).
fof(f11478,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,domain(X1)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2497,f11449]) ).
fof(f11479,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,coantidomain(X1)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2496,f11449]) ).
fof(f11480,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,antidomain(X1)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2495,f11449]) ).
fof(f11481,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,c(X1)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2494,f11449]) ).
fof(f11482,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,codomain(X1)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2493,f11449]) ).
fof(f11483,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,divergence(X1)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2492,f11449]) ).
fof(f11484,plain,
! [X0,X1] : multiplication(multiplication(addition(X0,one),X1),omega(X1)) = multiplication(addition(multiplication(X0,X1),one),omega(X1)),
inference(paramodulation,[status(thm)],[f232,f11449]) ).
fof(f11485,plain,
! [X0,X1] : multiplication(multiplication(addition(one,X0),X1),omega(X1)) = multiplication(addition(multiplication(X0,X1),one),omega(X1)),
inference(paramodulation,[status(thm)],[f207,f11449]) ).
fof(f11486,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(X1,one)),omega(X0)) = multiplication(addition(multiplication(X0,X1),one),omega(X0)),
inference(paramodulation,[status(thm)],[f192,f11449]) ).
fof(f11487,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(one,X1)),omega(X0)) = multiplication(addition(multiplication(X0,X1),one),omega(X0)),
inference(paramodulation,[status(thm)],[f162,f11449]) ).
fof(f11488,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(addition(X1,X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f1329,f11449]) ).
fof(f11489,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = multiplication(addition(addition(X1,X0),one),omega(X1)),
inference(paramodulation,[status(thm)],[f1026,f11449]) ).
fof(f11490,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = multiplication(addition(addition(X0,X1),one),omega(X1)),
inference(paramodulation,[status(thm)],[f1005,f11449]) ).
fof(f11491,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(addition(X0,X1),one),omega(X0)),
inference(paramodulation,[status(thm)],[f105,f11449]) ).
fof(f11492,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(addition(X0,X1),one),omega(X2)),
inference(paramodulation,[status(thm)],[f97,f11449]) ).
fof(f11493,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = multiplication(addition(addition(X2,X0),one),omega(X1)),
inference(paramodulation,[status(thm)],[f97,f11449]) ).
fof(f11497,plain,
! [X0] : multiplication(X0,omega(X0)) = multiplication(addition(X0,one),omega(X0)),
inference(paramodulation,[status(thm)],[f38,f11449]) ).
fof(f11501,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(X1,X0),omega(X0)),
inference(paramodulation,[status(thm)],[f10882,f11449]) ).
fof(f11503,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X0)) = multiplication(addition(X2,addition(X1,one)),omega(X0)),
inference(paramodulation,[status(thm)],[f103,f11449]) ).
fof(f11504,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X0)) = multiplication(addition(X1,addition(X2,one)),omega(X0)),
inference(paramodulation,[status(thm)],[f36,f11449]) ).
fof(f11506,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(one,X1),omega(X0)),
inference(paramodulation,[status(thm)],[f35,f11449]) ).
fof(f11507,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(one,X1),omega(X0)),
inference(paramodulation,[status(thm)],[f35,f11449]) ).
fof(f11508,plain,
! [X0] : multiplication(addition(X0,one),omega(X0)) = multiplication(one,omega(X0)),
inference(paramodulation,[status(thm)],[f38,f11449]) ).
fof(f11513,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,omega(X1))),omega(X1))
| ~ leq(multiplication(addition(X0,one),omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f11449,f290]) ).
fof(f11514,plain,
! [X0,X1] :
( multiplication(addition(X1,one),omega(X0)) != multiplication(X1,omega(X0))
| leq(multiplication(X0,omega(X0)),multiplication(X1,omega(X0))) ),
inference(paramodulation,[status(thm)],[f11449,f241]) ).
fof(f11515,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(omega(X0),omega(multiplication(addition(X1,one),omega(X0))))) = omega(multiplication(addition(X0,X1),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f308]) ).
fof(f11516,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(X2,X1))),X3),omega(X2))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,one),omega(X2))),X3),omega(X2)) ),
inference(paramodulation,[status(thm)],[f11449,f296]) ).
fof(f11517,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X1,X0)),multiplication(addition(X1,X0),omega(X1))),omega(X1))
| ~ leq(multiplication(addition(X0,one),omega(X1)),omega(X1)) ),
inference(paramodulation,[status(thm)],[f11449,f295]) ).
fof(f11518,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X2,X1)),X0),omega(X2))
| ~ leq(addition(X0,multiplication(addition(X1,one),omega(X2))),omega(X2)) ),
inference(paramodulation,[status(thm)],[f11449,f293]) ).
fof(f11519,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(omega(X0),star(multiplication(addition(X0,X1),omega(X0)))))),star(multiplication(addition(X1,one),omega(X0)))),
inference(paramodulation,[status(thm)],[f11449,f252]) ).
fof(f11520,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,X1),multiplication(omega(X0),star(multiplication(addition(X1,one),omega(X0)))))),star(multiplication(addition(X0,X1),omega(X0)))),
inference(paramodulation,[status(thm)],[f11449,f252]) ).
fof(f11521,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,omega(X1)),addition(multiplication(addition(X2,one),omega(X1)),X3)) = addition(multiplication(addition(X0,addition(X1,X2)),omega(X1)),X3),
inference(paramodulation,[status(thm)],[f11449,f219]) ).
fof(f11522,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),omega(X1)),addition(multiplication(X2,omega(X1)),X3)) = addition(multiplication(addition(addition(X1,X0),X2),omega(X1)),X3),
inference(paramodulation,[status(thm)],[f11449,f219]) ).
fof(f11523,plain,
! [X0,X1] : multiplication(addition(addition(X0,X1),one),omega(X0)) = addition(omega(X0),multiplication(addition(X1,one),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f232]) ).
fof(f11524,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,X3))),omega(X2)) = addition(multiplication(X0,omega(X2)),multiplication(X1,multiplication(addition(X3,one),omega(X2)))),
inference(paramodulation,[status(thm)],[f11449,f211]) ).
fof(f11525,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,X1),multiplication(X2,X3)),omega(X0)) = addition(multiplication(addition(X1,one),omega(X0)),multiplication(X2,multiplication(X3,omega(X0)))),
inference(paramodulation,[status(thm)],[f11449,f211]) ).
fof(f11526,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),omega(X0)) = addition(omega(X0),multiplication(addition(X1,one),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f207]) ).
fof(f11527,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),omega(X2)) = addition(multiplication(X0,multiplication(X1,omega(X2))),multiplication(addition(X3,one),omega(X2))),
inference(paramodulation,[status(thm)],[f11449,f204]) ).
fof(f11528,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(X1)) = addition(multiplication(X0,multiplication(addition(X2,one),omega(X1))),multiplication(X3,omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f204]) ).
fof(f11529,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),omega(X0)) = addition(multiplication(X2,omega(X0)),multiplication(addition(X1,one),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f201]) ).
fof(f11530,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = addition(multiplication(addition(X2,one),omega(X1)),multiplication(X0,omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f201]) ).
fof(f11531,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),addition(multiplication(addition(X1,one),omega(X0)),X3)) = addition(multiplication(addition(X0,X1),addition(X2,omega(X0))),X3),
inference(paramodulation,[status(thm)],[f11449,f170]) ).
fof(f11532,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),omega(X1)),addition(multiplication(addition(X1,X0),X2),X3)) = addition(multiplication(addition(X1,X0),addition(omega(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f11449,f170]) ).
fof(f11533,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(omega(X0),one)) = addition(addition(X0,X1),multiplication(addition(X1,one),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f192]) ).
fof(f11534,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,omega(X0))) = addition(addition(X0,X1),multiplication(addition(X1,one),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f162]) ).
fof(f11535,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X0),X2)) = addition(multiplication(addition(X0,X1),X2),multiplication(addition(X1,one),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f153]) ).
fof(f11536,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X0))) = addition(multiplication(addition(X1,one),omega(X0)),multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f11449,f153]) ).
fof(f11537,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(omega(X0),coantidomain(multiplication(addition(X1,one),omega(X0))))) = zero,
inference(paramodulation,[status(thm)],[f11449,f144]) ).
fof(f11538,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),multiplication(addition(X1,one),omega(X0))) = zero,
inference(paramodulation,[status(thm)],[f11449,f136]) ).
fof(f11539,plain,
! [X0,X1] : addition(coantidomain(multiplication(addition(X0,one),omega(X1))),coantidomain(multiplication(codomain(addition(X1,X0)),omega(X1)))) = coantidomain(multiplication(codomain(addition(X1,X0)),omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f615]) ).
fof(f11540,plain,
! [X0,X1] : addition(antidomain(multiplication(addition(X0,one),omega(X1))),antidomain(multiplication(addition(X1,X0),domain(omega(X1))))) = antidomain(multiplication(addition(X1,X0),domain(omega(X1)))),
inference(paramodulation,[status(thm)],[f11449,f479]) ).
fof(f11541,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(addition(X0,X1)),multiplication(star(addition(X0,X1)),X2)))
| ~ leq(omega(X0),addition(multiplication(addition(X1,one),omega(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f11449,f58]) ).
fof(f11542,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(omega(X1))),addition(X1,X0))
| ~ leq(addition(multiplication(addition(X0,one),omega(X1)),X2),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f11449,f55]) ).
fof(f11543,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,X0)),X2),omega(X1))
| ~ leq(addition(multiplication(addition(X0,one),omega(X1)),X2),omega(X1)) ),
inference(paramodulation,[status(thm)],[f11449,f53]) ).
fof(f11544,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = addition(multiplication(X0,omega(X1)),multiplication(addition(X2,one),omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f43]) ).
fof(f11545,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X2),omega(X0)) = addition(multiplication(addition(X1,one),omega(X0)),multiplication(X2,omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f43]) ).
fof(f11546,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X0))) = addition(multiplication(addition(X0,X1),X2),multiplication(addition(X1,one),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f42]) ).
fof(f11547,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X0),X2)) = addition(multiplication(addition(X1,one),omega(X0)),multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f11449,f42]) ).
fof(f11548,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(multiplication(addition(X1,one),omega(X0)),X2),
inference(paramodulation,[status(thm)],[f11449,f39]) ).
fof(f11550,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = multiplication(addition(X1,X0),omega(X1)),
inference(paramodulation,[status(thm)],[f11449,f10882]) ).
fof(f11551,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(one,omega(X0))),omega(X0))
| ~ leq(multiplication(addition(X0,X1),omega(X0)),omega(X0)) ),
inference(paramodulation,[status(thm)],[f11449,f290]) ).
fof(f11552,plain,
! [X0,X1] :
( multiplication(addition(X1,X0),omega(X1)) != multiplication(one,omega(X1))
| leq(multiplication(X0,omega(X1)),multiplication(one,omega(X1))) ),
inference(paramodulation,[status(thm)],[f11449,f241]) ).
fof(f11553,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(omega(X1),omega(multiplication(addition(X1,X0),omega(X1))))) = omega(multiplication(addition(X0,one),omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f308]) ).
fof(f11554,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,addition(X2,one))),X3),omega(X1))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,X2),omega(X1))),X3),omega(X1)) ),
inference(paramodulation,[status(thm)],[f11449,f296]) ).
fof(f11555,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X1,one)),multiplication(addition(X1,one),omega(X0))),omega(X0))
| ~ leq(multiplication(addition(X0,X1),omega(X0)),omega(X0)) ),
inference(paramodulation,[status(thm)],[f11449,f295]) ).
fof(f11556,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X2,one)),X0),omega(X1))
| ~ leq(addition(X0,multiplication(addition(X1,X2),omega(X1))),omega(X1)) ),
inference(paramodulation,[status(thm)],[f11449,f293]) ).
fof(f11557,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,one),multiplication(omega(X1),star(multiplication(addition(X0,one),omega(X1)))))),star(multiplication(addition(X1,X0),omega(X1)))),
inference(paramodulation,[status(thm)],[f11449,f252]) ).
fof(f11558,plain,
! [X0,X1] : leq(addition(one,multiplication(addition(X0,one),multiplication(omega(X1),star(multiplication(addition(X1,X0),omega(X1)))))),star(multiplication(addition(X0,one),omega(X1)))),
inference(paramodulation,[status(thm)],[f11449,f252]) ).
fof(f11559,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,omega(X1)),addition(multiplication(addition(X1,X2),omega(X1)),X3)) = addition(multiplication(addition(X0,addition(X2,one)),omega(X1)),X3),
inference(paramodulation,[status(thm)],[f11449,f219]) ).
fof(f11560,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),omega(X0)),addition(multiplication(X2,omega(X0)),X3)) = addition(multiplication(addition(addition(X1,one),X2),omega(X0)),X3),
inference(paramodulation,[status(thm)],[f11449,f219]) ).
fof(f11561,plain,
! [X0,X1] : multiplication(addition(addition(X0,one),one),omega(X1)) = addition(omega(X1),multiplication(addition(X1,X0),omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f232]) ).
fof(f11562,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,one))),omega(X3)) = addition(multiplication(X0,omega(X3)),multiplication(X1,multiplication(addition(X3,X2),omega(X3)))),
inference(paramodulation,[status(thm)],[f11449,f211]) ).
fof(f11563,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,one),multiplication(X1,X2)),omega(X3)) = addition(multiplication(addition(X3,X0),omega(X3)),multiplication(X1,multiplication(X2,omega(X3)))),
inference(paramodulation,[status(thm)],[f11449,f211]) ).
fof(f11564,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),omega(X1)) = addition(omega(X1),multiplication(addition(X1,X0),omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f207]) ).
fof(f11565,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,one)),omega(X3)) = addition(multiplication(X0,multiplication(X1,omega(X3))),multiplication(addition(X3,X2),omega(X3))),
inference(paramodulation,[status(thm)],[f11449,f204]) ).
fof(f11566,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,one)),X2),omega(X3)) = addition(multiplication(X0,multiplication(addition(X3,X1),omega(X3))),multiplication(X2,omega(X3))),
inference(paramodulation,[status(thm)],[f11449,f204]) ).
fof(f11567,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),omega(X2)) = addition(multiplication(X1,omega(X2)),multiplication(addition(X2,X0),omega(X2))),
inference(paramodulation,[status(thm)],[f11449,f201]) ).
fof(f11568,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = addition(multiplication(addition(X2,X1),omega(X2)),multiplication(X0,omega(X2))),
inference(paramodulation,[status(thm)],[f11449,f201]) ).
fof(f11569,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),X1),addition(multiplication(addition(X2,X0),omega(X2)),X3)) = addition(multiplication(addition(X0,one),addition(X1,omega(X2))),X3),
inference(paramodulation,[status(thm)],[f11449,f170]) ).
fof(f11570,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),omega(X0)),addition(multiplication(addition(X1,one),X2),X3)) = addition(multiplication(addition(X1,one),addition(omega(X0),X2)),X3),
inference(paramodulation,[status(thm)],[f11449,f170]) ).
fof(f11571,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(omega(X1),one)) = addition(addition(X0,one),multiplication(addition(X1,X0),omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f192]) ).
fof(f11572,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,omega(X1))) = addition(addition(X0,one),multiplication(addition(X1,X0),omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f162]) ).
fof(f11573,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(omega(X1),X2)) = addition(multiplication(addition(X0,one),X2),multiplication(addition(X1,X0),omega(X1))),
inference(paramodulation,[status(thm)],[f11449,f153]) ).
fof(f11574,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,omega(X2))) = addition(multiplication(addition(X2,X0),omega(X2)),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f11449,f153]) ).
fof(f11575,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(omega(X1),coantidomain(multiplication(addition(X1,X0),omega(X1))))) = zero,
inference(paramodulation,[status(thm)],[f11449,f144]) ).
fof(f11576,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,one)),multiplication(addition(X1,X0),omega(X1))) = zero,
inference(paramodulation,[status(thm)],[f11449,f136]) ).
fof(f11577,plain,
! [X0,X1] : addition(coantidomain(multiplication(addition(X0,X1),omega(X0))),coantidomain(multiplication(codomain(addition(X1,one)),omega(X0)))) = coantidomain(multiplication(codomain(addition(X1,one)),omega(X0))),
inference(paramodulation,[status(thm)],[f11449,f615]) ).
fof(f11578,plain,
! [X0,X1] : addition(antidomain(multiplication(addition(X0,X1),omega(X0))),antidomain(multiplication(addition(X1,one),domain(omega(X0))))) = antidomain(multiplication(addition(X1,one),domain(omega(X0)))),
inference(paramodulation,[status(thm)],[f11449,f479]) ).
fof(f11579,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),X2)))
| ~ leq(omega(X0),addition(multiplication(addition(X0,X1),omega(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f11449,f58]) ).
fof(f11580,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(omega(X0))),addition(X1,one))
| ~ leq(addition(multiplication(addition(X0,X1),omega(X0)),X2),addition(X1,one)) ),
inference(paramodulation,[status(thm)],[f11449,f55]) ).
fof(f11581,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,one)),X2),omega(X0))
| ~ leq(addition(multiplication(addition(X0,X1),omega(X0)),X2),omega(X0)) ),
inference(paramodulation,[status(thm)],[f11449,f53]) ).
fof(f11582,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = addition(multiplication(X0,omega(X2)),multiplication(addition(X2,X1),omega(X2))),
inference(paramodulation,[status(thm)],[f11449,f43]) ).
fof(f11583,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),omega(X2)) = addition(multiplication(addition(X2,X0),omega(X2)),multiplication(X1,omega(X2))),
inference(paramodulation,[status(thm)],[f11449,f43]) ).
fof(f11584,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,omega(X2))) = addition(multiplication(addition(X0,one),X1),multiplication(addition(X2,X0),omega(X2))),
inference(paramodulation,[status(thm)],[f11449,f42]) ).
fof(f11585,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(omega(X1),X2)) = addition(multiplication(addition(X1,X0),omega(X1)),multiplication(addition(X0,one),X2)),
inference(paramodulation,[status(thm)],[f11449,f42]) ).
fof(f11586,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(omega(X1),X2)) = multiplication(multiplication(addition(X1,X0),omega(X1)),X2),
inference(paramodulation,[status(thm)],[f11449,f39]) ).
fof(f11598,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(codomain(X0),X1)),omega(coantidomain(multiplication(X0,X1)))) = multiplication(addition(one,coantidomain(multiplication(codomain(X0),X1))),omega(coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f35,f11456]) ).
fof(f11599,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(codomain(X0),X1)),omega(coantidomain(multiplication(X0,X1)))) = multiplication(one,omega(coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1377,f11598]) ).
fof(f11600,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(codomain(X0),X1)),omega(coantidomain(multiplication(X0,X1)))) = omega(coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f41,f11599]) ).
fof(f11604,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),omega(antidomain(multiplication(X0,X1)))) = multiplication(addition(one,antidomain(multiplication(X0,domain(X1)))),omega(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f35,f11458]) ).
fof(f11605,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),omega(antidomain(multiplication(X0,X1)))) = multiplication(one,omega(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1379,f11604]) ).
fof(f11606,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),omega(antidomain(multiplication(X0,X1)))) = omega(antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f41,f11605]) ).
fof(f11607,plain,
! [X0] : multiplication(c(X0),omega(antidomain(X0))) = multiplication(addition(one,c(X0)),omega(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f11459]) ).
fof(f11608,plain,
! [X0] : multiplication(c(X0),omega(antidomain(X0))) = multiplication(one,omega(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f1471,f11607]) ).
fof(f11609,plain,
! [X0] : multiplication(c(X0),omega(antidomain(X0))) = omega(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f41,f11608]) ).
fof(f11613,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,omega(multiplication(X0,multiplication(X1,X3))))) = multiplication(addition(multiplication(X2,X3),one),omega(multiplication(X0,multiplication(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f39,f11461]) ).
fof(f11614,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,omega(multiplication(X0,multiplication(X1,X3))))) = multiplication(addition(one,multiplication(X2,X3)),omega(multiplication(X0,multiplication(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f35,f11613]) ).
fof(f11615,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X1),X2),X3),omega(multiplication(X0,X2))) = multiplication(addition(X3,addition(multiplication(X1,X2),one)),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f11462]) ).
fof(f11616,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(addition(X0,X1),X2),X3),omega(multiplication(X0,X2))) = multiplication(addition(X3,addition(one,multiplication(X1,X2))),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f35,f11615]) ).
fof(f11617,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(multiplication(X0,X1))) = multiplication(addition(X3,addition(multiplication(X0,X2),one)),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f11463]) ).
fof(f11618,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(multiplication(X0,X1))) = multiplication(addition(X3,addition(one,multiplication(X0,X2))),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f11617]) ).
fof(f11619,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,omega(multiplication(X0,X3)))) = multiplication(addition(multiplication(X1,multiplication(X2,X3)),one),omega(multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f39,f11464]) ).
fof(f11620,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,omega(multiplication(X0,X3)))) = multiplication(addition(one,multiplication(X1,multiplication(X2,X3))),omega(multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f35,f11619]) ).
fof(f11621,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X1,X2)))) = multiplication(addition(multiplication(X0,X2),one),omega(multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f11465]) ).
fof(f11622,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X1,X2)))) = multiplication(addition(one,multiplication(X0,X2)),omega(multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f35,f11621]) ).
fof(f11623,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),omega(multiplication(X0,X2)))) = multiplication(addition(multiplication(X0,X1),one),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f11466]) ).
fof(f11624,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),omega(multiplication(X0,X2)))) = multiplication(addition(one,multiplication(X0,X1)),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f35,f11623]) ).
fof(f11625,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X0,X2)))) = multiplication(addition(multiplication(X1,X2),one),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f11467]) ).
fof(f11626,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(X2,omega(multiplication(X0,X2)))) = multiplication(addition(one,multiplication(X1,X2)),omega(multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f35,f11625]) ).
fof(f11627,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),omega(multiplication(X0,X1)))) = multiplication(addition(multiplication(X0,X2),one),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f39,f11468]) ).
fof(f11628,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,X2),omega(multiplication(X0,X1)))) = multiplication(addition(one,multiplication(X0,X2)),omega(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f11627]) ).
fof(f11634,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(domain(X1),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11472]) ).
fof(f11635,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(domain(X1),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11634]) ).
fof(f11636,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(coantidomain(X1),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11473]) ).
fof(f11637,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(coantidomain(X1),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11636]) ).
fof(f11638,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(antidomain(X1),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11474]) ).
fof(f11639,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(antidomain(X1),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11638]) ).
fof(f11640,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(c(X1),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11475]) ).
fof(f11641,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(c(X1),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11640]) ).
fof(f11642,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(codomain(X1),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11476]) ).
fof(f11643,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(codomain(X1),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11642]) ).
fof(f11644,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(divergence(X1),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11477]) ).
fof(f11645,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(divergence(X1),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11644]) ).
fof(f11646,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(X0,domain(X1)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11478]) ).
fof(f11647,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(X0,domain(X1))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11646]) ).
fof(f11648,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(X0,coantidomain(X1)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11479]) ).
fof(f11649,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(X0,coantidomain(X1))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11648]) ).
fof(f11650,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(X0,antidomain(X1)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11480]) ).
fof(f11651,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(X0,antidomain(X1))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11650]) ).
fof(f11652,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(X0,c(X1)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11481]) ).
fof(f11653,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(X0,c(X1))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11652]) ).
fof(f11654,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(X0,codomain(X1)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11482]) ).
fof(f11655,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(X0,codomain(X1))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11654]) ).
fof(f11656,plain,
! [X0,X1] : omega(X0) = multiplication(addition(multiplication(X0,divergence(X1)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11483]) ).
fof(f11657,plain,
! [X0,X1] : omega(X0) = multiplication(addition(one,multiplication(X0,divergence(X1))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11656]) ).
fof(f11658,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,omega(X1))) = multiplication(addition(multiplication(X0,X1),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f39,f11484]) ).
fof(f11659,plain,
! [X0,X1] : multiplication(addition(X0,one),omega(X1)) = multiplication(addition(multiplication(X0,X1),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f56,f11658]) ).
fof(f11660,plain,
! [X0,X1] : multiplication(addition(X0,one),omega(X1)) = multiplication(addition(one,multiplication(X0,X1)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f35,f11659]) ).
fof(f11661,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,omega(X1))) = multiplication(addition(multiplication(X0,X1),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f39,f11485]) ).
fof(f11662,plain,
! [X0,X1] : multiplication(addition(one,X0),omega(X1)) = multiplication(addition(multiplication(X0,X1),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f56,f11661]) ).
fof(f11663,plain,
! [X0,X1] : multiplication(addition(one,X0),omega(X1)) = multiplication(addition(one,multiplication(X0,X1)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f35,f11662]) ).
fof(f11664,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),omega(X0))) = multiplication(addition(multiplication(X0,X1),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f39,f11486]) ).
fof(f11665,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),omega(X0))) = multiplication(addition(one,multiplication(X0,X1)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11664]) ).
fof(f11666,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),omega(X0))) = multiplication(addition(multiplication(X0,X1),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f39,f11487]) ).
fof(f11667,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),omega(X0))) = multiplication(addition(one,multiplication(X0,X1)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f11666]) ).
fof(f11668,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(X0,addition(X1,one)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f103,f11488]) ).
fof(f11669,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = multiplication(addition(X0,addition(X1,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11489]) ).
fof(f11670,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = multiplication(addition(X1,addition(X0,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11490]) ).
fof(f11671,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = multiplication(addition(X1,addition(X0,one)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f103,f11491]) ).
fof(f11672,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X2)) = multiplication(addition(X1,addition(X0,one)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f11492]) ).
fof(f11673,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = multiplication(addition(X0,addition(X2,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11493]) ).
fof(f11676,plain,
! [X0] : omega(X0) = multiplication(addition(X0,one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f11497]) ).
fof(f11688,plain,
! [X0] : multiplication(addition(X0,one),omega(X0)) = omega(X0),
inference(forward_demodulation,[status(thm)],[f41,f11508]) ).
fof(f11699,plain,
! [X0,X1] :
( multiplication(addition(X1,one),omega(X0)) != multiplication(X1,omega(X0))
| leq(omega(X0),multiplication(X1,omega(X0))) ),
inference(forward_demodulation,[status(thm)],[f56,f11514]) ).
fof(f11700,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X1,one)),omega(X2)),X3) = addition(multiplication(addition(X0,addition(X2,X1)),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f219,f11521]) ).
fof(f11701,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(addition(X0,one),X1),omega(X2)),X3) = addition(multiplication(addition(addition(X2,X0),X1),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f219,f11522]) ).
fof(f11702,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,addition(X0,X1)),omega(X2)),X3) = addition(multiplication(addition(addition(X2,X0),X1),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11701]) ).
fof(f11703,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,addition(X0,X1)),omega(X2)),X3) = addition(multiplication(addition(X0,addition(X2,X1)),omega(X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11702]) ).
fof(f11704,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),omega(X1)) = addition(omega(X1),multiplication(addition(X0,one),omega(X1))),
inference(forward_demodulation,[status(thm)],[f103,f11523]) ).
fof(f11705,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),omega(X1)) = multiplication(addition(addition(X0,one),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f232,f11704]) ).
fof(f11706,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),omega(X1)) = multiplication(addition(one,addition(X0,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11705]) ).
fof(f11707,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),omega(X1)) = multiplication(addition(one,X0),omega(X1)),
inference(forward_demodulation,[status(thm)],[f1329,f11706]) ).
fof(f11708,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,X3))),omega(X2)) = multiplication(addition(X0,multiplication(X1,addition(X3,one))),omega(X2)),
inference(forward_demodulation,[status(thm)],[f211,f11524]) ).
fof(f11709,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,multiplication(X2,X3))),omega(X1)) = addition(multiplication(addition(X0,one),omega(X1)),multiplication(X2,multiplication(X3,omega(X1)))),
inference(forward_demodulation,[status(thm)],[f103,f11525]) ).
fof(f11710,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,multiplication(X2,X3))),omega(X1)) = multiplication(addition(addition(X0,one),multiplication(X2,X3)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f211,f11709]) ).
fof(f11711,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,multiplication(X2,X3))),omega(X1)) = multiplication(addition(one,addition(X0,multiplication(X2,X3))),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11710]) ).
fof(f11712,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),omega(X0)) = multiplication(addition(addition(X1,one),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f232,f11526]) ).
fof(f11713,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),omega(X0)) = multiplication(addition(one,addition(X1,one)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f103,f11712]) ).
fof(f11714,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),omega(X0)) = multiplication(addition(one,X1),omega(X0)),
inference(forward_demodulation,[status(thm)],[f1329,f11713]) ).
fof(f11715,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),omega(X2)) = multiplication(addition(multiplication(X0,X1),addition(X3,one)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f204,f11527]) ).
fof(f11716,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),omega(X2)) = multiplication(addition(one,addition(multiplication(X0,X1),X3)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f97,f11715]) ).
fof(f11717,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X2)),X3),omega(X1)) = multiplication(addition(multiplication(X0,addition(X2,one)),X3),omega(X1)),
inference(forward_demodulation,[status(thm)],[f204,f11528]) ).
fof(f11718,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = addition(multiplication(X2,omega(X1)),multiplication(addition(X0,one),omega(X1))),
inference(forward_demodulation,[status(thm)],[f103,f11529]) ).
fof(f11719,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = multiplication(addition(addition(X0,one),X2),omega(X1)),
inference(forward_demodulation,[status(thm)],[f201,f11718]) ).
fof(f11720,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = multiplication(addition(one,addition(X0,X2)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11719]) ).
fof(f11721,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = multiplication(addition(X0,addition(X2,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f201,f11530]) ).
fof(f11722,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,omega(X0))) = addition(addition(X0,X1),multiplication(addition(X1,one),omega(X0))),
inference(forward_demodulation,[status(thm)],[f35,f11533]) ).
fof(f11723,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,omega(X0))) = addition(X1,addition(X0,multiplication(addition(X1,one),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f11722]) ).
fof(f11724,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,omega(X0))) = addition(X1,addition(X0,multiplication(addition(X1,one),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f103,f11534]) ).
fof(f11725,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = multiplication(addition(addition(X2,one),X0),omega(X1)),
inference(forward_demodulation,[status(thm)],[f201,f11544]) ).
fof(f11726,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = multiplication(addition(one,addition(X2,X0)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11725]) ).
fof(f11727,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = addition(multiplication(addition(X0,one),omega(X1)),multiplication(X2,omega(X1))),
inference(forward_demodulation,[status(thm)],[f103,f11545]) ).
fof(f11728,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),omega(X1)) = multiplication(addition(X2,addition(X0,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f201,f11727]) ).
fof(f11729,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(addition(X1,one),multiplication(omega(X0),X2)),
inference(forward_demodulation,[status(thm)],[f39,f11548]) ).
fof(f11732,plain,
! [X0,X1] :
( leq(multiplication(star(X1),omega(X0)),omega(X0))
| ~ leq(multiplication(addition(X0,X1),omega(X0)),omega(X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f11551]) ).
fof(f11733,plain,
! [X0,X1] :
( multiplication(addition(X1,X0),omega(X1)) != multiplication(one,omega(X1))
| leq(multiplication(X0,omega(X1)),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f11552]) ).
fof(f11734,plain,
! [X0,X1] :
( multiplication(addition(X1,X0),omega(X1)) != omega(X1)
| leq(multiplication(X0,omega(X1)),omega(X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f11733]) ).
fof(f11735,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X1,X2)),omega(X1)),X3) = addition(multiplication(addition(X0,addition(X2,one)),omega(X1)),X3),
inference(forward_demodulation,[status(thm)],[f219,f11559]) ).
fof(f11736,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(addition(X0,X1),X2),omega(X0)),X3) = addition(multiplication(addition(addition(X1,one),X2),omega(X0)),X3),
inference(forward_demodulation,[status(thm)],[f219,f11560]) ).
fof(f11737,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X1,X2)),omega(X1)),X3) = addition(multiplication(addition(addition(X0,one),X2),omega(X1)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11736]) ).
fof(f11738,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X1,X2)),omega(X1)),X3) = addition(multiplication(addition(one,addition(X0,X2)),omega(X1)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11737]) ).
fof(f11739,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),omega(X1)) = addition(omega(X1),multiplication(addition(X1,X0),omega(X1))),
inference(forward_demodulation,[status(thm)],[f103,f11561]) ).
fof(f11740,plain,
! [X0,X1] : multiplication(addition(one,X0),omega(X1)) = addition(omega(X1),multiplication(addition(X1,X0),omega(X1))),
inference(forward_demodulation,[status(thm)],[f1329,f11739]) ).
fof(f11741,plain,
! [X0,X1] : multiplication(addition(one,X0),omega(X1)) = multiplication(addition(addition(X1,X0),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f232,f11740]) ).
fof(f11742,plain,
! [X0,X1] : multiplication(addition(one,X0),omega(X1)) = multiplication(addition(X0,addition(X1,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11741]) ).
fof(f11743,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,one))),omega(X3)) = multiplication(addition(X0,multiplication(X1,addition(X3,X2))),omega(X3)),
inference(forward_demodulation,[status(thm)],[f211,f11562]) ).
fof(f11744,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),omega(X3)) = addition(multiplication(addition(X3,X0),omega(X3)),multiplication(X1,multiplication(X2,omega(X3)))),
inference(forward_demodulation,[status(thm)],[f103,f11563]) ).
fof(f11745,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),omega(X3)) = multiplication(addition(addition(X3,X0),multiplication(X1,X2)),omega(X3)),
inference(forward_demodulation,[status(thm)],[f211,f11744]) ).
fof(f11746,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(X0,multiplication(X1,X2))),omega(X3)) = multiplication(addition(X0,addition(X3,multiplication(X1,X2))),omega(X3)),
inference(forward_demodulation,[status(thm)],[f103,f11745]) ).
fof(f11747,plain,
! [X0,X1] : multiplication(addition(one,X0),omega(X1)) = addition(omega(X1),multiplication(addition(X1,X0),omega(X1))),
inference(forward_demodulation,[status(thm)],[f1329,f11564]) ).
fof(f11748,plain,
! [X0,X1] : multiplication(addition(one,X0),omega(X1)) = multiplication(addition(addition(X1,X0),one),omega(X1)),
inference(forward_demodulation,[status(thm)],[f232,f11747]) ).
fof(f11749,plain,
! [X0,X1] : multiplication(addition(one,X0),omega(X1)) = multiplication(addition(X0,addition(X1,one)),omega(X1)),
inference(forward_demodulation,[status(thm)],[f103,f11748]) ).
fof(f11750,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(multiplication(X0,X1),X2)),omega(X3)) = addition(multiplication(X0,multiplication(X1,omega(X3))),multiplication(addition(X3,X2),omega(X3))),
inference(forward_demodulation,[status(thm)],[f97,f11565]) ).
fof(f11751,plain,
! [X0,X1,X2,X3] : multiplication(addition(one,addition(multiplication(X0,X1),X2)),omega(X3)) = multiplication(addition(multiplication(X0,X1),addition(X3,X2)),omega(X3)),
inference(forward_demodulation,[status(thm)],[f204,f11750]) ).
fof(f11752,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,one)),X2),omega(X3)) = multiplication(addition(multiplication(X0,addition(X3,X1)),X2),omega(X3)),
inference(forward_demodulation,[status(thm)],[f204,f11566]) ).
fof(f11753,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = addition(multiplication(X1,omega(X2)),multiplication(addition(X2,X0),omega(X2))),
inference(forward_demodulation,[status(thm)],[f103,f11567]) ).
fof(f11754,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = multiplication(addition(addition(X2,X0),X1),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f11753]) ).
fof(f11755,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = multiplication(addition(X0,addition(X2,X1)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f11754]) ).
fof(f11756,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = multiplication(addition(X0,addition(X2,X1)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f11568]) ).
fof(f11757,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,omega(X1))) = addition(addition(X0,one),multiplication(addition(X1,X0),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f11571]) ).
fof(f11758,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,omega(X1))) = addition(one,addition(X0,multiplication(addition(X1,X0),omega(X1)))),
inference(forward_demodulation,[status(thm)],[f103,f11757]) ).
fof(f11759,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,omega(X1))) = addition(one,addition(X0,multiplication(addition(X1,X0),omega(X1)))),
inference(forward_demodulation,[status(thm)],[f103,f11572]) ).
fof(f11760,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = multiplication(addition(addition(X2,X1),X0),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f11582]) ).
fof(f11761,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),omega(X2)) = multiplication(addition(X1,addition(X2,X0)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f103,f11760]) ).
fof(f11762,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = addition(multiplication(addition(X2,X0),omega(X2)),multiplication(X1,omega(X2))),
inference(forward_demodulation,[status(thm)],[f103,f11583]) ).
fof(f11763,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),omega(X2)) = multiplication(addition(X1,addition(X2,X0)),omega(X2)),
inference(forward_demodulation,[status(thm)],[f201,f11762]) ).
fof(f11764,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(omega(X1),X2)) = multiplication(addition(X1,X0),multiplication(omega(X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f11586]) ).
fof(f11767,plain,
! [X0,X1,X2] : multiplication(backward_box(X0,X1),domain_difference(backward_diamond(X0,c(X1)),X2)) = zero,
inference(paramodulation,[status(thm)],[f72,f1585]) ).
fof(f11768,plain,
! [X0,X1,X2] : multiplication(forward_box(X0,X1),domain_difference(forward_diamond(X0,c(X1)),X2)) = zero,
inference(paramodulation,[status(thm)],[f71,f1585]) ).
fof(f11770,plain,
! [X0,X1] : multiplication(antidomain(c(X0)),domain_difference(antidomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f547,f1585]) ).
fof(f11771,plain,
! [X0,X1] : multiplication(domain(c(X0)),domain_difference(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f362,f1585]) ).
fof(f11784,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,c(X2))),X1),domain_difference(X2,X3))
| ~ leq(addition(multiplication(X0,zero),X1),domain_difference(X2,X3)) ),
inference(paramodulation,[status(thm)],[f1585,f296]) ).
fof(f11786,plain,
! [X0,X1,X2] :
( leq(multiplication(star(c(X1)),X0),domain_difference(X1,X2))
| ~ leq(addition(X0,zero),domain_difference(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1585,f293]) ).
fof(f11789,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,domain_difference(X1,X2)),addition(zero,X3)) = addition(multiplication(addition(X0,c(X1)),domain_difference(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f1585,f219]) ).
fof(f11790,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(X0,domain_difference(X1,X2)),X3)) = addition(multiplication(addition(c(X1),X0),domain_difference(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f1585,f219]) ).
fof(f11792,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,c(X2))),domain_difference(X2,X3)) = addition(multiplication(X0,domain_difference(X2,X3)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f1585,f211]) ).
fof(f11793,plain,
! [X0,X1,X2,X3] : multiplication(addition(c(X0),multiplication(X1,X2)),domain_difference(X0,X3)) = addition(zero,multiplication(X1,multiplication(X2,domain_difference(X0,X3)))),
inference(paramodulation,[status(thm)],[f1585,f211]) ).
fof(f11795,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),c(X2)),domain_difference(X2,X3)) = addition(multiplication(X0,multiplication(X1,domain_difference(X2,X3))),zero),
inference(paramodulation,[status(thm)],[f1585,f204]) ).
fof(f11796,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,c(X1)),X2),domain_difference(X1,X3)) = addition(multiplication(X0,zero),multiplication(X2,domain_difference(X1,X3))),
inference(paramodulation,[status(thm)],[f1585,f204]) ).
fof(f11797,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),X1),domain_difference(X0,X2)) = addition(multiplication(X1,domain_difference(X0,X2)),zero),
inference(paramodulation,[status(thm)],[f1585,f201]) ).
fof(f11798,plain,
! [X0,X1,X2] : multiplication(addition(X0,c(X1)),domain_difference(X1,X2)) = addition(zero,multiplication(X0,domain_difference(X1,X2))),
inference(paramodulation,[status(thm)],[f1585,f201]) ).
fof(f11799,plain,
! [X0,X1,X2,X3] : addition(multiplication(c(X0),X1),addition(zero,X2)) = addition(multiplication(c(X0),addition(X1,domain_difference(X0,X3))),X2),
inference(paramodulation,[status(thm)],[f1585,f170]) ).
fof(f11800,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(c(X0),X1),X2)) = addition(multiplication(c(X0),addition(domain_difference(X0,X3),X1)),X2),
inference(paramodulation,[status(thm)],[f1585,f170]) ).
fof(f11801,plain,
! [X0,X1] : multiplication(c(X0),addition(domain_difference(X0,X1),one)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f1585,f192]) ).
fof(f11802,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f1585,f162]) ).
fof(f11803,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = addition(multiplication(c(X0),X2),zero),
inference(paramodulation,[status(thm)],[f1585,f153]) ).
fof(f11804,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f1585,f153]) ).
fof(f11807,plain,
! [X0,X1] : addition(coantidomain(zero),coantidomain(multiplication(codomain(c(X0)),domain_difference(X0,X1)))) = coantidomain(multiplication(codomain(c(X0)),domain_difference(X0,X1))),
inference(paramodulation,[status(thm)],[f1585,f615]) ).
fof(f11808,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(c(X0),domain(domain_difference(X0,X1))))) = antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),
inference(paramodulation,[status(thm)],[f1585,f479]) ).
fof(f11809,plain,
! [X0,X1,X2] :
( leq(domain_difference(X0,X1),addition(omega(c(X0)),multiplication(star(c(X0)),X2)))
| ~ leq(domain_difference(X0,X1),addition(zero,X2)) ),
inference(paramodulation,[status(thm)],[f1585,f58]) ).
fof(f11810,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain_difference(X1,X2))),c(X1))
| ~ leq(addition(zero,X0),c(X1)) ),
inference(paramodulation,[status(thm)],[f1585,f55]) ).
fof(f11811,plain,
! [X0,X1,X2] :
( leq(multiplication(star(c(X1)),X0),domain_difference(X1,X2))
| ~ leq(addition(zero,X0),domain_difference(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1585,f53]) ).
fof(f11812,plain,
! [X0,X1,X2] : multiplication(addition(X0,c(X1)),domain_difference(X1,X2)) = addition(multiplication(X0,domain_difference(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f1585,f43]) ).
fof(f11813,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),X1),domain_difference(X0,X2)) = addition(zero,multiplication(X1,domain_difference(X0,X2))),
inference(paramodulation,[status(thm)],[f1585,f43]) ).
fof(f11814,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f1585,f42]) ).
fof(f11815,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = addition(zero,multiplication(c(X0),X2)),
inference(paramodulation,[status(thm)],[f1585,f42]) ).
fof(f11816,plain,
! [X0,X1,X2] : multiplication(c(X0),multiplication(domain_difference(X0,X1),X2)) = multiplication(zero,X2),
inference(paramodulation,[status(thm)],[f1585,f39]) ).
fof(f11825,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X3,c(X1))),X0),domain_difference(X1,X2))
| ~ leq(addition(zero,X0),domain_difference(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f11784]) ).
fof(f11826,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X3,c(X1))),X0),domain_difference(X1,X2))
| ~ leq(X0,domain_difference(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f11825]) ).
fof(f11828,plain,
! [X0,X1,X2] :
( leq(multiplication(star(c(X1)),X0),domain_difference(X1,X2))
| ~ leq(X0,domain_difference(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f37,f11786]) ).
fof(f11841,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(X1,domain_difference(X2,X3)))) = addition(multiplication(addition(X1,c(X2)),domain_difference(X2,X3)),X0),
inference(forward_demodulation,[status(thm)],[f97,f11789]) ).
fof(f11842,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,domain_difference(X2,X3))) = addition(multiplication(addition(X1,c(X2)),domain_difference(X2,X3)),X0),
inference(forward_demodulation,[status(thm)],[f80,f11841]) ).
fof(f11843,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,domain_difference(X1,X2)),X3) = addition(multiplication(addition(c(X1),X0),domain_difference(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f80,f11790]) ).
fof(f11847,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,c(X2))),domain_difference(X2,X3)) = addition(multiplication(X0,domain_difference(X2,X3)),zero),
inference(forward_demodulation,[status(thm)],[f44,f11792]) ).
fof(f11848,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,c(X2))),domain_difference(X2,X3)) = multiplication(X0,domain_difference(X2,X3)),
inference(forward_demodulation,[status(thm)],[f37,f11847]) ).
fof(f11849,plain,
! [X0,X1,X2,X3] : multiplication(addition(c(X0),multiplication(X1,X2)),domain_difference(X0,X3)) = multiplication(X1,multiplication(X2,domain_difference(X0,X3))),
inference(forward_demodulation,[status(thm)],[f80,f11793]) ).
fof(f11852,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),c(X2)),domain_difference(X2,X3)) = multiplication(X0,multiplication(X1,domain_difference(X2,X3))),
inference(forward_demodulation,[status(thm)],[f37,f11795]) ).
fof(f11853,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,c(X1)),X2),domain_difference(X1,X3)) = addition(zero,multiplication(X2,domain_difference(X1,X3))),
inference(forward_demodulation,[status(thm)],[f44,f11796]) ).
fof(f11854,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,c(X1)),X2),domain_difference(X1,X3)) = multiplication(X2,domain_difference(X1,X3)),
inference(forward_demodulation,[status(thm)],[f80,f11853]) ).
fof(f11855,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),X1),domain_difference(X0,X2)) = multiplication(X1,domain_difference(X0,X2)),
inference(forward_demodulation,[status(thm)],[f37,f11797]) ).
fof(f11856,plain,
! [X0,X1,X2] : multiplication(addition(X0,c(X1)),domain_difference(X1,X2)) = multiplication(X0,domain_difference(X1,X2)),
inference(forward_demodulation,[status(thm)],[f80,f11798]) ).
fof(f11857,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(c(X1),X2))) = addition(multiplication(c(X1),addition(X2,domain_difference(X1,X3))),X0),
inference(forward_demodulation,[status(thm)],[f97,f11799]) ).
fof(f11858,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(c(X1),X2)) = addition(multiplication(c(X1),addition(X2,domain_difference(X1,X3))),X0),
inference(forward_demodulation,[status(thm)],[f80,f11857]) ).
fof(f11859,plain,
! [X0,X1,X2,X3] : addition(multiplication(c(X0),X1),X2) = addition(multiplication(c(X0),addition(domain_difference(X0,X3),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f11800]) ).
fof(f11860,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = addition(c(X0),zero),
inference(forward_demodulation,[status(thm)],[f35,f11801]) ).
fof(f11861,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = c(X0),
inference(forward_demodulation,[status(thm)],[f37,f11860]) ).
fof(f11862,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = c(X0),
inference(forward_demodulation,[status(thm)],[f37,f11802]) ).
fof(f11863,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = multiplication(c(X0),X2),
inference(forward_demodulation,[status(thm)],[f37,f11803]) ).
fof(f11864,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f11804]) ).
fof(f11867,plain,
! [X0,X1] : addition(one,coantidomain(multiplication(codomain(c(X0)),domain_difference(X0,X1)))) = coantidomain(multiplication(codomain(c(X0)),domain_difference(X0,X1))),
inference(forward_demodulation,[status(thm)],[f696,f11807]) ).
fof(f11868,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(c(X0)),domain_difference(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1377,f11867]) ).
fof(f11869,plain,
! [X0,X1] : addition(one,antidomain(multiplication(c(X0),domain(domain_difference(X0,X1))))) = antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f577,f11808]) ).
fof(f11870,plain,
! [X0,X1] : one = antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1379,f11869]) ).
fof(f11871,plain,
! [X0,X1,X2] :
( leq(domain_difference(X0,X1),addition(omega(c(X0)),multiplication(star(c(X0)),X2)))
| ~ leq(domain_difference(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f11809]) ).
fof(f11872,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain_difference(X1,X2))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f11810]) ).
fof(f11873,plain,
! [X0,X1,X2] :
( leq(multiplication(star(c(X1)),X0),domain_difference(X1,X2))
| ~ leq(X0,domain_difference(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f11811]) ).
fof(f11874,plain,
! [X0,X1,X2] : multiplication(addition(X0,c(X1)),domain_difference(X1,X2)) = multiplication(X0,domain_difference(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f11812]) ).
fof(f11875,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),X1),domain_difference(X0,X2)) = multiplication(X1,domain_difference(X0,X2)),
inference(forward_demodulation,[status(thm)],[f80,f11813]) ).
fof(f11876,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f11814]) ).
fof(f11877,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = multiplication(c(X0),X2),
inference(forward_demodulation,[status(thm)],[f80,f11815]) ).
fof(f11878,plain,
! [X0,X1,X2] : multiplication(c(X0),multiplication(domain_difference(X0,X1),X2)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f11816]) ).
fof(f11879,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,omega(multiplication(X0,X1))))) = addition(omega(multiplication(X0,X1)),multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f39,f321]) ).
fof(f11885,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(omega(X0),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f103,f321]) ).
fof(f11886,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(omega(X0),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f321]) ).
fof(f11888,plain,
! [X0,X1] : multiplication(X0,addition(omega(X0),X1)) = addition(omega(X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f321]) ).
fof(f11889,plain,
! [X0,X1] : multiplication(X0,addition(omega(X0),X1)) = addition(omega(X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f321]) ).
fof(f11890,plain,
! [X0] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,omega(X0))),
inference(paramodulation,[status(thm)],[f38,f321]) ).
fof(f11892,plain,
! [X0,X1,X2] : leq(addition(omega(forward_diamond(X0,X1)),multiplication(forward_diamond(X0,X1),X2)),addition(X2,omega(forward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f321,f7010]) ).
fof(f11893,plain,
! [X0,X1,X2] : leq(addition(omega(forward_box(X0,X1)),multiplication(forward_box(X0,X1),X2)),addition(X2,omega(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f321,f6659]) ).
fof(f11894,plain,
! [X0,X1,X2] : leq(addition(omega(backward_box(X0,X1)),multiplication(backward_box(X0,X1),X2)),addition(X2,omega(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f321,f6658]) ).
fof(f11895,plain,
! [X0,X1,X2] : leq(addition(omega(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),X2)),addition(X2,omega(backward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f321,f6519]) ).
fof(f11896,plain,
! [X0,X1] : leq(addition(omega(divergence(X0)),multiplication(divergence(X0),X1)),addition(X1,omega(divergence(X0)))),
inference(paramodulation,[status(thm)],[f321,f5965]) ).
fof(f11897,plain,
! [X0,X1] : addition(X0,omega(divergence(X1))) = addition(addition(X0,omega(divergence(X1))),addition(omega(divergence(X1)),multiplication(divergence(X1),X0))),
inference(paramodulation,[status(thm)],[f321,f4511]) ).
fof(f11898,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,addition(X2,omega(addition(X0,X1))))),addition(X2,omega(addition(X0,X1))))
| ~ leq(addition(omega(addition(X0,X1)),multiplication(addition(X0,X1),X2)),addition(X2,omega(addition(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f321,f290]) ).
fof(f11899,plain,
! [X0,X1,X2] :
( addition(omega(addition(X0,X2)),multiplication(addition(X0,X2),X1)) != multiplication(X2,addition(X1,omega(addition(X0,X2))))
| leq(multiplication(X0,addition(X1,omega(addition(X0,X2)))),multiplication(X2,addition(X1,omega(addition(X0,X2))))) ),
inference(paramodulation,[status(thm)],[f321,f241]) ).
fof(f11900,plain,
! [X0,X1] : leq(addition(omega(codomain(X0)),multiplication(codomain(X0),X1)),addition(X1,omega(codomain(X0)))),
inference(paramodulation,[status(thm)],[f321,f6393]) ).
fof(f11901,plain,
! [X0,X1] : addition(X0,omega(codomain(X1))) = addition(addition(X0,omega(codomain(X1))),addition(omega(codomain(X1)),multiplication(codomain(X1),X0))),
inference(paramodulation,[status(thm)],[f321,f4512]) ).
fof(f11902,plain,
! [X0,X1] : backward_diamond(addition(X0,omega(codomain(X1))),X1) = codomain(addition(omega(codomain(X1)),multiplication(codomain(X1),X0))),
inference(paramodulation,[status(thm)],[f321,f70]) ).
fof(f11903,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,addition(X1,omega(codomain(X0))))),coantidomain(addition(omega(codomain(X0)),multiplication(codomain(X0),X1)))) = coantidomain(multiplication(codomain(X0),addition(X1,omega(codomain(X0))))),
inference(paramodulation,[status(thm)],[f321,f615]) ).
fof(f11904,plain,
! [X0,X1] : leq(addition(omega(c(X0)),multiplication(c(X0),X1)),addition(X1,omega(c(X0)))),
inference(paramodulation,[status(thm)],[f321,f6526]) ).
fof(f11905,plain,
! [X0,X1] : addition(X0,omega(c(X1))) = addition(addition(X0,omega(c(X1))),addition(omega(c(X1)),multiplication(c(X1),X0))),
inference(paramodulation,[status(thm)],[f321,f4513]) ).
fof(f11906,plain,
! [X0,X1] : leq(addition(omega(coantidomain(X0)),multiplication(coantidomain(X0),X1)),addition(X1,omega(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f321,f7158]) ).
fof(f11907,plain,
! [X0,X1] : addition(X0,omega(coantidomain(X1))) = addition(addition(X0,omega(coantidomain(X1))),addition(omega(coantidomain(X1)),multiplication(coantidomain(X1),X0))),
inference(paramodulation,[status(thm)],[f321,f4515]) ).
fof(f11908,plain,
! [X0,X1] : multiplication(X0,addition(omega(coantidomain(X0)),multiplication(coantidomain(X0),X1))) = zero,
inference(paramodulation,[status(thm)],[f321,f151]) ).
fof(f11909,plain,
! [X0,X1] : addition(X0,omega(domain(X1))) = addition(addition(X0,omega(domain(X1))),addition(omega(domain(X1)),multiplication(domain(X1),X0))),
inference(paramodulation,[status(thm)],[f321,f4516]) ).
fof(f11910,plain,
! [X0,X1] : leq(addition(omega(domain(X0)),multiplication(domain(X0),X1)),addition(X1,omega(domain(X0)))),
inference(paramodulation,[status(thm)],[f321,f6808]) ).
fof(f11911,plain,
! [X0,X1] : leq(addition(X0,omega(star(X1))),addition(omega(star(X1)),multiplication(star(X1),X0))),
inference(paramodulation,[status(thm)],[f321,f8451]) ).
fof(f11912,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,omega(multiplication(X0,X1))))) = addition(omega(multiplication(X0,X1)),multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f321,f39]) ).
fof(f11914,plain,
! [X0,X1] : leq(addition(omega(antidomain(X0)),multiplication(antidomain(X0),X1)),addition(X1,omega(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f321,f6667]) ).
fof(f11915,plain,
! [X0,X1] : addition(X0,omega(antidomain(X1))) = addition(addition(X0,omega(antidomain(X1))),addition(omega(antidomain(X1)),multiplication(antidomain(X1),X0))),
inference(paramodulation,[status(thm)],[f321,f4514]) ).
fof(f11922,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,omega(X0)),omega(addition(omega(X0),multiplication(X0,X1))))) = omega(multiplication(X0,addition(X1,omega(X0)))),
inference(paramodulation,[status(thm)],[f321,f308]) ).
fof(f11923,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),addition(X2,omega(X1)))
| ~ leq(addition(multiplication(X0,addition(omega(X1),multiplication(X1,X2))),X3),addition(X2,omega(X1))) ),
inference(paramodulation,[status(thm)],[f321,f296]) ).
fof(f11924,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,addition(X1,omega(X0)))),addition(X1,omega(X0)))
| ~ leq(addition(omega(X0),multiplication(X0,X1)),addition(X1,omega(X0))) ),
inference(paramodulation,[status(thm)],[f321,f295]) ).
fof(f11925,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),addition(X2,omega(X1)))
| ~ leq(addition(X0,addition(omega(X1),multiplication(X1,X2))),addition(X2,omega(X1))) ),
inference(paramodulation,[status(thm)],[f321,f293]) ).
fof(f11926,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,omega(X0)),star(multiplication(X0,addition(X1,omega(X0))))))),star(addition(omega(X0),multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f321,f252]) ).
fof(f11927,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,omega(X0)),star(addition(omega(X0),multiplication(X0,X1)))))),star(multiplication(X0,addition(X1,omega(X0))))),
inference(paramodulation,[status(thm)],[f321,f252]) ).
fof(f11928,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,omega(X2))),addition(addition(omega(X2),multiplication(X2,X1)),X3)) = addition(multiplication(addition(X0,X2),addition(X1,omega(X2))),X3),
inference(paramodulation,[status(thm)],[f321,f219]) ).
fof(f11929,plain,
! [X0,X1,X2,X3] : addition(addition(omega(X0),multiplication(X0,X1)),addition(multiplication(X2,addition(X1,omega(X0))),X3)) = addition(multiplication(addition(X0,X2),addition(X1,omega(X0))),X3),
inference(paramodulation,[status(thm)],[f321,f219]) ).
fof(f11930,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,omega(X0))) = addition(addition(X1,omega(X0)),addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f321,f232]) ).
fof(f11931,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,omega(X2))) = addition(multiplication(X0,addition(X3,omega(X2))),multiplication(X1,addition(omega(X2),multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f321,f211]) ).
fof(f11932,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,omega(X0))) = addition(addition(omega(X0),multiplication(X0,X3)),multiplication(X1,multiplication(X2,addition(X3,omega(X0))))),
inference(paramodulation,[status(thm)],[f321,f211]) ).
fof(f11933,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,omega(X0))) = addition(addition(X1,omega(X0)),addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f321,f207]) ).
fof(f11934,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,omega(X2))) = addition(multiplication(X0,multiplication(X1,addition(X3,omega(X2)))),addition(omega(X2),multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f321,f204]) ).
fof(f11935,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,omega(X1))) = addition(multiplication(X0,addition(omega(X1),multiplication(X1,X3))),multiplication(X2,addition(X3,omega(X1)))),
inference(paramodulation,[status(thm)],[f321,f204]) ).
fof(f11936,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X0))) = addition(multiplication(X1,addition(X2,omega(X0))),addition(omega(X0),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f321,f201]) ).
fof(f11937,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X1))) = addition(addition(omega(X1),multiplication(X1,X2)),multiplication(X0,addition(X2,omega(X1)))),
inference(paramodulation,[status(thm)],[f321,f201]) ).
fof(f11938,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(omega(X0),multiplication(X0,X2)),X3)) = addition(multiplication(X0,addition(X1,addition(X2,omega(X0)))),X3),
inference(paramodulation,[status(thm)],[f321,f170]) ).
fof(f11939,plain,
! [X0,X1,X2,X3] : addition(addition(omega(X0),multiplication(X0,X1)),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(addition(X1,omega(X0)),X2)),X3),
inference(paramodulation,[status(thm)],[f321,f170]) ).
fof(f11940,plain,
! [X0,X1] : multiplication(X0,addition(addition(X1,omega(X0)),one)) = addition(X0,addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f321,f192]) ).
fof(f11941,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,omega(X0)))) = addition(X0,addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f321,f162]) ).
fof(f11942,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,omega(X0)),X2)) = addition(multiplication(X0,X2),addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f321,f153]) ).
fof(f11943,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(addition(omega(X0),multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f321,f153]) ).
fof(f11944,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,omega(X0)),coantidomain(addition(omega(X0),multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f321,f144]) ).
fof(f11945,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(omega(X0),multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f321,f136]) ).
fof(f11946,plain,
! [X0,X1] : addition(coantidomain(addition(omega(X0),multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),addition(X1,omega(X0))))) = coantidomain(multiplication(codomain(X0),addition(X1,omega(X0)))),
inference(paramodulation,[status(thm)],[f321,f615]) ).
fof(f11947,plain,
! [X0,X1] : addition(antidomain(addition(omega(X0),multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(X1,omega(X0)))))) = antidomain(multiplication(X0,domain(addition(X1,omega(X0))))),
inference(paramodulation,[status(thm)],[f321,f479]) ).
fof(f11948,plain,
! [X0,X1,X2] :
( leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,omega(X1)),addition(addition(omega(X1),multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f321,f58]) ).
fof(f11949,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,omega(X0)))),X0)
| ~ leq(addition(addition(omega(X0),multiplication(X0,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f321,f55]) ).
fof(f11950,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(X1,omega(X0)))
| ~ leq(addition(addition(omega(X0),multiplication(X0,X1)),X2),addition(X1,omega(X0))) ),
inference(paramodulation,[status(thm)],[f321,f53]) ).
fof(f11951,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X1))) = addition(multiplication(X0,addition(X2,omega(X1))),addition(omega(X1),multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f321,f43]) ).
fof(f11952,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X0))) = addition(addition(omega(X0),multiplication(X0,X2)),multiplication(X1,addition(X2,omega(X0)))),
inference(paramodulation,[status(thm)],[f321,f43]) ).
fof(f11953,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(multiplication(X0,X1),addition(omega(X0),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f321,f42]) ).
fof(f11954,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,omega(X0)),X2)) = addition(addition(omega(X0),multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f321,f42]) ).
fof(f11955,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,omega(X0)),X2)) = multiplication(addition(omega(X0),multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f321,f39]) ).
fof(f11956,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,omega(multiplication(X0,X1))))) = addition(omega(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f11879]) ).
fof(f11968,plain,
! [X0] : omega(X0) = addition(omega(X0),multiplication(X0,omega(X0))),
inference(forward_demodulation,[status(thm)],[f56,f11890]) ).
fof(f11969,plain,
! [X0] : omega(X0) = multiplication(addition(X0,one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f232,f11968]) ).
fof(f11973,plain,
! [X0,X1] : addition(X0,omega(divergence(X1))) = addition(omega(divergence(X1)),addition(X0,addition(omega(divergence(X1)),multiplication(divergence(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f11897]) ).
fof(f11974,plain,
! [X0,X1] : addition(X0,omega(codomain(X1))) = addition(omega(codomain(X1)),addition(X0,addition(omega(codomain(X1)),multiplication(codomain(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f11901]) ).
fof(f11975,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,addition(X1,omega(codomain(X0))))),coantidomain(addition(omega(codomain(X0)),multiplication(codomain(X0),X1)))) = coantidomain(addition(omega(codomain(X0)),multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f321,f11903]) ).
fof(f11976,plain,
! [X0,X1] : addition(X0,omega(c(X1))) = addition(omega(c(X1)),addition(X0,addition(omega(c(X1)),multiplication(c(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f11905]) ).
fof(f11977,plain,
! [X0,X1] : addition(X0,omega(coantidomain(X1))) = addition(omega(coantidomain(X1)),addition(X0,addition(omega(coantidomain(X1)),multiplication(coantidomain(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f11907]) ).
fof(f11978,plain,
! [X0,X1] : addition(X0,omega(domain(X1))) = addition(omega(domain(X1)),addition(X0,addition(omega(domain(X1)),multiplication(domain(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f11909]) ).
fof(f11979,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,omega(multiplication(X0,X1))))) = addition(omega(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f11912]) ).
fof(f11982,plain,
! [X0,X1] : addition(X0,omega(antidomain(X1))) = addition(omega(antidomain(X1)),addition(X0,addition(omega(antidomain(X1)),multiplication(antidomain(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f11915]) ).
fof(f11993,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,omega(X0)),omega(addition(omega(X0),multiplication(X0,X1))))) = omega(addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f321,f11922]) ).
fof(f11994,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(omega(X0),multiplication(X0,X1))),addition(X1,omega(X0)))
| ~ leq(addition(omega(X0),multiplication(X0,X1)),addition(X1,omega(X0))) ),
inference(forward_demodulation,[status(thm)],[f321,f11924]) ).
fof(f11995,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,omega(X0)),star(addition(omega(X0),multiplication(X0,X1)))))),star(addition(omega(X0),multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f321,f11926]) ).
fof(f11996,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(X1,omega(X0)),star(addition(omega(X0),multiplication(X0,X1)))))),star(addition(omega(X0),multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f321,f11927]) ).
fof(f11997,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,omega(X2))),addition(multiplication(X2,X1),addition(omega(X2),X3))) = addition(multiplication(addition(X0,X2),addition(X1,omega(X2))),X3),
inference(forward_demodulation,[status(thm)],[f103,f11928]) ).
fof(f11998,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(omega(X0),X2),multiplication(X3,addition(X1,omega(X0))))) = addition(multiplication(addition(X3,X0),addition(X1,omega(X0))),X2),
inference(forward_demodulation,[status(thm)],[f97,f11997]) ).
fof(f11999,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,addition(omega(X0),multiplication(X3,addition(X1,omega(X0)))))) = addition(multiplication(addition(X3,X0),addition(X1,omega(X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f11998]) ).
fof(f12000,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(omega(X0),addition(multiplication(X2,addition(X1,omega(X0))),X3))) = addition(multiplication(addition(X0,X2),addition(X1,omega(X0))),X3),
inference(forward_demodulation,[status(thm)],[f103,f11929]) ).
fof(f12001,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(addition(multiplication(X1,addition(X2,omega(X0))),X3),multiplication(X0,X2))) = addition(multiplication(addition(X0,X1),addition(X2,omega(X0))),X3),
inference(forward_demodulation,[status(thm)],[f97,f12000]) ).
fof(f12002,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,addition(multiplication(X2,addition(X3,omega(X0))),multiplication(X0,X3)))) = addition(multiplication(addition(X0,X2),addition(X3,omega(X0))),X1),
inference(forward_demodulation,[status(thm)],[f103,f12001]) ).
fof(f12003,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,addition(multiplication(X0,X2),multiplication(X3,addition(X2,omega(X0)))))) = addition(multiplication(addition(X0,X3),addition(X2,omega(X0))),X1),
inference(forward_demodulation,[status(thm)],[f35,f12002]) ).
fof(f12004,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,omega(X0))) = addition(omega(X0),addition(X1,addition(omega(X0),multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f11930]) ).
fof(f12005,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,omega(X0))) = addition(multiplication(X0,X3),addition(omega(X0),multiplication(X1,multiplication(X2,addition(X3,omega(X0)))))),
inference(forward_demodulation,[status(thm)],[f103,f11932]) ).
fof(f12006,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,omega(X0))) = addition(omega(X0),addition(multiplication(X1,multiplication(X2,addition(X3,omega(X0)))),multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f97,f12005]) ).
fof(f12007,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,omega(X0))) = addition(omega(X0),addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,addition(X3,omega(X0)))))),
inference(forward_demodulation,[status(thm)],[f35,f12006]) ).
fof(f12008,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,omega(X0))) = addition(omega(X0),addition(X1,addition(omega(X0),multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f11933]) ).
fof(f12009,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,omega(X2))) = addition(omega(X2),addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,addition(X3,omega(X2)))))),
inference(forward_demodulation,[status(thm)],[f97,f11934]) ).
fof(f12010,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X0))) = addition(omega(X0),addition(multiplication(X0,X2),multiplication(X1,addition(X2,omega(X0))))),
inference(forward_demodulation,[status(thm)],[f97,f11936]) ).
fof(f12011,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X1))) = addition(multiplication(X1,X2),addition(omega(X1),multiplication(X0,addition(X2,omega(X1))))),
inference(forward_demodulation,[status(thm)],[f103,f11937]) ).
fof(f12012,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X1))) = addition(omega(X1),addition(multiplication(X0,addition(X2,omega(X1))),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f97,f12011]) ).
fof(f12013,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X1))) = addition(omega(X1),addition(multiplication(X1,X2),multiplication(X0,addition(X2,omega(X1))))),
inference(forward_demodulation,[status(thm)],[f35,f12012]) ).
fof(f12014,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),addition(omega(X0),X3))) = addition(multiplication(X0,addition(X1,addition(X2,omega(X0)))),X3),
inference(forward_demodulation,[status(thm)],[f103,f11938]) ).
fof(f12015,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),addition(omega(X0),X3)) = addition(multiplication(X0,addition(X1,addition(X2,omega(X0)))),X3),
inference(forward_demodulation,[status(thm)],[f170,f12014]) ).
fof(f12016,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(X2,addition(X3,omega(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f97,f12015]) ).
fof(f12017,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(omega(X0),addition(multiplication(X0,X2),X3))) = addition(multiplication(X0,addition(addition(X1,omega(X0)),X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f11939]) ).
fof(f12018,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(addition(multiplication(X0,X1),X2),multiplication(X0,X3))) = addition(multiplication(X0,addition(addition(X3,omega(X0)),X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f12017]) ).
fof(f12019,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,addition(multiplication(X0,X2),multiplication(X0,X3)))) = addition(multiplication(X0,addition(addition(X3,omega(X0)),X2)),X1),
inference(forward_demodulation,[status(thm)],[f103,f12018]) ).
fof(f12020,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(addition(X2,omega(X0)),X3)),X1),
inference(forward_demodulation,[status(thm)],[f153,f12019]) ).
fof(f12021,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(omega(X0),addition(X2,X3))),X1),
inference(forward_demodulation,[status(thm)],[f103,f12020]) ).
fof(f12022,plain,
! [X0,X1] : multiplication(X0,addition(omega(X0),addition(X1,one))) = addition(X0,addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f11940]) ).
fof(f12023,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(omega(X0),X1))) = addition(X0,addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f12022]) ).
fof(f12024,plain,
! [X0,X1,X2] : multiplication(X0,addition(omega(X0),addition(X1,X2))) = addition(multiplication(X0,X2),addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f11942]) ).
fof(f12025,plain,
! [X0,X1,X2] : multiplication(X0,addition(omega(X0),addition(X1,X2))) = addition(omega(X0),addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f12024]) ).
fof(f12026,plain,
! [X0,X1,X2] : multiplication(X0,addition(omega(X0),addition(X1,X2))) = addition(omega(X0),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f12025]) ).
fof(f12027,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(multiplication(X0,X2),addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f11943]) ).
fof(f12028,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(omega(X0),addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f12027]) ).
fof(f12029,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(omega(X0),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f12028]) ).
fof(f12030,plain,
! [X0,X1,X2] :
( leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,omega(X1)),addition(multiplication(X1,X0),addition(omega(X1),X2))) ),
inference(forward_demodulation,[status(thm)],[f103,f11948]) ).
fof(f12031,plain,
! [X0,X1,X2] :
( leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,omega(X1)),addition(omega(X1),addition(X2,multiplication(X1,X0)))) ),
inference(forward_demodulation,[status(thm)],[f97,f12030]) ).
fof(f12032,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,omega(X0)))),X0)
| ~ leq(addition(multiplication(X0,X1),addition(omega(X0),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f103,f11949]) ).
fof(f12033,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(addition(X2,omega(X0)))),X0)
| ~ leq(addition(omega(X0),addition(X1,multiplication(X0,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f97,f12032]) ).
fof(f12034,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(X1,omega(X0)))
| ~ leq(addition(multiplication(X0,X1),addition(omega(X0),X2)),addition(X1,omega(X0))) ),
inference(forward_demodulation,[status(thm)],[f103,f11950]) ).
fof(f12035,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X1),addition(X2,omega(X0)))
| ~ leq(addition(omega(X0),addition(X1,multiplication(X0,X2))),addition(X2,omega(X0))) ),
inference(forward_demodulation,[status(thm)],[f97,f12034]) ).
fof(f12036,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X1))) = addition(omega(X1),addition(multiplication(X1,X2),multiplication(X0,addition(X2,omega(X1))))),
inference(forward_demodulation,[status(thm)],[f97,f11951]) ).
fof(f12037,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X0))) = addition(multiplication(X0,X2),addition(omega(X0),multiplication(X1,addition(X2,omega(X0))))),
inference(forward_demodulation,[status(thm)],[f103,f11952]) ).
fof(f12038,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X0))) = addition(omega(X0),addition(multiplication(X1,addition(X2,omega(X0))),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f12037]) ).
fof(f12039,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,omega(X0))) = addition(omega(X0),addition(multiplication(X0,X2),multiplication(X1,addition(X2,omega(X0))))),
inference(forward_demodulation,[status(thm)],[f35,f12038]) ).
fof(f12040,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(omega(X0),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f11953]) ).
fof(f12041,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(omega(X0),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f153,f12040]) ).
fof(f12042,plain,
! [X0,X1,X2] : multiplication(X0,addition(omega(X0),addition(X1,X2))) = addition(addition(omega(X0),multiplication(X0,X1)),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f11954]) ).
fof(f12043,plain,
! [X0,X1,X2] : multiplication(X0,addition(omega(X0),addition(X1,X2))) = addition(multiplication(X0,X1),addition(omega(X0),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f12042]) ).
fof(f12044,plain,
! [X0,X1,X2] : multiplication(X0,addition(omega(X0),addition(X1,X2))) = addition(omega(X0),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f12043]) ).
fof(f12045,plain,
! [X0,X1,X2] : multiplication(X0,addition(omega(X0),addition(X1,X2))) = addition(omega(X0),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f153,f12044]) ).
fof(f12046,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(omega(X2),multiplication(star(X2),one))),
inference(resolution,[status(thm)],[f1907,f58]) ).
fof(f12047,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,one))),forward_diamond(X1,X2)),addition(X0,one)),
inference(resolution,[status(thm)],[f1907,f304]) ).
fof(f12048,plain,
! [X0,X1,X2] : addition(forward_diamond(X0,X1),addition(X2,one)) = addition(X2,one),
inference(resolution,[status(thm)],[f1907,f48]) ).
fof(f12057,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f103,f1907]) ).
fof(f12058,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f36,f1907]) ).
fof(f12060,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f35,f1907]) ).
fof(f12061,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f35,f1907]) ).
fof(f12063,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(omega(X2),star(X2))),
inference(forward_demodulation,[status(thm)],[f40,f12046]) ).
fof(f12064,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(star(X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f35,f12063]) ).
fof(f12065,plain,
! [X0,X1,X2] : addition(one,addition(forward_diamond(X0,X1),X2)) = addition(X2,one),
inference(forward_demodulation,[status(thm)],[f97,f12048]) ).
fof(f12066,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(omega(X2),multiplication(star(X2),one))),
inference(resolution,[status(thm)],[f2028,f58]) ).
fof(f12067,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,one))),backward_box(X1,X2)),addition(X0,one)),
inference(resolution,[status(thm)],[f2028,f304]) ).
fof(f12068,plain,
! [X0,X1,X2] : addition(backward_box(X0,X1),addition(X2,one)) = addition(X2,one),
inference(resolution,[status(thm)],[f2028,f48]) ).
fof(f12072,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f103,f2028]) ).
fof(f12073,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f36,f2028]) ).
fof(f12075,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f35,f2028]) ).
fof(f12076,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f35,f2028]) ).
fof(f12078,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(omega(X2),star(X2))),
inference(forward_demodulation,[status(thm)],[f40,f12066]) ).
fof(f12079,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(star(X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f35,f12078]) ).
fof(f12080,plain,
! [X0,X1,X2] : addition(one,addition(backward_box(X0,X1),X2)) = addition(X2,one),
inference(forward_demodulation,[status(thm)],[f97,f12068]) ).
fof(f12081,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(omega(X2),multiplication(star(X2),one))),
inference(resolution,[status(thm)],[f2052,f58]) ).
fof(f12082,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,one))),forward_box(X1,X2)),addition(X0,one)),
inference(resolution,[status(thm)],[f2052,f304]) ).
fof(f12083,plain,
! [X0,X1,X2] : addition(forward_box(X0,X1),addition(X2,one)) = addition(X2,one),
inference(resolution,[status(thm)],[f2052,f48]) ).
fof(f12088,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f103,f2052]) ).
fof(f12089,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f36,f2052]) ).
fof(f12091,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f35,f2052]) ).
fof(f12092,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f35,f2052]) ).
fof(f12094,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(omega(X2),star(X2))),
inference(forward_demodulation,[status(thm)],[f40,f12081]) ).
fof(f12095,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(star(X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f35,f12094]) ).
fof(f12096,plain,
! [X0,X1,X2] : addition(one,addition(forward_box(X0,X1),X2)) = addition(X2,one),
inference(forward_demodulation,[status(thm)],[f97,f12083]) ).
fof(f12097,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(omega(X2),multiplication(star(X2),one))),
inference(resolution,[status(thm)],[f2078,f58]) ).
fof(f12098,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,one))),backward_diamond(X1,X2)),addition(X0,one)),
inference(resolution,[status(thm)],[f2078,f304]) ).
fof(f12099,plain,
! [X0,X1,X2] : addition(backward_diamond(X0,X1),addition(X2,one)) = addition(X2,one),
inference(resolution,[status(thm)],[f2078,f48]) ).
fof(f12106,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f103,f2078]) ).
fof(f12107,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f36,f2078]) ).
fof(f12109,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f35,f2078]) ).
fof(f12110,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f35,f2078]) ).
fof(f12112,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(omega(X2),star(X2))),
inference(forward_demodulation,[status(thm)],[f40,f12097]) ).
fof(f12113,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(star(X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f35,f12112]) ).
fof(f12114,plain,
! [X0,X1,X2] : addition(one,addition(backward_diamond(X0,X1),X2)) = addition(X2,one),
inference(forward_demodulation,[status(thm)],[f97,f12099]) ).
fof(f12115,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(omega(multiplication(X0,X1)),X2))) = addition(omega(multiplication(X0,X1)),multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f39,f318]) ).
fof(f12122,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(domain(X1),omega(X0)))),
inference(paramodulation,[status(thm)],[f4516,f318]) ).
fof(f12123,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(coantidomain(X1),omega(X0)))),
inference(paramodulation,[status(thm)],[f4515,f318]) ).
fof(f12124,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(antidomain(X1),omega(X0)))),
inference(paramodulation,[status(thm)],[f4514,f318]) ).
fof(f12125,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(c(X1),omega(X0)))),
inference(paramodulation,[status(thm)],[f4513,f318]) ).
fof(f12126,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(codomain(X1),omega(X0)))),
inference(paramodulation,[status(thm)],[f4512,f318]) ).
fof(f12127,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(divergence(X1),omega(X0)))),
inference(paramodulation,[status(thm)],[f4511,f318]) ).
fof(f12128,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),domain(X1)))),
inference(paramodulation,[status(thm)],[f2497,f318]) ).
fof(f12129,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f2496,f318]) ).
fof(f12130,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),antidomain(X1)))),
inference(paramodulation,[status(thm)],[f2495,f318]) ).
fof(f12131,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),c(X1)))),
inference(paramodulation,[status(thm)],[f2494,f318]) ).
fof(f12132,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),codomain(X1)))),
inference(paramodulation,[status(thm)],[f2493,f318]) ).
fof(f12133,plain,
! [X0,X1] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),divergence(X1)))),
inference(paramodulation,[status(thm)],[f2492,f318]) ).
fof(f12134,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),omega(X0))) = addition(omega(X0),multiplication(X0,multiplication(X1,omega(X0)))),
inference(paramodulation,[status(thm)],[f232,f318]) ).
fof(f12135,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),omega(X0))) = addition(omega(X0),multiplication(X0,multiplication(X1,omega(X0)))),
inference(paramodulation,[status(thm)],[f207,f318]) ).
fof(f12136,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(X0),addition(X1,one))) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),X1))),
inference(paramodulation,[status(thm)],[f192,f318]) ).
fof(f12137,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(X0),addition(one,X1))) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),X1))),
inference(paramodulation,[status(thm)],[f162,f318]) ).
fof(f12142,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,omega(X0)))) = addition(omega(X0),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f97,f318]) ).
fof(f12143,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f97,f318]) ).
fof(f12147,plain,
! [X0] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,omega(X0))),
inference(paramodulation,[status(thm)],[f38,f318]) ).
fof(f12149,plain,
! [X0,X1,X2] : leq(addition(omega(forward_diamond(X0,X1)),multiplication(forward_diamond(X0,X1),X2)),addition(omega(forward_diamond(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f318,f7010]) ).
fof(f12150,plain,
! [X0,X1,X2] : leq(addition(omega(forward_box(X0,X1)),multiplication(forward_box(X0,X1),X2)),addition(omega(forward_box(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f318,f6659]) ).
fof(f12151,plain,
! [X0,X1,X2] : leq(addition(omega(backward_box(X0,X1)),multiplication(backward_box(X0,X1),X2)),addition(omega(backward_box(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f318,f6658]) ).
fof(f12152,plain,
! [X0,X1,X2] : leq(addition(omega(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),X2)),addition(omega(backward_diamond(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f318,f6519]) ).
fof(f12153,plain,
! [X0,X1] : leq(addition(omega(divergence(X0)),multiplication(divergence(X0),X1)),addition(omega(divergence(X0)),X1)),
inference(paramodulation,[status(thm)],[f318,f5965]) ).
fof(f12154,plain,
! [X0,X1] : addition(omega(divergence(X0)),X1) = addition(addition(omega(divergence(X0)),X1),addition(omega(divergence(X0)),multiplication(divergence(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f4511]) ).
fof(f12155,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,addition(omega(addition(X0,X1)),X2))),addition(omega(addition(X0,X1)),X2))
| ~ leq(addition(omega(addition(X0,X1)),multiplication(addition(X0,X1),X2)),addition(omega(addition(X0,X1)),X2)) ),
inference(paramodulation,[status(thm)],[f318,f290]) ).
fof(f12156,plain,
! [X0,X1,X2] :
( addition(omega(addition(X0,X1)),multiplication(addition(X0,X1),X2)) != multiplication(X1,addition(omega(addition(X0,X1)),X2))
| leq(multiplication(X0,addition(omega(addition(X0,X1)),X2)),multiplication(X1,addition(omega(addition(X0,X1)),X2))) ),
inference(paramodulation,[status(thm)],[f318,f241]) ).
fof(f12157,plain,
! [X0,X1] : leq(addition(omega(codomain(X0)),multiplication(codomain(X0),X1)),addition(omega(codomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f318,f6393]) ).
fof(f12158,plain,
! [X0,X1] : addition(omega(codomain(X0)),X1) = addition(addition(omega(codomain(X0)),X1),addition(omega(codomain(X0)),multiplication(codomain(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f4512]) ).
fof(f12159,plain,
! [X0,X1] : backward_diamond(addition(omega(codomain(X0)),X1),X0) = codomain(addition(omega(codomain(X0)),multiplication(codomain(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f70]) ).
fof(f12160,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,addition(omega(codomain(X0)),X1))),coantidomain(addition(omega(codomain(X0)),multiplication(codomain(X0),X1)))) = coantidomain(multiplication(codomain(X0),addition(omega(codomain(X0)),X1))),
inference(paramodulation,[status(thm)],[f318,f615]) ).
fof(f12161,plain,
! [X0,X1] : leq(addition(omega(c(X0)),multiplication(c(X0),X1)),addition(omega(c(X0)),X1)),
inference(paramodulation,[status(thm)],[f318,f6526]) ).
fof(f12162,plain,
! [X0,X1] : addition(omega(c(X0)),X1) = addition(addition(omega(c(X0)),X1),addition(omega(c(X0)),multiplication(c(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f4513]) ).
fof(f12163,plain,
! [X0,X1] : leq(addition(omega(coantidomain(X0)),multiplication(coantidomain(X0),X1)),addition(omega(coantidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f318,f7158]) ).
fof(f12164,plain,
! [X0,X1] : addition(omega(coantidomain(X0)),X1) = addition(addition(omega(coantidomain(X0)),X1),addition(omega(coantidomain(X0)),multiplication(coantidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f4515]) ).
fof(f12165,plain,
! [X0,X1] : multiplication(X0,addition(omega(coantidomain(X0)),multiplication(coantidomain(X0),X1))) = zero,
inference(paramodulation,[status(thm)],[f318,f151]) ).
fof(f12166,plain,
! [X0,X1] : addition(omega(domain(X0)),X1) = addition(addition(omega(domain(X0)),X1),addition(omega(domain(X0)),multiplication(domain(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f4516]) ).
fof(f12167,plain,
! [X0,X1] : leq(addition(omega(domain(X0)),multiplication(domain(X0),X1)),addition(omega(domain(X0)),X1)),
inference(paramodulation,[status(thm)],[f318,f6808]) ).
fof(f12168,plain,
! [X0,X1] : leq(addition(omega(star(X0)),X1),addition(omega(star(X0)),multiplication(star(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f8451]) ).
fof(f12169,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(omega(multiplication(X0,X1)),X2))) = addition(omega(multiplication(X0,X1)),multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f318,f39]) ).
fof(f12171,plain,
! [X0,X1] : leq(addition(omega(antidomain(X0)),multiplication(antidomain(X0),X1)),addition(omega(antidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f318,f6667]) ).
fof(f12172,plain,
! [X0,X1] : addition(omega(antidomain(X0)),X1) = addition(addition(omega(antidomain(X0)),X1),addition(omega(antidomain(X0)),multiplication(antidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f4514]) ).
fof(f12180,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(omega(X0),X1),omega(addition(omega(X0),multiplication(X0,X1))))) = omega(multiplication(X0,addition(omega(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f308]) ).
fof(f12181,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),addition(omega(X1),X2))
| ~ leq(addition(multiplication(X0,addition(omega(X1),multiplication(X1,X2))),X3),addition(omega(X1),X2)) ),
inference(paramodulation,[status(thm)],[f318,f296]) ).
fof(f12182,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,addition(omega(X0),X1))),addition(omega(X0),X1))
| ~ leq(addition(omega(X0),multiplication(X0,X1)),addition(omega(X0),X1)) ),
inference(paramodulation,[status(thm)],[f318,f295]) ).
fof(f12183,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),addition(omega(X1),X2))
| ~ leq(addition(X0,addition(omega(X1),multiplication(X1,X2))),addition(omega(X1),X2)) ),
inference(paramodulation,[status(thm)],[f318,f293]) ).
fof(f12184,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(omega(X0),X1),star(multiplication(X0,addition(omega(X0),X1)))))),star(addition(omega(X0),multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f318,f252]) ).
fof(f12185,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(omega(X0),X1),star(addition(omega(X0),multiplication(X0,X1)))))),star(multiplication(X0,addition(omega(X0),X1)))),
inference(paramodulation,[status(thm)],[f318,f252]) ).
fof(f12186,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(omega(X1),X2)),addition(addition(omega(X1),multiplication(X1,X2)),X3)) = addition(multiplication(addition(X0,X1),addition(omega(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f318,f219]) ).
fof(f12187,plain,
! [X0,X1,X2,X3] : addition(addition(omega(X0),multiplication(X0,X1)),addition(multiplication(X2,addition(omega(X0),X1)),X3)) = addition(multiplication(addition(X0,X2),addition(omega(X0),X1)),X3),
inference(paramodulation,[status(thm)],[f318,f219]) ).
fof(f12188,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(omega(X0),X1)) = addition(addition(omega(X0),X1),addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f318,f232]) ).
fof(f12189,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(omega(X2),X3)) = addition(multiplication(X0,addition(omega(X2),X3)),multiplication(X1,addition(omega(X2),multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f318,f211]) ).
fof(f12190,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(omega(X0),X3)) = addition(addition(omega(X0),multiplication(X0,X3)),multiplication(X1,multiplication(X2,addition(omega(X0),X3)))),
inference(paramodulation,[status(thm)],[f318,f211]) ).
fof(f12191,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(omega(X0),X1)) = addition(addition(omega(X0),X1),addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f318,f207]) ).
fof(f12192,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(omega(X2),X3)) = addition(multiplication(X0,multiplication(X1,addition(omega(X2),X3))),addition(omega(X2),multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f318,f204]) ).
fof(f12193,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(omega(X1),X3)) = addition(multiplication(X0,addition(omega(X1),multiplication(X1,X3))),multiplication(X2,addition(omega(X1),X3))),
inference(paramodulation,[status(thm)],[f318,f204]) ).
fof(f12194,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X0),X2)) = addition(multiplication(X1,addition(omega(X0),X2)),addition(omega(X0),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f318,f201]) ).
fof(f12195,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X1),X2)) = addition(addition(omega(X1),multiplication(X1,X2)),multiplication(X0,addition(omega(X1),X2))),
inference(paramodulation,[status(thm)],[f318,f201]) ).
fof(f12196,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(omega(X0),multiplication(X0,X2)),X3)) = addition(multiplication(X0,addition(X1,addition(omega(X0),X2))),X3),
inference(paramodulation,[status(thm)],[f318,f170]) ).
fof(f12197,plain,
! [X0,X1,X2,X3] : addition(addition(omega(X0),multiplication(X0,X1)),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(addition(omega(X0),X1),X2)),X3),
inference(paramodulation,[status(thm)],[f318,f170]) ).
fof(f12198,plain,
! [X0,X1] : multiplication(X0,addition(addition(omega(X0),X1),one)) = addition(X0,addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f318,f192]) ).
fof(f12199,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(omega(X0),X1))) = addition(X0,addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f318,f162]) ).
fof(f12200,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(omega(X0),X1),X2)) = addition(multiplication(X0,X2),addition(omega(X0),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f318,f153]) ).
fof(f12201,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(addition(omega(X0),multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f318,f153]) ).
fof(f12202,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(omega(X0),X1),coantidomain(addition(omega(X0),multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f318,f144]) ).
fof(f12203,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(omega(X0),multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f318,f136]) ).
fof(f12204,plain,
! [X0,X1] : addition(coantidomain(addition(omega(X0),multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),addition(omega(X0),X1)))) = coantidomain(multiplication(codomain(X0),addition(omega(X0),X1))),
inference(paramodulation,[status(thm)],[f318,f615]) ).
fof(f12205,plain,
! [X0,X1] : addition(antidomain(addition(omega(X0),multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(omega(X0),X1))))) = antidomain(multiplication(X0,domain(addition(omega(X0),X1)))),
inference(paramodulation,[status(thm)],[f318,f479]) ).
fof(f12206,plain,
! [X0,X1,X2] :
( leq(addition(omega(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(addition(omega(X0),X1),addition(addition(omega(X0),multiplication(X0,X1)),X2)) ),
inference(paramodulation,[status(thm)],[f318,f58]) ).
fof(f12207,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(omega(X0),X1))),X0)
| ~ leq(addition(addition(omega(X0),multiplication(X0,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f318,f55]) ).
fof(f12208,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(omega(X0),X1))
| ~ leq(addition(addition(omega(X0),multiplication(X0,X1)),X2),addition(omega(X0),X1)) ),
inference(paramodulation,[status(thm)],[f318,f53]) ).
fof(f12209,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X1),X2)) = addition(multiplication(X0,addition(omega(X1),X2)),addition(omega(X1),multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f318,f43]) ).
fof(f12210,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X0),X2)) = addition(addition(omega(X0),multiplication(X0,X2)),multiplication(X1,addition(omega(X0),X2))),
inference(paramodulation,[status(thm)],[f318,f43]) ).
fof(f12211,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(multiplication(X0,X1),addition(omega(X0),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f318,f42]) ).
fof(f12212,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(omega(X0),X1),X2)) = addition(addition(omega(X0),multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f318,f42]) ).
fof(f12213,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(omega(X0),X1),X2)) = multiplication(addition(omega(X0),multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f318,f39]) ).
fof(f12214,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(omega(multiplication(X0,X1)),X2))) = addition(omega(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f12115]) ).
fof(f12223,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(domain(X1),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f12122]) ).
fof(f12224,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(coantidomain(X1),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f12123]) ).
fof(f12225,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(antidomain(X1),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f12124]) ).
fof(f12226,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(c(X1),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f12125]) ).
fof(f12227,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(codomain(X1),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f12126]) ).
fof(f12228,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(divergence(X1),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f12127]) ).
fof(f12229,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f56,f12128]) ).
fof(f12230,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),coantidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f56,f12129]) ).
fof(f12231,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),antidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f56,f12130]) ).
fof(f12232,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),c(X1)))),
inference(forward_demodulation,[status(thm)],[f56,f12131]) ).
fof(f12233,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),codomain(X1)))),
inference(forward_demodulation,[status(thm)],[f56,f12132]) ).
fof(f12234,plain,
! [X0,X1] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(omega(X0),divergence(X1)))),
inference(forward_demodulation,[status(thm)],[f56,f12133]) ).
fof(f12249,plain,
! [X0] : omega(X0) = addition(omega(X0),multiplication(X0,omega(X0))),
inference(forward_demodulation,[status(thm)],[f56,f12147]) ).
fof(f12250,plain,
! [X0] : omega(X0) = multiplication(addition(X0,one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f232,f12249]) ).
fof(f12254,plain,
! [X0,X1] : addition(omega(divergence(X0)),X1) = addition(X1,addition(omega(divergence(X0)),addition(omega(divergence(X0)),multiplication(divergence(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12154]) ).
fof(f12255,plain,
! [X0,X1] : addition(omega(divergence(X0)),X1) = addition(X1,addition(multiplication(divergence(X0),X1),omega(divergence(X0)))),
inference(forward_demodulation,[status(thm)],[f1026,f12254]) ).
fof(f12256,plain,
! [X0,X1] : addition(omega(divergence(X0)),X1) = addition(X1,addition(omega(divergence(X0)),multiplication(divergence(X0),X1))),
inference(forward_demodulation,[status(thm)],[f35,f12255]) ).
fof(f12257,plain,
! [X0,X1] : addition(omega(codomain(X0)),X1) = addition(X1,addition(omega(codomain(X0)),addition(omega(codomain(X0)),multiplication(codomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12158]) ).
fof(f12258,plain,
! [X0,X1] : addition(omega(codomain(X0)),X1) = addition(X1,addition(multiplication(codomain(X0),X1),omega(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1026,f12257]) ).
fof(f12259,plain,
! [X0,X1] : addition(omega(codomain(X0)),X1) = addition(X1,addition(omega(codomain(X0)),multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f35,f12258]) ).
fof(f12260,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,addition(omega(codomain(X0)),X1))),coantidomain(addition(omega(codomain(X0)),multiplication(codomain(X0),X1)))) = coantidomain(addition(omega(codomain(X0)),multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f318,f12160]) ).
fof(f12261,plain,
! [X0,X1] : addition(omega(c(X0)),X1) = addition(X1,addition(omega(c(X0)),addition(omega(c(X0)),multiplication(c(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12162]) ).
fof(f12262,plain,
! [X0,X1] : addition(omega(c(X0)),X1) = addition(X1,addition(multiplication(c(X0),X1),omega(c(X0)))),
inference(forward_demodulation,[status(thm)],[f1026,f12261]) ).
fof(f12263,plain,
! [X0,X1] : addition(omega(c(X0)),X1) = addition(X1,addition(omega(c(X0)),multiplication(c(X0),X1))),
inference(forward_demodulation,[status(thm)],[f35,f12262]) ).
fof(f12264,plain,
! [X0,X1] : addition(omega(coantidomain(X0)),X1) = addition(X1,addition(omega(coantidomain(X0)),addition(omega(coantidomain(X0)),multiplication(coantidomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12164]) ).
fof(f12265,plain,
! [X0,X1] : addition(omega(coantidomain(X0)),X1) = addition(X1,addition(multiplication(coantidomain(X0),X1),omega(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1026,f12264]) ).
fof(f12266,plain,
! [X0,X1] : addition(omega(coantidomain(X0)),X1) = addition(X1,addition(omega(coantidomain(X0)),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f35,f12265]) ).
fof(f12267,plain,
! [X0,X1] : addition(omega(domain(X0)),X1) = addition(X1,addition(omega(domain(X0)),addition(omega(domain(X0)),multiplication(domain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12166]) ).
fof(f12268,plain,
! [X0,X1] : addition(omega(domain(X0)),X1) = addition(X1,addition(multiplication(domain(X0),X1),omega(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f1026,f12267]) ).
fof(f12269,plain,
! [X0,X1] : addition(omega(domain(X0)),X1) = addition(X1,addition(omega(domain(X0)),multiplication(domain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f35,f12268]) ).
fof(f12270,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(omega(multiplication(X0,X1)),X2))) = addition(omega(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f12169]) ).
fof(f12273,plain,
! [X0,X1] : addition(omega(antidomain(X0)),X1) = addition(X1,addition(omega(antidomain(X0)),addition(omega(antidomain(X0)),multiplication(antidomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12172]) ).
fof(f12274,plain,
! [X0,X1] : addition(omega(antidomain(X0)),X1) = addition(X1,addition(multiplication(antidomain(X0),X1),omega(antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1026,f12273]) ).
fof(f12275,plain,
! [X0,X1] : addition(omega(antidomain(X0)),X1) = addition(X1,addition(omega(antidomain(X0)),multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f35,f12274]) ).
fof(f12283,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(omega(X0),X1),omega(addition(omega(X0),multiplication(X0,X1))))) = omega(addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f318,f12180]) ).
fof(f12284,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(omega(X0),multiplication(X0,X1))),addition(omega(X0),X1))
| ~ leq(addition(omega(X0),multiplication(X0,X1)),addition(omega(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f318,f12182]) ).
fof(f12285,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(omega(X0),X1),star(addition(omega(X0),multiplication(X0,X1)))))),star(addition(omega(X0),multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f318,f12184]) ).
fof(f12286,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(addition(omega(X0),X1),star(addition(omega(X0),multiplication(X0,X1)))))),star(addition(omega(X0),multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f318,f12185]) ).
fof(f12287,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(omega(X1),X2)),addition(multiplication(X1,X2),addition(omega(X1),X3))) = addition(multiplication(addition(X0,X1),addition(omega(X1),X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f12186]) ).
fof(f12288,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(omega(X0),X2),multiplication(X3,addition(omega(X0),X1)))) = addition(multiplication(addition(X3,X0),addition(omega(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f12287]) ).
fof(f12289,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,addition(omega(X0),multiplication(X3,addition(omega(X0),X1))))) = addition(multiplication(addition(X3,X0),addition(omega(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f103,f12288]) ).
fof(f12290,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(omega(X0),addition(multiplication(X2,addition(omega(X0),X1)),X3))) = addition(multiplication(addition(X0,X2),addition(omega(X0),X1)),X3),
inference(forward_demodulation,[status(thm)],[f103,f12187]) ).
fof(f12291,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(addition(multiplication(X1,addition(omega(X0),X2)),X3),multiplication(X0,X2))) = addition(multiplication(addition(X0,X1),addition(omega(X0),X2)),X3),
inference(forward_demodulation,[status(thm)],[f97,f12290]) ).
fof(f12292,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,addition(multiplication(X2,addition(omega(X0),X3)),multiplication(X0,X3)))) = addition(multiplication(addition(X0,X2),addition(omega(X0),X3)),X1),
inference(forward_demodulation,[status(thm)],[f103,f12291]) ).
fof(f12293,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,addition(multiplication(X0,X2),multiplication(X3,addition(omega(X0),X2))))) = addition(multiplication(addition(X0,X3),addition(omega(X0),X2)),X1),
inference(forward_demodulation,[status(thm)],[f35,f12292]) ).
fof(f12294,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(omega(X0),X1)) = addition(X1,addition(omega(X0),addition(omega(X0),multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12188]) ).
fof(f12295,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(omega(X0),X1)) = addition(X1,addition(multiplication(X0,X1),omega(X0))),
inference(forward_demodulation,[status(thm)],[f1026,f12294]) ).
fof(f12296,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(omega(X0),X1)) = addition(X1,addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f12295]) ).
fof(f12297,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(omega(X0),X3)) = addition(multiplication(X0,X3),addition(omega(X0),multiplication(X1,multiplication(X2,addition(omega(X0),X3))))),
inference(forward_demodulation,[status(thm)],[f103,f12190]) ).
fof(f12298,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(omega(X0),X3)) = addition(omega(X0),addition(multiplication(X1,multiplication(X2,addition(omega(X0),X3))),multiplication(X0,X3))),
inference(forward_demodulation,[status(thm)],[f97,f12297]) ).
fof(f12299,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(omega(X0),X3)) = addition(omega(X0),addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,addition(omega(X0),X3))))),
inference(forward_demodulation,[status(thm)],[f35,f12298]) ).
fof(f12300,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(omega(X0),X1)) = addition(X1,addition(omega(X0),addition(omega(X0),multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12191]) ).
fof(f12301,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(omega(X0),X1)) = addition(X1,addition(multiplication(X0,X1),omega(X0))),
inference(forward_demodulation,[status(thm)],[f1026,f12300]) ).
fof(f12302,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(omega(X0),X1)) = addition(X1,addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f12301]) ).
fof(f12303,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(omega(X2),X3)) = addition(omega(X2),addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,addition(omega(X2),X3))))),
inference(forward_demodulation,[status(thm)],[f97,f12192]) ).
fof(f12304,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X0),X2)) = addition(omega(X0),addition(multiplication(X0,X2),multiplication(X1,addition(omega(X0),X2)))),
inference(forward_demodulation,[status(thm)],[f97,f12194]) ).
fof(f12305,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X1),X2)) = addition(multiplication(X1,X2),addition(omega(X1),multiplication(X0,addition(omega(X1),X2)))),
inference(forward_demodulation,[status(thm)],[f103,f12195]) ).
fof(f12306,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X1),X2)) = addition(omega(X1),addition(multiplication(X0,addition(omega(X1),X2)),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f97,f12305]) ).
fof(f12307,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X1),X2)) = addition(omega(X1),addition(multiplication(X1,X2),multiplication(X0,addition(omega(X1),X2)))),
inference(forward_demodulation,[status(thm)],[f35,f12306]) ).
fof(f12308,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),addition(omega(X0),X3))) = addition(multiplication(X0,addition(X1,addition(omega(X0),X2))),X3),
inference(forward_demodulation,[status(thm)],[f103,f12196]) ).
fof(f12309,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),addition(omega(X0),X3)) = addition(multiplication(X0,addition(X1,addition(omega(X0),X2))),X3),
inference(forward_demodulation,[status(thm)],[f170,f12308]) ).
fof(f12310,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(X2,addition(omega(X0),X3))),X1),
inference(forward_demodulation,[status(thm)],[f97,f12309]) ).
fof(f12311,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(omega(X0),addition(multiplication(X0,X2),X3))) = addition(multiplication(X0,addition(addition(omega(X0),X1),X2)),X3),
inference(forward_demodulation,[status(thm)],[f103,f12197]) ).
fof(f12312,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(addition(multiplication(X0,X1),X2),multiplication(X0,X3))) = addition(multiplication(X0,addition(addition(omega(X0),X3),X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f12311]) ).
fof(f12313,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,addition(multiplication(X0,X2),multiplication(X0,X3)))) = addition(multiplication(X0,addition(addition(omega(X0),X3),X2)),X1),
inference(forward_demodulation,[status(thm)],[f103,f12312]) ).
fof(f12314,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(addition(omega(X0),X2),X3)),X1),
inference(forward_demodulation,[status(thm)],[f153,f12313]) ).
fof(f12315,plain,
! [X0,X1,X2,X3] : addition(omega(X0),addition(X1,multiplication(X0,addition(X2,X3)))) = addition(multiplication(X0,addition(X2,addition(omega(X0),X3))),X1),
inference(forward_demodulation,[status(thm)],[f103,f12314]) ).
fof(f12316,plain,
! [X0,X1] : multiplication(X0,addition(X1,addition(omega(X0),one))) = addition(X0,addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f12198]) ).
fof(f12317,plain,
! [X0,X1] : multiplication(X0,addition(X1,addition(one,omega(X0)))) = addition(X0,addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f12316]) ).
fof(f12318,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(multiplication(X0,X2),addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f12200]) ).
fof(f12319,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f12318]) ).
fof(f12320,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f12319]) ).
fof(f12321,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(multiplication(X0,X2),addition(omega(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f103,f12201]) ).
fof(f12322,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f12321]) ).
fof(f12323,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f12322]) ).
fof(f12324,plain,
! [X0,X1,X2] :
( leq(addition(omega(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(addition(omega(X0),X1),addition(multiplication(X0,X1),addition(omega(X0),X2))) ),
inference(forward_demodulation,[status(thm)],[f103,f12206]) ).
fof(f12325,plain,
! [X0,X1,X2] :
( leq(addition(omega(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(addition(omega(X0),X1),addition(omega(X0),addition(X2,multiplication(X0,X1)))) ),
inference(forward_demodulation,[status(thm)],[f97,f12324]) ).
fof(f12326,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(omega(X0),X1))),X0)
| ~ leq(addition(multiplication(X0,X1),addition(omega(X0),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f103,f12207]) ).
fof(f12327,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(addition(omega(X0),X2))),X0)
| ~ leq(addition(omega(X0),addition(X1,multiplication(X0,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f97,f12326]) ).
fof(f12328,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(omega(X0),X1))
| ~ leq(addition(multiplication(X0,X1),addition(omega(X0),X2)),addition(omega(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f103,f12208]) ).
fof(f12329,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X1),addition(omega(X0),X2))
| ~ leq(addition(omega(X0),addition(X1,multiplication(X0,X2))),addition(omega(X0),X2)) ),
inference(forward_demodulation,[status(thm)],[f97,f12328]) ).
fof(f12330,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X1),X2)) = addition(omega(X1),addition(multiplication(X1,X2),multiplication(X0,addition(omega(X1),X2)))),
inference(forward_demodulation,[status(thm)],[f97,f12209]) ).
fof(f12331,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X0),X2)) = addition(multiplication(X0,X2),addition(omega(X0),multiplication(X1,addition(omega(X0),X2)))),
inference(forward_demodulation,[status(thm)],[f103,f12210]) ).
fof(f12332,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X0),X2)) = addition(omega(X0),addition(multiplication(X1,addition(omega(X0),X2)),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f97,f12331]) ).
fof(f12333,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(omega(X0),X2)) = addition(omega(X0),addition(multiplication(X0,X2),multiplication(X1,addition(omega(X0),X2)))),
inference(forward_demodulation,[status(thm)],[f35,f12332]) ).
fof(f12334,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f12211]) ).
fof(f12335,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f153,f12334]) ).
fof(f12336,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(addition(omega(X0),multiplication(X0,X1)),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f103,f12212]) ).
fof(f12337,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(multiplication(X0,X1),addition(omega(X0),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f103,f12336]) ).
fof(f12338,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f97,f12337]) ).
fof(f12339,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(omega(X0),X2))) = addition(omega(X0),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f153,f12338]) ).
fof(f12341,plain,
! [X0,X1] : c(backward_diamond(X0,c(X1))) = multiplication(backward_box(X0,X1),c(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f72,f2211]) ).
fof(f12342,plain,
! [X0,X1] : c(forward_diamond(X0,c(X1))) = multiplication(forward_box(X0,X1),c(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f71,f2211]) ).
fof(f12344,plain,
! [X0] : c(antidomain(X0)) = multiplication(antidomain(c(X0)),c(antidomain(X0))),
inference(paramodulation,[status(thm)],[f547,f2211]) ).
fof(f12345,plain,
! [X0] : c(domain(X0)) = multiplication(domain(c(X0)),c(domain(X0))),
inference(paramodulation,[status(thm)],[f362,f2211]) ).
fof(f12348,plain,
! [X0,X1] : c(backward_diamond(X0,c(X1))) = multiplication(c(backward_diamond(X0,c(X1))),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f72,f2211]) ).
fof(f12349,plain,
! [X0,X1] : c(forward_diamond(X0,c(X1))) = multiplication(c(forward_diamond(X0,c(X1))),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f71,f2211]) ).
fof(f12351,plain,
! [X0] : c(antidomain(X0)) = multiplication(c(antidomain(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f547,f2211]) ).
fof(f12352,plain,
! [X0] : c(domain(X0)) = multiplication(c(domain(X0)),domain(c(X0))),
inference(paramodulation,[status(thm)],[f362,f2211]) ).
fof(f12359,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,c(X1))),X2),c(X1))
| ~ leq(addition(multiplication(X0,c(X1)),X2),c(X1)) ),
inference(paramodulation,[status(thm)],[f2211,f296]) ).
fof(f12360,plain,
! [X0] :
( leq(multiplication(star(c(X0)),multiplication(c(X0),c(X0))),c(X0))
| ~ leq(c(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2211,f295]) ).
fof(f12361,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),c(X1))
| ~ leq(addition(X0,c(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f2211,f293]) ).
fof(f12362,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(c(X0),star(multiplication(c(X0),c(X0)))))),star(c(X0))),
inference(paramodulation,[status(thm)],[f2211,f252]) ).
fof(f12363,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(c(X0),star(c(X0))))),star(multiplication(c(X0),c(X0)))),
inference(paramodulation,[status(thm)],[f2211,f252]) ).
fof(f12364,plain,
! [X0,X1,X2] : addition(multiplication(X0,c(X1)),addition(c(X1),X2)) = addition(multiplication(addition(X0,c(X1)),c(X1)),X2),
inference(paramodulation,[status(thm)],[f2211,f219]) ).
fof(f12365,plain,
! [X0,X1,X2] : addition(c(X0),addition(multiplication(X1,c(X0)),X2)) = addition(multiplication(addition(c(X0),X1),c(X0)),X2),
inference(paramodulation,[status(thm)],[f2211,f219]) ).
fof(f12367,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),c(X2)) = addition(multiplication(X0,c(X2)),multiplication(X1,c(X2))),
inference(paramodulation,[status(thm)],[f2211,f211]) ).
fof(f12368,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),c(X0)) = addition(c(X0),multiplication(X1,multiplication(X2,c(X0)))),
inference(paramodulation,[status(thm)],[f2211,f211]) ).
fof(f12370,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),c(X2)) = addition(multiplication(X0,multiplication(X1,c(X2))),c(X2)),
inference(paramodulation,[status(thm)],[f2211,f204]) ).
fof(f12371,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),c(X1)) = addition(multiplication(X0,c(X1)),multiplication(X2,c(X1))),
inference(paramodulation,[status(thm)],[f2211,f204]) ).
fof(f12372,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = addition(multiplication(X1,c(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f2211,f201]) ).
fof(f12373,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = addition(c(X1),multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f2211,f201]) ).
fof(f12374,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(c(X0),X2)) = addition(multiplication(c(X0),addition(X1,c(X0))),X2),
inference(paramodulation,[status(thm)],[f2211,f170]) ).
fof(f12375,plain,
! [X0,X1,X2] : addition(c(X0),addition(multiplication(c(X0),X1),X2)) = addition(multiplication(c(X0),addition(c(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f2211,f170]) ).
fof(f12378,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = addition(multiplication(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f2211,f153]) ).
fof(f12379,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = addition(c(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f2211,f153]) ).
fof(f12382,plain,
! [X0] : addition(coantidomain(c(X0)),coantidomain(multiplication(codomain(c(X0)),c(X0)))) = coantidomain(multiplication(codomain(c(X0)),c(X0))),
inference(paramodulation,[status(thm)],[f2211,f615]) ).
fof(f12383,plain,
! [X0] : addition(antidomain(c(X0)),antidomain(multiplication(c(X0),domain(c(X0))))) = antidomain(multiplication(c(X0),domain(c(X0)))),
inference(paramodulation,[status(thm)],[f2211,f479]) ).
fof(f12384,plain,
! [X0,X1] :
( leq(c(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(c(X0),addition(c(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2211,f58]) ).
fof(f12385,plain,
! [X0,X1] :
( leq(multiplication(X1,star(c(X0))),c(X0))
| ~ leq(addition(c(X0),X1),c(X0)) ),
inference(paramodulation,[status(thm)],[f2211,f55]) ).
fof(f12386,plain,
! [X0,X1] :
( leq(multiplication(star(c(X0)),X1),c(X0))
| ~ leq(addition(c(X0),X1),c(X0)) ),
inference(paramodulation,[status(thm)],[f2211,f53]) ).
fof(f12387,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = addition(multiplication(X0,c(X1)),c(X1)),
inference(paramodulation,[status(thm)],[f2211,f43]) ).
fof(f12388,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = addition(c(X0),multiplication(X1,c(X0))),
inference(paramodulation,[status(thm)],[f2211,f43]) ).
fof(f12389,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = addition(multiplication(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f2211,f42]) ).
fof(f12390,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = addition(c(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f2211,f42]) ).
fof(f12391,plain,
! [X0,X1] : multiplication(c(X0),multiplication(c(X0),X1)) = multiplication(c(X0),X1),
inference(paramodulation,[status(thm)],[f2211,f39]) ).
fof(f12393,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),c(backward_diamond(X0,c(X1)))),
inference(forward_demodulation,[status(thm)],[f72,f12341]) ).
fof(f12394,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f72,f12393]) ).
fof(f12395,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),c(forward_diamond(X0,c(X1)))),
inference(forward_demodulation,[status(thm)],[f71,f12342]) ).
fof(f12396,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f71,f12395]) ).
fof(f12399,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),c(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f547,f12344]) ).
fof(f12400,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f547,f12399]) ).
fof(f12401,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),c(domain(X0))),
inference(forward_demodulation,[status(thm)],[f362,f12345]) ).
fof(f12402,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f362,f12401]) ).
fof(f12405,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(c(backward_diamond(X0,c(X1))),backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f72,f12348]) ).
fof(f12406,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f72,f12405]) ).
fof(f12407,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(c(forward_diamond(X0,c(X1))),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f71,f12349]) ).
fof(f12408,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f71,f12407]) ).
fof(f12411,plain,
! [X0] : antidomain(c(X0)) = multiplication(c(antidomain(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f547,f12351]) ).
fof(f12412,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f547,f12411]) ).
fof(f12413,plain,
! [X0] : domain(c(X0)) = multiplication(c(domain(X0)),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f362,f12352]) ).
fof(f12414,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f362,f12413]) ).
fof(f12418,plain,
! [X0] :
( leq(multiplication(star(c(X0)),c(X0)),c(X0))
| ~ leq(c(X0),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f2211,f12360]) ).
fof(f12419,plain,
! [X0] : leq(multiplication(star(c(X0)),c(X0)),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f12418,f239]) ).
fof(f12420,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(c(X0),star(c(X0))))),star(c(X0))),
inference(forward_demodulation,[status(thm)],[f2211,f12362]) ).
fof(f12421,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(c(X0),star(c(X0))))),star(c(X0))),
inference(forward_demodulation,[status(thm)],[f2211,f12363]) ).
fof(f12422,plain,
! [X0,X1,X2] : addition(c(X0),addition(X1,multiplication(X2,c(X0)))) = addition(multiplication(addition(X2,c(X0)),c(X0)),X1),
inference(forward_demodulation,[status(thm)],[f97,f12364]) ).
fof(f12426,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),c(X2)) = multiplication(addition(X1,X0),c(X2)),
inference(forward_demodulation,[status(thm)],[f201,f12367]) ).
fof(f12429,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),c(X2)) = addition(c(X2),multiplication(X0,multiplication(X1,c(X2)))),
inference(forward_demodulation,[status(thm)],[f35,f12370]) ).
fof(f12430,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),c(X1)) = multiplication(addition(X2,X0),c(X1)),
inference(forward_demodulation,[status(thm)],[f201,f12371]) ).
fof(f12431,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = addition(c(X0),multiplication(X1,c(X0))),
inference(forward_demodulation,[status(thm)],[f35,f12372]) ).
fof(f12432,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = multiplication(addition(X1,one),c(X0)),
inference(forward_demodulation,[status(thm)],[f232,f12431]) ).
fof(f12433,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = multiplication(addition(X0,one),c(X1)),
inference(forward_demodulation,[status(thm)],[f232,f12373]) ).
fof(f12434,plain,
! [X0,X1,X2] : addition(c(X0),addition(X1,multiplication(c(X0),X2))) = addition(multiplication(c(X0),addition(X2,c(X0))),X1),
inference(forward_demodulation,[status(thm)],[f97,f12374]) ).
fof(f12440,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = addition(c(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f12378]) ).
fof(f12441,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f12440]) ).
fof(f12442,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f12379]) ).
fof(f12444,plain,
! [X0,X1] : leq(c(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f12384,f1324]) ).
fof(f12445,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = addition(c(X1),multiplication(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f35,f12387]) ).
fof(f12446,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = multiplication(addition(X0,one),c(X1)),
inference(forward_demodulation,[status(thm)],[f232,f12445]) ).
fof(f12447,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = multiplication(addition(X1,one),c(X0)),
inference(forward_demodulation,[status(thm)],[f232,f12388]) ).
fof(f12448,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = addition(c(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f12389]) ).
fof(f12449,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f12448]) ).
fof(f12450,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f12390]) ).
fof(f12452,plain,
! [X0,X1] : domain(multiplication(X0,domain(X1))) = multiplication(forward_diamond(X0,X1),domain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f69,f2215]) ).
fof(f12454,plain,
! [X0] : domain(domain(X0)) = multiplication(antidomain(c(X0)),domain(domain(X0))),
inference(paramodulation,[status(thm)],[f196,f2215]) ).
fof(f12458,plain,
! [X0,X1] : domain(multiplication(X0,domain(X1))) = multiplication(domain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f69,f2215]) ).
fof(f12460,plain,
! [X0] : domain(domain(X0)) = multiplication(domain(domain(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f196,f2215]) ).
fof(f12467,plain,
! [X0] : forward_diamond(domain(X0),X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f2215,f69]) ).
fof(f12470,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,domain(X1))),X2),domain(X1))
| ~ leq(addition(multiplication(X0,domain(X1)),X2),domain(X1)) ),
inference(paramodulation,[status(thm)],[f2215,f296]) ).
fof(f12471,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),multiplication(domain(X0),domain(X0))),domain(X0))
| ~ leq(domain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2215,f295]) ).
fof(f12472,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),domain(X1))
| ~ leq(addition(X0,domain(X1)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f2215,f293]) ).
fof(f12473,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(domain(X0),star(multiplication(domain(X0),domain(X0)))))),star(domain(X0))),
inference(paramodulation,[status(thm)],[f2215,f252]) ).
fof(f12474,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(domain(X0),star(domain(X0))))),star(multiplication(domain(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f2215,f252]) ).
fof(f12475,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),addition(domain(X1),X2)) = addition(multiplication(addition(X0,domain(X1)),domain(X1)),X2),
inference(paramodulation,[status(thm)],[f2215,f219]) ).
fof(f12476,plain,
! [X0,X1,X2] : addition(domain(X0),addition(multiplication(X1,domain(X0)),X2)) = addition(multiplication(addition(domain(X0),X1),domain(X0)),X2),
inference(paramodulation,[status(thm)],[f2215,f219]) ).
fof(f12478,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),multiplication(X1,domain(X2))),
inference(paramodulation,[status(thm)],[f2215,f211]) ).
fof(f12479,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),multiplication(X1,X2)),domain(X0)) = addition(domain(X0),multiplication(X1,multiplication(X2,domain(X0)))),
inference(paramodulation,[status(thm)],[f2215,f211]) ).
fof(f12481,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),domain(X2)) = addition(multiplication(X0,multiplication(X1,domain(X2))),domain(X2)),
inference(paramodulation,[status(thm)],[f2215,f204]) ).
fof(f12482,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),domain(X1)) = addition(multiplication(X0,domain(X1)),multiplication(X2,domain(X1))),
inference(paramodulation,[status(thm)],[f2215,f204]) ).
fof(f12483,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = addition(multiplication(X1,domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f2215,f201]) ).
fof(f12484,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = addition(domain(X1),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f2215,f201]) ).
fof(f12485,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),addition(domain(X0),X2)) = addition(multiplication(domain(X0),addition(X1,domain(X0))),X2),
inference(paramodulation,[status(thm)],[f2215,f170]) ).
fof(f12486,plain,
! [X0,X1,X2] : addition(domain(X0),addition(multiplication(domain(X0),X1),X2)) = addition(multiplication(domain(X0),addition(domain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f2215,f170]) ).
fof(f12489,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = addition(multiplication(domain(X0),X1),domain(X0)),
inference(paramodulation,[status(thm)],[f2215,f153]) ).
fof(f12490,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = addition(domain(X0),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f2215,f153]) ).
fof(f12493,plain,
! [X0] : addition(coantidomain(domain(X0)),coantidomain(multiplication(codomain(domain(X0)),domain(X0)))) = coantidomain(multiplication(codomain(domain(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f2215,f615]) ).
fof(f12494,plain,
! [X0] : addition(antidomain(domain(X0)),antidomain(multiplication(domain(X0),domain(domain(X0))))) = antidomain(multiplication(domain(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f2215,f479]) ).
fof(f12495,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),X1)))
| ~ leq(domain(X0),addition(domain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2215,f58]) ).
fof(f12496,plain,
! [X0,X1] :
( leq(multiplication(X1,star(domain(X0))),domain(X0))
| ~ leq(addition(domain(X0),X1),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2215,f55]) ).
fof(f12497,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X0)),X1),domain(X0))
| ~ leq(addition(domain(X0),X1),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2215,f53]) ).
fof(f12498,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = addition(multiplication(X0,domain(X1)),domain(X1)),
inference(paramodulation,[status(thm)],[f2215,f43]) ).
fof(f12499,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = addition(domain(X0),multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f2215,f43]) ).
fof(f12500,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = addition(multiplication(domain(X0),X1),domain(X0)),
inference(paramodulation,[status(thm)],[f2215,f42]) ).
fof(f12501,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = addition(domain(X0),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f2215,f42]) ).
fof(f12502,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(domain(X0),X1)) = multiplication(domain(X0),X1),
inference(paramodulation,[status(thm)],[f2215,f39]) ).
fof(f12505,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),domain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f69,f12452]) ).
fof(f12506,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),forward_diamond(X0,X1)),
inference(forward_demodulation,[status(thm)],[f69,f12505]) ).
fof(f12508,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f196,f12454]) ).
fof(f12509,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f196,f12508]) ).
fof(f12516,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(domain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)),
inference(forward_demodulation,[status(thm)],[f69,f12458]) ).
fof(f12517,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),forward_diamond(X0,X1)),
inference(forward_demodulation,[status(thm)],[f69,f12516]) ).
fof(f12519,plain,
! [X0] : antidomain(c(X0)) = multiplication(domain(domain(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f196,f12460]) ).
fof(f12520,plain,
! [X0] : antidomain(c(X0)) = domain_difference(domain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f68,f12519]) ).
fof(f12524,plain,
! [X0] : forward_diamond(domain(X0),X0) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f196,f12467]) ).
fof(f12533,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),domain(X0)),domain(X0))
| ~ leq(domain(X0),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2215,f12471]) ).
fof(f12534,plain,
! [X0] : leq(multiplication(star(domain(X0)),domain(X0)),domain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f12533,f239]) ).
fof(f12535,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(domain(X0),star(domain(X0))))),star(domain(X0))),
inference(forward_demodulation,[status(thm)],[f2215,f12473]) ).
fof(f12536,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(domain(X0),star(domain(X0))))),star(domain(X0))),
inference(forward_demodulation,[status(thm)],[f2215,f12474]) ).
fof(f12537,plain,
! [X0,X1,X2] : addition(domain(X0),addition(X1,multiplication(X2,domain(X0)))) = addition(multiplication(addition(X2,domain(X0)),domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f97,f12475]) ).
fof(f12541,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),domain(X2)) = multiplication(addition(X1,X0),domain(X2)),
inference(forward_demodulation,[status(thm)],[f201,f12478]) ).
fof(f12544,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),domain(X2)) = addition(domain(X2),multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f35,f12481]) ).
fof(f12545,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),domain(X1)) = multiplication(addition(X2,X0),domain(X1)),
inference(forward_demodulation,[status(thm)],[f201,f12482]) ).
fof(f12546,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = addition(domain(X0),multiplication(X1,domain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f12483]) ).
fof(f12547,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = multiplication(addition(X1,one),domain(X0)),
inference(forward_demodulation,[status(thm)],[f232,f12546]) ).
fof(f12548,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = multiplication(addition(X0,one),domain(X1)),
inference(forward_demodulation,[status(thm)],[f232,f12484]) ).
fof(f12549,plain,
! [X0,X1,X2] : addition(domain(X0),addition(X1,multiplication(domain(X0),X2))) = addition(multiplication(domain(X0),addition(X2,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f97,f12485]) ).
fof(f12555,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = addition(domain(X0),multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f12489]) ).
fof(f12556,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = multiplication(domain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f12555]) ).
fof(f12557,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = multiplication(domain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f12490]) ).
fof(f12559,plain,
! [X0] : addition(c(X0),antidomain(multiplication(domain(X0),domain(domain(X0))))) = antidomain(multiplication(domain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f67,f12494]) ).
fof(f12560,plain,
! [X0] : addition(c(X0),antidomain(multiplication(domain(X0),antidomain(c(X0))))) = antidomain(multiplication(domain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f12559]) ).
fof(f12561,plain,
! [X0] : addition(c(X0),antidomain(domain_difference(X0,c(X0)))) = antidomain(multiplication(domain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f68,f12560]) ).
fof(f12562,plain,
! [X0] : addition(c(X0),antidomain(domain_difference(X0,c(X0)))) = antidomain(multiplication(domain(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f12561]) ).
fof(f12563,plain,
! [X0] : addition(c(X0),antidomain(domain_difference(X0,c(X0)))) = antidomain(domain_difference(X0,c(X0))),
inference(forward_demodulation,[status(thm)],[f68,f12562]) ).
fof(f12564,plain,
! [X0,X1] : leq(domain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f12495,f1324]) ).
fof(f12565,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = addition(domain(X1),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f35,f12498]) ).
fof(f12566,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = multiplication(addition(X0,one),domain(X1)),
inference(forward_demodulation,[status(thm)],[f232,f12565]) ).
fof(f12567,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = multiplication(addition(X1,one),domain(X0)),
inference(forward_demodulation,[status(thm)],[f232,f12499]) ).
fof(f12568,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = addition(domain(X0),multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f12500]) ).
fof(f12569,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = multiplication(domain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f12568]) ).
fof(f12570,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = multiplication(domain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f12501]) ).
fof(f12571,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),X2))) = multiplication(omega(multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f39,f319]) ).
fof(f12577,plain,
! [X0,X1] : multiplication(X0,addition(omega(omega(X0)),multiplication(omega(X0),X1))) = multiplication(omega(X0),addition(omega(omega(X0)),X1)),
inference(paramodulation,[status(thm)],[f318,f319]) ).
fof(f12579,plain,
! [X0,X1] : multiplication(X0,addition(omega(omega(X0)),multiplication(omega(X0),X1))) = multiplication(omega(X0),addition(X1,omega(omega(X0)))),
inference(paramodulation,[status(thm)],[f321,f319]) ).
fof(f12581,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(omega(X0)),X1)) = multiplication(omega(X0),multiplication(omega(omega(X0)),X1)),
inference(paramodulation,[status(thm)],[f319,f319]) ).
fof(f12583,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(omega(X0),X1))) = multiplication(omega(X0),multiplication(X1,omega(multiplication(omega(X0),X1)))),
inference(paramodulation,[status(thm)],[f308,f319]) ).
fof(f12586,plain,
! [X0] : multiplication(X0,omega(omega(X0))) = multiplication(omega(X0),omega(omega(X0))),
inference(paramodulation,[status(thm)],[f56,f319]) ).
fof(f12597,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,multiplication(omega(addition(X0,X1)),X2))),multiplication(omega(addition(X0,X1)),X2))
| ~ leq(multiplication(omega(addition(X0,X1)),X2),multiplication(omega(addition(X0,X1)),X2)) ),
inference(paramodulation,[status(thm)],[f319,f290]) ).
fof(f12598,plain,
! [X0,X1,X2] :
( multiplication(omega(addition(X0,X1)),X2) != multiplication(X1,multiplication(omega(addition(X0,X1)),X2))
| leq(multiplication(X0,multiplication(omega(addition(X0,X1)),X2)),multiplication(X1,multiplication(omega(addition(X0,X1)),X2))) ),
inference(paramodulation,[status(thm)],[f319,f241]) ).
fof(f12601,plain,
! [X0,X1] : backward_diamond(multiplication(omega(codomain(X0)),X1),X0) = codomain(multiplication(omega(codomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f319,f70]) ).
fof(f12602,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,multiplication(omega(codomain(X0)),X1))),coantidomain(multiplication(omega(codomain(X0)),X1))) = coantidomain(multiplication(codomain(X0),multiplication(omega(codomain(X0)),X1))),
inference(paramodulation,[status(thm)],[f319,f615]) ).
fof(f12607,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(coantidomain(X0)),X1)) = zero,
inference(paramodulation,[status(thm)],[f319,f151]) ).
fof(f12611,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),X2))) = multiplication(omega(multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f319,f39]) ).
fof(f12620,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,omega(X1))),X2) = addition(multiplication(X0,X2),multiplication(omega(X1),X2)),
inference(paramodulation,[status(thm)],[f319,f211]) ).
fof(f12621,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,omega(X0)),X1),X2) = addition(multiplication(omega(X0),X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f319,f204]) ).
fof(f12623,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),multiplication(omega(X1),X2))
| ~ leq(addition(multiplication(X0,multiplication(omega(X1),X2)),X3),multiplication(omega(X1),X2)) ),
inference(paramodulation,[status(thm)],[f319,f296]) ).
fof(f12624,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(omega(X0),X1))),multiplication(omega(X0),X1))
| ~ leq(multiplication(omega(X0),X1),multiplication(omega(X0),X1)) ),
inference(paramodulation,[status(thm)],[f319,f295]) ).
fof(f12625,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),multiplication(omega(X1),X2))
| ~ leq(addition(X0,multiplication(omega(X1),X2)),multiplication(omega(X1),X2)) ),
inference(paramodulation,[status(thm)],[f319,f293]) ).
fof(f12628,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(omega(X1),X2)),addition(multiplication(omega(X1),X2),X3)) = addition(multiplication(addition(X0,X1),multiplication(omega(X1),X2)),X3),
inference(paramodulation,[status(thm)],[f319,f219]) ).
fof(f12629,plain,
! [X0,X1,X2,X3] : addition(multiplication(omega(X0),X1),addition(multiplication(X2,multiplication(omega(X0),X1)),X3)) = addition(multiplication(addition(X0,X2),multiplication(omega(X0),X1)),X3),
inference(paramodulation,[status(thm)],[f319,f219]) ).
fof(f12630,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(omega(X0),X1)) = addition(multiplication(omega(X0),X1),multiplication(omega(X0),X1)),
inference(paramodulation,[status(thm)],[f319,f232]) ).
fof(f12631,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(omega(X2),X3)) = addition(multiplication(X0,multiplication(omega(X2),X3)),multiplication(X1,multiplication(omega(X2),X3))),
inference(paramodulation,[status(thm)],[f319,f211]) ).
fof(f12632,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(omega(X0),X3)) = addition(multiplication(omega(X0),X3),multiplication(X1,multiplication(X2,multiplication(omega(X0),X3)))),
inference(paramodulation,[status(thm)],[f319,f211]) ).
fof(f12633,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(omega(X0),X1)) = addition(multiplication(omega(X0),X1),multiplication(omega(X0),X1)),
inference(paramodulation,[status(thm)],[f319,f207]) ).
fof(f12634,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(omega(X2),X3)) = addition(multiplication(X0,multiplication(X1,multiplication(omega(X2),X3))),multiplication(omega(X2),X3)),
inference(paramodulation,[status(thm)],[f319,f204]) ).
fof(f12635,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(omega(X1),X3)) = addition(multiplication(X0,multiplication(omega(X1),X3)),multiplication(X2,multiplication(omega(X1),X3))),
inference(paramodulation,[status(thm)],[f319,f204]) ).
fof(f12636,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = addition(multiplication(X1,multiplication(omega(X0),X2)),multiplication(omega(X0),X2)),
inference(paramodulation,[status(thm)],[f319,f201]) ).
fof(f12637,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = addition(multiplication(omega(X1),X2),multiplication(X0,multiplication(omega(X1),X2))),
inference(paramodulation,[status(thm)],[f319,f201]) ).
fof(f12638,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(omega(X0),X2),X3)) = addition(multiplication(X0,addition(X1,multiplication(omega(X0),X2))),X3),
inference(paramodulation,[status(thm)],[f319,f170]) ).
fof(f12639,plain,
! [X0,X1,X2,X3] : addition(multiplication(omega(X0),X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(multiplication(omega(X0),X1),X2)),X3),
inference(paramodulation,[status(thm)],[f319,f170]) ).
fof(f12640,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(omega(X0),X1),one)) = addition(X0,multiplication(omega(X0),X1)),
inference(paramodulation,[status(thm)],[f319,f192]) ).
fof(f12641,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(omega(X0),X1))) = addition(X0,multiplication(omega(X0),X1)),
inference(paramodulation,[status(thm)],[f319,f162]) ).
fof(f12642,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(omega(X0),X1),X2)) = addition(multiplication(X0,X2),multiplication(omega(X0),X1)),
inference(paramodulation,[status(thm)],[f319,f153]) ).
fof(f12643,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(omega(X0),X2))) = addition(multiplication(omega(X0),X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f319,f153]) ).
fof(f12645,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(omega(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f319,f136]) ).
fof(f12646,plain,
! [X0,X1] : addition(coantidomain(multiplication(omega(X0),X1)),coantidomain(multiplication(codomain(X0),multiplication(omega(X0),X1)))) = coantidomain(multiplication(codomain(X0),multiplication(omega(X0),X1))),
inference(paramodulation,[status(thm)],[f319,f615]) ).
fof(f12647,plain,
! [X0,X1] : addition(antidomain(multiplication(omega(X0),X1)),antidomain(multiplication(X0,domain(multiplication(omega(X0),X1))))) = antidomain(multiplication(X0,domain(multiplication(omega(X0),X1)))),
inference(paramodulation,[status(thm)],[f319,f479]) ).
fof(f12648,plain,
! [X0,X1,X2] :
( leq(multiplication(omega(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(multiplication(omega(X0),X1),addition(multiplication(omega(X0),X1),X2)) ),
inference(paramodulation,[status(thm)],[f319,f58]) ).
fof(f12649,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(multiplication(omega(X0),X1))),X0)
| ~ leq(addition(multiplication(omega(X0),X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f319,f55]) ).
fof(f12650,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),multiplication(omega(X0),X1))
| ~ leq(addition(multiplication(omega(X0),X1),X2),multiplication(omega(X0),X1)) ),
inference(paramodulation,[status(thm)],[f319,f53]) ).
fof(f12651,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = addition(multiplication(X0,multiplication(omega(X1),X2)),multiplication(omega(X1),X2)),
inference(paramodulation,[status(thm)],[f319,f43]) ).
fof(f12652,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = addition(multiplication(omega(X0),X2),multiplication(X1,multiplication(omega(X0),X2))),
inference(paramodulation,[status(thm)],[f319,f43]) ).
fof(f12653,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(omega(X0),X2))) = addition(multiplication(X0,X1),multiplication(omega(X0),X2)),
inference(paramodulation,[status(thm)],[f319,f42]) ).
fof(f12654,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(omega(X0),X1),X2)) = addition(multiplication(omega(X0),X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f319,f42]) ).
fof(f12661,plain,
! [X0,X1] : multiplication(X0,addition(omega(omega(X0)),multiplication(omega(X0),X1))) = addition(omega(omega(X0)),multiplication(omega(X0),X1)),
inference(forward_demodulation,[status(thm)],[f318,f12577]) ).
fof(f12663,plain,
! [X0,X1] : multiplication(X0,addition(omega(omega(X0)),multiplication(omega(X0),X1))) = addition(omega(omega(X0)),multiplication(omega(X0),X1)),
inference(forward_demodulation,[status(thm)],[f321,f12579]) ).
fof(f12665,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(omega(X0)),X1)) = multiplication(omega(omega(X0)),X1),
inference(forward_demodulation,[status(thm)],[f319,f12581]) ).
fof(f12667,plain,
! [X0,X1] : multiplication(X0,omega(multiplication(omega(X0),X1))) = omega(multiplication(omega(X0),X1)),
inference(forward_demodulation,[status(thm)],[f308,f12583]) ).
fof(f12670,plain,
! [X0] : multiplication(X0,omega(omega(X0))) = omega(omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f12586]) ).
fof(f12677,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(X1,multiplication(omega(addition(X0,X1)),X2))),multiplication(omega(addition(X0,X1)),X2)),
inference(forward_subsumption_resolution,[status(thm)],[f12597,f239]) ).
fof(f12679,plain,
! [X0,X1] : addition(coantidomain(multiplication(omega(codomain(X0)),X1)),coantidomain(multiplication(X0,multiplication(omega(codomain(X0)),X1)))) = coantidomain(multiplication(codomain(X0),multiplication(omega(codomain(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f35,f12602]) ).
fof(f12680,plain,
! [X0,X1] : addition(coantidomain(multiplication(omega(codomain(X0)),X1)),coantidomain(multiplication(X0,multiplication(omega(codomain(X0)),X1)))) = coantidomain(multiplication(omega(codomain(X0)),X1)),
inference(forward_demodulation,[status(thm)],[f319,f12679]) ).
fof(f12692,plain,
! [X0,X1,X2] : multiplication(addition(X0,omega(X1)),X2) = addition(multiplication(X0,X2),multiplication(omega(X1),X2)),
inference(forward_demodulation,[status(thm)],[f56,f12620]) ).
fof(f12693,plain,
! [X0,X1,X2] : multiplication(addition(X0,omega(X1)),X2) = multiplication(addition(omega(X1),X0),X2),
inference(forward_demodulation,[status(thm)],[f201,f12692]) ).
fof(f12694,plain,
! [X0,X1,X2] : multiplication(addition(omega(X0),X1),X2) = addition(multiplication(omega(X0),X2),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f56,f12621]) ).
fof(f12695,plain,
! [X0,X1,X2] : multiplication(addition(omega(X0),X1),X2) = multiplication(addition(X1,omega(X0)),X2),
inference(forward_demodulation,[status(thm)],[f201,f12694]) ).
fof(f12699,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(omega(X0),X1)),multiplication(omega(X0),X1))
| ~ leq(multiplication(omega(X0),X1),multiplication(omega(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f319,f12624]) ).
fof(f12700,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(omega(X0),X1)),multiplication(omega(X0),X1)),
inference(forward_subsumption_resolution,[status(thm)],[f12699,f239]) ).
fof(f12707,plain,
! [X0,X1,X2,X3] : addition(multiplication(omega(X0),X1),addition(X2,multiplication(X3,multiplication(omega(X0),X1)))) = addition(multiplication(addition(X3,X0),multiplication(omega(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f97,f12628]) ).
fof(f12708,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(omega(X0),X1)) = multiplication(addition(omega(X0),omega(X0)),X1),
inference(forward_demodulation,[status(thm)],[f201,f12630]) ).
fof(f12709,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(omega(X0),X1)) = multiplication(omega(X0),X1),
inference(forward_demodulation,[status(thm)],[f38,f12708]) ).
fof(f12710,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),multiplication(omega(X2),X3)) = multiplication(addition(X1,X0),multiplication(omega(X2),X3)),
inference(forward_demodulation,[status(thm)],[f201,f12631]) ).
fof(f12711,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(omega(X0),X1)) = multiplication(addition(omega(X0),omega(X0)),X1),
inference(forward_demodulation,[status(thm)],[f201,f12633]) ).
fof(f12712,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(omega(X0),X1)) = multiplication(omega(X0),X1),
inference(forward_demodulation,[status(thm)],[f38,f12711]) ).
fof(f12713,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(omega(X2),X3)) = addition(multiplication(omega(X2),X3),multiplication(X0,multiplication(X1,multiplication(omega(X2),X3)))),
inference(forward_demodulation,[status(thm)],[f35,f12634]) ).
fof(f12714,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),multiplication(omega(X1),X3)) = multiplication(addition(X2,X0),multiplication(omega(X1),X3)),
inference(forward_demodulation,[status(thm)],[f201,f12635]) ).
fof(f12715,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(addition(multiplication(X1,omega(X0)),omega(X0)),X2),
inference(forward_demodulation,[status(thm)],[f204,f12636]) ).
fof(f12716,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(addition(omega(X0),multiplication(X1,omega(X0))),X2),
inference(forward_demodulation,[status(thm)],[f35,f12715]) ).
fof(f12717,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(multiplication(addition(X1,one),omega(X0)),X2),
inference(forward_demodulation,[status(thm)],[f232,f12716]) ).
fof(f12718,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(addition(X1,one),multiplication(omega(X0),X2)),
inference(forward_demodulation,[status(thm)],[f39,f12717]) ).
fof(f12719,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(addition(omega(X1),multiplication(X0,omega(X1))),X2),
inference(forward_demodulation,[status(thm)],[f211,f12637]) ).
fof(f12720,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(multiplication(addition(X0,one),omega(X1)),X2),
inference(forward_demodulation,[status(thm)],[f232,f12719]) ).
fof(f12721,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(addition(X0,one),multiplication(omega(X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f12720]) ).
fof(f12722,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(omega(X0),X1))) = addition(X0,multiplication(omega(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f12640]) ).
fof(f12725,plain,
! [X0,X1,X2] : leq(multiplication(omega(X0),X1),addition(omega(X0),multiplication(star(X0),X2))),
inference(forward_subsumption_resolution,[status(thm)],[f12648,f1324]) ).
fof(f12726,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(addition(multiplication(X0,omega(X1)),omega(X1)),X2),
inference(forward_demodulation,[status(thm)],[f204,f12651]) ).
fof(f12727,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(addition(omega(X1),multiplication(X0,omega(X1))),X2),
inference(forward_demodulation,[status(thm)],[f35,f12726]) ).
fof(f12728,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(multiplication(addition(X0,one),omega(X1)),X2),
inference(forward_demodulation,[status(thm)],[f232,f12727]) ).
fof(f12729,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X1),X2)) = multiplication(addition(X0,one),multiplication(omega(X1),X2)),
inference(forward_demodulation,[status(thm)],[f39,f12728]) ).
fof(f12730,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(addition(omega(X0),multiplication(X1,omega(X0))),X2),
inference(forward_demodulation,[status(thm)],[f211,f12652]) ).
fof(f12731,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(multiplication(addition(X1,one),omega(X0)),X2),
inference(forward_demodulation,[status(thm)],[f232,f12730]) ).
fof(f12732,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(omega(X0),X2)) = multiplication(addition(X1,one),multiplication(omega(X0),X2)),
inference(forward_demodulation,[status(thm)],[f39,f12731]) ).
fof(f12740,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),backward_diamond(X2,X3)))),
inference(paramodulation,[status(thm)],[f103,f2488]) ).
fof(f12741,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),backward_diamond(X2,X3)))),
inference(paramodulation,[status(thm)],[f36,f2488]) ).
fof(f12747,plain,
! [X0,X1,X2] : addition(antidomain(backward_diamond(X0,X1)),X2) = addition(addition(antidomain(backward_diamond(X0,X1)),X2),multiplication(X2,backward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f224,f2488]) ).
fof(f12750,plain,
! [X0,X1] : domain(backward_diamond(X0,X1)) = addition(domain(backward_diamond(X0,X1)),backward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f4146,f2488]) ).
fof(f12762,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(omega(X0),backward_diamond(X1,X2))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2488,f314]) ).
fof(f12765,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),backward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f2488,f224]) ).
fof(f12766,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(multiplication(one,backward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f2488,f207]) ).
fof(f12775,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),backward_diamond(X3,X4))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2488,f296]) ).
fof(f12778,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),backward_diamond(X3,X4))),
inference(paramodulation,[status(thm)],[f2488,f219]) ).
fof(f12779,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),backward_diamond(X3,X4))),
inference(paramodulation,[status(thm)],[f2488,f170]) ).
fof(f12780,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),backward_diamond(X2,X3)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2488,f58]) ).
fof(f12781,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,X1),backward_diamond(X2,X3)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2488,f55]) ).
fof(f12782,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),backward_diamond(X2,X3))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2488,f53]) ).
fof(f12783,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X1,X0),backward_diamond(X2,X3)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2488,f103]) ).
fof(f12784,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X0,X1),backward_diamond(X2,X3)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2488,f36]) ).
fof(f12786,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X0),backward_diamond(X1,X2))
| ~ leq(X0,backward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f2488,f293]) ).
fof(f12791,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,backward_diamond(X1,X2)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2488,f11449]) ).
fof(f12793,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(X0,backward_diamond(X1,X2)))) = multiplication(addition(X0,one),omega(multiplication(X0,backward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f2488,f10882]) ).
fof(f12798,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2488,f302]) ).
fof(f12799,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,backward_diamond(X2,X3)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2488,f291]) ).
fof(f12800,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,backward_diamond(X2,X3)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2488,f290]) ).
fof(f12801,plain,
! [X0,X1,X2,X3] :
( addition(X0,X1) != multiplication(X1,backward_diamond(X2,X3))
| leq(addition(X0,X1),multiplication(X1,backward_diamond(X2,X3))) ),
inference(paramodulation,[status(thm)],[f2488,f243]) ).
fof(f12802,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,backward_diamond(X2,X3)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,backward_diamond(X2,X3)))) ),
inference(paramodulation,[status(thm)],[f2488,f242]) ).
fof(f12803,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(X0,backward_diamond(X2,X3)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,backward_diamond(X2,X3)),X1)) ),
inference(paramodulation,[status(thm)],[f2488,f241]) ).
fof(f12805,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,backward_diamond(X1,X2)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2488,f226]) ).
fof(f12809,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(X3,X0)),
inference(paramodulation,[status(thm)],[f2488,f1420]) ).
fof(f12813,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,backward_diamond(X1,X2)),addition(X0,X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2488,f103]) ).
fof(f12814,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,backward_diamond(X1,X2)),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f2488,f97]) ).
fof(f12815,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(X1,backward_diamond(X2,X3)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2488,f97]) ).
fof(f12817,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_diamond(X1,X2))
| leq(X0,multiplication(X0,backward_diamond(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2488,f49]) ).
fof(f12818,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,backward_diamond(X1,X2)),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2488,f36]) ).
fof(f12831,plain,
! [X0,X1,X2] : addition(antidomain(backward_diamond(X0,X1)),X2) = addition(X2,addition(antidomain(backward_diamond(X0,X1)),multiplication(X2,backward_diamond(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12747]) ).
fof(f12834,plain,
! [X0,X1] : domain(backward_diamond(X0,X1)) = addition(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f12750]) ).
fof(f12842,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(omega(X0),backward_diamond(X1,X2))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f12762,f239]) ).
fof(f12844,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(antidomain(X0),backward_diamond(X1,X2)),X0),
inference(forward_demodulation,[status(thm)],[f59,f12765]) ).
fof(f12845,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f12844]) ).
fof(f12846,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(multiplication(one,backward_diamond(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f41,f12766]) ).
fof(f12847,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(one,multiplication(backward_diamond(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f39,f12846]) ).
fof(f12848,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f41,f12847]) ).
fof(f12854,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),backward_diamond(X3,X4)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f12775]) ).
fof(f12855,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,backward_diamond(X3,X4))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f12854]) ).
fof(f12857,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),backward_diamond(X3,X4))),
inference(forward_demodulation,[status(thm)],[f201,f12778]) ).
fof(f12858,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,backward_diamond(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f12857]) ).
fof(f12859,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),backward_diamond(X3,X4))),
inference(forward_demodulation,[status(thm)],[f153,f12779]) ).
fof(f12860,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,backward_diamond(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f12859]) ).
fof(f12861,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,backward_diamond(X3,X4)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f12860]) ).
fof(f12862,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,backward_diamond(X3,X4)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f12861]) ).
fof(f12863,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,backward_diamond(X2,X3))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f12780]) ).
fof(f12864,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X1),multiplication(backward_diamond(X2,X3),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f12781]) ).
fof(f12865,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(backward_diamond(X2,X3),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f12864]) ).
fof(f12866,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,backward_diamond(X2,X3)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f12782]) ).
fof(f12873,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(multiplication(X0,backward_diamond(X1,X2)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f12791]) ).
fof(f12874,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(one,multiplication(X0,backward_diamond(X1,X2))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f12873]) ).
fof(f12883,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(backward_diamond(X2,X3),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f12800]) ).
fof(f12884,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(X0,backward_diamond(X2,X3)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(backward_diamond(X2,X3),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f12803]) ).
fof(f12885,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(backward_diamond(X2,X3),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(backward_diamond(X2,X3),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f12884]) ).
fof(f12886,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(X0,backward_diamond(X1,X2)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f12805]) ).
fof(f12887,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(backward_diamond(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f12886]) ).
fof(f12890,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,backward_diamond(X2,X3)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f12813]) ).
fof(f12891,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(X1,backward_diamond(X2,X3)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f12815]) ).
fof(f12898,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),forward_box(X2,X3)))),
inference(paramodulation,[status(thm)],[f103,f2489]) ).
fof(f12899,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),forward_box(X2,X3)))),
inference(paramodulation,[status(thm)],[f36,f2489]) ).
fof(f12905,plain,
! [X0,X1,X2] : addition(antidomain(forward_box(X0,X1)),X2) = addition(addition(antidomain(forward_box(X0,X1)),X2),multiplication(X2,forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f224,f2489]) ).
fof(f12908,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = addition(domain(forward_box(X0,X1)),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f4146,f2489]) ).
fof(f12918,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(omega(X0),forward_box(X1,X2))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2489,f314]) ).
fof(f12921,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),forward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f2489,f224]) ).
fof(f12922,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(multiplication(one,forward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f2489,f207]) ).
fof(f12931,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),forward_box(X3,X4))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2489,f296]) ).
fof(f12934,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),forward_box(X3,X4))),
inference(paramodulation,[status(thm)],[f2489,f219]) ).
fof(f12935,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),forward_box(X3,X4))),
inference(paramodulation,[status(thm)],[f2489,f170]) ).
fof(f12936,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),forward_box(X2,X3)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2489,f58]) ).
fof(f12937,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,X1),forward_box(X2,X3)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2489,f55]) ).
fof(f12938,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),forward_box(X2,X3))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2489,f53]) ).
fof(f12939,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X1,X0),forward_box(X2,X3)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2489,f103]) ).
fof(f12940,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X0,X1),forward_box(X2,X3)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2489,f36]) ).
fof(f12942,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X0),forward_box(X1,X2))
| ~ leq(X0,forward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f2489,f293]) ).
fof(f12947,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,forward_box(X1,X2)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2489,f11449]) ).
fof(f12949,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(X0,forward_box(X1,X2)))) = multiplication(addition(X0,one),omega(multiplication(X0,forward_box(X1,X2)))),
inference(paramodulation,[status(thm)],[f2489,f10882]) ).
fof(f12954,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_box(X1,X2))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2489,f302]) ).
fof(f12955,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,forward_box(X2,X3)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2489,f291]) ).
fof(f12956,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,forward_box(X2,X3)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2489,f290]) ).
fof(f12957,plain,
! [X0,X1,X2,X3] :
( addition(X0,X1) != multiplication(X1,forward_box(X2,X3))
| leq(addition(X0,X1),multiplication(X1,forward_box(X2,X3))) ),
inference(paramodulation,[status(thm)],[f2489,f243]) ).
fof(f12958,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,forward_box(X2,X3)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,forward_box(X2,X3)))) ),
inference(paramodulation,[status(thm)],[f2489,f242]) ).
fof(f12959,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(X0,forward_box(X2,X3)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,forward_box(X2,X3)),X1)) ),
inference(paramodulation,[status(thm)],[f2489,f241]) ).
fof(f12961,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,forward_box(X1,X2)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2489,f226]) ).
fof(f12965,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,forward_box(X1,X2)),addition(X3,X0)),
inference(paramodulation,[status(thm)],[f2489,f1420]) ).
fof(f12969,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,forward_box(X1,X2)),addition(X0,X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2489,f103]) ).
fof(f12970,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,forward_box(X1,X2)),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f2489,f97]) ).
fof(f12971,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(X1,forward_box(X2,X3)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2489,f97]) ).
fof(f12973,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_box(X1,X2))
| leq(X0,multiplication(X0,forward_box(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2489,f49]) ).
fof(f12974,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,forward_box(X1,X2)),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2489,f36]) ).
fof(f12987,plain,
! [X0,X1,X2] : addition(antidomain(forward_box(X0,X1)),X2) = addition(X2,addition(antidomain(forward_box(X0,X1)),multiplication(X2,forward_box(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f12905]) ).
fof(f12990,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = addition(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f12908]) ).
fof(f12999,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(omega(X0),forward_box(X1,X2))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f12918,f239]) ).
fof(f13001,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(antidomain(X0),forward_box(X1,X2)),X0),
inference(forward_demodulation,[status(thm)],[f59,f12921]) ).
fof(f13002,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f13001]) ).
fof(f13003,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(multiplication(one,forward_box(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f41,f12922]) ).
fof(f13004,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(one,multiplication(forward_box(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f39,f13003]) ).
fof(f13005,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f41,f13004]) ).
fof(f13011,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),forward_box(X3,X4)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f12931]) ).
fof(f13012,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,forward_box(X3,X4))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f13011]) ).
fof(f13014,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),forward_box(X3,X4))),
inference(forward_demodulation,[status(thm)],[f201,f12934]) ).
fof(f13015,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,forward_box(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f13014]) ).
fof(f13016,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),forward_box(X3,X4))),
inference(forward_demodulation,[status(thm)],[f153,f12935]) ).
fof(f13017,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,forward_box(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f13016]) ).
fof(f13018,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,forward_box(X3,X4)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f13017]) ).
fof(f13019,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,forward_box(X3,X4)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f13018]) ).
fof(f13020,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,forward_box(X2,X3))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f12936]) ).
fof(f13021,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X1),multiplication(forward_box(X2,X3),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f12937]) ).
fof(f13022,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(forward_box(X2,X3),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13021]) ).
fof(f13023,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,forward_box(X2,X3)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f12938]) ).
fof(f13030,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(multiplication(X0,forward_box(X1,X2)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f12947]) ).
fof(f13031,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(one,multiplication(X0,forward_box(X1,X2))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f13030]) ).
fof(f13040,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(forward_box(X2,X3),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f12956]) ).
fof(f13041,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(X0,forward_box(X2,X3)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(forward_box(X2,X3),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f12959]) ).
fof(f13042,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(forward_box(X2,X3),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(forward_box(X2,X3),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f13041]) ).
fof(f13043,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(X0,forward_box(X1,X2)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f12961]) ).
fof(f13044,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(forward_box(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f13043]) ).
fof(f13047,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,forward_box(X2,X3)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f12969]) ).
fof(f13048,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(X1,forward_box(X2,X3)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f12971]) ).
fof(f13050,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(X0,star(X0))),one)
| ~ leq(addition(X0,multiplication(X1,X0)),one) ),
inference(paramodulation,[status(thm)],[f207,f340]) ).
fof(f13051,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),antidomain(X1))
| ~ leq(multiplication(X0,X1),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f224,f340]) ).
fof(f13052,plain,
! [X0,X1] :
( leq(multiplication(one,multiplication(omega(X0),star(omega(X0)))),X1)
| ~ leq(multiplication(addition(X0,X1),omega(X0)),X1) ),
inference(paramodulation,[status(thm)],[f11449,f340]) ).
fof(f13053,plain,
! [X0,X1] :
( leq(multiplication(one,multiplication(omega(X1),star(omega(X1)))),X0)
| ~ leq(multiplication(addition(X0,X1),omega(X1)),X0) ),
inference(paramodulation,[status(thm)],[f10882,f340]) ).
fof(f13054,plain,
! [X0,X1] :
( leq(multiplication(one,multiplication(X0,star(X0))),X1)
| ~ leq(addition(X0,multiplication(X1,X0)),X1) ),
inference(paramodulation,[status(thm)],[f232,f340]) ).
fof(f13056,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(omega(X1),star(omega(X1)))),X1)
| ~ leq(multiplication(addition(X0,one),omega(X1)),X1) ),
inference(paramodulation,[status(thm)],[f11449,f340]) ).
fof(f13057,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(omega(X1),star(omega(X1)))),X0)
| ~ leq(multiplication(addition(X0,one),omega(X1)),X0) ),
inference(paramodulation,[status(thm)],[f10882,f340]) ).
fof(f13059,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(coantidomain(X1),star(coantidomain(X1)))),X1)
| ~ leq(multiplication(X0,coantidomain(X1)),X1) ),
inference(paramodulation,[status(thm)],[f226,f340]) ).
fof(f13060,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(codomain(addition(X0,X1)),star(codomain(addition(X0,X1))))),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2309,f340]) ).
fof(f13061,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(addition(omega(addition(X0,X1)),X2),star(addition(omega(addition(X0,X1)),X2)))),X0)
| ~ leq(addition(omega(addition(X0,X1)),multiplication(addition(X0,X1),X2)),X0) ),
inference(paramodulation,[status(thm)],[f318,f340]) ).
fof(f13062,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(addition(coantidomain(addition(X0,X1)),X2),star(addition(coantidomain(addition(X0,X1)),X2)))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f181,f340]) ).
fof(f13063,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(addition(X2,omega(addition(X0,X1))),star(addition(X2,omega(addition(X0,X1)))))),X0)
| ~ leq(addition(omega(addition(X0,X1)),multiplication(addition(X0,X1),X2)),X0) ),
inference(paramodulation,[status(thm)],[f321,f340]) ).
fof(f13064,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(addition(X2,coantidomain(addition(X0,X1))),star(addition(X2,coantidomain(addition(X0,X1)))))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f190,f340]) ).
fof(f13065,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(multiplication(omega(addition(X0,X1)),X2),star(multiplication(omega(addition(X0,X1)),X2)))),X0)
| ~ leq(multiplication(omega(addition(X0,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f319,f340]) ).
fof(f13066,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(multiplication(coantidomain(addition(X0,X1)),X2),star(multiplication(coantidomain(addition(X0,X1)),X2)))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f151,f340]) ).
fof(f13067,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(multiplication(X2,omega(multiplication(addition(X0,X1),X2))),star(multiplication(X2,omega(multiplication(addition(X0,X1),X2)))))),X0)
| ~ leq(omega(multiplication(addition(X0,X1),X2)),X0) ),
inference(paramodulation,[status(thm)],[f308,f340]) ).
fof(f13068,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(multiplication(X2,coantidomain(multiplication(addition(X0,X1),X2))),star(multiplication(X2,coantidomain(multiplication(addition(X0,X1),X2)))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f144,f340]) ).
fof(f13069,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(omega(coantidomain(addition(X0,X1))),star(omega(coantidomain(addition(X0,X1)))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f1813,f340]) ).
fof(f13070,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(omega(addition(X0,X1)),star(omega(addition(X0,X1))))),X0)
| ~ leq(omega(addition(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f56,f340]) ).
fof(f13071,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(coantidomain(addition(X0,X1)),star(coantidomain(addition(X0,X1))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f63,f340]) ).
fof(f13073,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(one,star(one))),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f40,f340]) ).
fof(f13074,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,star(X1))),one)
| ~ leq(multiplication(star(X0),X1),one) ),
inference(paramodulation,[status(thm)],[f7563,f340]) ).
fof(f13075,plain,
! [X0,X1] :
( leq(multiplication(multiplication(star(X0),addition(X0,one)),multiplication(X1,star(X1))),one)
| ~ leq(multiplication(star(X0),X1),one) ),
inference(paramodulation,[status(thm)],[f7789,f340]) ).
fof(f13076,plain,
! [X0,X1] :
( leq(multiplication(multiplication(addition(X0,one),star(X0)),multiplication(X1,star(X1))),one)
| ~ leq(multiplication(star(X0),X1),one) ),
inference(paramodulation,[status(thm)],[f7510,f340]) ).
fof(f13077,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1504,f340]) ).
fof(f13078,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1497,f340]) ).
fof(f13079,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1492,f340]) ).
fof(f13080,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1485,f340]) ).
fof(f13081,plain,
! [X0,X1] :
( leq(multiplication(divergence(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1488,f340]) ).
fof(f13082,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1477,f340]) ).
fof(f13083,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1471,f340]) ).
fof(f13084,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1379,f340]) ).
fof(f13085,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1377,f340]) ).
fof(f13086,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1375,f340]) ).
fof(f13087,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),domain(X1))
| ~ leq(multiplication(one,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f569,f340]) ).
fof(f13088,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(multiplication(codomain(X0),X1)),multiplication(X2,star(X2))),coantidomain(multiplication(X0,X1)))
| ~ leq(multiplication(coantidomain(multiplication(codomain(X0),X1)),X2),coantidomain(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f615,f340]) ).
fof(f13089,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),coantidomain(X1))
| ~ leq(multiplication(one,X0),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f683,f340]) ).
fof(f13090,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(multiplication(X0,domain(X1))),multiplication(X2,star(X2))),antidomain(multiplication(X0,X1)))
| ~ leq(multiplication(antidomain(multiplication(X0,domain(X1))),X2),antidomain(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f479,f340]) ).
fof(f13091,plain,
! [X0,X1] :
( leq(multiplication(c(X0),multiplication(X1,star(X1))),antidomain(X0))
| ~ leq(multiplication(c(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f514,f340]) ).
fof(f13092,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),antidomain(X1))
| ~ leq(multiplication(one,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f558,f340]) ).
fof(f13093,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X2,X3),multiplication(X4,star(X4))),multiplication(X0,multiplication(X1,X3)))
| ~ leq(multiplication(multiplication(addition(multiplication(X0,X1),X2),X3),X4),multiplication(X0,multiplication(X1,X3))) ),
inference(paramodulation,[status(thm)],[f204,f340]) ).
fof(f13094,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(addition(multiplication(X1,X2),X3),multiplication(X4,star(X4))),multiplication(X0,X2))
| ~ leq(multiplication(addition(multiplication(addition(X0,X1),X2),X3),X4),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f219,f340]) ).
fof(f13095,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(addition(multiplication(X0,X2),X3),multiplication(X4,star(X4))),multiplication(X0,X1))
| ~ leq(multiplication(addition(multiplication(X0,addition(X1,X2)),X3),X4),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f170,f340]) ).
fof(f13096,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X1,multiplication(X2,X3)),multiplication(X4,star(X4))),multiplication(X0,X3))
| ~ leq(multiplication(multiplication(addition(X0,multiplication(X1,X2)),X3),X4),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f211,f340]) ).
fof(f13097,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X2),multiplication(X3,star(X3))),multiplication(X1,X2))
| ~ leq(multiplication(multiplication(addition(X0,X1),X2),X3),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f201,f340]) ).
fof(f13098,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X1),multiplication(X3,star(X3))),multiplication(X0,X2))
| ~ leq(multiplication(multiplication(X0,addition(X1,X2)),X3),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f153,f340]) ).
fof(f13099,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X1,X2),multiplication(X3,star(X3))),multiplication(X0,X2))
| ~ leq(multiplication(multiplication(addition(X0,X1),X2),X3),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f43,f340]) ).
fof(f13100,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X2),multiplication(X3,star(X3))),multiplication(X0,X1))
| ~ leq(multiplication(multiplication(X0,addition(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f42,f340]) ).
fof(f13101,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X2,multiplication(X3,star(X3))),addition(X1,X0))
| ~ leq(multiplication(addition(X0,addition(X1,X2)),X3),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f103,f340]) ).
fof(f13102,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X2,multiplication(X3,star(X3))),addition(X0,X1))
| ~ leq(multiplication(addition(X0,addition(X1,X2)),X3),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f36,f340]) ).
fof(f13103,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),zero)
| ~ leq(multiplication(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f80,f340]) ).
fof(f13104,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(domain(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4516,f340]) ).
fof(f13105,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(coantidomain(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4515,f340]) ).
fof(f13106,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(antidomain(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4514,f340]) ).
fof(f13107,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(c(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4513,f340]) ).
fof(f13108,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(codomain(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4512,f340]) ).
fof(f13109,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(divergence(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4511,f340]) ).
fof(f13110,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,forward_box(X2,X3)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2489,f340]) ).
fof(f13111,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,backward_diamond(X2,X3)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2488,f340]) ).
fof(f13112,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,domain(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2497,f340]) ).
fof(f13113,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,coantidomain(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2496,f340]) ).
fof(f13114,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,antidomain(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2495,f340]) ).
fof(f13115,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,c(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2494,f340]) ).
fof(f13116,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,codomain(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2493,f340]) ).
fof(f13117,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,divergence(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2492,f340]) ).
fof(f13118,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(multiplication(addition(X0,one),X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f232,f340]) ).
fof(f13119,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(multiplication(addition(one,X0),X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f207,f340]) ).
fof(f13120,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(multiplication(X0,addition(X1,one)),X2),X0) ),
inference(paramodulation,[status(thm)],[f192,f340]) ).
fof(f13121,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(multiplication(X0,addition(one,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f162,f340]) ).
fof(f13122,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X1,X0),multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f1329,f340]) ).
fof(f13123,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X1,X0),multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f1026,f340]) ).
fof(f13124,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,X1),multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f1005,f340]) ).
fof(f13125,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,X1),multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f105,f340]) ).
fof(f13126,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X0,X1),multiplication(X3,star(X3))),X2)
| ~ leq(multiplication(addition(X0,addition(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f97,f340]) ).
fof(f13127,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X2,X0),multiplication(X3,star(X3))),X1)
| ~ leq(multiplication(addition(X0,addition(X1,X2)),X3),X1) ),
inference(paramodulation,[status(thm)],[f97,f340]) ).
fof(f13129,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f35,f340]) ).
fof(f13130,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f35,f340]) ).
fof(f13131,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f38,f340]) ).
fof(f13132,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),star(omega(X0))),X1)
| ~ leq(multiplication(addition(X0,X1),omega(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f41,f13052]) ).
fof(f13133,plain,
! [X0,X1] :
( leq(multiplication(omega(X1),star(omega(X1))),X0)
| ~ leq(multiplication(addition(X0,X1),omega(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f41,f13053]) ).
fof(f13134,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),X1)
| ~ leq(addition(X0,multiplication(X1,X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f41,f13054]) ).
fof(f13136,plain,
! [X0,X1] :
( leq(multiplication(omega(X1),star(omega(X1))),X0)
| ~ leq(multiplication(addition(X0,one),omega(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f319,f13057]) ).
fof(f13138,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(omega(addition(X0,X1)),multiplication(X2,star(multiplication(omega(addition(X0,X1)),X2))))),X0)
| ~ leq(multiplication(omega(addition(X0,X1)),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13065]) ).
fof(f13139,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(coantidomain(addition(X0,X1)),multiplication(X2,star(multiplication(coantidomain(addition(X0,X1)),X2))))),X0)
| ~ leq(zero,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13066]) ).
fof(f13140,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(coantidomain(addition(X1,X0)),multiplication(X2,star(multiplication(coantidomain(addition(X1,X0)),X2))))),X1),
inference(forward_subsumption_resolution,[status(thm)],[f13139,f240]) ).
fof(f13141,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,multiplication(omega(multiplication(addition(X0,X1),X2)),star(multiplication(X2,omega(multiplication(addition(X0,X1),X2))))))),X0)
| ~ leq(omega(multiplication(addition(X0,X1),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13067]) ).
fof(f13142,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,multiplication(coantidomain(multiplication(addition(X0,X1),X2)),star(multiplication(X2,coantidomain(multiplication(addition(X0,X1),X2))))))),X0)
| ~ leq(zero,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13068]) ).
fof(f13143,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(addition(X2,X0),X1)),star(multiplication(X1,coantidomain(multiplication(addition(X2,X0),X1))))))),X2),
inference(forward_subsumption_resolution,[status(thm)],[f13142,f240]) ).
fof(f13144,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(omega(coantidomain(addition(X1,X0))),star(omega(coantidomain(addition(X1,X0)))))),X1),
inference(forward_subsumption_resolution,[status(thm)],[f13069,f240]) ).
fof(f13145,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(coantidomain(addition(X1,X0)),star(coantidomain(addition(X1,X0))))),X1),
inference(forward_subsumption_resolution,[status(thm)],[f13071,f240]) ).
fof(f13147,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f41,f13073]) ).
fof(f13148,plain,
! [X0,X1] :
( leq(multiplication(X1,one),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f13147]) ).
fof(f13149,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f40,f13148]) ).
fof(f13150,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(addition(X0,one),multiplication(X1,star(X1)))),one)
| ~ leq(multiplication(star(X0),X1),one) ),
inference(forward_demodulation,[status(thm)],[f39,f13075]) ).
fof(f13151,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,one),multiplication(star(X0),multiplication(X1,star(X1)))),one)
| ~ leq(multiplication(star(X0),X1),one) ),
inference(forward_demodulation,[status(thm)],[f39,f13076]) ).
fof(f13152,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13077]) ).
fof(f13153,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13078]) ).
fof(f13154,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13079]) ).
fof(f13155,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13080]) ).
fof(f13156,plain,
! [X0,X1] :
( leq(multiplication(divergence(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13081]) ).
fof(f13157,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13082]) ).
fof(f13158,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13083]) ).
fof(f13159,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13084]) ).
fof(f13160,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13085]) ).
fof(f13161,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f13086]) ).
fof(f13162,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f13087]) ).
fof(f13163,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f13089]) ).
fof(f13164,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f13092]) ).
fof(f13165,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X2,X3),multiplication(X4,star(X4))),multiplication(X0,multiplication(X1,X3)))
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,X4)),multiplication(X0,multiplication(X1,X3))) ),
inference(forward_demodulation,[status(thm)],[f39,f13093]) ).
fof(f13166,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X2,multiplication(X3,multiplication(X4,star(X4)))),multiplication(X0,multiplication(X1,X3)))
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),multiplication(X3,X4)),multiplication(X0,multiplication(X1,X3))) ),
inference(forward_demodulation,[status(thm)],[f39,f13165]) ).
fof(f13167,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X1,multiplication(X2,X3)),multiplication(X4,star(X4))),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),multiplication(X0,X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f13096]) ).
fof(f13168,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X1,multiplication(multiplication(X2,X3),multiplication(X4,star(X4)))),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),multiplication(X0,X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f13167]) ).
fof(f13169,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,star(X4))))),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),multiplication(X0,X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f13168]) ).
fof(f13170,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X2),multiplication(X3,star(X3))),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f13097]) ).
fof(f13171,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X2,multiplication(X3,star(X3)))),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f13170]) ).
fof(f13172,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X1),multiplication(X3,star(X3))),multiplication(X0,X2))
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f13098]) ).
fof(f13173,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X3,star(X3)))),multiplication(X0,X2))
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f13172]) ).
fof(f13174,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X1,X2),multiplication(X3,star(X3))),multiplication(X0,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f13099]) ).
fof(f13175,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(X2,multiplication(X3,star(X3)))),multiplication(X0,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f13174]) ).
fof(f13176,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X2),multiplication(X3,star(X3))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f13100]) ).
fof(f13177,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X2,multiplication(X3,star(X3)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f13176]) ).
fof(f13178,plain,
! [X0,X1,X2] :
( leq(multiplication(domain(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13104]) ).
fof(f13179,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13105]) ).
fof(f13180,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13106]) ).
fof(f13181,plain,
! [X0,X1,X2] :
( leq(multiplication(c(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13107]) ).
fof(f13182,plain,
! [X0,X1,X2] :
( leq(multiplication(codomain(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13108]) ).
fof(f13183,plain,
! [X0,X1,X2] :
( leq(multiplication(divergence(X2),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13109]) ).
fof(f13184,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(forward_box(X2,X3),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13110]) ).
fof(f13185,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(backward_diamond(X2,X3),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13111]) ).
fof(f13186,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(domain(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13112]) ).
fof(f13187,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(coantidomain(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13113]) ).
fof(f13188,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(antidomain(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13114]) ).
fof(f13189,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(c(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13115]) ).
fof(f13190,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(codomain(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13116]) ).
fof(f13191,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(divergence(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13117]) ).
fof(f13192,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f13118]) ).
fof(f13193,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X1)
| ~ leq(multiplication(addition(X0,one),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f13192]) ).
fof(f13194,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f13119]) ).
fof(f13195,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X1)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f13194]) ).
fof(f13196,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,one),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13120]) ).
fof(f13197,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,one),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13196]) ).
fof(f13198,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(X0,multiplication(addition(one,X1),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13121]) ).
fof(f13199,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X0)
| ~ leq(multiplication(X0,multiplication(addition(one,X1),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13198]) ).
fof(f13206,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),backward_box(X2,X3)))),
inference(paramodulation,[status(thm)],[f103,f2490]) ).
fof(f13207,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),backward_box(X2,X3)))),
inference(paramodulation,[status(thm)],[f36,f2490]) ).
fof(f13213,plain,
! [X0,X1,X2] : addition(antidomain(backward_box(X0,X1)),X2) = addition(addition(antidomain(backward_box(X0,X1)),X2),multiplication(X2,backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f224,f2490]) ).
fof(f13216,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = addition(domain(backward_box(X0,X1)),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f4146,f2490]) ).
fof(f13225,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(omega(X0),backward_box(X1,X2))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2490,f314]) ).
fof(f13228,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),backward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f2490,f224]) ).
fof(f13229,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(multiplication(one,backward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f2490,f207]) ).
fof(f13238,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),backward_box(X3,X4))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2490,f296]) ).
fof(f13241,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),backward_box(X3,X4))),
inference(paramodulation,[status(thm)],[f2490,f219]) ).
fof(f13242,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),backward_box(X3,X4))),
inference(paramodulation,[status(thm)],[f2490,f170]) ).
fof(f13243,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),backward_box(X2,X3)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2490,f58]) ).
fof(f13244,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,X1),backward_box(X2,X3)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2490,f55]) ).
fof(f13245,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),backward_box(X2,X3))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2490,f53]) ).
fof(f13246,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X1,X0),backward_box(X2,X3)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2490,f103]) ).
fof(f13247,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X0,X1),backward_box(X2,X3)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2490,f36]) ).
fof(f13249,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X0),backward_box(X1,X2))
| ~ leq(X0,backward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f2490,f293]) ).
fof(f13254,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,backward_box(X2,X3)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2490,f340]) ).
fof(f13255,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,backward_box(X1,X2)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2490,f11449]) ).
fof(f13257,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(X0,backward_box(X1,X2)))) = multiplication(addition(X0,one),omega(multiplication(X0,backward_box(X1,X2)))),
inference(paramodulation,[status(thm)],[f2490,f10882]) ).
fof(f13262,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_box(X1,X2))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2490,f302]) ).
fof(f13263,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,backward_box(X2,X3)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2490,f291]) ).
fof(f13264,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,backward_box(X2,X3)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2490,f290]) ).
fof(f13265,plain,
! [X0,X1,X2,X3] :
( addition(X0,X1) != multiplication(X1,backward_box(X2,X3))
| leq(addition(X0,X1),multiplication(X1,backward_box(X2,X3))) ),
inference(paramodulation,[status(thm)],[f2490,f243]) ).
fof(f13266,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,backward_box(X2,X3)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,backward_box(X2,X3)))) ),
inference(paramodulation,[status(thm)],[f2490,f242]) ).
fof(f13267,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(X0,backward_box(X2,X3)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,backward_box(X2,X3)),X1)) ),
inference(paramodulation,[status(thm)],[f2490,f241]) ).
fof(f13269,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,backward_box(X1,X2)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2490,f226]) ).
fof(f13273,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,backward_box(X1,X2)),addition(X3,X0)),
inference(paramodulation,[status(thm)],[f2490,f1420]) ).
fof(f13277,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,backward_box(X1,X2)),addition(X0,X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2490,f103]) ).
fof(f13278,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,backward_box(X1,X2)),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f2490,f97]) ).
fof(f13279,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(X1,backward_box(X2,X3)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2490,f97]) ).
fof(f13281,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_box(X1,X2))
| leq(X0,multiplication(X0,backward_box(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2490,f49]) ).
fof(f13282,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,backward_box(X1,X2)),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2490,f36]) ).
fof(f13295,plain,
! [X0,X1,X2] : addition(antidomain(backward_box(X0,X1)),X2) = addition(X2,addition(antidomain(backward_box(X0,X1)),multiplication(X2,backward_box(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f13213]) ).
fof(f13298,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = addition(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f13216]) ).
fof(f13306,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(omega(X0),backward_box(X1,X2))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f13225,f239]) ).
fof(f13308,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(antidomain(X0),backward_box(X1,X2)),X0),
inference(forward_demodulation,[status(thm)],[f59,f13228]) ).
fof(f13309,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f13308]) ).
fof(f13310,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(multiplication(one,backward_box(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f41,f13229]) ).
fof(f13311,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(one,multiplication(backward_box(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f39,f13310]) ).
fof(f13312,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f41,f13311]) ).
fof(f13318,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),backward_box(X3,X4)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f13238]) ).
fof(f13319,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,backward_box(X3,X4))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f13318]) ).
fof(f13321,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),backward_box(X3,X4))),
inference(forward_demodulation,[status(thm)],[f201,f13241]) ).
fof(f13322,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,backward_box(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f13321]) ).
fof(f13323,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),backward_box(X3,X4))),
inference(forward_demodulation,[status(thm)],[f153,f13242]) ).
fof(f13324,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,backward_box(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f13323]) ).
fof(f13325,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,backward_box(X3,X4)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f13324]) ).
fof(f13326,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,backward_box(X3,X4)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f13325]) ).
fof(f13327,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,backward_box(X2,X3))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f13243]) ).
fof(f13328,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X1),multiplication(backward_box(X2,X3),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13244]) ).
fof(f13329,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(backward_box(X2,X3),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13328]) ).
fof(f13330,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,backward_box(X2,X3)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f13245]) ).
fof(f13337,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(backward_box(X2,X3),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13254]) ).
fof(f13338,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(multiplication(X0,backward_box(X1,X2)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f13255]) ).
fof(f13339,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(one,multiplication(X0,backward_box(X1,X2))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f13338]) ).
fof(f13348,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(backward_box(X2,X3),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f13264]) ).
fof(f13349,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(X0,backward_box(X2,X3)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(backward_box(X2,X3),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f13267]) ).
fof(f13350,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(backward_box(X2,X3),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(backward_box(X2,X3),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f13349]) ).
fof(f13351,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(X0,backward_box(X1,X2)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f13269]) ).
fof(f13352,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(backward_box(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f13351]) ).
fof(f13355,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,backward_box(X2,X3)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f13277]) ).
fof(f13356,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(X1,backward_box(X2,X3)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f13279]) ).
fof(f13363,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),forward_diamond(X2,X3)))),
inference(paramodulation,[status(thm)],[f103,f2491]) ).
fof(f13364,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),forward_diamond(X2,X3)))),
inference(paramodulation,[status(thm)],[f36,f2491]) ).
fof(f13370,plain,
! [X0,X1,X2] : addition(antidomain(forward_diamond(X0,X1)),X2) = addition(addition(antidomain(forward_diamond(X0,X1)),X2),multiplication(X2,forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f224,f2491]) ).
fof(f13373,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = addition(domain(forward_diamond(X0,X1)),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f4146,f2491]) ).
fof(f13387,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(omega(X0),forward_diamond(X1,X2))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f2491,f314]) ).
fof(f13390,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),forward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f2491,f224]) ).
fof(f13391,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(multiplication(one,forward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f2491,f207]) ).
fof(f13400,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(multiplication(X0,multiplication(X1,X2)),forward_diamond(X3,X4))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f2491,f296]) ).
fof(f13403,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),forward_diamond(X3,X4))),
inference(paramodulation,[status(thm)],[f2491,f219]) ).
fof(f13404,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),forward_diamond(X3,X4))),
inference(paramodulation,[status(thm)],[f2491,f170]) ).
fof(f13405,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X0),forward_diamond(X2,X3)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2491,f58]) ).
fof(f13406,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,X1),forward_diamond(X2,X3)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2491,f55]) ).
fof(f13407,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),forward_diamond(X2,X3))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2491,f53]) ).
fof(f13408,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X1,X0),forward_diamond(X2,X3)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2491,f103]) ).
fof(f13409,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X0,X1),forward_diamond(X2,X3)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2491,f36]) ).
fof(f13411,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X0),forward_diamond(X1,X2))
| ~ leq(X0,forward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f2491,f293]) ).
fof(f13416,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,forward_diamond(X2,X3)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2491,f340]) ).
fof(f13417,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(X0,forward_diamond(X1,X2)),one),omega(X0)),
inference(paramodulation,[status(thm)],[f2491,f11449]) ).
fof(f13419,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(X0,forward_diamond(X1,X2)))) = multiplication(addition(X0,one),omega(multiplication(X0,forward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f2491,f10882]) ).
fof(f13424,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2491,f302]) ).
fof(f13425,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,forward_diamond(X2,X3)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2491,f291]) ).
fof(f13426,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,forward_diamond(X2,X3)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2491,f290]) ).
fof(f13427,plain,
! [X0,X1,X2,X3] :
( addition(X0,X1) != multiplication(X1,forward_diamond(X2,X3))
| leq(addition(X0,X1),multiplication(X1,forward_diamond(X2,X3))) ),
inference(paramodulation,[status(thm)],[f2491,f243]) ).
fof(f13428,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,forward_diamond(X2,X3)))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,forward_diamond(X2,X3)))) ),
inference(paramodulation,[status(thm)],[f2491,f242]) ).
fof(f13429,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(X0,forward_diamond(X2,X3)),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,forward_diamond(X2,X3)),X1)) ),
inference(paramodulation,[status(thm)],[f2491,f241]) ).
fof(f13431,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,forward_diamond(X1,X2)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2491,f226]) ).
fof(f13435,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(X3,X0)),
inference(paramodulation,[status(thm)],[f2491,f1420]) ).
fof(f13439,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,forward_diamond(X1,X2)),addition(X0,X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2491,f103]) ).
fof(f13440,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,forward_diamond(X1,X2)),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f2491,f97]) ).
fof(f13441,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(X1,forward_diamond(X2,X3)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2491,f97]) ).
fof(f13443,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_diamond(X1,X2))
| leq(X0,multiplication(X0,forward_diamond(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2491,f49]) ).
fof(f13444,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,forward_diamond(X1,X2)),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2491,f36]) ).
fof(f13457,plain,
! [X0,X1,X2] : addition(antidomain(forward_diamond(X0,X1)),X2) = addition(X2,addition(antidomain(forward_diamond(X0,X1)),multiplication(X2,forward_diamond(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f13370]) ).
fof(f13460,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = addition(forward_diamond(X0,X1),domain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f13373]) ).
fof(f13469,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(omega(X0),forward_diamond(X1,X2))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f13387,f239]) ).
fof(f13471,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(antidomain(X0),forward_diamond(X1,X2)),X0),
inference(forward_demodulation,[status(thm)],[f59,f13390]) ).
fof(f13472,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f13471]) ).
fof(f13473,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(multiplication(one,forward_diamond(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f41,f13391]) ).
fof(f13474,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(one,multiplication(forward_diamond(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f39,f13473]) ).
fof(f13475,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f41,f13474]) ).
fof(f13481,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(multiplication(X1,X2),forward_diamond(X3,X4)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f13400]) ).
fof(f13482,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,multiplication(X2,forward_diamond(X3,X4))))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f13481]) ).
fof(f13484,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),forward_diamond(X3,X4))),
inference(forward_demodulation,[status(thm)],[f201,f13403]) ).
fof(f13485,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,forward_diamond(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f13484]) ).
fof(f13486,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),forward_diamond(X3,X4))),
inference(forward_demodulation,[status(thm)],[f153,f13404]) ).
fof(f13487,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,forward_diamond(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f39,f13486]) ).
fof(f13488,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,forward_diamond(X3,X4)),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f153,f13487]) ).
fof(f13489,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(multiplication(X1,forward_diamond(X3,X4)),X2))),
inference(forward_demodulation,[status(thm)],[f97,f13488]) ).
fof(f13490,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,forward_diamond(X2,X3))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f13405]) ).
fof(f13491,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X1),multiplication(forward_diamond(X2,X3),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13406]) ).
fof(f13492,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(forward_diamond(X2,X3),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13491]) ).
fof(f13493,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,forward_diamond(X2,X3)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f13407]) ).
fof(f13500,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(forward_diamond(X2,X3),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13416]) ).
fof(f13501,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(multiplication(X0,forward_diamond(X1,X2)),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f13417]) ).
fof(f13502,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(one,multiplication(X0,forward_diamond(X1,X2))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f13501]) ).
fof(f13511,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(forward_diamond(X2,X3),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f13426]) ).
fof(f13512,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(X0,forward_diamond(X2,X3)),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(forward_diamond(X2,X3),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f13429]) ).
fof(f13513,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(forward_diamond(X2,X3),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(forward_diamond(X2,X3),X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f13512]) ).
fof(f13514,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(X0,forward_diamond(X1,X2)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f13431]) ).
fof(f13515,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(forward_diamond(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f13514]) ).
fof(f13518,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,forward_diamond(X2,X3)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f13439]) ).
fof(f13519,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(X1,forward_diamond(X2,X3)),X0)),
inference(forward_demodulation,[status(thm)],[f97,f13441]) ).
fof(f13521,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(X0,addition(one,X1)))),X0),multiplication(X0,addition(one,X1))),
inference(resolution,[status(thm)],[f2478,f304]) ).
fof(f13522,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = multiplication(X0,addition(one,X1)),
inference(resolution,[status(thm)],[f2478,f48]) ).
fof(f13523,plain,
! [X0,X1] : leq(addition(antidomain(addition(one,X0)),X1),multiplication(X1,addition(one,X0))),
inference(paramodulation,[status(thm)],[f224,f2478]) ).
fof(f13524,plain,
! [X0,X1] : leq(addition(X0,antidomain(addition(one,X1))),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f230,f2478]) ).
fof(f13525,plain,
! [X0] : leq(c(addition(one,X0)),zero),
inference(paramodulation,[status(thm)],[f4265,f2478]) ).
fof(f13527,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f39,f2478]) ).
fof(f13530,plain,
! [X0] : leq(antidomain(addition(one,X0)),zero),
inference(paramodulation,[status(thm)],[f59,f2478]) ).
fof(f13567,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f1026,f2478]) ).
fof(f13568,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f1005,f2478]) ).
fof(f13570,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f97,f2478]) ).
fof(f13571,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f97,f2478]) ).
fof(f13573,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f35,f2478]) ).
fof(f13574,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f35,f2478]) ).
fof(f13614,plain,
! [X0,X1] : c(backward_diamond(X0,c(X1))) = multiplication(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f72,f2633]) ).
fof(f13615,plain,
! [X0,X1] : c(forward_diamond(X0,c(X1))) = multiplication(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f71,f2633]) ).
fof(f13617,plain,
! [X0] : c(antidomain(X0)) = multiplication(antidomain(c(X0)),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f547,f2633]) ).
fof(f13618,plain,
! [X0] : c(domain(X0)) = multiplication(domain(c(X0)),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f362,f2633]) ).
fof(f13622,plain,
! [X0] : c(domain(X0)) = multiplication(c(domain(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f67,f2633]) ).
fof(f13623,plain,
! [X0] : c(antidomain(X0)) = multiplication(c(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f62,f2633]) ).
fof(f13625,plain,
! [X0] : leq(c(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f2633,f6526]) ).
fof(f13626,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f2633,f4513]) ).
fof(f13629,plain,
! [X0] : multiplication(c(X0),multiplication(antidomain(X0),omega(c(X0)))) = omega(multiplication(c(X0),antidomain(X0))),
inference(paramodulation,[status(thm)],[f2633,f308]) ).
fof(f13630,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,c(X1))),X2),antidomain(X1))
| ~ leq(addition(multiplication(X0,c(X1)),X2),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f2633,f296]) ).
fof(f13631,plain,
! [X0] :
( leq(multiplication(star(c(X0)),multiplication(c(X0),antidomain(X0))),antidomain(X0))
| ~ leq(c(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f2633,f295]) ).
fof(f13632,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),antidomain(X1))
| ~ leq(addition(X0,c(X1)),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f2633,f293]) ).
fof(f13633,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(multiplication(c(X0),antidomain(X0)))))),star(c(X0))),
inference(paramodulation,[status(thm)],[f2633,f252]) ).
fof(f13634,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(c(X0))))),star(multiplication(c(X0),antidomain(X0)))),
inference(paramodulation,[status(thm)],[f2633,f252]) ).
fof(f13635,plain,
! [X0,X1,X2] : addition(multiplication(X0,antidomain(X1)),addition(c(X1),X2)) = addition(multiplication(addition(X0,c(X1)),antidomain(X1)),X2),
inference(paramodulation,[status(thm)],[f2633,f219]) ).
fof(f13636,plain,
! [X0,X1,X2] : addition(c(X0),addition(multiplication(X1,antidomain(X0)),X2)) = addition(multiplication(addition(c(X0),X1),antidomain(X0)),X2),
inference(paramodulation,[status(thm)],[f2633,f219]) ).
fof(f13637,plain,
! [X0] : multiplication(addition(c(X0),one),antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f2633,f232]) ).
fof(f13638,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),antidomain(X2)) = addition(multiplication(X0,antidomain(X2)),multiplication(X1,c(X2))),
inference(paramodulation,[status(thm)],[f2633,f211]) ).
fof(f13639,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),antidomain(X0)) = addition(c(X0),multiplication(X1,multiplication(X2,antidomain(X0)))),
inference(paramodulation,[status(thm)],[f2633,f211]) ).
fof(f13640,plain,
! [X0] : multiplication(addition(one,c(X0)),antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f2633,f207]) ).
fof(f13641,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),antidomain(X2)) = addition(multiplication(X0,multiplication(X1,antidomain(X2))),c(X2)),
inference(paramodulation,[status(thm)],[f2633,f204]) ).
fof(f13642,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),antidomain(X1)) = addition(multiplication(X0,c(X1)),multiplication(X2,antidomain(X1))),
inference(paramodulation,[status(thm)],[f2633,f204]) ).
fof(f13643,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(multiplication(X1,antidomain(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f2633,f201]) ).
fof(f13644,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(c(X1),multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f2633,f201]) ).
fof(f13645,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(c(X0),X2)) = addition(multiplication(c(X0),addition(X1,antidomain(X0))),X2),
inference(paramodulation,[status(thm)],[f2633,f170]) ).
fof(f13646,plain,
! [X0,X1,X2] : addition(c(X0),addition(multiplication(c(X0),X1),X2)) = addition(multiplication(c(X0),addition(antidomain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f2633,f170]) ).
fof(f13649,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(multiplication(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f2633,f153]) ).
fof(f13650,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(c(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f2633,f153]) ).
fof(f13651,plain,
! [X0] : multiplication(c(X0),multiplication(antidomain(X0),coantidomain(c(X0)))) = zero,
inference(paramodulation,[status(thm)],[f2633,f144]) ).
fof(f13653,plain,
! [X0] : addition(coantidomain(c(X0)),coantidomain(multiplication(codomain(c(X0)),antidomain(X0)))) = coantidomain(multiplication(codomain(c(X0)),antidomain(X0))),
inference(paramodulation,[status(thm)],[f2633,f615]) ).
fof(f13655,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(antidomain(X0),addition(c(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2633,f58]) ).
fof(f13656,plain,
! [X0,X1] :
( leq(multiplication(X1,star(antidomain(X0))),c(X0))
| ~ leq(addition(c(X0),X1),c(X0)) ),
inference(paramodulation,[status(thm)],[f2633,f55]) ).
fof(f13657,plain,
! [X0,X1] :
( leq(multiplication(star(c(X0)),X1),antidomain(X0))
| ~ leq(addition(c(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f2633,f53]) ).
fof(f13658,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(multiplication(X0,antidomain(X1)),c(X1)),
inference(paramodulation,[status(thm)],[f2633,f43]) ).
fof(f13659,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(c(X0),multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f2633,f43]) ).
fof(f13660,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(multiplication(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f2633,f42]) ).
fof(f13661,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(c(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f2633,f42]) ).
fof(f13662,plain,
! [X0,X1] : multiplication(c(X0),multiplication(antidomain(X0),X1)) = multiplication(c(X0),X1),
inference(paramodulation,[status(thm)],[f2633,f39]) ).
fof(f13664,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))),
inference(forward_demodulation,[status(thm)],[f72,f13614]) ).
fof(f13665,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))),
inference(forward_demodulation,[status(thm)],[f71,f13615]) ).
fof(f13668,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f547,f13617]) ).
fof(f13669,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f13668]) ).
fof(f13670,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),antidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f362,f13618]) ).
fof(f13671,plain,
! [X0] : domain(c(X0)) = domain_difference(c(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f68,f13670]) ).
fof(f13676,plain,
! [X0] : domain(c(X0)) = multiplication(c(domain(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f362,f13622]) ).
fof(f13677,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f362,f13676]) ).
fof(f13678,plain,
! [X0] : domain(c(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f4146,f13677]) ).
fof(f13679,plain,
! [X0] : antidomain(c(X0)) = multiplication(c(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f547,f13623]) ).
fof(f13680,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f547,f13679]) ).
fof(f13682,plain,
! [X0] : multiplication(c(X0),multiplication(antidomain(X0),omega(c(X0)))) = omega(c(X0)),
inference(forward_demodulation,[status(thm)],[f2633,f13629]) ).
fof(f13683,plain,
! [X0] :
( leq(multiplication(star(c(X0)),c(X0)),antidomain(X0))
| ~ leq(c(X0),antidomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2633,f13631]) ).
fof(f13684,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(c(X0))))),star(c(X0))),
inference(forward_demodulation,[status(thm)],[f2633,f13633]) ).
fof(f13685,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(c(X0))))),star(c(X0))),
inference(forward_demodulation,[status(thm)],[f2633,f13634]) ).
fof(f13686,plain,
! [X0,X1,X2] : addition(c(X0),addition(X1,multiplication(X2,antidomain(X0)))) = addition(multiplication(addition(X2,c(X0)),antidomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f97,f13635]) ).
fof(f13687,plain,
! [X0] : multiplication(addition(one,c(X0)),antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f35,f13637]) ).
fof(f13688,plain,
! [X0] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f1471,f13687]) ).
fof(f13689,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f41,f13688]) ).
fof(f13690,plain,
! [X0] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f1471,f13640]) ).
fof(f13691,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f41,f13690]) ).
fof(f13692,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),antidomain(X2)) = addition(c(X2),multiplication(X0,multiplication(X1,antidomain(X2)))),
inference(forward_demodulation,[status(thm)],[f35,f13641]) ).
fof(f13693,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(c(X0),multiplication(X1,antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f13643]) ).
fof(f13694,plain,
! [X0,X1,X2] : addition(c(X0),addition(X1,multiplication(c(X0),X2))) = addition(multiplication(c(X0),addition(X2,antidomain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f97,f13645]) ).
fof(f13700,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(c(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f13649]) ).
fof(f13701,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f13700]) ).
fof(f13702,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f13650]) ).
fof(f13707,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(c(X1),multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f35,f13658]) ).
fof(f13708,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(c(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f13660]) ).
fof(f13709,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f13708]) ).
fof(f13710,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f192,f13661]) ).
fof(f13711,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(antidomain(addition(X1,X2)),X0),multiplication(X2,star(X1))),addition(antidomain(addition(X1,X2)),X0))
| ~ leq(multiplication(X0,addition(X1,X2)),addition(antidomain(addition(X1,X2)),X0)) ),
inference(paramodulation,[status(thm)],[f224,f341]) ).
fof(f13712,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,antidomain(addition(X1,X2))),multiplication(X2,star(X1))),addition(X0,antidomain(addition(X1,X2))))
| ~ leq(multiplication(X0,addition(X1,X2)),addition(X0,antidomain(addition(X1,X2)))) ),
inference(paramodulation,[status(thm)],[f230,f341]) ).
fof(f13713,plain,
! [X0,X1] :
( leq(multiplication(c(addition(X0,X1)),multiplication(X1,star(X0))),c(addition(X0,X1)))
| ~ leq(zero,c(addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f4265,f341]) ).
fof(f13714,plain,
! [X0,X1] :
( leq(multiplication(domain(addition(X0,X1)),multiplication(X1,star(X0))),domain(addition(X0,X1)))
| ~ leq(addition(X0,X1),domain(addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f4146,f341]) ).
fof(f13715,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X1),multiplication(X3,star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f39,f341]) ).
fof(f13717,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X0),multiplication(X1,star(X0))),antidomain(X0))
| ~ leq(multiplication(antidomain(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f177,f341]) ).
fof(f13718,plain,
! [X0,X1] :
( leq(multiplication(antidomain(addition(X0,X1)),multiplication(X1,star(X0))),antidomain(addition(X0,X1)))
| ~ leq(zero,antidomain(addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f59,f341]) ).
fof(f13719,plain,
! [X0,X1] :
( leq(multiplication(zero,multiplication(X0,star(X1))),zero)
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f45,f341]) ).
fof(f13720,plain,
! [X0,X1] :
( leq(multiplication(one,multiplication(X1,star(X0))),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f41,f341]) ).
fof(f13721,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(omega(X0)))),X0)
| ~ leq(addition(omega(X0),multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f318,f341]) ).
fof(f13722,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(one))),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f162,f341]) ).
fof(f13723,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(coantidomain(X0)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f181,f341]) ).
fof(f13724,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(omega(X0),star(X1))),X0)
| ~ leq(addition(omega(X0),multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f321,f341]) ).
fof(f13725,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(one,star(X1))),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f192,f341]) ).
fof(f13728,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(multiplication(star(X1),addition(X1,one)),star(one))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(paramodulation,[status(thm)],[f7789,f341]) ).
fof(f13729,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(multiplication(addition(X1,one),star(X1)),star(one))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(paramodulation,[status(thm)],[f7510,f341]) ).
fof(f13740,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(c(X1),star(domain(X1)))),X0)
| ~ leq(multiplication(X0,one),X0) ),
inference(paramodulation,[status(thm)],[f569,f341]) ).
fof(f13741,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(coantidomain(multiplication(codomain(X1),X2)),star(coantidomain(multiplication(X1,X2))))),X0)
| ~ leq(multiplication(X0,coantidomain(multiplication(codomain(X1),X2))),X0) ),
inference(paramodulation,[status(thm)],[f615,f341]) ).
fof(f13742,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(codomain(X1),star(coantidomain(X1)))),X0)
| ~ leq(multiplication(X0,one),X0) ),
inference(paramodulation,[status(thm)],[f683,f341]) ).
fof(f13743,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(antidomain(multiplication(X1,domain(X2))),star(antidomain(multiplication(X1,X2))))),X0)
| ~ leq(multiplication(X0,antidomain(multiplication(X1,domain(X2)))),X0) ),
inference(paramodulation,[status(thm)],[f479,f341]) ).
fof(f13744,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(c(X1),star(antidomain(X1)))),X0)
| ~ leq(multiplication(X0,c(X1)),X0) ),
inference(paramodulation,[status(thm)],[f514,f341]) ).
fof(f13745,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(domain(X1),star(antidomain(X1)))),X0)
| ~ leq(multiplication(X0,one),X0) ),
inference(paramodulation,[status(thm)],[f558,f341]) ).
fof(f13746,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(multiplication(X3,X4),star(multiplication(X1,multiplication(X2,X4))))),X0)
| ~ leq(multiplication(X0,multiplication(addition(multiplication(X1,X2),X3),X4)),X0) ),
inference(paramodulation,[status(thm)],[f204,f341]) ).
fof(f13747,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(addition(multiplication(X2,X3),X4),star(multiplication(X1,X3)))),X0)
| ~ leq(multiplication(X0,addition(multiplication(addition(X1,X2),X3),X4)),X0) ),
inference(paramodulation,[status(thm)],[f219,f341]) ).
fof(f13748,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(addition(multiplication(X1,X3),X4),star(multiplication(X1,X2)))),X0)
| ~ leq(multiplication(X0,addition(multiplication(X1,addition(X2,X3)),X4)),X0) ),
inference(paramodulation,[status(thm)],[f170,f341]) ).
fof(f13749,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(multiplication(X2,multiplication(X3,X4)),star(multiplication(X1,X4)))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,multiplication(X2,X3)),X4)),X0) ),
inference(paramodulation,[status(thm)],[f211,f341]) ).
fof(f13750,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X3),star(multiplication(X2,X3)))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),X0) ),
inference(paramodulation,[status(thm)],[f201,f341]) ).
fof(f13751,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(multiplication(X1,X3)))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),X0) ),
inference(paramodulation,[status(thm)],[f153,f341]) ).
fof(f13752,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X2,X3),star(multiplication(X1,X3)))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),X0) ),
inference(paramodulation,[status(thm)],[f43,f341]) ).
fof(f13753,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X3),star(multiplication(X1,X2)))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),X0) ),
inference(paramodulation,[status(thm)],[f42,f341]) ).
fof(f13754,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X3,star(addition(X2,X1)))),X0)
| ~ leq(multiplication(X0,addition(X1,addition(X2,X3))),X0) ),
inference(paramodulation,[status(thm)],[f103,f341]) ).
fof(f13755,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X3,star(addition(X1,X2)))),X0)
| ~ leq(multiplication(X0,addition(X1,addition(X2,X3))),X0) ),
inference(paramodulation,[status(thm)],[f36,f341]) ).
fof(f13757,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(domain(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4516,f341]) ).
fof(f13758,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(coantidomain(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4515,f341]) ).
fof(f13759,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(antidomain(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4514,f341]) ).
fof(f13760,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(c(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4513,f341]) ).
fof(f13761,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(codomain(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4512,f341]) ).
fof(f13762,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(divergence(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4511,f341]) ).
fof(f13763,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,forward_diamond(X2,X3)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2491,f341]) ).
fof(f13764,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,backward_box(X2,X3)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2490,f341]) ).
fof(f13765,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,forward_box(X2,X3)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2489,f341]) ).
fof(f13766,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,backward_diamond(X2,X3)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2488,f341]) ).
fof(f13767,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,domain(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2497,f341]) ).
fof(f13768,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,coantidomain(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2496,f341]) ).
fof(f13769,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,antidomain(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2495,f341]) ).
fof(f13770,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,c(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2494,f341]) ).
fof(f13771,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,codomain(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2493,f341]) ).
fof(f13772,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,divergence(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2492,f341]) ).
fof(f13773,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(X2))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,one),X2)),X0) ),
inference(paramodulation,[status(thm)],[f232,f341]) ).
fof(f13774,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(X2))),X0)
| ~ leq(multiplication(X0,multiplication(addition(one,X1),X2)),X0) ),
inference(paramodulation,[status(thm)],[f207,f341]) ).
fof(f13775,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(X1))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,one))),X0) ),
inference(paramodulation,[status(thm)],[f192,f341]) ).
fof(f13776,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(X1))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X0) ),
inference(paramodulation,[status(thm)],[f162,f341]) ).
fof(f13777,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(addition(X2,X1),star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f1329,f341]) ).
fof(f13778,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(addition(X2,X1),star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f1026,f341]) ).
fof(f13779,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(addition(X1,X2),star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f1005,f341]) ).
fof(f13780,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(addition(X1,X2),star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f105,f341]) ).
fof(f13781,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(addition(X1,X2),star(X3))),X0)
| ~ leq(multiplication(X0,addition(X1,addition(X2,X3))),X0) ),
inference(paramodulation,[status(thm)],[f97,f341]) ).
fof(f13782,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(addition(X3,X1),star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,addition(X2,X3))),X0) ),
inference(paramodulation,[status(thm)],[f97,f341]) ).
fof(f13784,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f35,f341]) ).
fof(f13785,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f35,f341]) ).
fof(f13786,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f38,f341]) ).
fof(f13787,plain,
! [X0,X1] : leq(multiplication(c(addition(X0,X1)),multiplication(X1,star(X0))),c(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f13713,f240]) ).
fof(f13788,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X3,star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f13715]) ).
fof(f13790,plain,
! [X0,X1] : leq(multiplication(antidomain(addition(X0,X1)),multiplication(X1,star(X0))),antidomain(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f13718,f240]) ).
fof(f13791,definition,
! [X0,X1] :
( sQ28_spl
<=> leq(multiplication(zero,multiplication(X0,star(X1))),zero) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f13794,plain,
( sQ28_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f13719,f7983,f13791]) ).
fof(f13795,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(forward_demodulation,[status(thm)],[f41,f13720]) ).
fof(f13796,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,one)),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f13722]) ).
fof(f13797,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f40,f13796]) ).
fof(f13798,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),star(X1)),X0)
| ~ leq(addition(omega(X0),multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f319,f13724]) ).
fof(f13799,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f41,f13725]) ).
fof(f13802,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(star(X1),multiplication(addition(X1,one),star(one)))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13728]) ).
fof(f13803,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(star(X1),multiplication(addition(X1,one),one))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f13802]) ).
fof(f13804,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(star(X1),addition(one,multiplication(X1,one)))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f232,f13803]) ).
fof(f13805,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(star(X1),addition(one,X1))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f40,f13804]) ).
fof(f13806,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(X1,one),multiplication(star(X1),star(one)))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13729]) ).
fof(f13807,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(X1,one),multiplication(star(X1),one))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f13806]) ).
fof(f13808,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(X1,one),star(X1))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f40,f13807]) ).
fof(f13839,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(c(X1),star(domain(X1)))),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f13740]) ).
fof(f13840,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(c(X1),star(domain(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f13839,f239]) ).
fof(f13841,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(coantidomain(multiplication(codomain(X1),X2)),star(coantidomain(multiplication(X1,X2))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f13741,f4627]) ).
fof(f13842,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(codomain(X1),star(coantidomain(X1)))),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f13742]) ).
fof(f13843,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(codomain(X1),star(coantidomain(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f13842,f239]) ).
fof(f13844,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(antidomain(multiplication(X1,domain(X2))),star(antidomain(multiplication(X1,X2))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f13743,f3749]) ).
fof(f13845,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(c(X1),star(antidomain(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f13744,f3652]) ).
fof(f13846,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(domain(X1),star(antidomain(X1)))),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f13745]) ).
fof(f13847,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(domain(X1),star(antidomain(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f13846,f239]) ).
fof(f13848,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(X3,multiplication(X4,star(multiplication(X1,multiplication(X2,X4)))))),X0)
| ~ leq(multiplication(X0,multiplication(addition(multiplication(X1,X2),X3),X4)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13746]) ).
fof(f13849,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(X2,multiplication(multiplication(X3,X4),star(multiplication(X1,X4))))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,multiplication(X2,X3)),X4)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13749]) ).
fof(f13850,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(X2,multiplication(X3,multiplication(X4,star(multiplication(X1,X4)))))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,multiplication(X2,X3)),X4)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13849]) ).
fof(f13851,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X3,star(multiplication(X2,X3))))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13750]) ).
fof(f13852,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X1,X3))))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13751]) ).
fof(f13853,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X2,multiplication(X3,star(multiplication(X1,X3))))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,X2),X3)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13752]) ).
fof(f13854,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X3,star(multiplication(X1,X2))))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,X3))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13753]) ).
fof(f13856,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(domain(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13757]) ).
fof(f13857,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(coantidomain(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13758]) ).
fof(f13858,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(antidomain(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13759]) ).
fof(f13859,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(c(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13760]) ).
fof(f13860,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(codomain(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13761]) ).
fof(f13861,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(divergence(X2),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13762]) ).
fof(f13862,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(forward_diamond(X2,X3),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13763]) ).
fof(f13863,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(backward_box(X2,X3),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13764]) ).
fof(f13864,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(forward_box(X2,X3),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13765]) ).
fof(f13865,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(backward_diamond(X2,X3),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13766]) ).
fof(f13866,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(domain(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13767]) ).
fof(f13867,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(coantidomain(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13768]) ).
fof(f13868,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(antidomain(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13769]) ).
fof(f13869,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(c(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13770]) ).
fof(f13870,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(codomain(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13771]) ).
fof(f13871,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(divergence(X2),star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13772]) ).
fof(f13872,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X0)
| ~ leq(multiplication(X0,multiplication(addition(X1,one),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13773]) ).
fof(f13873,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X0)
| ~ leq(multiplication(X0,multiplication(addition(one,X1),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13774]) ).
fof(f13874,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X1)))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(X2,one))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13775]) ).
fof(f13875,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X1)))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f13776]) ).
fof(f13881,plain,
! [X0] : c(X0) = c(domain(X0)),
inference(backward_demodulation,[status(thm)],[f13678,f362]) ).
fof(f13883,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f72,f13678]) ).
fof(f13884,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f71,f13678]) ).
fof(f13886,plain,
! [X0] : domain(antidomain(c(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f547,f13678]) ).
fof(f13895,plain,
! [X0] : leq(c(X0),antidomain(c(c(X0)))),
inference(paramodulation,[status(thm)],[f13678,f4249]) ).
fof(f13899,plain,
! [X0,X1] : leq(domain_difference(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f13678,f3834]) ).
fof(f13904,plain,
! [X0] : addition(c(X0),c(c(X0))) = one,
inference(paramodulation,[status(thm)],[f13678,f569]) ).
fof(f13905,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(c(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(c(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),c(X2))) != addition(forward_diamond(X1,domain(X0)),domain(c(X2))) ),
inference(paramodulation,[status(thm)],[f13678,f75]) ).
fof(f13906,plain,
! [X0,X1,X2] :
( addition(domain(c(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(c(X0)),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,domain(c(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f13678,f75]) ).
fof(f13907,plain,
! [X0,X1,X2] :
( addition(domain(c(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,domain(c(X0))),domain(X2))) != addition(forward_diamond(X1,domain(c(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f13678,f75]) ).
fof(f13908,plain,
! [X0,X1] : forward_diamond(X0,c(X1)) = domain(multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f13678,f69]) ).
fof(f13909,plain,
! [X0,X1] : domain_difference(c(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f13678,f68]) ).
fof(f13910,plain,
! [X0] : addition(antidomain(c(X0)),c(X0)) = one,
inference(paramodulation,[status(thm)],[f13678,f558]) ).
fof(f13916,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f72,f13883]) ).
fof(f13917,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f71,f13884]) ).
fof(f13919,plain,
! [X0] : c(c(X0)) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f361,f13886]) ).
fof(f13920,plain,
! [X0] : c(c(X0)) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f547,f13919]) ).
fof(f13927,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(c(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(c(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),c(X2))) != addition(forward_diamond(X1,domain(X0)),c(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13905]) ).
fof(f13928,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),c(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(c(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),c(X2))) != addition(forward_diamond(X1,domain(X0)),c(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13927]) ).
fof(f13929,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),c(X2)))) = addition(divergence(X1),forward_diamond(star(X1),c(X2)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),c(X2))) != addition(forward_diamond(X1,domain(X0)),c(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13928]) ).
fof(f13930,plain,
! [X0,X1,X2] :
( addition(domain(c(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,domain(c(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13906]) ).
fof(f13931,plain,
! [X0,X1,X2] :
( addition(domain(c(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,c(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13930]) ).
fof(f13932,plain,
! [X0,X1,X2] :
( addition(c(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,c(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13931]) ).
fof(f13933,plain,
! [X0,X1,X2] :
( addition(domain(c(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,domain(c(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13907]) ).
fof(f13934,plain,
! [X0,X1,X2] :
( addition(domain(c(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,c(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13933]) ).
fof(f13935,plain,
! [X0,X1,X2] :
( addition(c(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(c(X0),addition(forward_diamond(X1,c(X0)),domain(X2))) != addition(forward_diamond(X1,c(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f13678,f13934]) ).
fof(f13936,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f35,f13910]) ).
fof(f13939,plain,
! [X0] : leq(multiplication(star(antidomain(antidomain(X0))),c(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f13625,f304]) ).
fof(f13940,plain,
! [X0] : addition(c(X0),antidomain(X0)) = antidomain(X0),
inference(resolution,[status(thm)],[f13625,f48]) ).
fof(f13942,plain,
! [X0,X1] : leq(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f72,f13625]) ).
fof(f13943,plain,
! [X0,X1] : leq(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f71,f13625]) ).
fof(f13945,plain,
! [X0] : leq(antidomain(c(X0)),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f547,f13625]) ).
fof(f13952,plain,
! [X0] : leq(multiplication(star(domain(X0)),c(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f13939]) ).
fof(f13953,plain,
! [X0] : addition(antidomain(X0),c(X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f13940]) ).
fof(f13956,plain,
! [X0] : leq(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f13945]) ).
fof(f13964,plain,
! [X0,X1] : c(multiplication(X0,domain(X1))) = c(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f69,f13881]) ).
fof(f13974,plain,
! [X0,X1] : multiplication(c(X0),domain_difference(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f13881,f1585]) ).
fof(f13990,plain,
! [X0] : forward_box(c(c(X0)),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f13881,f976]) ).
fof(f13991,plain,
! [X0] : addition(domain(domain(X0)),c(X0)) = one,
inference(paramodulation,[status(thm)],[f13881,f569]) ).
fof(f13992,plain,
! [X0] : forward_diamond(c(X0),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f13881,f770]) ).
fof(f13993,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f13881,f72]) ).
fof(f13994,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f13881,f71]) ).
fof(f13995,plain,
! [X0] : multiplication(c(X0),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f13881,f197]) ).
fof(f14015,plain,
! [X0] : addition(c(X0),domain(domain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f35,f13991]) ).
fof(f14016,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f196,f14015]) ).
fof(f14017,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f72,f13993]) ).
fof(f14018,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f71,f13994]) ).
fof(f14019,plain,
! [X0] : multiplication(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f196,f13995]) ).
fof(f14025,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = multiplication(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13916,f2215]) ).
fof(f14026,plain,
! [X0,X1] : leq(domain(backward_box(X0,X1)),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13916,f7000]) ).
fof(f14027,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(domain(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f13916,f7000]) ).
fof(f14029,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f13916,f4516]) ).
fof(f14031,plain,
! [X0,X1] : leq(backward_box(X0,X1),antidomain(c(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f13916,f4249]) ).
fof(f14033,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f13916,f4146]) ).
fof(f14035,plain,
! [X0,X1,X2] : leq(domain_difference(backward_box(X0,X1),X2),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f13916,f3834]) ).
fof(f14036,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f13916,f2403]) ).
fof(f14040,plain,
! [X0,X1] : addition(backward_box(X0,X1),c(backward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f13916,f569]) ).
fof(f14041,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(backward_box(X2,X3))))) = addition(divergence(X1),forward_diamond(star(X1),domain(backward_box(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),backward_box(X2,X3))) != addition(forward_diamond(X1,domain(X0)),domain(backward_box(X2,X3))) ),
inference(paramodulation,[status(thm)],[f13916,f75]) ).
fof(f14042,plain,
! [X0,X1,X2,X3] :
( addition(domain(backward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(domain(backward_box(X0,X1)),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(backward_box(X0,X1))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f13916,f75]) ).
fof(f14043,plain,
! [X0,X1,X2,X3] :
( addition(domain(backward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,domain(backward_box(X0,X1))),domain(X3))) != addition(forward_diamond(X2,domain(backward_box(X0,X1))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f13916,f75]) ).
fof(f14044,plain,
! [X0,X1,X2] : forward_diamond(X0,backward_box(X1,X2)) = domain(multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f13916,f69]) ).
fof(f14045,plain,
! [X0,X1,X2] : domain_difference(backward_box(X0,X1),X2) = multiplication(backward_box(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f13916,f68]) ).
fof(f14046,plain,
! [X0,X1] : addition(antidomain(backward_box(X0,X1)),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f13916,f558]) ).
fof(f14049,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = antidomain(c(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13916,f196]) ).
fof(f14050,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f13916,f67]) ).
fof(f14055,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13916,f14025]) ).
fof(f14056,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f13916,f14055]) ).
fof(f14057,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13916,f14026]) ).
fof(f14058,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13916,f14027]) ).
fof(f14059,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(backward_box(X2,X3))))) = addition(divergence(X1),forward_diamond(star(X1),domain(backward_box(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),backward_box(X2,X3))) != addition(forward_diamond(X1,domain(X0)),backward_box(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14041]) ).
fof(f14060,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),backward_box(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),domain(backward_box(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),backward_box(X2,X3))) != addition(forward_diamond(X1,domain(X0)),backward_box(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14059]) ).
fof(f14061,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),backward_box(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),backward_box(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),backward_box(X2,X3))) != addition(forward_diamond(X1,domain(X0)),backward_box(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14060]) ).
fof(f14062,plain,
! [X0,X1,X2,X3] :
( addition(domain(backward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(backward_box(X0,X1))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14042]) ).
fof(f14063,plain,
! [X0,X1,X2,X3] :
( addition(domain(backward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14062]) ).
fof(f14064,plain,
! [X0,X1,X2,X3] :
( addition(backward_box(X0,X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14063]) ).
fof(f14065,plain,
! [X0,X1,X2,X3] :
( addition(domain(backward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(backward_box(X0,X1))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14043]) ).
fof(f14066,plain,
! [X0,X1,X2,X3] :
( addition(domain(backward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14065]) ).
fof(f14067,plain,
! [X0,X1,X2,X3] :
( addition(backward_box(X0,X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f14066]) ).
fof(f14068,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f35,f14046]) ).
fof(f14070,plain,
! [X0,X1] : backward_box(X0,X1) = antidomain(c(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13916,f14049]) ).
fof(f14072,plain,
! [X0] :
( leq(multiplication(one,star(addition(X0,one))),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f7789,f329]) ).
fof(f14073,plain,
! [X0] :
( leq(multiplication(one,star(star(X0))),addition(X0,one))
| ~ leq(star(X0),addition(X0,one)) ),
inference(paramodulation,[status(thm)],[f7510,f329]) ).
fof(f14074,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X3)),star(X3)),X2)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),X2) ),
inference(paramodulation,[status(thm)],[f204,f329]) ).
fof(f14075,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X3),star(multiplication(X2,X3))),X1)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X1) ),
inference(paramodulation,[status(thm)],[f211,f329]) ).
fof(f14078,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X2)),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f43,f329]) ).
fof(f14079,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),star(X2)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f42,f329]) ).
fof(f14080,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X1,X0),star(X3)),X2)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X3))),X2) ),
inference(paramodulation,[status(thm)],[f103,f329]) ).
fof(f14081,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X0,X1),star(X3)),X2)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X3))),X2) ),
inference(paramodulation,[status(thm)],[f36,f329]) ).
fof(f14083,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(paramodulation,[status(thm)],[f4516,f329]) ).
fof(f14084,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f4515,f329]) ).
fof(f14085,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f4514,f329]) ).
fof(f14086,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),c(X1))
| ~ leq(X0,c(X1)) ),
inference(paramodulation,[status(thm)],[f4513,f329]) ).
fof(f14087,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(paramodulation,[status(thm)],[f4512,f329]) ).
fof(f14088,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),divergence(X1))
| ~ leq(X0,divergence(X1)) ),
inference(paramodulation,[status(thm)],[f4511,f329]) ).
fof(f14089,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(forward_diamond(X1,X2))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2491,f329]) ).
fof(f14090,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(backward_box(X1,X2))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2490,f329]) ).
fof(f14091,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(forward_box(X1,X2))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2489,f329]) ).
fof(f14092,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(backward_diamond(X1,X2))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2488,f329]) ).
fof(f14093,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2497,f329]) ).
fof(f14094,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2496,f329]) ).
fof(f14095,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2495,f329]) ).
fof(f14096,plain,
! [X0,X1] :
( leq(multiplication(X0,star(c(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2494,f329]) ).
fof(f14097,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2493,f329]) ).
fof(f14098,plain,
! [X0,X1] :
( leq(multiplication(X0,star(divergence(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2492,f329]) ).
fof(f14099,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X1)),X0)
| ~ leq(multiplication(addition(X0,one),X1),X0) ),
inference(paramodulation,[status(thm)],[f232,f329]) ).
fof(f14100,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X1)),X0)
| ~ leq(multiplication(addition(one,X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f207,f329]) ).
fof(f14101,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,one)),X0) ),
inference(paramodulation,[status(thm)],[f192,f329]) ).
fof(f14102,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),X0)
| ~ leq(multiplication(X0,addition(one,X1)),X0) ),
inference(paramodulation,[status(thm)],[f162,f329]) ).
fof(f14105,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f38,f329]) ).
fof(f14106,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),addition(one,X2))
| ~ leq(addition(X0,addition(X1,multiplication(X2,X1))),addition(one,X2)) ),
inference(paramodulation,[status(thm)],[f207,f329]) ).
fof(f14107,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),addition(antidomain(X2),X1))
| ~ leq(addition(X0,multiplication(X1,X2)),addition(antidomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f224,f329]) ).
fof(f14108,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(omega(X1))),addition(X2,one))
| ~ leq(addition(X0,multiplication(addition(X1,X2),omega(X1))),addition(X2,one)) ),
inference(paramodulation,[status(thm)],[f11449,f329]) ).
fof(f14109,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(omega(X2))),addition(X1,one))
| ~ leq(addition(X0,multiplication(addition(X1,X2),omega(X2))),addition(X1,one)) ),
inference(paramodulation,[status(thm)],[f10882,f329]) ).
fof(f14110,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),addition(X2,one))
| ~ leq(addition(X0,addition(X1,multiplication(X2,X1))),addition(X2,one)) ),
inference(paramodulation,[status(thm)],[f232,f329]) ).
fof(f14111,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),addition(X1,antidomain(X2)))
| ~ leq(addition(X0,multiplication(X1,X2)),addition(X1,antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f230,f329]) ).
fof(f14112,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(omega(X2))),addition(X2,X1))
| ~ leq(addition(X0,multiplication(addition(X1,one),omega(X2))),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f11449,f329]) ).
fof(f14113,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(omega(X2))),addition(X1,X2))
| ~ leq(addition(X0,multiplication(addition(X1,one),omega(X2))),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f10882,f329]) ).
fof(f14114,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(coantidomain(X2))),addition(X1,X2))
| ~ leq(addition(X0,multiplication(X1,coantidomain(X2))),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f233,f329]) ).
fof(f14115,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(coantidomain(X2))),addition(X2,X1))
| ~ leq(addition(X0,multiplication(X1,coantidomain(X2))),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f226,f329]) ).
fof(f14116,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),c(X1))
| ~ leq(addition(X0,c(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f2633,f329]) ).
fof(f14117,plain,
! [X0,X1] :
( leq(multiplication(X0,star(c(X1))),c(X1))
| ~ leq(addition(X0,c(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f2211,f329]) ).
fof(f14118,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain_difference(X1,X2))),c(X1))
| ~ leq(addition(X0,zero),c(X1)) ),
inference(paramodulation,[status(thm)],[f1585,f329]) ).
fof(f14119,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(addition(X0,zero),c(X1)) ),
inference(paramodulation,[status(thm)],[f197,f329]) ).
fof(f14120,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),c(X1))
| ~ leq(addition(X0,zero),c(X1)) ),
inference(paramodulation,[status(thm)],[f4265,f329]) ).
fof(f14121,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),coantidomain(X1))
| ~ leq(addition(X0,zero),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f195,f329]) ).
fof(f14122,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),domain(X1))
| ~ leq(addition(X0,domain(X1)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f2215,f329]) ).
fof(f14123,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(antidomain(X2))),domain(X1))
| ~ leq(addition(X0,domain_difference(X1,X2)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f68,f329]) ).
fof(f14124,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),domain(X1))
| ~ leq(addition(X0,X1),domain(X1)) ),
inference(paramodulation,[status(thm)],[f4146,f329]) ).
fof(f14125,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X3)),multiplication(X1,X2))
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f39,f329]) ).
fof(f14126,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(X2,X1))),antidomain(X1))
| ~ leq(addition(X0,multiplication(antidomain(X1),X2)),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f186,f329]) ).
fof(f14127,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(X1,X2))),antidomain(X1))
| ~ leq(addition(X0,multiplication(antidomain(X1),X2)),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f177,f329]) ).
fof(f14128,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(X1))),antidomain(X1))
| ~ leq(addition(X0,zero),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f1569,f329]) ).
fof(f14129,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X1,X2))),antidomain(X1))
| ~ leq(addition(X0,zero),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f136,f329]) ).
fof(f14130,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),antidomain(X1))
| ~ leq(addition(X0,zero),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f59,f329]) ).
fof(f14131,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(addition(X0,zero),zero) ),
inference(paramodulation,[status(thm)],[f45,f329]) ).
fof(f14132,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f41,f329]) ).
fof(f14133,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2309,f329]) ).
fof(f14134,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(omega(X1),X2))),X1)
| ~ leq(addition(X0,addition(omega(X1),multiplication(X1,X2))),X1) ),
inference(paramodulation,[status(thm)],[f318,f329]) ).
fof(f14135,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(one,X2))),X1)
| ~ leq(addition(X0,addition(X1,multiplication(X1,X2))),X1) ),
inference(paramodulation,[status(thm)],[f162,f329]) ).
fof(f14136,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(coantidomain(X1),X2))),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f181,f329]) ).
fof(f14137,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(X2,omega(X1)))),X1)
| ~ leq(addition(X0,addition(omega(X1),multiplication(X1,X2))),X1) ),
inference(paramodulation,[status(thm)],[f321,f329]) ).
fof(f14138,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(X2,one))),X1)
| ~ leq(addition(X0,addition(X1,multiplication(X1,X2))),X1) ),
inference(paramodulation,[status(thm)],[f192,f329]) ).
fof(f14139,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(X2,coantidomain(X1)))),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f190,f329]) ).
fof(f14140,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(omega(X1),X2))),X1)
| ~ leq(addition(X0,multiplication(omega(X1),X2)),X1) ),
inference(paramodulation,[status(thm)],[f319,f329]) ).
fof(f14141,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(coantidomain(X1),X2))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f151,f329]) ).
fof(f14142,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,omega(multiplication(X1,X2))))),X1)
| ~ leq(addition(X0,omega(multiplication(X1,X2))),X1) ),
inference(paramodulation,[status(thm)],[f308,f329]) ).
fof(f14143,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,coantidomain(multiplication(X1,X2))))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f144,f329]) ).
fof(f14144,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(coantidomain(X1)))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f1813,f329]) ).
fof(f14145,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(X1))),X1)
| ~ leq(addition(X0,omega(X1)),X1) ),
inference(paramodulation,[status(thm)],[f56,f329]) ).
fof(f14146,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f63,f329]) ).
fof(f14148,plain,
! [X0,X1] :
( leq(multiplication(X0,star(one)),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f40,f329]) ).
fof(f14150,plain,
! [X0] :
( leq(star(addition(X0,one)),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f14072]) ).
fof(f14151,plain,
! [X0] : leq(star(addition(X0,one)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14150,f239]) ).
fof(f14152,plain,
! [X0] :
( leq(star(star(X0)),addition(X0,one))
| ~ leq(star(X0),addition(X0,one)) ),
inference(forward_demodulation,[status(thm)],[f41,f14073]) ).
fof(f14153,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X3),star(X3))),X2)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f14074]) ).
fof(f14154,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X3,star(X3)))),X2)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),X2) ),
inference(forward_demodulation,[status(thm)],[f39,f14153]) ).
fof(f14155,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X3,star(multiplication(X2,X3)))),X1)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f14075]) ).
fof(f14158,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f14078]) ).
fof(f14159,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f14079]) ).
fof(f14161,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(forward_diamond(X1,X2))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14089,f239]) ).
fof(f14162,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(backward_box(X1,X2))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14090,f239]) ).
fof(f14163,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(forward_box(X1,X2))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14091,f239]) ).
fof(f14164,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(backward_diamond(X1,X2))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14092,f239]) ).
fof(f14165,plain,
! [X0,X1] : leq(multiplication(X0,star(domain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14093,f239]) ).
fof(f14166,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14094,f239]) ).
fof(f14167,plain,
! [X0,X1] : leq(multiplication(X0,star(antidomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14095,f239]) ).
fof(f14168,plain,
! [X0,X1] : leq(multiplication(X0,star(c(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14096,f239]) ).
fof(f14169,plain,
! [X0,X1] : leq(multiplication(X0,star(codomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14097,f239]) ).
fof(f14170,plain,
! [X0,X1] : leq(multiplication(X0,star(divergence(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14098,f239]) ).
fof(f14171,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f14105]) ).
fof(f14172,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain_difference(X1,X2))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f14118]) ).
fof(f14173,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f14119]) ).
fof(f14174,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f14120]) ).
fof(f14175,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f14121]) ).
fof(f14176,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f14128]) ).
fof(f14177,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X1,X2))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f14129]) ).
fof(f14178,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f14130]) ).
fof(f14179,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f14131]) ).
fof(f14180,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(coantidomain(X1),X2))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f14141]) ).
fof(f14181,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,coantidomain(multiplication(X1,X2))))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f14143]) ).
fof(f14182,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(coantidomain(X1)))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f14144]) ).
fof(f14183,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f14146]) ).
fof(f14186,plain,
! [X0,X1] :
( leq(multiplication(X0,one),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f9603,f14148]) ).
fof(f14187,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(addition(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f40,f14186]) ).
fof(f14194,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = multiplication(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13917,f2215]) ).
fof(f14195,plain,
! [X0,X1] : leq(domain(forward_box(X0,X1)),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13917,f7000]) ).
fof(f14196,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(domain(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f13917,f7000]) ).
fof(f14198,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f13917,f4516]) ).
fof(f14200,plain,
! [X0,X1] : leq(forward_box(X0,X1),antidomain(c(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f13917,f4249]) ).
fof(f14202,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f13917,f4146]) ).
fof(f14204,plain,
! [X0,X1,X2] : leq(domain_difference(forward_box(X0,X1),X2),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f13917,f3834]) ).
fof(f14205,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f13917,f2403]) ).
fof(f14209,plain,
! [X0,X1] : addition(forward_box(X0,X1),c(forward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f13917,f569]) ).
fof(f14210,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(forward_box(X2,X3))))) = addition(divergence(X1),forward_diamond(star(X1),domain(forward_box(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_box(X2,X3))) != addition(forward_diamond(X1,domain(X0)),domain(forward_box(X2,X3))) ),
inference(paramodulation,[status(thm)],[f13917,f75]) ).
fof(f14211,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(domain(forward_box(X0,X1)),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(forward_box(X0,X1))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f13917,f75]) ).
fof(f14212,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,domain(forward_box(X0,X1))),domain(X3))) != addition(forward_diamond(X2,domain(forward_box(X0,X1))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f13917,f75]) ).
fof(f14213,plain,
! [X0,X1,X2] : forward_diamond(X0,forward_box(X1,X2)) = domain(multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f13917,f69]) ).
fof(f14214,plain,
! [X0,X1,X2] : domain_difference(forward_box(X0,X1),X2) = multiplication(forward_box(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f13917,f68]) ).
fof(f14215,plain,
! [X0,X1] : addition(antidomain(forward_box(X0,X1)),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f13917,f558]) ).
fof(f14218,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = antidomain(c(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13917,f196]) ).
fof(f14219,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f13917,f67]) ).
fof(f14225,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13917,f14194]) ).
fof(f14226,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f13917,f14225]) ).
fof(f14227,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13917,f14195]) ).
fof(f14228,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13917,f14196]) ).
fof(f14229,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(forward_box(X2,X3))))) = addition(divergence(X1),forward_diamond(star(X1),domain(forward_box(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_box(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_box(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14210]) ).
fof(f14230,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_box(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),domain(forward_box(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_box(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_box(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14229]) ).
fof(f14231,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_box(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),forward_box(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_box(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_box(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14230]) ).
fof(f14232,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(forward_box(X0,X1))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14211]) ).
fof(f14233,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14232]) ).
fof(f14234,plain,
! [X0,X1,X2,X3] :
( addition(forward_box(X0,X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14233]) ).
fof(f14235,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(forward_box(X0,X1))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14212]) ).
fof(f14236,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14235]) ).
fof(f14237,plain,
! [X0,X1,X2,X3] :
( addition(forward_box(X0,X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f14236]) ).
fof(f14238,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f35,f14215]) ).
fof(f14240,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(c(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13917,f14218]) ).
fof(f14241,plain,
! [X0] : forward_box(antidomain(c(X0)),X0) = one,
inference(backward_demodulation,[status(thm)],[f13920,f976]) ).
fof(f14245,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(c(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f72,f13920]) ).
fof(f14246,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(c(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f71,f13920]) ).
fof(f14252,plain,
! [X0] : c(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f13920,f2633]) ).
fof(f14254,plain,
! [X0] : c(c(X0)) = multiplication(antidomain(c(X0)),c(c(X0))),
inference(paramodulation,[status(thm)],[f13920,f2211]) ).
fof(f14255,plain,
! [X0,X1] : multiplication(antidomain(c(X0)),domain_difference(c(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f13920,f1585]) ).
fof(f14272,plain,
! [X0] : forward_diamond(antidomain(c(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f13920,f770]) ).
fof(f14273,plain,
! [X0,X1] : backward_box(X0,c(X1)) = c(backward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f13920,f72]) ).
fof(f14274,plain,
! [X0,X1] : forward_box(X0,c(X1)) = c(forward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f13920,f71]) ).
fof(f14279,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f72,f14245]) ).
fof(f14280,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f71,f14246]) ).
fof(f14291,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f13920,f14252]) ).
fof(f14294,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),c(c(X0))),
inference(forward_demodulation,[status(thm)],[f13920,f14254]) ).
fof(f14295,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f13920,f14294]) ).
fof(f14306,plain,
! [X0] : leq(multiplication(star(antidomain(domain(X0))),antidomain(c(X0))),domain(X0)),
inference(resolution,[status(thm)],[f13956,f304]) ).
fof(f14307,plain,
! [X0] : addition(antidomain(c(X0)),domain(X0)) = domain(X0),
inference(resolution,[status(thm)],[f13956,f48]) ).
fof(f14311,plain,
! [X0,X1] : leq(antidomain(backward_box(X0,X1)),domain(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f72,f13956]) ).
fof(f14312,plain,
! [X0,X1] : leq(antidomain(forward_box(X0,X1)),domain(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f71,f13956]) ).
fof(f14316,plain,
! [X0,X1] : leq(antidomain(c(forward_box(X0,X1))),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f13917,f13956]) ).
fof(f14317,plain,
! [X0,X1] : leq(antidomain(c(backward_box(X0,X1))),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f13916,f13956]) ).
fof(f14320,plain,
! [X0,X1] : leq(antidomain(c(multiplication(X0,domain(X1)))),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f69,f13956]) ).
fof(f14325,plain,
! [X0] : leq(multiplication(star(c(X0)),antidomain(c(X0))),domain(X0)),
inference(forward_demodulation,[status(thm)],[f67,f14306]) ).
fof(f14326,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f35,f14307]) ).
fof(f14356,plain,
! [X0,X1] : leq(multiplication(forward_diamond(X0,X1),multiplication(forward_diamond(X0,X1),star(forward_diamond(X0,X1)))),forward_diamond(X0,X1)),
inference(resolution,[status(thm)],[f343,f7010]) ).
fof(f14357,plain,
! [X0,X1] : leq(multiplication(forward_box(X0,X1),multiplication(forward_box(X0,X1),star(forward_box(X0,X1)))),forward_box(X0,X1)),
inference(resolution,[status(thm)],[f343,f6659]) ).
fof(f14358,plain,
! [X0,X1] : leq(multiplication(backward_box(X0,X1),multiplication(backward_box(X0,X1),star(backward_box(X0,X1)))),backward_box(X0,X1)),
inference(resolution,[status(thm)],[f343,f6658]) ).
fof(f14359,plain,
! [X0,X1] : leq(multiplication(backward_diamond(X0,X1),multiplication(backward_diamond(X0,X1),star(backward_diamond(X0,X1)))),backward_diamond(X0,X1)),
inference(resolution,[status(thm)],[f343,f6519]) ).
fof(f14360,plain,
! [X0] : leq(multiplication(coantidomain(X0),multiplication(coantidomain(X0),star(coantidomain(X0)))),coantidomain(X0)),
inference(resolution,[status(thm)],[f343,f7158]) ).
fof(f14361,plain,
! [X0] : leq(multiplication(domain(X0),multiplication(domain(X0),star(domain(X0)))),domain(X0)),
inference(resolution,[status(thm)],[f343,f6808]) ).
fof(f14362,plain,
! [X0] : leq(multiplication(antidomain(X0),multiplication(antidomain(X0),star(antidomain(X0)))),antidomain(X0)),
inference(resolution,[status(thm)],[f343,f6667]) ).
fof(f14363,plain,
! [X0] : leq(multiplication(c(X0),multiplication(c(X0),star(c(X0)))),c(X0)),
inference(resolution,[status(thm)],[f343,f6526]) ).
fof(f14364,plain,
! [X0] : leq(multiplication(codomain(X0),multiplication(codomain(X0),star(codomain(X0)))),codomain(X0)),
inference(resolution,[status(thm)],[f343,f6393]) ).
fof(f14365,plain,
! [X0] : leq(multiplication(divergence(X0),multiplication(divergence(X0),star(divergence(X0)))),divergence(X0)),
inference(resolution,[status(thm)],[f343,f5965]) ).
fof(f14366,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(forward_diamond(X1,X2),star(forward_diamond(X1,X2)))),X0),
inference(resolution,[status(thm)],[f343,f4077]) ).
fof(f14367,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(forward_box(X1,X2),star(forward_box(X1,X2)))),X0),
inference(resolution,[status(thm)],[f343,f3741]) ).
fof(f14368,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(backward_box(X1,X2),star(backward_box(X1,X2)))),X0),
inference(resolution,[status(thm)],[f343,f3740]) ).
fof(f14369,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(backward_diamond(X1,X2),star(backward_diamond(X1,X2)))),X0),
inference(resolution,[status(thm)],[f343,f3497]) ).
fof(f14370,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(coantidomain(X1),star(coantidomain(X1)))),X0),
inference(resolution,[status(thm)],[f343,f4627]) ).
fof(f14371,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(domain(X1),star(domain(X1)))),X0),
inference(resolution,[status(thm)],[f343,f3841]) ).
fof(f14372,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(antidomain(X1),star(antidomain(X1)))),X0),
inference(resolution,[status(thm)],[f343,f3749]) ).
fof(f14373,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(c(X1),star(c(X1)))),X0),
inference(resolution,[status(thm)],[f343,f3652]) ).
fof(f14374,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(codomain(X1),star(codomain(X1)))),X0),
inference(resolution,[status(thm)],[f343,f3411]) ).
fof(f14375,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(divergence(X1),star(divergence(X1)))),X0),
inference(resolution,[status(thm)],[f343,f3330]) ).
fof(f14376,plain,
! [X0,X1] :
( leq(multiplication(addition(one,X1),multiplication(X0,star(X0))),addition(one,X1))
| ~ leq(addition(X0,multiplication(X1,X0)),addition(one,X1)) ),
inference(paramodulation,[status(thm)],[f207,f343]) ).
fof(f14377,plain,
! [X0,X1] :
( leq(multiplication(addition(antidomain(X1),X0),multiplication(X1,star(X1))),addition(antidomain(X1),X0))
| ~ leq(multiplication(X0,X1),addition(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f224,f343]) ).
fof(f14378,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,one),multiplication(omega(X0),star(omega(X0)))),addition(X1,one))
| ~ leq(multiplication(addition(X0,X1),omega(X0)),addition(X1,one)) ),
inference(paramodulation,[status(thm)],[f11449,f343]) ).
fof(f14379,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,one),multiplication(omega(X1),star(omega(X1)))),addition(X0,one))
| ~ leq(multiplication(addition(X0,X1),omega(X1)),addition(X0,one)) ),
inference(paramodulation,[status(thm)],[f10882,f343]) ).
fof(f14380,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,one),multiplication(X0,star(X0))),addition(X1,one))
| ~ leq(addition(X0,multiplication(X1,X0)),addition(X1,one)) ),
inference(paramodulation,[status(thm)],[f232,f343]) ).
fof(f14381,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,antidomain(X1)),multiplication(X1,star(X1))),addition(X0,antidomain(X1)))
| ~ leq(multiplication(X0,X1),addition(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f230,f343]) ).
fof(f14382,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,X0),multiplication(omega(X1),star(omega(X1)))),addition(X1,X0))
| ~ leq(multiplication(addition(X0,one),omega(X1)),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f11449,f343]) ).
fof(f14383,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,X1),multiplication(omega(X1),star(omega(X1)))),addition(X0,X1))
| ~ leq(multiplication(addition(X0,one),omega(X1)),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f10882,f343]) ).
fof(f14384,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,X1),multiplication(coantidomain(X1),star(coantidomain(X1)))),addition(X0,X1))
| ~ leq(multiplication(X0,coantidomain(X1)),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f233,f343]) ).
fof(f14385,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,X0),multiplication(coantidomain(X1),star(coantidomain(X1)))),addition(X1,X0))
| ~ leq(multiplication(X0,coantidomain(X1)),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f226,f343]) ).
fof(f14386,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0)))),c(X0))
| ~ leq(c(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2633,f343]) ).
fof(f14387,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(c(X0),star(c(X0)))),c(X0))
| ~ leq(c(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2211,f343]) ).
fof(f14388,plain,
! [X0,X1] :
( leq(multiplication(c(X0),multiplication(domain_difference(X0,X1),star(domain_difference(X0,X1)))),c(X0))
| ~ leq(zero,c(X0)) ),
inference(paramodulation,[status(thm)],[f1585,f343]) ).
fof(f14389,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(domain(X0),star(domain(X0)))),c(X0))
| ~ leq(zero,c(X0)) ),
inference(paramodulation,[status(thm)],[f197,f343]) ).
fof(f14390,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(X0,star(X0))),c(X0))
| ~ leq(zero,c(X0)) ),
inference(paramodulation,[status(thm)],[f4265,f343]) ).
fof(f14391,plain,
! [X0] :
( leq(multiplication(coantidomain(X0),multiplication(codomain(X0),star(codomain(X0)))),coantidomain(X0))
| ~ leq(zero,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f195,f343]) ).
fof(f14392,plain,
! [X0] :
( leq(multiplication(domain(X0),multiplication(domain(X0),star(domain(X0)))),domain(X0))
| ~ leq(domain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2215,f343]) ).
fof(f14393,plain,
! [X0,X1] :
( leq(multiplication(domain(X0),multiplication(antidomain(X1),star(antidomain(X1)))),domain(X0))
| ~ leq(domain_difference(X0,X1),domain(X0)) ),
inference(paramodulation,[status(thm)],[f68,f343]) ).
fof(f14394,plain,
! [X0] :
( leq(multiplication(domain(X0),multiplication(X0,star(X0))),domain(X0))
| ~ leq(X0,domain(X0)) ),
inference(paramodulation,[status(thm)],[f4146,f343]) ).
fof(f14395,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f39,f343]) ).
fof(f14396,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X0),multiplication(addition(X1,X0),star(addition(X1,X0)))),antidomain(X0))
| ~ leq(multiplication(antidomain(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f186,f343]) ).
fof(f14397,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X0),multiplication(addition(X0,X1),star(addition(X0,X1)))),antidomain(X0))
| ~ leq(multiplication(antidomain(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f177,f343]) ).
fof(f14398,plain,
! [X0] :
( leq(multiplication(antidomain(X0),multiplication(omega(X0),star(omega(X0)))),antidomain(X0))
| ~ leq(zero,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f1569,f343]) ).
fof(f14401,plain,
! [X0] :
( leq(multiplication(zero,multiplication(X0,star(X0))),zero)
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f45,f343]) ).
fof(f14402,plain,
! [X0] :
( leq(multiplication(one,multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f41,f343]) ).
fof(f14403,plain,
! [X0] :
( leq(multiplication(X0,multiplication(codomain(X0),star(codomain(X0)))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2309,f343]) ).
fof(f14404,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(omega(X0),X1),star(addition(omega(X0),X1)))),X0)
| ~ leq(addition(omega(X0),multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f318,f343]) ).
fof(f14405,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(one,X1),star(addition(one,X1)))),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f162,f343]) ).
fof(f14406,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(coantidomain(X0),X1),star(addition(coantidomain(X0),X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f181,f343]) ).
fof(f14407,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(X1,omega(X0)),star(addition(X1,omega(X0))))),X0)
| ~ leq(addition(omega(X0),multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f321,f343]) ).
fof(f14408,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(X1,one),star(addition(X1,one)))),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f192,f343]) ).
fof(f14409,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(X1,coantidomain(X0)),star(addition(X1,coantidomain(X0))))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f190,f343]) ).
fof(f14410,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(multiplication(omega(X0),X1),star(multiplication(omega(X0),X1)))),X0)
| ~ leq(multiplication(omega(X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f319,f343]) ).
fof(f14412,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(multiplication(X1,omega(multiplication(X0,X1))),star(multiplication(X1,omega(multiplication(X0,X1)))))),X0)
| ~ leq(omega(multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f308,f343]) ).
fof(f14413,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(multiplication(X1,coantidomain(multiplication(X0,X1))),star(multiplication(X1,coantidomain(multiplication(X0,X1)))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f144,f343]) ).
fof(f14414,plain,
! [X0] :
( leq(multiplication(X0,multiplication(omega(coantidomain(X0)),star(omega(coantidomain(X0))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f1813,f343]) ).
fof(f14415,plain,
! [X0] :
( leq(multiplication(X0,multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f56,f343]) ).
fof(f14419,plain,
! [X0] : leq(multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0)))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14386,f239]) ).
fof(f14420,plain,
! [X0] : leq(multiplication(c(X0),multiplication(c(X0),star(c(X0)))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14387,f239]) ).
fof(f14421,plain,
! [X0,X1] : leq(multiplication(c(X0),multiplication(domain_difference(X0,X1),star(domain_difference(X0,X1)))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14388,f240]) ).
fof(f14422,plain,
! [X0] : leq(multiplication(c(X0),multiplication(domain(X0),star(domain(X0)))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14389,f240]) ).
fof(f14423,plain,
! [X0] : leq(multiplication(c(X0),multiplication(X0,star(X0))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14390,f240]) ).
fof(f14424,plain,
! [X0] : leq(multiplication(coantidomain(X0),multiplication(codomain(X0),star(codomain(X0)))),coantidomain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14391,f240]) ).
fof(f14425,plain,
! [X0] : leq(multiplication(domain(X0),multiplication(domain(X0),star(domain(X0)))),domain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14392,f239]) ).
fof(f14426,plain,
! [X0,X1] : leq(multiplication(domain(X0),multiplication(antidomain(X1),star(antidomain(X1)))),domain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14393,f3834]) ).
fof(f14427,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14395]) ).
fof(f14428,plain,
! [X0] : leq(multiplication(antidomain(X0),multiplication(omega(X0),star(omega(X0)))),antidomain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f14398,f240]) ).
fof(f14430,definition,
! [X0] :
( sQ29_spl
<=> leq(multiplication(zero,multiplication(X0,star(X0))),zero) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f14433,plain,
( sQ29_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f14401,f7983,f14430]) ).
fof(f14434,plain,
! [X0] :
( leq(multiplication(X0,star(X0)),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f41,f14402]) ).
fof(f14435,plain,
! [X0] : leq(multiplication(X0,multiplication(codomain(X0),star(codomain(X0)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14403,f239]) ).
fof(f14436,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(omega(X0),multiplication(X1,star(multiplication(omega(X0),X1))))),X0)
| ~ leq(multiplication(omega(X0),X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f14410]) ).
fof(f14437,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(X1,star(multiplication(omega(X0),X1)))),X0)
| ~ leq(multiplication(omega(X0),X1),X0) ),
inference(forward_demodulation,[status(thm)],[f319,f14436]) ).
fof(f14439,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),star(multiplication(X1,omega(multiplication(X0,X1))))))),X0)
| ~ leq(omega(multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f14412]) ).
fof(f14440,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),star(multiplication(X1,coantidomain(multiplication(X0,X1))))))),X0)
| ~ leq(zero,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f14413]) ).
fof(f14441,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),star(multiplication(X1,coantidomain(multiplication(X0,X1))))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14440,f240]) ).
fof(f14442,plain,
! [X0] : leq(multiplication(X0,multiplication(omega(coantidomain(X0)),star(omega(coantidomain(X0))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14414,f240]) ).
fof(f14443,plain,
! [X0] :
( leq(multiplication(omega(X0),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f319,f14415]) ).
fof(f14449,plain,
! [X0] : forward_diamond(antidomain(c(X0)),domain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f13920,f13992]) ).
fof(f14450,plain,
! [X0] : forward_diamond(c(X0),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f13881,f13992]) ).
fof(f14452,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f72,f13992]) ).
fof(f14453,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f71,f13992]) ).
fof(f14455,plain,
! [X0] : forward_diamond(antidomain(c(X0)),domain(antidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f547,f13992]) ).
fof(f14461,plain,
! [X0,X1] : forward_diamond(c(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f69,f13992]) ).
fof(f14463,plain,
! [X0] : forward_diamond(c(domain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f196,f13992]) ).
fof(f14464,plain,
! [X0] : forward_diamond(c(antidomain(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f361,f13992]) ).
fof(f14466,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(c(X0)),forward_diamond(star(c(X0)),domain(X1)))) = addition(divergence(c(X0)),forward_diamond(star(c(X0)),domain(X1)))
| addition(domain(X0),addition(zero,domain(X1))) != addition(forward_diamond(c(X0),domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f13992,f75]) ).
fof(f14475,plain,
! [X0] : forward_diamond(antidomain(c(X0)),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f13678,f14449]) ).
fof(f14476,plain,
! [X0] : forward_diamond(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f196,f14450]) ).
fof(f14480,plain,
! [X0] : forward_diamond(antidomain(c(X0)),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f361,f14455]) ).
fof(f14483,plain,
! [X0] : forward_diamond(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f13881,f14463]) ).
fof(f14484,plain,
! [X0] : forward_diamond(antidomain(c(X0)),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f547,f14464]) ).
fof(f14485,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))) = addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))
| addition(zero,addition(domain(X0),domain(X1))) != addition(forward_diamond(c(X1),domain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f14466]) ).
fof(f14486,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))) = addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))
| addition(domain(X0),domain(X1)) != addition(forward_diamond(c(X1),domain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f14485]) ).
fof(f14487,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))) = addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))
| addition(domain(X0),domain(X1)) != addition(zero,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f13992,f14486]) ).
fof(f14488,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))) = addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f80,f14487]) ).
fof(f14497,plain,
! [X0,X1,X2] : backward_box(X0,forward_diamond(X1,X2)) = backward_box(X0,multiplication(X1,domain(X2))),
inference(paramodulation,[status(thm)],[f69,f14017]) ).
fof(f14499,plain,
! [X0,X1] : backward_box(X0,antidomain(c(X1))) = backward_box(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f196,f14017]) ).
fof(f14500,plain,
! [X0,X1] : backward_box(X0,c(X1)) = backward_box(X0,antidomain(X1)),
inference(paramodulation,[status(thm)],[f361,f14017]) ).
fof(f14512,plain,
! [X0,X1] : backward_box(X0,antidomain(c(X1))) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f14017,f14499]) ).
fof(f14519,plain,
! [X0,X1,X2] : forward_box(X0,forward_diamond(X1,X2)) = forward_box(X0,multiplication(X1,domain(X2))),
inference(paramodulation,[status(thm)],[f69,f14018]) ).
fof(f14521,plain,
! [X0,X1] : forward_box(X0,antidomain(c(X1))) = forward_box(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f196,f14018]) ).
fof(f14522,plain,
! [X0,X1] : forward_box(X0,c(X1)) = forward_box(X0,antidomain(X1)),
inference(paramodulation,[status(thm)],[f361,f14018]) ).
fof(f14534,plain,
! [X0,X1] : forward_box(X0,antidomain(c(X1))) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f14018,f14521]) ).
fof(f14537,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(addition(multiplication(X1,multiplication(X2,X3)),X4),star(X3)),multiplication(X0,X2))
| ~ leq(addition(multiplication(addition(X0,X1),multiplication(X2,X3)),X4),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f219,f332]) ).
fof(f14538,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(addition(multiplication(X0,X3),X4),star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,addition(multiplication(X1,X2),X3)),X4),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f170,f332]) ).
fof(f14539,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X1,multiplication(X2,multiplication(X3,X4))),star(X4)),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f211,f332]) ).
fof(f14540,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X2,X3)),star(X3)),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f201,f332]) ).
fof(f14541,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X1),star(X3)),multiplication(X0,X2))
| ~ leq(multiplication(X0,addition(X1,multiplication(X2,X3))),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f153,f332]) ).
fof(f14542,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X1,multiplication(X2,X3)),star(X3)),multiplication(X0,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f43,f332]) ).
fof(f14543,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,X3),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,addition(multiplication(X1,X2),X3)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f42,f332]) ).
fof(f14544,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(domain(X3),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4516,f332]) ).
fof(f14545,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(coantidomain(X3),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4515,f332]) ).
fof(f14546,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(antidomain(X3),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4514,f332]) ).
fof(f14547,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(c(X3),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4513,f332]) ).
fof(f14548,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(codomain(X3),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4512,f332]) ).
fof(f14549,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(divergence(X3),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4511,f332]) ).
fof(f14550,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),forward_diamond(X3,X4)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2491,f332]) ).
fof(f14551,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),backward_box(X3,X4)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2490,f332]) ).
fof(f14552,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),forward_box(X3,X4)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2489,f332]) ).
fof(f14553,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),backward_diamond(X3,X4)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2488,f332]) ).
fof(f14554,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),domain(X3)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2497,f332]) ).
fof(f14555,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),coantidomain(X3)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2496,f332]) ).
fof(f14556,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),antidomain(X3)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2495,f332]) ).
fof(f14557,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),c(X3)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2494,f332]) ).
fof(f14558,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),codomain(X3)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2493,f332]) ).
fof(f14559,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),divergence(X3)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2492,f332]) ).
fof(f14560,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,multiplication(X2,X3))),star(X3)),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,one),multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f232,f332]) ).
fof(f14561,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,multiplication(X2,X3))),star(X3)),multiplication(X1,X2))
| ~ leq(multiplication(addition(one,X0),multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f207,f332]) ).
fof(f14562,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),X3),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(multiplication(X0,multiplication(X1,X2)),addition(X3,one)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f192,f332]) ).
fof(f14563,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),X3),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X3)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f162,f332]) ).
fof(f14564,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X3,multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1329,f332]) ).
fof(f14565,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(multiplication(X1,multiplication(X2,X3)),X0),star(X3)),multiplication(X1,X2))
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1026,f332]) ).
fof(f14566,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X0,multiplication(X1,multiplication(X2,X3))),star(X3)),multiplication(X1,X2))
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1005,f332]) ).
fof(f14567,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(multiplication(X0,multiplication(X1,X2)),X3),star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f105,f332]) ).
fof(f14568,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(addition(X0,X1),star(X4)),multiplication(X2,X3))
| ~ leq(addition(X0,addition(X1,multiplication(X2,multiplication(X3,X4)))),multiplication(X2,X3)) ),
inference(paramodulation,[status(thm)],[f97,f332]) ).
fof(f14569,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(addition(X4,X0),star(X3)),multiplication(X1,X2))
| ~ leq(addition(X0,addition(multiplication(X1,multiplication(X2,X3)),X4)),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f97,f332]) ).
fof(f14571,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X3)),multiplication(X1,X2))
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f35,f332]) ).
fof(f14572,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X3)),multiplication(X1,X2))
| ~ leq(addition(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f35,f332]) ).
fof(f14573,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f38,f332]) ).
fof(f14574,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(antidomain(multiplication(X1,X2)),X0),X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(addition(antidomain(multiplication(X1,X2)),X0),X1)) ),
inference(paramodulation,[status(thm)],[f224,f332]) ).
fof(f14575,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,antidomain(multiplication(X1,X2))),X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(addition(X0,antidomain(multiplication(X1,X2))),X1)) ),
inference(paramodulation,[status(thm)],[f230,f332]) ).
fof(f14576,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(c(multiplication(X1,X2)),X1))
| ~ leq(addition(zero,X0),multiplication(c(multiplication(X1,X2)),X1)) ),
inference(paramodulation,[status(thm)],[f4265,f332]) ).
fof(f14577,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(domain(multiplication(X0,X1)),X0))
| ~ leq(addition(multiplication(X0,X1),X2),multiplication(domain(multiplication(X0,X1)),X0)) ),
inference(paramodulation,[status(thm)],[f4146,f332]) ).
fof(f14578,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X4,star(X3)),multiplication(multiplication(X0,X1),X2))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),multiplication(multiplication(X0,X1),X2)) ),
inference(paramodulation,[status(thm)],[f39,f332]) ).
fof(f14579,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(antidomain(X1),X1))
| ~ leq(addition(zero,X0),multiplication(antidomain(X1),X1)) ),
inference(paramodulation,[status(thm)],[f136,f332]) ).
fof(f14580,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(antidomain(multiplication(X1,X2)),X1))
| ~ leq(addition(zero,X0),multiplication(antidomain(multiplication(X1,X2)),X1)) ),
inference(paramodulation,[status(thm)],[f59,f332]) ).
fof(f14581,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(zero,X1))
| ~ leq(addition(zero,X0),multiplication(zero,X1)) ),
inference(paramodulation,[status(thm)],[f45,f332]) ).
fof(f14584,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,coantidomain(X1)))
| ~ leq(addition(zero,X0),multiplication(X1,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f151,f332]) ).
fof(f14585,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(omega(multiplication(X0,X1)))),multiplication(X0,X1))
| ~ leq(addition(omega(multiplication(X0,X1)),X2),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f308,f332]) ).
fof(f14586,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(coantidomain(multiplication(X1,X2)))),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f144,f332]) ).
fof(f14587,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X1)),multiplication(X0,addition(one,X2)))
| ~ leq(addition(multiplication(X0,addition(X1,multiplication(X2,X1))),X3),multiplication(X0,addition(one,X2))) ),
inference(paramodulation,[status(thm)],[f207,f332]) ).
fof(f14588,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,addition(antidomain(X2),X1)))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,addition(antidomain(X2),X1))) ),
inference(paramodulation,[status(thm)],[f224,f332]) ).
fof(f14589,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(omega(X1))),multiplication(X0,addition(X2,one)))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,X2),omega(X1))),X3),multiplication(X0,addition(X2,one))) ),
inference(paramodulation,[status(thm)],[f11449,f332]) ).
fof(f14590,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(omega(X2))),multiplication(X0,addition(X1,one)))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,X2),omega(X2))),X3),multiplication(X0,addition(X1,one))) ),
inference(paramodulation,[status(thm)],[f10882,f332]) ).
fof(f14591,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X1)),multiplication(X0,addition(X2,one)))
| ~ leq(addition(multiplication(X0,addition(X1,multiplication(X2,X1))),X3),multiplication(X0,addition(X2,one))) ),
inference(paramodulation,[status(thm)],[f232,f332]) ).
fof(f14592,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,addition(X1,antidomain(X2))))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,addition(X1,antidomain(X2)))) ),
inference(paramodulation,[status(thm)],[f230,f332]) ).
fof(f14593,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(omega(X2))),multiplication(X0,addition(X2,X1)))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,one),omega(X2))),X3),multiplication(X0,addition(X2,X1))) ),
inference(paramodulation,[status(thm)],[f11449,f332]) ).
fof(f14594,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(omega(X2))),multiplication(X0,addition(X1,X2)))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,one),omega(X2))),X3),multiplication(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f10882,f332]) ).
fof(f14595,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(coantidomain(X2))),multiplication(X0,addition(X1,X2)))
| ~ leq(addition(multiplication(X0,multiplication(X1,coantidomain(X2))),X3),multiplication(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f233,f332]) ).
fof(f14596,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(coantidomain(X2))),multiplication(X0,addition(X2,X1)))
| ~ leq(addition(multiplication(X0,multiplication(X1,coantidomain(X2))),X3),multiplication(X0,addition(X2,X1))) ),
inference(paramodulation,[status(thm)],[f226,f332]) ).
fof(f14597,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(antidomain(X1))),multiplication(X0,c(X1)))
| ~ leq(addition(multiplication(X0,c(X1)),X2),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f2633,f332]) ).
fof(f14598,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(c(X1))),multiplication(X0,c(X1)))
| ~ leq(addition(multiplication(X0,c(X1)),X2),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f2211,f332]) ).
fof(f14599,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,star(domain_difference(X2,X3))),multiplication(X0,c(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,c(X2))) ),
inference(paramodulation,[status(thm)],[f1585,f332]) ).
fof(f14600,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(domain(X2))),multiplication(X0,c(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,c(X2))) ),
inference(paramodulation,[status(thm)],[f197,f332]) ).
fof(f14601,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X2)),multiplication(X0,c(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,c(X2))) ),
inference(paramodulation,[status(thm)],[f4265,f332]) ).
fof(f14602,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(codomain(X2))),multiplication(X0,coantidomain(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,coantidomain(X2))) ),
inference(paramodulation,[status(thm)],[f195,f332]) ).
fof(f14603,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(domain(X1))),multiplication(X0,domain(X1)))
| ~ leq(addition(multiplication(X0,domain(X1)),X2),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f2215,f332]) ).
fof(f14604,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(antidomain(X2))),multiplication(X0,domain(X1)))
| ~ leq(addition(multiplication(X0,domain_difference(X1,X2)),X3),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f68,f332]) ).
fof(f14605,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(X0,domain(X1)))
| ~ leq(addition(multiplication(X0,X1),X2),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f4146,f332]) ).
fof(f14606,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X4,star(X3)),multiplication(X0,multiplication(X1,X2)))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),multiplication(X0,multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f39,f332]) ).
fof(f14607,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(addition(X2,X1))),multiplication(X0,antidomain(X1)))
| ~ leq(addition(multiplication(X0,multiplication(antidomain(X1),X2)),X3),multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f186,f332]) ).
fof(f14608,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(addition(X1,X2))),multiplication(X0,antidomain(X1)))
| ~ leq(addition(multiplication(X0,multiplication(antidomain(X1),X2)),X3),multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f177,f332]) ).
fof(f14609,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(omega(X2))),multiplication(X0,antidomain(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f1569,f332]) ).
fof(f14610,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,star(multiplication(X2,X3))),multiplication(X0,antidomain(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f136,f332]) ).
fof(f14611,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X2)),multiplication(X0,antidomain(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f59,f332]) ).
fof(f14612,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X2)),multiplication(X0,zero))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,zero)) ),
inference(paramodulation,[status(thm)],[f45,f332]) ).
fof(f14614,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(codomain(X1))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,X1),X2),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2309,f332]) ).
fof(f14615,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(addition(omega(X1),X2))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,addition(omega(X1),multiplication(X1,X2))),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f318,f332]) ).
fof(f14616,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(addition(one,X2))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,addition(X1,multiplication(X1,X2))),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f162,f332]) ).
fof(f14617,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(addition(coantidomain(X1),X2))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f181,f332]) ).
fof(f14618,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(addition(X2,omega(X1)))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,addition(omega(X1),multiplication(X1,X2))),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f321,f332]) ).
fof(f14619,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(addition(X2,one))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,addition(X1,multiplication(X1,X2))),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f192,f332]) ).
fof(f14620,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(addition(X2,coantidomain(X1)))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f190,f332]) ).
fof(f14621,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(multiplication(omega(X1),X2))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(omega(X1),X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f319,f332]) ).
fof(f14622,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,star(multiplication(coantidomain(X2),X3))),multiplication(X0,X2))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f151,f332]) ).
fof(f14623,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(multiplication(X2,omega(multiplication(X1,X2))))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,omega(multiplication(X1,X2))),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f308,f332]) ).
fof(f14624,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,star(multiplication(X3,coantidomain(multiplication(X2,X3))))),multiplication(X0,X2))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f144,f332]) ).
fof(f14625,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(omega(coantidomain(X2)))),multiplication(X0,X2))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f1813,f332]) ).
fof(f14626,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(omega(X1))),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,omega(X1)),X2),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f56,f332]) ).
fof(f14627,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(coantidomain(X2))),multiplication(X0,X2))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f63,f332]) ).
fof(f14629,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(one)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,X1),X2),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f40,f332]) ).
fof(f14630,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(one,X0),X1))
| ~ leq(addition(multiplication(addition(one,X0),multiplication(X1,X2)),X3),addition(X1,multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f207,f332]) ).
fof(f14631,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(antidomain(X0),X1),X0))
| ~ leq(addition(multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)),X3),multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f224,f332]) ).
fof(f14632,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,one),omega(X1)))
| ~ leq(addition(multiplication(addition(X0,one),multiplication(omega(X1),X2)),X3),multiplication(addition(X1,X0),omega(X1))) ),
inference(paramodulation,[status(thm)],[f11449,f332]) ).
fof(f14633,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,one),omega(X1)))
| ~ leq(addition(multiplication(addition(X0,one),multiplication(omega(X1),X2)),X3),multiplication(addition(X0,X1),omega(X1))) ),
inference(paramodulation,[status(thm)],[f10882,f332]) ).
fof(f14634,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,one),X1))
| ~ leq(addition(multiplication(addition(X0,one),multiplication(X1,X2)),X3),addition(X1,multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f232,f332]) ).
fof(f14635,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,antidomain(X1)),X1))
| ~ leq(addition(multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f230,f332]) ).
fof(f14636,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,X1),omega(X0)))
| ~ leq(addition(multiplication(addition(X0,X1),multiplication(omega(X0),X2)),X3),multiplication(addition(X1,one),omega(X0))) ),
inference(paramodulation,[status(thm)],[f11449,f332]) ).
fof(f14637,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,X1),omega(X1)))
| ~ leq(addition(multiplication(addition(X0,X1),multiplication(omega(X1),X2)),X3),multiplication(addition(X0,one),omega(X1))) ),
inference(paramodulation,[status(thm)],[f10882,f332]) ).
fof(f14638,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,X1),coantidomain(X1)))
| ~ leq(addition(multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)),X3),multiplication(X0,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f233,f332]) ).
fof(f14639,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(addition(X0,X1),coantidomain(X0)))
| ~ leq(addition(multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)),X3),multiplication(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f226,f332]) ).
fof(f14640,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(c(X0),antidomain(X0)))
| ~ leq(addition(multiplication(c(X0),multiplication(antidomain(X0),X1)),X2),c(X0)) ),
inference(paramodulation,[status(thm)],[f2633,f332]) ).
fof(f14641,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(c(X0),c(X0)))
| ~ leq(addition(multiplication(c(X0),multiplication(c(X0),X1)),X2),c(X0)) ),
inference(paramodulation,[status(thm)],[f2211,f332]) ).
fof(f14642,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(c(X0),domain_difference(X0,X1)))
| ~ leq(addition(multiplication(c(X0),multiplication(domain_difference(X0,X1),X2)),X3),zero) ),
inference(paramodulation,[status(thm)],[f1585,f332]) ).
fof(f14643,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(c(X0),domain(X0)))
| ~ leq(addition(multiplication(c(X0),multiplication(domain(X0),X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f197,f332]) ).
fof(f14644,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(c(X0),X0))
| ~ leq(addition(multiplication(c(X0),multiplication(X0,X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f4265,f332]) ).
fof(f14645,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(coantidomain(X0),codomain(X0)))
| ~ leq(addition(multiplication(coantidomain(X0),multiplication(codomain(X0),X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f195,f332]) ).
fof(f14646,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(domain(X0),domain(X0)))
| ~ leq(addition(multiplication(domain(X0),multiplication(domain(X0),X1)),X2),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2215,f332]) ).
fof(f14647,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(domain(X0),antidomain(X1)))
| ~ leq(addition(multiplication(domain(X0),multiplication(antidomain(X1),X2)),X3),domain_difference(X0,X1)) ),
inference(paramodulation,[status(thm)],[f68,f332]) ).
fof(f14648,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(domain(X0),X0))
| ~ leq(addition(multiplication(domain(X0),multiplication(X0,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f4146,f332]) ).
fof(f14649,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X4,star(X3)),multiplication(multiplication(X0,X1),X2))
| ~ leq(addition(multiplication(multiplication(X0,X1),multiplication(X2,X3)),X4),multiplication(X0,multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f39,f332]) ).
fof(f14650,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(antidomain(X0),addition(X1,X0)))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(addition(X1,X0),X2)),X3),multiplication(antidomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f186,f332]) ).
fof(f14651,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(antidomain(X0),addition(X0,X1)))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(addition(X0,X1),X2)),X3),multiplication(antidomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f177,f332]) ).
fof(f14652,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(antidomain(X0),omega(X0)))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(omega(X0),X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f1569,f332]) ).
fof(f14653,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(antidomain(X0),multiplication(X0,X1)))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(multiplication(X0,X1),X2)),X3),zero) ),
inference(paramodulation,[status(thm)],[f136,f332]) ).
fof(f14654,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(antidomain(X0),X0))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(X0,X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f59,f332]) ).
fof(f14655,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(zero,X0))
| ~ leq(addition(multiplication(zero,multiplication(X0,X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f45,f332]) ).
fof(f14657,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(X0,codomain(X0)))
| ~ leq(addition(multiplication(X0,multiplication(codomain(X0),X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f2309,f332]) ).
fof(f14658,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,addition(omega(X0),X1)))
| ~ leq(addition(multiplication(X0,multiplication(addition(omega(X0),X1),X2)),X3),addition(omega(X0),multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f318,f332]) ).
fof(f14659,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,addition(one,X1)))
| ~ leq(addition(multiplication(X0,multiplication(addition(one,X1),X2)),X3),addition(X0,multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f162,f332]) ).
fof(f14660,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,addition(coantidomain(X0),X1)))
| ~ leq(addition(multiplication(X0,multiplication(addition(coantidomain(X0),X1),X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f181,f332]) ).
fof(f14661,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,addition(X1,omega(X0))))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,omega(X0)),X2)),X3),addition(omega(X0),multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f321,f332]) ).
fof(f14662,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,addition(X1,one)))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,one),X2)),X3),addition(X0,multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f192,f332]) ).
fof(f14663,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,addition(X1,coantidomain(X0))))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,coantidomain(X0)),X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f190,f332]) ).
fof(f14665,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,multiplication(coantidomain(X0),X1)))
| ~ leq(addition(multiplication(X0,multiplication(multiplication(coantidomain(X0),X1),X2)),X3),zero) ),
inference(paramodulation,[status(thm)],[f151,f332]) ).
fof(f14666,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))))
| ~ leq(addition(multiplication(X0,multiplication(multiplication(X1,omega(multiplication(X0,X1))),X2)),X3),omega(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f308,f332]) ).
fof(f14667,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))))
| ~ leq(addition(multiplication(X0,multiplication(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)),X3),zero) ),
inference(paramodulation,[status(thm)],[f144,f332]) ).
fof(f14668,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(X0,omega(coantidomain(X0))))
| ~ leq(addition(multiplication(X0,multiplication(omega(coantidomain(X0)),X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f1813,f332]) ).
fof(f14670,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(X0,coantidomain(X0)))
| ~ leq(addition(multiplication(X0,multiplication(coantidomain(X0),X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f63,f332]) ).
fof(f14671,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(X0,zero))
| ~ leq(addition(multiplication(X0,multiplication(zero,X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f44,f332]) ).
fof(f14674,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X1,multiplication(multiplication(X2,multiplication(X3,X4)),star(X4))),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),multiplication(X0,X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f14539]) ).
fof(f14675,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X1,multiplication(X2,multiplication(multiplication(X3,X4),star(X4)))),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),multiplication(X0,X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f14674]) ).
fof(f14676,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,star(X4))))),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),multiplication(X3,X4)),multiplication(X0,X3)) ),
inference(forward_demodulation,[status(thm)],[f39,f14675]) ).
fof(f14677,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X2,X3),star(X3))),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14540]) ).
fof(f14678,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X2,multiplication(X3,star(X3)))),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14677]) ).
fof(f14679,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,star(X3))),multiplication(X0,X2))
| ~ leq(multiplication(X0,addition(X1,multiplication(X2,X3))),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14541]) ).
fof(f14680,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(multiplication(X2,X3),star(X3))),multiplication(X0,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14542]) ).
fof(f14681,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(X2,multiplication(X3,star(X3)))),multiplication(X0,X2))
| ~ leq(multiplication(addition(X0,X1),multiplication(X2,X3)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14680]) ).
fof(f14682,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X3,star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,addition(multiplication(X1,X2),X3)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14543]) ).
fof(f14683,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(domain(X3),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14544]) ).
fof(f14684,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(domain(X3),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14683]) ).
fof(f14685,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(domain(X3),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14684]) ).
fof(f14686,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(coantidomain(X3),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14545]) ).
fof(f14687,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(coantidomain(X3),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14686]) ).
fof(f14688,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(coantidomain(X3),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14687]) ).
fof(f14689,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(antidomain(X3),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14546]) ).
fof(f14690,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(antidomain(X3),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14689]) ).
fof(f14691,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(antidomain(X3),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14690]) ).
fof(f14692,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(c(X3),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14547]) ).
fof(f14693,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(c(X3),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14692]) ).
fof(f14694,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(c(X3),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14693]) ).
fof(f14695,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(codomain(X3),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14548]) ).
fof(f14696,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(codomain(X3),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14695]) ).
fof(f14697,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(codomain(X3),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14696]) ).
fof(f14698,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(divergence(X3),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14549]) ).
fof(f14699,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(divergence(X3),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14698]) ).
fof(f14700,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(divergence(X3),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14699]) ).
fof(f14701,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(forward_diamond(X3,X4),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14550]) ).
fof(f14702,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(forward_diamond(X3,X4),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14701]) ).
fof(f14703,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(forward_diamond(X3,X4),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14702]) ).
fof(f14704,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(backward_box(X3,X4),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14551]) ).
fof(f14705,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(backward_box(X3,X4),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14704]) ).
fof(f14706,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(backward_box(X3,X4),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14705]) ).
fof(f14707,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(forward_box(X3,X4),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14552]) ).
fof(f14708,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(forward_box(X3,X4),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14707]) ).
fof(f14709,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(forward_box(X3,X4),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14708]) ).
fof(f14710,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(backward_diamond(X3,X4),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14553]) ).
fof(f14711,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(backward_diamond(X3,X4),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14710]) ).
fof(f14712,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(backward_diamond(X3,X4),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14711]) ).
fof(f14713,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(domain(X3),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14554]) ).
fof(f14714,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(domain(X3),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14713]) ).
fof(f14715,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(domain(X3),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14714]) ).
fof(f14716,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(coantidomain(X3),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14555]) ).
fof(f14717,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(coantidomain(X3),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14716]) ).
fof(f14718,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(coantidomain(X3),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14717]) ).
fof(f14719,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(antidomain(X3),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14556]) ).
fof(f14720,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(antidomain(X3),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14719]) ).
fof(f14721,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(antidomain(X3),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14720]) ).
fof(f14722,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(c(X3),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14557]) ).
fof(f14723,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(c(X3),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14722]) ).
fof(f14724,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(c(X3),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14723]) ).
fof(f14725,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(codomain(X3),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14558]) ).
fof(f14726,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(codomain(X3),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14725]) ).
fof(f14727,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(codomain(X3),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14726]) ).
fof(f14728,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(divergence(X3),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14559]) ).
fof(f14729,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(divergence(X3),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14728]) ).
fof(f14730,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(divergence(X3),star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14729]) ).
fof(f14731,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,multiplication(X2,X3)),star(X3))),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,one),multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14560]) ).
fof(f14732,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(multiplication(X2,X3),star(X3)))),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,one),multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14731]) ).
fof(f14733,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(X3,star(X3))))),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,one),multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14732]) ).
fof(f14734,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,multiplication(X2,X3)),star(X3))),multiplication(X1,X2))
| ~ leq(multiplication(addition(one,X0),multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14561]) ).
fof(f14735,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(multiplication(X2,X3),star(X3)))),multiplication(X1,X2))
| ~ leq(multiplication(addition(one,X0),multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14734]) ).
fof(f14736,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(X3,star(X3))))),multiplication(X1,X2))
| ~ leq(multiplication(addition(one,X0),multiplication(X1,multiplication(X2,X3))),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f39,f14735]) ).
fof(f14737,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),X3),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(multiplication(X1,X2),addition(X3,one))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14562]) ).
fof(f14738,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),X3),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(X3,one)))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14737]) ).
fof(f14739,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(X3,star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(X3,one)))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14738]) ).
fof(f14740,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(X3,star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(X3,one)))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14739]) ).
fof(f14741,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(X3,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(X3,one)))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14740]) ).
fof(f14742,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),X3),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(multiplication(X1,X2),addition(one,X3))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14563]) ).
fof(f14743,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(multiplication(X0,multiplication(X1,X2)),X3),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X3)))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14742]) ).
fof(f14744,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),multiplication(X3,star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X3)))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14743]) ).
fof(f14745,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),multiplication(X3,star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X3)))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14744]) ).
fof(f14746,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,multiplication(X3,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X3)))),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14745]) ).
fof(f14748,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14573]) ).
fof(f14749,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f14748]) ).
fof(f14750,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(c(multiplication(X1,X2)),X1))
| ~ leq(X0,multiplication(c(multiplication(X1,X2)),X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f14576]) ).
fof(f14751,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X4,star(X3)),multiplication(multiplication(X0,X1),X2))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),multiplication(X0,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f14578]) ).
fof(f14752,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X4,star(X3)),multiplication(X0,multiplication(X1,X2)))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),multiplication(X0,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f14751]) ).
fof(f14753,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(antidomain(X1),X1))
| ~ leq(X0,multiplication(antidomain(X1),X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f14579]) ).
fof(f14754,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),X2))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f59,f14753]) ).
fof(f14755,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f59,f14754]) ).
fof(f14756,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(antidomain(multiplication(X1,X2)),X1))
| ~ leq(X0,multiplication(antidomain(multiplication(X1,X2)),X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f14580]) ).
fof(f14757,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(zero,X1))
| ~ leq(X0,multiplication(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f14581]) ).
fof(f14758,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(zero,X2))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f45,f14757]) ).
fof(f14759,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f45,f14758]) ).
fof(f14764,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,coantidomain(X1)))
| ~ leq(X0,multiplication(X1,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f80,f14584]) ).
fof(f14765,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,coantidomain(X2)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f63,f14764]) ).
fof(f14766,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f63,f14765]) ).
fof(f14767,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(coantidomain(multiplication(X1,X2)))),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f14586]) ).
fof(f14768,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(domain_difference(X2,X3))),multiplication(X1,c(X2)))
| ~ leq(addition(zero,X0),multiplication(X1,c(X2))) ),
inference(forward_demodulation,[status(thm)],[f44,f14599]) ).
fof(f14769,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(domain_difference(X2,X3))),multiplication(X1,c(X2)))
| ~ leq(X0,multiplication(X1,c(X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f14768]) ).
fof(f14770,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain(X2))),multiplication(X1,c(X2)))
| ~ leq(addition(zero,X0),multiplication(X1,c(X2))) ),
inference(forward_demodulation,[status(thm)],[f44,f14600]) ).
fof(f14771,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain(X2))),multiplication(X1,c(X2)))
| ~ leq(X0,multiplication(X1,c(X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f14770]) ).
fof(f14772,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,c(X2)))
| ~ leq(addition(zero,X0),multiplication(X1,c(X2))) ),
inference(forward_demodulation,[status(thm)],[f44,f14601]) ).
fof(f14773,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,c(X2)))
| ~ leq(X0,multiplication(X1,c(X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f14772]) ).
fof(f14774,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(codomain(X2))),multiplication(X1,coantidomain(X2)))
| ~ leq(addition(zero,X0),multiplication(X1,coantidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f44,f14602]) ).
fof(f14775,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(codomain(X2))),multiplication(X1,coantidomain(X2)))
| ~ leq(X0,multiplication(X1,coantidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f14774]) ).
fof(f14776,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(omega(X2))),multiplication(X1,antidomain(X2)))
| ~ leq(addition(zero,X0),multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f44,f14609]) ).
fof(f14777,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(omega(X2))),multiplication(X1,antidomain(X2)))
| ~ leq(X0,multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f14776]) ).
fof(f14778,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(multiplication(X2,X3))),multiplication(X1,antidomain(X2)))
| ~ leq(addition(zero,X0),multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f44,f14610]) ).
fof(f14779,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(multiplication(X2,X3))),multiplication(X1,antidomain(X2)))
| ~ leq(X0,multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f14778]) ).
fof(f14780,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,antidomain(X2)))
| ~ leq(addition(zero,X0),multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f44,f14611]) ).
fof(f14781,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,antidomain(X2)))
| ~ leq(X0,multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f14780]) ).
fof(f14782,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,zero))
| ~ leq(addition(zero,X0),multiplication(X1,zero)) ),
inference(forward_demodulation,[status(thm)],[f44,f14612]) ).
fof(f14783,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,zero))
| ~ leq(X0,multiplication(X1,zero)) ),
inference(forward_demodulation,[status(thm)],[f80,f14782]) ).
fof(f14784,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,zero))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f44,f14783]) ).
fof(f14785,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f44,f14784]) ).
fof(f14788,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(multiplication(coantidomain(X2),X3))),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f14622]) ).
fof(f14789,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(multiplication(coantidomain(X2),X3))),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f14788]) ).
fof(f14790,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(multiplication(X3,coantidomain(multiplication(X2,X3))))),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f14624]) ).
fof(f14791,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(multiplication(X3,coantidomain(multiplication(X2,X3))))),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f14790]) ).
fof(f14792,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(omega(coantidomain(X2)))),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f14625]) ).
fof(f14793,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(omega(coantidomain(X2)))),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f14792]) ).
fof(f14794,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(coantidomain(X2))),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f14627]) ).
fof(f14795,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(coantidomain(X2))),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f14794]) ).
fof(f14799,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,one),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,X1),X2),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f9603,f14629]) ).
fof(f14800,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,X1),X2),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f40,f14799]) ).
fof(f14801,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X1,X0))
| ~ leq(addition(multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)),X3),multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f224,f14631]) ).
fof(f14802,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f230,f14635]) ).
fof(f14803,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,coantidomain(X1)))
| ~ leq(addition(multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)),X3),multiplication(X0,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f233,f14638]) ).
fof(f14804,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X1,coantidomain(X0)))
| ~ leq(addition(multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)),X3),multiplication(X1,coantidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f226,f14639]) ).
fof(f14805,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),c(X0))
| ~ leq(addition(multiplication(c(X0),multiplication(antidomain(X0),X1)),X2),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f2633,f14640]) ).
fof(f14806,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),c(X0))
| ~ leq(addition(multiplication(c(X0),multiplication(c(X0),X1)),X2),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f2211,f14641]) ).
fof(f14807,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),zero)
| ~ leq(addition(multiplication(c(X0),multiplication(domain_difference(X0,X1),X2)),X3),zero) ),
inference(forward_demodulation,[status(thm)],[f1585,f14642]) ).
fof(f14808,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),zero)
| ~ leq(addition(multiplication(c(X0),multiplication(domain(X0),X1)),X2),zero) ),
inference(forward_demodulation,[status(thm)],[f197,f14643]) ).
fof(f14809,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),zero)
| ~ leq(addition(multiplication(c(X0),multiplication(X0,X1)),X2),zero) ),
inference(forward_demodulation,[status(thm)],[f4265,f14644]) ).
fof(f14810,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),zero)
| ~ leq(addition(multiplication(coantidomain(X0),multiplication(codomain(X0),X1)),X2),zero) ),
inference(forward_demodulation,[status(thm)],[f195,f14645]) ).
fof(f14811,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),domain(X0))
| ~ leq(addition(multiplication(domain(X0),multiplication(domain(X0),X1)),X2),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2215,f14646]) ).
fof(f14812,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),domain_difference(X0,X1))
| ~ leq(addition(multiplication(domain(X0),multiplication(antidomain(X1),X2)),X3),domain_difference(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f68,f14647]) ).
fof(f14813,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(domain(X0),multiplication(X0,X1)),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f4146,f14648]) ).
fof(f14814,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X4,star(X3)),multiplication(multiplication(X0,X1),X2))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),multiplication(X0,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f14649]) ).
fof(f14815,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X4,star(X3)),multiplication(X0,multiplication(X1,X2)))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(X2,X3))),X4),multiplication(X0,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f39,f14814]) ).
fof(f14816,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(antidomain(X0),X1))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(addition(X1,X0),X2)),X3),multiplication(antidomain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f186,f14650]) ).
fof(f14817,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(antidomain(X0),X1))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(addition(X0,X1),X2)),X3),multiplication(antidomain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f177,f14651]) ).
fof(f14818,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),zero)
| ~ leq(addition(multiplication(antidomain(X0),multiplication(omega(X0),X1)),X2),zero) ),
inference(forward_demodulation,[status(thm)],[f1569,f14652]) ).
fof(f14819,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(antidomain(X0),multiplication(X0,X1)))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(X0,multiplication(X1,X2))),X3),zero) ),
inference(forward_demodulation,[status(thm)],[f39,f14653]) ).
fof(f14820,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),multiplication(X2,X3)))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f136,f14819]) ).
fof(f14821,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),multiplication(X2,X3)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f14820]) ).
fof(f14822,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f136,f14821]) ).
fof(f14823,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),X2))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f136,f14654]) ).
fof(f14824,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),X2))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f14823]) ).
fof(f14825,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f59,f14824]) ).
fof(f14826,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(zero,X2))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f45,f14655]) ).
fof(f14827,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(zero,X2))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f14826]) ).
fof(f14828,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f45,f14827]) ).
fof(f14831,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,multiplication(codomain(X0),X1)),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f2309,f14657]) ).
fof(f14832,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),addition(omega(X0),multiplication(X0,X1)))
| ~ leq(addition(multiplication(X0,multiplication(addition(omega(X0),X1),X2)),X3),addition(omega(X0),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f318,f14658]) ).
fof(f14833,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(addition(coantidomain(X0),X1),X2)),X3),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f181,f14660]) ).
fof(f14834,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),addition(omega(X0),multiplication(X0,X1)))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,omega(X0)),X2)),X3),addition(omega(X0),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f321,f14661]) ).
fof(f14835,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(addition(X1,coantidomain(X0)),X2)),X3),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f190,f14663]) ).
fof(f14839,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,multiplication(coantidomain(X0),X1)))
| ~ leq(addition(multiplication(X0,multiplication(coantidomain(X0),multiplication(X1,X2))),X3),zero) ),
inference(forward_demodulation,[status(thm)],[f39,f14665]) ).
fof(f14840,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X1)),multiplication(X2,multiplication(coantidomain(X2),X3)))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f151,f14839]) ).
fof(f14841,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X1)),multiplication(X2,multiplication(coantidomain(X2),X3)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f14840]) ).
fof(f14842,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f151,f14841]) ).
fof(f14843,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),X2))),X3),omega(multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f14666]) ).
fof(f14844,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),omega(multiplication(X0,X1)))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(omega(multiplication(X0,X1)),X2))),X3),omega(multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f308,f14843]) ).
fof(f14845,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))))
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))),X3),zero) ),
inference(forward_demodulation,[status(thm)],[f39,f14667]) ).
fof(f14846,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),zero)
| ~ leq(addition(multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))),X3),zero) ),
inference(forward_demodulation,[status(thm)],[f144,f14845]) ).
fof(f14847,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),zero)
| ~ leq(addition(multiplication(X0,multiplication(omega(coantidomain(X0)),X1)),X2),zero) ),
inference(forward_demodulation,[status(thm)],[f1813,f14668]) ).
fof(f14850,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,coantidomain(X2)))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f151,f14670]) ).
fof(f14851,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,coantidomain(X2)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f14850]) ).
fof(f14852,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f63,f14851]) ).
fof(f14853,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X2)),multiplication(X0,zero))
| ~ leq(addition(multiplication(X0,zero),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f45,f14671]) ).
fof(f14854,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,zero))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f14853]) ).
fof(f14855,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,zero))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f80,f14854]) ).
fof(f14856,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f44,f14855]) ).
fof(f14862,plain,
! [X0] : forward_box(antidomain(antidomain(c(X0))),c(X0)) = one,
inference(paramodulation,[status(thm)],[f13920,f14241]) ).
fof(f14865,plain,
! [X0,X1] : forward_box(antidomain(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f72,f14241]) ).
fof(f14866,plain,
! [X0,X1] : forward_box(antidomain(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f71,f14241]) ).
fof(f14868,plain,
! [X0] : forward_box(antidomain(antidomain(c(X0))),antidomain(X0)) = one,
inference(paramodulation,[status(thm)],[f547,f14241]) ).
fof(f14882,plain,
! [X0] : forward_box(domain(c(X0)),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f62,f14862]) ).
fof(f14883,plain,
! [X0] : forward_box(c(X0),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f13678,f14882]) ).
fof(f14886,plain,
! [X0] : forward_box(domain(c(X0)),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f62,f14868]) ).
fof(f14887,plain,
! [X0] : forward_box(c(X0),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f13678,f14886]) ).
fof(f14893,plain,
! [X0] : forward_box(antidomain(c(X0)),c(c(X0))) = one,
inference(paramodulation,[status(thm)],[f13920,f14883]) ).
fof(f14896,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),c(backward_diamond(X0,c(X1)))) = one,
inference(paramodulation,[status(thm)],[f72,f14883]) ).
fof(f14897,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),c(forward_diamond(X0,c(X1)))) = one,
inference(paramodulation,[status(thm)],[f71,f14883]) ).
fof(f14899,plain,
! [X0] : forward_box(antidomain(c(X0)),c(antidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f547,f14883]) ).
fof(f14901,plain,
! [X0] : forward_box(c(c(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f13920,f14883]) ).
fof(f14904,plain,
! [X0,X1] : forward_box(c(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f72,f14883]) ).
fof(f14905,plain,
! [X0,X1] : forward_box(c(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f71,f14883]) ).
fof(f14907,plain,
! [X0] : forward_box(c(antidomain(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f547,f14883]) ).
fof(f14917,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f13920,f14893]) ).
fof(f14919,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f72,f14896]) ).
fof(f14920,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f71,f14897]) ).
fof(f14922,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f547,f14899]) ).
fof(f14923,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f13920,f14901]) ).
fof(f14926,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f72,f14904]) ).
fof(f14927,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f71,f14905]) ).
fof(f14928,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f547,f14907]) ).
fof(f14934,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f13920,f14887]) ).
fof(f14937,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))) = one,
inference(paramodulation,[status(thm)],[f72,f14887]) ).
fof(f14938,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))) = one,
inference(paramodulation,[status(thm)],[f71,f14887]) ).
fof(f14970,plain,
! [X0] : zero = antidomain(addition(one,X0)),
inference(paramodulation,[status(thm)],[f40,f2635]) ).
fof(f14985,plain,
! [X0,X1] : zero = multiplication(antidomain(coantidomain(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f615,f2635]) ).
fof(f14987,plain,
! [X0,X1] : zero = multiplication(antidomain(antidomain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f479,f2635]) ).
fof(f14988,plain,
! [X0] : zero = multiplication(antidomain(c(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f514,f2635]) ).
fof(f14990,plain,
! [X0,X1,X2,X3] : zero = multiplication(antidomain(multiplication(addition(multiplication(X0,X1),X2),X3)),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f204,f2635]) ).
fof(f14991,plain,
! [X0,X1,X2,X3] : zero = multiplication(antidomain(addition(multiplication(addition(X0,X1),X2),X3)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f219,f2635]) ).
fof(f14992,plain,
! [X0,X1,X2,X3] : zero = multiplication(antidomain(addition(multiplication(X0,addition(X1,X2)),X3)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f170,f2635]) ).
fof(f14993,plain,
! [X0,X1,X2,X3] : zero = multiplication(antidomain(multiplication(addition(X0,multiplication(X1,X2)),X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f211,f2635]) ).
fof(f14994,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(addition(X0,X1),X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f201,f2635]) ).
fof(f14995,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,addition(X1,X2))),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f153,f2635]) ).
fof(f14996,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(addition(X0,X1),X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f43,f2635]) ).
fof(f14997,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,addition(X1,X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f42,f2635]) ).
fof(f14998,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(X0,addition(X1,X2))),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f103,f2635]) ).
fof(f14999,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(X0,addition(X1,X2))),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f36,f2635]) ).
fof(f15017,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(addition(X0,one),X1)),X1),
inference(paramodulation,[status(thm)],[f232,f2635]) ).
fof(f15018,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(addition(one,X0),X1)),X1),
inference(paramodulation,[status(thm)],[f207,f2635]) ).
fof(f15019,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,addition(X1,one))),X0),
inference(paramodulation,[status(thm)],[f192,f2635]) ).
fof(f15020,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,addition(one,X1))),X0),
inference(paramodulation,[status(thm)],[f162,f2635]) ).
fof(f15022,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f1026,f2635]) ).
fof(f15023,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f1005,f2635]) ).
fof(f15025,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(X0,addition(X1,X2))),X2),
inference(paramodulation,[status(thm)],[f97,f2635]) ).
fof(f15026,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(X0,addition(X1,X2))),X1),
inference(paramodulation,[status(thm)],[f97,f2635]) ).
fof(f15028,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f35,f2635]) ).
fof(f15029,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f35,f2635]) ).
fof(f15049,plain,
! [X0,X1] : leq(antidomain(addition(addition(one,X0),X1)),zero),
inference(paramodulation,[status(thm)],[f2635,f2478]) ).
fof(f15050,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(addition(addition(X0,X1),X2)),multiplication(X1,star(X0))),antidomain(addition(addition(X0,X1),X2)))
| ~ leq(zero,antidomain(addition(addition(X0,X1),X2))) ),
inference(paramodulation,[status(thm)],[f2635,f341]) ).
fof(f15052,plain,
! [X0,X1,X2] :
( zero != multiplication(antidomain(addition(addition(X0,X1),X2)),X1)
| leq(multiplication(antidomain(addition(addition(X0,X1),X2)),X0),multiplication(antidomain(addition(addition(X0,X1),X2)),X1)) ),
inference(paramodulation,[status(thm)],[f2635,f242]) ).
fof(f15053,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X2)),multiplication(antidomain(addition(multiplication(X1,X2),X3)),X1))
| ~ leq(addition(zero,X0),multiplication(antidomain(addition(multiplication(X1,X2),X3)),X1)) ),
inference(paramodulation,[status(thm)],[f2635,f332]) ).
fof(f15054,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(antidomain(addition(multiplication(X2,X1),X3)),X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f2635,f296]) ).
fof(f15055,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(antidomain(addition(multiplication(X1,X2),X3)),X1)),X2) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f2635,f211]) ).
fof(f15056,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(antidomain(addition(multiplication(X0,X1),X2)),X0),X3),X1) = addition(zero,multiplication(X3,X1)),
inference(paramodulation,[status(thm)],[f2635,f204]) ).
fof(f15059,plain,
! [X0,X1] : forward_diamond(antidomain(addition(domain(X0),X1)),X0) = domain(zero),
inference(paramodulation,[status(thm)],[f2635,f69]) ).
fof(f15061,plain,
! [X0,X1] : leq(antidomain(addition(star(X0),X1)),zero),
inference(paramodulation,[status(thm)],[f2635,f8449]) ).
fof(f15066,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(antidomain(addition(X0,X1)),X0))
| ~ leq(addition(multiplication(antidomain(addition(X0,X1)),multiplication(X0,X2)),X3),zero) ),
inference(paramodulation,[status(thm)],[f2635,f332]) ).
fof(f15067,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,star(X2)),multiplication(X0,antidomain(addition(X2,X3))))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,antidomain(addition(X2,X3)))) ),
inference(paramodulation,[status(thm)],[f2635,f332]) ).
fof(f15068,plain,
! [X0,X1] :
( leq(multiplication(antidomain(addition(X0,X1)),multiplication(X0,star(X0))),antidomain(addition(X0,X1)))
| ~ leq(zero,antidomain(addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f2635,f343]) ).
fof(f15069,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),antidomain(addition(X1,X2)))
| ~ leq(addition(X0,zero),antidomain(addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2635,f329]) ).
fof(f15071,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,antidomain(addition(X2,X3)))),X1),X2)
| ~ leq(addition(multiplication(X0,zero),X1),X2) ),
inference(paramodulation,[status(thm)],[f2635,f296]) ).
fof(f15073,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(addition(X1,X2))),X0),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f2635,f293]) ).
fof(f15076,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(addition(X0,antidomain(addition(X1,X3))),X1),X2),
inference(paramodulation,[status(thm)],[f2635,f219]) ).
fof(f15077,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(addition(antidomain(addition(X1,X3)),X0),X1),X2),
inference(paramodulation,[status(thm)],[f2635,f219]) ).
fof(f15079,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(addition(X2,X3)))),X2) = addition(multiplication(X0,X2),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f2635,f211]) ).
fof(f15080,plain,
! [X0,X1,X2,X3] : multiplication(addition(antidomain(addition(X0,X1)),multiplication(X2,X3)),X0) = addition(zero,multiplication(X2,multiplication(X3,X0))),
inference(paramodulation,[status(thm)],[f2635,f211]) ).
fof(f15082,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),antidomain(addition(X2,X3))),X2) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f2635,f204]) ).
fof(f15083,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(addition(X1,X2))),X3),X1) = addition(multiplication(X0,zero),multiplication(X3,X1)),
inference(paramodulation,[status(thm)],[f2635,f204]) ).
fof(f15084,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(addition(X0,X1)),X2),X0) = addition(multiplication(X2,X0),zero),
inference(paramodulation,[status(thm)],[f2635,f201]) ).
fof(f15085,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(addition(X1,X2))),X1) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2635,f201]) ).
fof(f15086,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(addition(X0,X1)),X2),addition(zero,X3)) = addition(multiplication(antidomain(addition(X0,X1)),addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f2635,f170]) ).
fof(f15087,plain,
! [X0,X1,X2,X3] : addition(zero,addition(multiplication(antidomain(addition(X0,X1)),X2),X3)) = addition(multiplication(antidomain(addition(X0,X1)),addition(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f2635,f170]) ).
fof(f15088,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,one)) = addition(antidomain(addition(X0,X1)),zero),
inference(paramodulation,[status(thm)],[f2635,f192]) ).
fof(f15089,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(one,X0)) = addition(antidomain(addition(X0,X1)),zero),
inference(paramodulation,[status(thm)],[f2635,f162]) ).
fof(f15090,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,X2)) = addition(multiplication(antidomain(addition(X0,X1)),X2),zero),
inference(paramodulation,[status(thm)],[f2635,f153]) ).
fof(f15091,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X2,X0)) = addition(zero,multiplication(antidomain(addition(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f2635,f153]) ).
fof(f15094,plain,
! [X0,X1] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(addition(X0,X1))),X0))) = coantidomain(multiplication(codomain(antidomain(addition(X0,X1))),X0)),
inference(paramodulation,[status(thm)],[f2635,f615]) ).
fof(f15095,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0)))) = antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0))),
inference(paramodulation,[status(thm)],[f2635,f479]) ).
fof(f15096,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X0,X2))),multiplication(star(antidomain(addition(X0,X2))),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f2635,f58]) ).
fof(f15097,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),antidomain(addition(X1,X2)))
| ~ leq(addition(zero,X0),antidomain(addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2635,f55]) ).
fof(f15098,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(addition(X1,X2))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f2635,f53]) ).
fof(f15099,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(addition(X1,X2))),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f2635,f43]) ).
fof(f15100,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(addition(X0,X1)),X2),X0) = addition(zero,multiplication(X2,X0)),
inference(paramodulation,[status(thm)],[f2635,f43]) ).
fof(f15101,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X2,X0)) = addition(multiplication(antidomain(addition(X0,X1)),X2),zero),
inference(paramodulation,[status(thm)],[f2635,f42]) ).
fof(f15102,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,X2)) = addition(zero,multiplication(antidomain(addition(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f2635,f42]) ).
fof(f15103,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),multiplication(X0,X2)) = multiplication(zero,X2),
inference(paramodulation,[status(thm)],[f2635,f39]) ).
fof(f15110,plain,
! [X0,X1] : zero = multiplication(domain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f62,f14987]) ).
fof(f15111,plain,
! [X0,X1] : zero = domain_difference(multiplication(X0,domain(X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f68,f15110]) ).
fof(f15113,plain,
! [X0,X1] : leq(antidomain(addition(X0,addition(one,X1))),zero),
inference(forward_demodulation,[status(thm)],[f103,f15049]) ).
fof(f15114,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(addition(addition(X1,X0),X2)),multiplication(X0,star(X1))),antidomain(addition(addition(X1,X0),X2)))
| ~ leq(zero,antidomain(addition(X0,addition(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f103,f15050]) ).
fof(f15115,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(addition(X0,addition(X1,X2))),multiplication(X0,star(X1))),antidomain(addition(addition(X1,X0),X2)))
| ~ leq(zero,antidomain(addition(X0,addition(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f103,f15114]) ).
fof(f15116,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(addition(X0,addition(X1,X2))),multiplication(X0,star(X1))),antidomain(addition(X0,addition(X1,X2))))
| ~ leq(zero,antidomain(addition(X0,addition(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f103,f15115]) ).
fof(f15117,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(addition(X0,addition(X1,X2))),multiplication(X0,star(X1))),antidomain(addition(X0,addition(X1,X2)))),
inference(forward_subsumption_resolution,[status(thm)],[f15116,f240]) ).
fof(f15121,plain,
! [X0,X1,X2] :
( zero != multiplication(antidomain(addition(addition(X1,X0),X2)),X0)
| leq(multiplication(antidomain(addition(X0,addition(X1,X2))),X1),multiplication(antidomain(addition(addition(X1,X0),X2)),X0)) ),
inference(forward_demodulation,[status(thm)],[f103,f15052]) ).
fof(f15122,plain,
! [X0,X1,X2] :
( zero != multiplication(antidomain(addition(addition(X1,X0),X2)),X0)
| leq(multiplication(antidomain(addition(X0,addition(X1,X2))),X1),multiplication(antidomain(addition(X0,addition(X1,X2))),X0)) ),
inference(forward_demodulation,[status(thm)],[f103,f15121]) ).
fof(f15123,plain,
! [X0,X1,X2] :
( zero != multiplication(antidomain(addition(addition(X1,X0),X2)),X0)
| leq(multiplication(antidomain(addition(X0,addition(X1,X2))),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f2635,f15122]) ).
fof(f15124,plain,
! [X0,X1,X2] :
( zero != multiplication(antidomain(addition(X0,addition(X1,X2))),X0)
| leq(multiplication(antidomain(addition(X0,addition(X1,X2))),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f103,f15123]) ).
fof(f15125,plain,
! [X0,X1,X2] :
( zero != zero
| leq(multiplication(antidomain(addition(X0,addition(X1,X2))),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f2635,f15124]) ).
fof(f15126,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(addition(X0,addition(X1,X2))),X1),zero),
inference(trivial_equality_resolution,[status(thm)],[f15125]) ).
fof(f15127,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X2)),multiplication(antidomain(addition(multiplication(X1,X2),X3)),X1))
| ~ leq(X0,multiplication(antidomain(addition(multiplication(X1,X2),X3)),X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f15053]) ).
fof(f15128,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(antidomain(addition(multiplication(X2,X1),X3)),X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f15054]) ).
fof(f15129,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(antidomain(addition(multiplication(X1,X2),X3)),X1)),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f37,f15055]) ).
fof(f15130,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(antidomain(addition(multiplication(X0,X1),X2)),X0),X3),X1) = multiplication(X3,X1),
inference(forward_demodulation,[status(thm)],[f80,f15056]) ).
fof(f15131,plain,
! [X0,X1] : forward_diamond(antidomain(addition(domain(X0),X1)),X0) = zero,
inference(forward_demodulation,[status(thm)],[f607,f15059]) ).
fof(f15136,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),zero)
| ~ leq(addition(multiplication(antidomain(addition(X0,X1)),multiplication(X0,X2)),X3),zero) ),
inference(forward_demodulation,[status(thm)],[f2635,f15066]) ).
fof(f15137,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X2)),multiplication(X1,antidomain(addition(X2,X3))))
| ~ leq(addition(zero,X0),multiplication(X1,antidomain(addition(X2,X3)))) ),
inference(forward_demodulation,[status(thm)],[f44,f15067]) ).
fof(f15138,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X2)),multiplication(X1,antidomain(addition(X2,X3))))
| ~ leq(X0,multiplication(X1,antidomain(addition(X2,X3)))) ),
inference(forward_demodulation,[status(thm)],[f80,f15137]) ).
fof(f15139,plain,
! [X0,X1] : leq(multiplication(antidomain(addition(X0,X1)),multiplication(X0,star(X0))),antidomain(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f15068,f240]) ).
fof(f15140,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),antidomain(addition(X1,X2)))
| ~ leq(X0,antidomain(addition(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f37,f15069]) ).
fof(f15145,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X2,antidomain(addition(X1,X3)))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f44,f15071]) ).
fof(f15146,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X2,antidomain(addition(X1,X3)))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f15145]) ).
fof(f15148,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(addition(X1,X2))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f15073]) ).
fof(f15161,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(X1,X2))) = addition(multiplication(addition(X1,antidomain(addition(X2,X3))),X2),X0),
inference(forward_demodulation,[status(thm)],[f97,f15076]) ).
fof(f15162,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,X2)) = addition(multiplication(addition(X1,antidomain(addition(X2,X3))),X2),X0),
inference(forward_demodulation,[status(thm)],[f80,f15161]) ).
fof(f15163,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),X2) = addition(multiplication(addition(antidomain(addition(X1,X3)),X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f80,f15077]) ).
fof(f15167,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(addition(X2,X3)))),X2) = addition(multiplication(X0,X2),zero),
inference(forward_demodulation,[status(thm)],[f44,f15079]) ).
fof(f15168,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(addition(X2,X3)))),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f37,f15167]) ).
fof(f15169,plain,
! [X0,X1,X2,X3] : multiplication(addition(antidomain(addition(X0,X1)),multiplication(X2,X3)),X0) = multiplication(X2,multiplication(X3,X0)),
inference(forward_demodulation,[status(thm)],[f80,f15080]) ).
fof(f15172,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),antidomain(addition(X2,X3))),X2) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f15082]) ).
fof(f15173,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(addition(X1,X2))),X3),X1) = addition(zero,multiplication(X3,X1)),
inference(forward_demodulation,[status(thm)],[f44,f15083]) ).
fof(f15174,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(addition(X1,X2))),X3),X1) = multiplication(X3,X1),
inference(forward_demodulation,[status(thm)],[f80,f15173]) ).
fof(f15175,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(addition(X0,X1)),X2),X0) = multiplication(X2,X0),
inference(forward_demodulation,[status(thm)],[f37,f15084]) ).
fof(f15176,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(addition(X1,X2))),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f15085]) ).
fof(f15177,plain,
! [X0,X1,X2,X3] : addition(zero,addition(X0,multiplication(antidomain(addition(X1,X2)),X3))) = addition(multiplication(antidomain(addition(X1,X2)),addition(X3,X1)),X0),
inference(forward_demodulation,[status(thm)],[f97,f15086]) ).
fof(f15178,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(antidomain(addition(X1,X2)),X3)) = addition(multiplication(antidomain(addition(X1,X2)),addition(X3,X1)),X0),
inference(forward_demodulation,[status(thm)],[f80,f15177]) ).
fof(f15179,plain,
! [X0,X1,X2,X3] : addition(multiplication(antidomain(addition(X0,X1)),X2),X3) = addition(multiplication(antidomain(addition(X0,X1)),addition(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f80,f15087]) ).
fof(f15180,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,one)) = antidomain(addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f37,f15088]) ).
fof(f15181,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(one,X0)) = antidomain(addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f37,f15089]) ).
fof(f15182,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,X2)) = multiplication(antidomain(addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f37,f15090]) ).
fof(f15183,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X2,X0)) = multiplication(antidomain(addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f15091]) ).
fof(f15186,plain,
! [X0,X1] : addition(one,coantidomain(multiplication(codomain(antidomain(addition(X0,X1))),X0))) = coantidomain(multiplication(codomain(antidomain(addition(X0,X1))),X0)),
inference(forward_demodulation,[status(thm)],[f696,f15094]) ).
fof(f15187,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(antidomain(addition(X0,X1))),X0)),
inference(forward_demodulation,[status(thm)],[f1377,f15186]) ).
fof(f15188,plain,
! [X0,X1] : addition(one,antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0)))) = antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f577,f15095]) ).
fof(f15189,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1379,f15188]) ).
fof(f15190,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X0,X2))),multiplication(star(antidomain(addition(X0,X2))),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f15096]) ).
fof(f15191,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),antidomain(addition(X1,X2)))
| ~ leq(X0,antidomain(addition(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f15097]) ).
fof(f15192,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(addition(X1,X2))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f15098]) ).
fof(f15193,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(addition(X1,X2))),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f15099]) ).
fof(f15194,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(addition(X0,X1)),X2),X0) = multiplication(X2,X0),
inference(forward_demodulation,[status(thm)],[f80,f15100]) ).
fof(f15195,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X2,X0)) = multiplication(antidomain(addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f37,f15101]) ).
fof(f15196,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,X2)) = multiplication(antidomain(addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f15102]) ).
fof(f15197,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),multiplication(X0,X2)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f15103]) ).
fof(f15198,plain,
! [X0,X1] : leq(multiplication(domain_difference(X0,X1),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f344,f6998]) ).
fof(f15199,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(forward_diamond(X0,X1),antidomain(X2)),star(X2)),antidomain(X2)),
inference(resolution,[status(thm)],[f344,f7010]) ).
fof(f15200,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(forward_box(X0,X1),antidomain(X2)),star(X2)),antidomain(X2)),
inference(resolution,[status(thm)],[f344,f6659]) ).
fof(f15201,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(backward_box(X0,X1),antidomain(X2)),star(X2)),antidomain(X2)),
inference(resolution,[status(thm)],[f344,f6658]) ).
fof(f15202,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(backward_diamond(X0,X1),antidomain(X2)),star(X2)),antidomain(X2)),
inference(resolution,[status(thm)],[f344,f6519]) ).
fof(f15203,plain,
! [X0,X1] : leq(multiplication(multiplication(coantidomain(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f344,f7158]) ).
fof(f15204,plain,
! [X0,X1] : leq(multiplication(multiplication(domain(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f344,f6808]) ).
fof(f15205,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f344,f6667]) ).
fof(f15206,plain,
! [X0,X1] : leq(multiplication(multiplication(c(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f344,f6526]) ).
fof(f15207,plain,
! [X0,X1] : leq(multiplication(multiplication(codomain(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f344,f6393]) ).
fof(f15208,plain,
! [X0,X1] : leq(multiplication(multiplication(divergence(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f344,f5965]) ).
fof(f15209,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(antidomain(X0),forward_diamond(X1,X2)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f4077]) ).
fof(f15210,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(antidomain(X0),forward_box(X1,X2)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f3741]) ).
fof(f15211,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(antidomain(X0),backward_box(X1,X2)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f3740]) ).
fof(f15212,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(antidomain(X0),backward_diamond(X1,X2)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f3497]) ).
fof(f15213,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),coantidomain(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f4627]) ).
fof(f15214,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),domain(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f3841]) ).
fof(f15215,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),antidomain(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f3749]) ).
fof(f15216,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),c(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f3652]) ).
fof(f15217,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),codomain(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f3411]) ).
fof(f15218,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),divergence(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f3330]) ).
fof(f15219,plain,
! [X0] : leq(multiplication(c(X0),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f13625]) ).
fof(f15220,plain,
! [X0] : leq(multiplication(domain(X0),star(c(X0))),antidomain(c(X0))),
inference(resolution,[status(thm)],[f344,f4249]) ).
fof(f15222,plain,
! [X0] : leq(multiplication(antidomain(X0),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f344,f239]) ).
fof(f15223,plain,
! [X0,X1] :
( leq(multiplication(X0,star(star(X1))),antidomain(star(X1)))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f8455,f344]) ).
fof(f15225,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(domain(X1)))
| ~ leq(X0,c(X1)) ),
inference(paramodulation,[status(thm)],[f67,f344]) ).
fof(f15226,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),antidomain(antidomain(X1)))
| ~ leq(X0,domain(X1)) ),
inference(paramodulation,[status(thm)],[f62,f344]) ).
fof(f15228,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),multiplication(antidomain(X2),star(X2))),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f39,f15199]) ).
fof(f15229,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),multiplication(antidomain(X2),star(X2))),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f39,f15200]) ).
fof(f15230,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),multiplication(antidomain(X2),star(X2))),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f39,f15201]) ).
fof(f15231,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),multiplication(antidomain(X2),star(X2))),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f39,f15202]) ).
fof(f15232,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f39,f15203]) ).
fof(f15233,plain,
! [X0,X1] : leq(multiplication(domain(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f39,f15204]) ).
fof(f15234,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f39,f15205]) ).
fof(f15235,plain,
! [X0,X1] : leq(multiplication(c(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f39,f15206]) ).
fof(f15236,plain,
! [X0,X1] : leq(multiplication(codomain(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f39,f15207]) ).
fof(f15237,plain,
! [X0,X1] : leq(multiplication(divergence(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f39,f15208]) ).
fof(f15238,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),multiplication(forward_diamond(X1,X2),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15209]) ).
fof(f15239,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),multiplication(forward_box(X1,X2),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15210]) ).
fof(f15240,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),multiplication(backward_box(X1,X2),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15211]) ).
fof(f15241,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),multiplication(backward_diamond(X1,X2),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15212]) ).
fof(f15242,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(coantidomain(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15213]) ).
fof(f15243,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(domain(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15214]) ).
fof(f15244,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(antidomain(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15215]) ).
fof(f15245,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(c(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15216]) ).
fof(f15246,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(codomain(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15217]) ).
fof(f15247,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(divergence(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f15218]) ).
fof(f15249,plain,
! [X0,X1] :
( leq(multiplication(X0,star(star(X1))),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f8455,f15223]) ).
fof(f15252,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f67,f15225]) ).
fof(f15253,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f62,f15226]) ).
fof(f15287,plain,
! [X0] : zero = antidomain(addition(X0,one)),
inference(paramodulation,[status(thm)],[f1026,f14970]) ).
fof(f15290,plain,
! [X0,X1] : zero = antidomain(addition(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f97,f14970]) ).
fof(f15291,plain,
! [X0,X1] : zero = antidomain(addition(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f97,f14970]) ).
fof(f15297,plain,
! [X0,X1] :
( leq(multiplication(X0,star(addition(one,X1))),antidomain(addition(one,X1)))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f14970,f344]) ).
fof(f15298,plain,
! [X0] : forward_box(c(addition(one,X0)),zero) = one,
inference(paramodulation,[status(thm)],[f14970,f14887]) ).
fof(f15299,plain,
! [X0] : leq(c(addition(one,X0)),zero),
inference(paramodulation,[status(thm)],[f14970,f13625]) ).
fof(f15300,plain,
! [X0] : c(addition(one,X0)) = multiplication(c(addition(one,X0)),zero),
inference(paramodulation,[status(thm)],[f14970,f2633]) ).
fof(f15305,plain,
! [X0,X1] : leq(domain_difference(X0,addition(one,X1)),zero),
inference(paramodulation,[status(thm)],[f14970,f6998]) ).
fof(f15322,plain,
! [X0,X1] : domain_difference(X0,addition(one,X1)) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f14970,f68]) ).
fof(f15323,plain,
! [X0] : addition(zero,domain(addition(one,X0))) = one,
inference(paramodulation,[status(thm)],[f14970,f558]) ).
fof(f15324,plain,
! [X0] : antidomain(c(addition(one,X0))) = c(zero),
inference(paramodulation,[status(thm)],[f14970,f547]) ).
fof(f15329,plain,
! [X0,X1] :
( leq(multiplication(X0,star(addition(one,X1))),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f14970,f15297]) ).
fof(f15330,plain,
! [X0] : c(addition(one,X0)) = zero,
inference(forward_demodulation,[status(thm)],[f44,f15300]) ).
fof(f15344,plain,
! [X0,X1] : domain_difference(X0,addition(one,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f44,f15322]) ).
fof(f15345,plain,
! [X0] : domain(addition(one,X0)) = one,
inference(forward_demodulation,[status(thm)],[f80,f15323]) ).
fof(f15346,plain,
! [X0] : antidomain(c(addition(one,X0))) = one,
inference(forward_demodulation,[status(thm)],[f597,f15324]) ).
fof(f15351,plain,
! [X0,X1] : zero = antidomain(addition(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f103,f15287]) ).
fof(f15352,plain,
! [X0,X1] : zero = antidomain(addition(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f36,f15287]) ).
fof(f15359,plain,
! [X0,X1] :
( leq(multiplication(X0,star(addition(X1,one))),antidomain(addition(X1,one)))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f15287,f344]) ).
fof(f15360,plain,
! [X0] : forward_box(c(addition(X0,one)),zero) = one,
inference(paramodulation,[status(thm)],[f15287,f14887]) ).
fof(f15361,plain,
! [X0] : leq(c(addition(X0,one)),zero),
inference(paramodulation,[status(thm)],[f15287,f13625]) ).
fof(f15362,plain,
! [X0] : c(addition(X0,one)) = multiplication(c(addition(X0,one)),zero),
inference(paramodulation,[status(thm)],[f15287,f2633]) ).
fof(f15367,plain,
! [X0,X1] : leq(domain_difference(X0,addition(X1,one)),zero),
inference(paramodulation,[status(thm)],[f15287,f6998]) ).
fof(f15384,plain,
! [X0,X1] : domain_difference(X0,addition(X1,one)) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f15287,f68]) ).
fof(f15385,plain,
! [X0] : addition(zero,domain(addition(X0,one))) = one,
inference(paramodulation,[status(thm)],[f15287,f558]) ).
fof(f15386,plain,
! [X0] : antidomain(c(addition(X0,one))) = c(zero),
inference(paramodulation,[status(thm)],[f15287,f547]) ).
fof(f15391,plain,
! [X0,X1] :
( leq(multiplication(X0,star(addition(X1,one))),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f15287,f15359]) ).
fof(f15392,plain,
! [X0] : c(addition(X0,one)) = zero,
inference(forward_demodulation,[status(thm)],[f44,f15362]) ).
fof(f15406,plain,
! [X0,X1] : domain_difference(X0,addition(X1,one)) = zero,
inference(forward_demodulation,[status(thm)],[f44,f15384]) ).
fof(f15407,plain,
! [X0] : domain(addition(X0,one)) = one,
inference(forward_demodulation,[status(thm)],[f80,f15385]) ).
fof(f15408,plain,
! [X0] : antidomain(c(addition(X0,one))) = one,
inference(forward_demodulation,[status(thm)],[f597,f15386]) ).
fof(f15519,plain,
! [X0,X1] : c(addition(X0,addition(X1,one))) = zero,
inference(paramodulation,[status(thm)],[f97,f15330]) ).
fof(f15520,plain,
! [X0,X1] : c(addition(X0,addition(one,X1))) = zero,
inference(paramodulation,[status(thm)],[f97,f15330]) ).
fof(f15528,plain,
! [X0] : forward_box(antidomain(zero),addition(one,X0)) = one,
inference(paramodulation,[status(thm)],[f15330,f14241]) ).
fof(f15530,plain,
! [X0] : leq(antidomain(zero),domain(addition(one,X0))),
inference(paramodulation,[status(thm)],[f15330,f13956]) ).
fof(f15555,plain,
! [X0,X1] : backward_box(X0,addition(one,X1)) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f15330,f72]) ).
fof(f15556,plain,
! [X0,X1] : forward_box(X0,addition(one,X1)) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f15330,f71]) ).
fof(f15560,plain,
! [X0] : forward_box(one,addition(one,X0)) = one,
inference(forward_demodulation,[status(thm)],[f577,f15528]) ).
fof(f15561,plain,
! [X0] : leq(one,domain(addition(one,X0))),
inference(forward_demodulation,[status(thm)],[f577,f15530]) ).
fof(f15582,plain,
! [X0,X1] : backward_box(X0,addition(one,X1)) = c(zero),
inference(forward_demodulation,[status(thm)],[f809,f15555]) ).
fof(f15583,plain,
! [X0,X1] : backward_box(X0,addition(one,X1)) = one,
inference(forward_demodulation,[status(thm)],[f597,f15582]) ).
fof(f15584,plain,
! [X0,X1] : forward_box(X0,addition(one,X1)) = c(zero),
inference(forward_demodulation,[status(thm)],[f776,f15556]) ).
fof(f15585,plain,
! [X0,X1] : forward_box(X0,addition(one,X1)) = one,
inference(forward_demodulation,[status(thm)],[f597,f15584]) ).
fof(f15619,plain,
! [X0,X1] : domain(addition(X0,addition(X1,one))) = one,
inference(paramodulation,[status(thm)],[f97,f15345]) ).
fof(f15620,plain,
! [X0,X1] : domain(addition(X0,addition(one,X1))) = one,
inference(paramodulation,[status(thm)],[f97,f15345]) ).
fof(f15641,plain,
! [X0,X1] : leq(domain_difference(addition(one,X0),X1),one),
inference(paramodulation,[status(thm)],[f15345,f3834]) ).
fof(f15647,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),one)) != addition(forward_diamond(X1,domain(X0)),domain(addition(one,X2))) ),
inference(paramodulation,[status(thm)],[f15345,f75]) ).
fof(f15648,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(addition(one,X0)),addition(forward_diamond(X1,one),domain(X2))) != addition(forward_diamond(X1,domain(addition(one,X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f15345,f75]) ).
fof(f15649,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X1)),addition(divergence(X0),forward_diamond(star(X0),domain(X2)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X2)))
| addition(one,addition(forward_diamond(X0,domain(addition(one,X1))),domain(X2))) != addition(forward_diamond(X0,domain(addition(one,X1))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f15345,f75]) ).
fof(f15650,plain,
! [X0,X1] : forward_diamond(X0,addition(one,X1)) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f15345,f69]) ).
fof(f15651,plain,
! [X0,X1] : domain_difference(addition(one,X0),X1) = multiplication(one,antidomain(X1)),
inference(paramodulation,[status(thm)],[f15345,f68]) ).
fof(f15653,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,addition(one,X1))),antidomain(multiplication(X0,one))) = antidomain(multiplication(X0,domain(addition(one,X1)))),
inference(paramodulation,[status(thm)],[f15345,f479]) ).
fof(f15678,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(forward_diamond(X1,domain(X0)),domain(addition(one,X2))) ),
inference(forward_demodulation,[status(thm)],[f97,f15647]) ).
fof(f15679,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(forward_diamond(X1,domain(X0)),one) ),
inference(forward_demodulation,[status(thm)],[f15345,f15678]) ).
fof(f15680,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(one,forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f15679]) ).
fof(f15681,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f1485,f15680]) ).
fof(f15682,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f15345,f15681]) ).
fof(f15683,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),domain(star(X1)))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f777,f15682]) ).
fof(f15684,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),one)) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f15683]) ).
fof(f15685,plain,
! [X0,X1,X2] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(one,X2))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f97,f15684]) ).
fof(f15686,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f15345,f15685]) ).
fof(f15687,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),domain(star(X1)))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f777,f15686]) ).
fof(f15688,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),one)
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f15687]) ).
fof(f15689,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(one,divergence(X1))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f35,f15688]) ).
fof(f15690,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = one
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f1488,f15689]) ).
fof(f15691,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(addition(one,X2))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15345,f15648]) ).
fof(f15692,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,domain(addition(one,X2))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f15691]) ).
fof(f15693,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15345,f15692]) ).
fof(f15694,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f15693]) ).
fof(f15695,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15345,f15694]) ).
fof(f15696,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(addition(one,X2))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15345,f15649]) ).
fof(f15697,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,domain(addition(one,X2))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f15696]) ).
fof(f15698,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15345,f15697]) ).
fof(f15699,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X2)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f15698]) ).
fof(f15700,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15345,f15699]) ).
fof(f15701,plain,
! [X0,X1] : forward_diamond(X0,addition(one,X1)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f40,f15650]) ).
fof(f15702,plain,
! [X0,X1] : domain_difference(addition(one,X0),X1) = antidomain(X1),
inference(forward_demodulation,[status(thm)],[f41,f15651]) ).
fof(f15704,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,one)),antidomain(multiplication(X0,addition(one,X1)))) = antidomain(multiplication(X0,domain(addition(one,X1)))),
inference(forward_demodulation,[status(thm)],[f35,f15653]) ).
fof(f15705,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(one,X1)))) = antidomain(multiplication(X0,domain(addition(one,X1)))),
inference(forward_demodulation,[status(thm)],[f40,f15704]) ).
fof(f15706,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(one,X1)))) = antidomain(multiplication(X0,one)),
inference(forward_demodulation,[status(thm)],[f15345,f15705]) ).
fof(f15707,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(one,X1)))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f40,f15706]) ).
fof(f15713,plain,
! [X0] :
( leq(multiplication(multiplication(star(X0),addition(X0,one)),star(one)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7789,f335]) ).
fof(f15714,plain,
! [X0] :
( leq(multiplication(multiplication(addition(X0,one),star(X0)),star(one)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7510,f335]) ).
fof(f15715,plain,
! [X0,X1] :
( leq(multiplication(backward_diamond(X0,X1),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1504,f335]) ).
fof(f15716,plain,
! [X0,X1] :
( leq(multiplication(forward_box(X0,X1),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1497,f335]) ).
fof(f15717,plain,
! [X0,X1] :
( leq(multiplication(backward_box(X0,X1),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1492,f335]) ).
fof(f15718,plain,
! [X0,X1] :
( leq(multiplication(forward_diamond(X0,X1),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1485,f335]) ).
fof(f15719,plain,
! [X0] :
( leq(multiplication(divergence(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1488,f335]) ).
fof(f15720,plain,
! [X0] :
( leq(multiplication(codomain(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1477,f335]) ).
fof(f15721,plain,
! [X0] :
( leq(multiplication(c(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1471,f335]) ).
fof(f15722,plain,
! [X0] :
( leq(multiplication(antidomain(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1379,f335]) ).
fof(f15723,plain,
! [X0] :
( leq(multiplication(coantidomain(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1377,f335]) ).
fof(f15724,plain,
! [X0] :
( leq(multiplication(domain(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1375,f335]) ).
fof(f15725,plain,
! [X0] :
( leq(multiplication(c(X0),star(domain(X0))),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f569,f335]) ).
fof(f15726,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(multiplication(codomain(X0),X1)),star(coantidomain(multiplication(X0,X1)))),one)
| ~ leq(coantidomain(multiplication(codomain(X0),X1)),one) ),
inference(paramodulation,[status(thm)],[f615,f335]) ).
fof(f15727,plain,
! [X0] :
( leq(multiplication(codomain(X0),star(coantidomain(X0))),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f683,f335]) ).
fof(f15728,plain,
! [X0,X1] :
( leq(multiplication(antidomain(multiplication(X0,domain(X1))),star(antidomain(multiplication(X0,X1)))),one)
| ~ leq(antidomain(multiplication(X0,domain(X1))),one) ),
inference(paramodulation,[status(thm)],[f479,f335]) ).
fof(f15729,plain,
! [X0] :
( leq(multiplication(c(X0),star(antidomain(X0))),one)
| ~ leq(c(X0),one) ),
inference(paramodulation,[status(thm)],[f514,f335]) ).
fof(f15730,plain,
! [X0] :
( leq(multiplication(domain(X0),star(antidomain(X0))),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f558,f335]) ).
fof(f15731,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X2,X3),star(multiplication(X0,multiplication(X1,X3)))),one)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),one) ),
inference(paramodulation,[status(thm)],[f204,f335]) ).
fof(f15732,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(multiplication(X1,X2),X3),star(multiplication(X0,X2))),one)
| ~ leq(addition(multiplication(addition(X0,X1),X2),X3),one) ),
inference(paramodulation,[status(thm)],[f219,f335]) ).
fof(f15733,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(multiplication(X0,X2),X3),star(multiplication(X0,X1))),one)
| ~ leq(addition(multiplication(X0,addition(X1,X2)),X3),one) ),
inference(paramodulation,[status(thm)],[f170,f335]) ).
fof(f15734,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X1,multiplication(X2,X3)),star(multiplication(X0,X3))),one)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),one) ),
inference(paramodulation,[status(thm)],[f211,f335]) ).
fof(f15735,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(multiplication(X1,X2))),one)
| ~ leq(multiplication(addition(X0,X1),X2),one) ),
inference(paramodulation,[status(thm)],[f201,f335]) ).
fof(f15736,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),star(multiplication(X0,X2))),one)
| ~ leq(multiplication(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f153,f335]) ).
fof(f15737,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X1,X2),star(multiplication(X0,X2))),one)
| ~ leq(multiplication(addition(X0,X1),X2),one) ),
inference(paramodulation,[status(thm)],[f43,f335]) ).
fof(f15738,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(multiplication(X0,X1))),one)
| ~ leq(multiplication(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f42,f335]) ).
fof(f15739,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,X0))),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f103,f335]) ).
fof(f15740,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X0,X1))),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f36,f335]) ).
fof(f15742,plain,
! [X0,X1] :
( leq(multiplication(multiplication(domain(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4516,f335]) ).
fof(f15743,plain,
! [X0,X1] :
( leq(multiplication(multiplication(coantidomain(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4515,f335]) ).
fof(f15744,plain,
! [X0,X1] :
( leq(multiplication(multiplication(antidomain(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4514,f335]) ).
fof(f15745,plain,
! [X0,X1] :
( leq(multiplication(multiplication(c(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4513,f335]) ).
fof(f15746,plain,
! [X0,X1] :
( leq(multiplication(multiplication(codomain(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4512,f335]) ).
fof(f15747,plain,
! [X0,X1] :
( leq(multiplication(multiplication(divergence(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4511,f335]) ).
fof(f15748,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,forward_diamond(X1,X2)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2491,f335]) ).
fof(f15749,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,backward_box(X1,X2)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2490,f335]) ).
fof(f15750,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,forward_box(X1,X2)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2489,f335]) ).
fof(f15751,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,backward_diamond(X1,X2)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2488,f335]) ).
fof(f15752,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,domain(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2497,f335]) ).
fof(f15753,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,coantidomain(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2496,f335]) ).
fof(f15754,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,antidomain(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2495,f335]) ).
fof(f15755,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,c(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2494,f335]) ).
fof(f15756,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,codomain(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2493,f335]) ).
fof(f15757,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,divergence(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2492,f335]) ).
fof(f15758,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),one)
| ~ leq(multiplication(addition(X0,one),X1),one) ),
inference(paramodulation,[status(thm)],[f232,f335]) ).
fof(f15760,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X0)),one)
| ~ leq(multiplication(X0,addition(X1,one)),one) ),
inference(paramodulation,[status(thm)],[f192,f335]) ).
fof(f15761,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X0)),one)
| ~ leq(multiplication(X0,addition(one,X1)),one) ),
inference(paramodulation,[status(thm)],[f162,f335]) ).
fof(f15762,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,X0),star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1329,f335]) ).
fof(f15763,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,X0),star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1026,f335]) ).
fof(f15764,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,X1),star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1005,f335]) ).
fof(f15765,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,X1),star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f105,f335]) ).
fof(f15766,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,X1),star(X2)),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f97,f335]) ).
fof(f15767,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X2,X0),star(X1)),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f97,f335]) ).
fof(f15769,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f35,f335]) ).
fof(f15770,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f35,f335]) ).
fof(f15771,plain,
! [X0] :
( leq(multiplication(X0,star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f38,f335]) ).
fof(f15773,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(addition(X0,one),star(one))),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15713]) ).
fof(f15774,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(addition(X0,one),one)),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f9603,f15773]) ).
fof(f15775,plain,
! [X0] :
( leq(multiplication(star(X0),addition(one,multiplication(X0,one))),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f232,f15774]) ).
fof(f15776,plain,
! [X0] :
( leq(multiplication(star(X0),addition(one,X0)),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f40,f15775]) ).
fof(f15777,plain,
! [X0] :
( leq(multiplication(addition(X0,one),multiplication(star(X0),star(one))),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15714]) ).
fof(f15778,plain,
! [X0] :
( leq(multiplication(addition(X0,one),multiplication(star(X0),one)),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f9603,f15777]) ).
fof(f15779,plain,
! [X0] :
( leq(multiplication(addition(X0,one),star(X0)),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f40,f15778]) ).
fof(f15780,definition,
! [X0,X1] :
( sQ30_spl
<=> leq(multiplication(backward_diamond(X0,X1),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f15783,plain,
( sQ30_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15715,f9301,f15780]) ).
fof(f15784,definition,
! [X0,X1] :
( sQ31_spl
<=> leq(multiplication(forward_box(X0,X1),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f15787,plain,
( sQ31_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15716,f9301,f15784]) ).
fof(f15788,definition,
! [X0,X1] :
( sQ32_spl
<=> leq(multiplication(backward_box(X0,X1),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f15791,plain,
( sQ32_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15717,f9301,f15788]) ).
fof(f15792,definition,
! [X0,X1] :
( sQ33_spl
<=> leq(multiplication(forward_diamond(X0,X1),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f15795,plain,
( sQ33_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15718,f9301,f15792]) ).
fof(f15796,definition,
! [X0] :
( sQ34_spl
<=> leq(multiplication(divergence(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f15799,plain,
( sQ34_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15719,f9301,f15796]) ).
fof(f15800,definition,
! [X0] :
( sQ35_spl
<=> leq(multiplication(codomain(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f15803,plain,
( sQ35_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15720,f9301,f15800]) ).
fof(f15804,definition,
! [X0] :
( sQ36_spl
<=> leq(multiplication(c(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f15807,plain,
( sQ36_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15721,f9301,f15804]) ).
fof(f15808,definition,
! [X0] :
( sQ37_spl
<=> leq(multiplication(antidomain(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f15811,plain,
( sQ37_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15722,f9301,f15808]) ).
fof(f15812,definition,
! [X0] :
( sQ38_spl
<=> leq(multiplication(coantidomain(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f15815,plain,
( sQ38_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15723,f9301,f15812]) ).
fof(f15816,definition,
! [X0] :
( sQ39_spl
<=> leq(multiplication(domain(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f15819,plain,
( sQ39_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15724,f9301,f15816]) ).
fof(f15820,definition,
! [X0] :
( sQ40_spl
<=> leq(multiplication(c(X0),star(domain(X0))),one) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f15821,plain,
! [X0] :
( ~ sQ40_spl
| leq(multiplication(c(X0),star(domain(X0))),one) ),
inference(component_clause,[status(thm)],[f15820]) ).
fof(f15823,plain,
( sQ40_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15725,f9301,f15820]) ).
fof(f15824,plain,
! [X0,X1] : leq(multiplication(coantidomain(multiplication(codomain(X0),X1)),star(coantidomain(multiplication(X0,X1)))),one),
inference(forward_subsumption_resolution,[status(thm)],[f15726,f1410]) ).
fof(f15825,definition,
! [X0] :
( sQ41_spl
<=> leq(multiplication(codomain(X0),star(coantidomain(X0))),one) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f15826,plain,
! [X0] :
( ~ sQ41_spl
| leq(multiplication(codomain(X0),star(coantidomain(X0))),one) ),
inference(component_clause,[status(thm)],[f15825]) ).
fof(f15828,plain,
( sQ41_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15727,f9301,f15825]) ).
fof(f15829,plain,
! [X0,X1] : leq(multiplication(antidomain(multiplication(X0,domain(X1))),star(antidomain(multiplication(X0,X1)))),one),
inference(forward_subsumption_resolution,[status(thm)],[f15728,f1412]) ).
fof(f15830,plain,
! [X0] : leq(multiplication(c(X0),star(antidomain(X0))),one),
inference(forward_subsumption_resolution,[status(thm)],[f15729,f1430]) ).
fof(f15831,definition,
! [X0] :
( sQ42_spl
<=> leq(multiplication(domain(X0),star(antidomain(X0))),one) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f15832,plain,
! [X0] :
( ~ sQ42_spl
| leq(multiplication(domain(X0),star(antidomain(X0))),one) ),
inference(component_clause,[status(thm)],[f15831]) ).
fof(f15834,plain,
( sQ42_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15730,f9301,f15831]) ).
fof(f15835,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X2,multiplication(X3,star(multiplication(X0,multiplication(X1,X3))))),one)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15731]) ).
fof(f15836,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(multiplication(X2,X3),star(multiplication(X0,X3)))),one)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15734]) ).
fof(f15837,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(X2,multiplication(X3,star(multiplication(X0,X3))))),one)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15836]) ).
fof(f15838,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(multiplication(X1,X2)))),one)
| ~ leq(multiplication(addition(X0,X1),X2),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15735]) ).
fof(f15839,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(multiplication(X0,X2)))),one)
| ~ leq(multiplication(X0,addition(X1,X2)),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15736]) ).
fof(f15840,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,star(multiplication(X0,X2)))),one)
| ~ leq(multiplication(addition(X0,X1),X2),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15737]) ).
fof(f15841,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(multiplication(X0,X1)))),one)
| ~ leq(multiplication(X0,addition(X1,X2)),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15738]) ).
fof(f15843,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15742]) ).
fof(f15844,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15743]) ).
fof(f15845,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15744]) ).
fof(f15846,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15745]) ).
fof(f15847,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15746]) ).
fof(f15848,plain,
! [X0,X1] :
( leq(multiplication(divergence(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15747]) ).
fof(f15849,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(forward_diamond(X1,X2),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15748]) ).
fof(f15850,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(backward_box(X1,X2),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15749]) ).
fof(f15851,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(forward_box(X1,X2),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15750]) ).
fof(f15852,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(backward_diamond(X1,X2),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15751]) ).
fof(f15853,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(domain(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15752]) ).
fof(f15854,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(coantidomain(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15753]) ).
fof(f15855,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(antidomain(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15754]) ).
fof(f15856,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(c(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15755]) ).
fof(f15857,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(codomain(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15756]) ).
fof(f15858,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(divergence(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f15757]) ).
fof(f15859,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),one)
| ~ leq(multiplication(addition(X0,one),X1),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15758]) ).
fof(f15861,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X0))),one)
| ~ leq(multiplication(X0,addition(X1,one)),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15760]) ).
fof(f15862,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X0))),one)
| ~ leq(multiplication(X0,addition(one,X1)),one) ),
inference(forward_demodulation,[status(thm)],[f39,f15761]) ).
fof(f15886,plain,
! [X0,X1] : c(addition(X0,addition(X1,one))) = zero,
inference(paramodulation,[status(thm)],[f103,f15392]) ).
fof(f15887,plain,
! [X0,X1] : c(addition(X0,addition(X1,one))) = zero,
inference(paramodulation,[status(thm)],[f36,f15392]) ).
fof(f15896,plain,
! [X0] : forward_box(antidomain(zero),addition(X0,one)) = one,
inference(paramodulation,[status(thm)],[f15392,f14241]) ).
fof(f15898,plain,
! [X0] : leq(antidomain(zero),domain(addition(X0,one))),
inference(paramodulation,[status(thm)],[f15392,f13956]) ).
fof(f15923,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f15392,f72]) ).
fof(f15924,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f15392,f71]) ).
fof(f15928,plain,
! [X0] : forward_box(one,addition(X0,one)) = one,
inference(forward_demodulation,[status(thm)],[f577,f15896]) ).
fof(f15929,plain,
! [X0] : leq(one,domain(addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f577,f15898]) ).
fof(f15950,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = c(zero),
inference(forward_demodulation,[status(thm)],[f809,f15923]) ).
fof(f15951,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = one,
inference(forward_demodulation,[status(thm)],[f597,f15950]) ).
fof(f15952,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = c(zero),
inference(forward_demodulation,[status(thm)],[f776,f15924]) ).
fof(f15953,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = one,
inference(forward_demodulation,[status(thm)],[f597,f15952]) ).
fof(f15955,plain,
! [X0,X1] : domain(addition(X0,addition(X1,one))) = one,
inference(paramodulation,[status(thm)],[f103,f15407]) ).
fof(f15956,plain,
! [X0,X1] : domain(addition(X0,addition(X1,one))) = one,
inference(paramodulation,[status(thm)],[f36,f15407]) ).
fof(f15978,plain,
! [X0,X1] : leq(domain_difference(addition(X0,one),X1),one),
inference(paramodulation,[status(thm)],[f15407,f3834]) ).
fof(f15984,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),one)) != addition(forward_diamond(X1,domain(X0)),domain(addition(X2,one))) ),
inference(paramodulation,[status(thm)],[f15407,f75]) ).
fof(f15985,plain,
! [X0,X1,X2] :
( addition(domain(addition(X0,one)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(addition(X0,one)),addition(forward_diamond(X1,one),domain(X2))) != addition(forward_diamond(X1,domain(addition(X0,one))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f15407,f75]) ).
fof(f15986,plain,
! [X0,X1,X2] :
( addition(domain(addition(X1,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X2)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X2)))
| addition(one,addition(forward_diamond(X0,domain(addition(X1,one))),domain(X2))) != addition(forward_diamond(X0,domain(addition(X1,one))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f15407,f75]) ).
fof(f15987,plain,
! [X0,X1] : forward_diamond(X0,addition(X1,one)) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f15407,f69]) ).
fof(f15988,plain,
! [X0,X1] : domain_difference(addition(X0,one),X1) = multiplication(one,antidomain(X1)),
inference(paramodulation,[status(thm)],[f15407,f68]) ).
fof(f15990,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,addition(X1,one))),antidomain(multiplication(X0,one))) = antidomain(multiplication(X0,domain(addition(X1,one)))),
inference(paramodulation,[status(thm)],[f15407,f479]) ).
fof(f16015,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(forward_diamond(X1,domain(X0)),domain(addition(X2,one))) ),
inference(forward_demodulation,[status(thm)],[f97,f15984]) ).
fof(f16016,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(forward_diamond(X1,domain(X0)),one) ),
inference(forward_demodulation,[status(thm)],[f15407,f16015]) ).
fof(f16017,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != addition(one,forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f16016]) ).
fof(f16018,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f1485,f16017]) ).
fof(f16019,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f15407,f16018]) ).
fof(f16020,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),domain(star(X1)))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f777,f16019]) ).
fof(f16021,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),one)) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f16020]) ).
fof(f16022,plain,
! [X0,X1,X2] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),domain(addition(X2,one))))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f97,f16021]) ).
fof(f16023,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f15407,f16022]) ).
fof(f16024,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),domain(star(X1)))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f777,f16023]) ).
fof(f16025,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),one)
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f16024]) ).
fof(f16026,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(one,divergence(X1))
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f35,f16025]) ).
fof(f16027,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = one
| addition(one,addition(domain(X0),forward_diamond(X1,domain(X0)))) != one ),
inference(forward_demodulation,[status(thm)],[f1488,f16026]) ).
fof(f16028,plain,
! [X0,X1,X2] :
( addition(domain(addition(X2,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(addition(X2,one))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15407,f15985]) ).
fof(f16029,plain,
! [X0,X1,X2] :
( addition(domain(addition(X2,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,domain(addition(X2,one))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f16028]) ).
fof(f16030,plain,
! [X0,X1,X2] :
( addition(domain(addition(X2,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15407,f16029]) ).
fof(f16031,plain,
! [X0,X1,X2] :
( addition(domain(addition(X2,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f16030]) ).
fof(f16032,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15407,f16031]) ).
fof(f16033,plain,
! [X0,X1,X2] :
( addition(domain(addition(X2,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,domain(addition(X2,one))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15407,f15986]) ).
fof(f16034,plain,
! [X0,X1,X2] :
( addition(domain(addition(X2,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,domain(addition(X2,one))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f16033]) ).
fof(f16035,plain,
! [X0,X1,X2] :
( addition(domain(addition(X2,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15407,f16034]) ).
fof(f16036,plain,
! [X0,X1,X2] :
( addition(domain(addition(X2,one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f16035]) ).
fof(f16037,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f15407,f16036]) ).
fof(f16038,plain,
! [X0,X1] : forward_diamond(X0,addition(X1,one)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f40,f15987]) ).
fof(f16039,plain,
! [X0,X1] : domain_difference(addition(X0,one),X1) = antidomain(X1),
inference(forward_demodulation,[status(thm)],[f41,f15988]) ).
fof(f16041,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,one)),antidomain(multiplication(X0,addition(X1,one)))) = antidomain(multiplication(X0,domain(addition(X1,one)))),
inference(forward_demodulation,[status(thm)],[f35,f15990]) ).
fof(f16042,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(X1,one)))) = antidomain(multiplication(X0,domain(addition(X1,one)))),
inference(forward_demodulation,[status(thm)],[f40,f16041]) ).
fof(f16043,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(X1,one)))) = antidomain(multiplication(X0,one)),
inference(forward_demodulation,[status(thm)],[f15407,f16042]) ).
fof(f16044,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(X1,one)))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f40,f16043]) ).
fof(f16049,plain,
! [X0,X1] :
( leq(multiplication(multiplication(domain(X1),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4516,f336]) ).
fof(f16050,plain,
! [X0,X1] :
( leq(multiplication(multiplication(coantidomain(X1),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4515,f336]) ).
fof(f16051,plain,
! [X0,X1] :
( leq(multiplication(multiplication(antidomain(X1),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4514,f336]) ).
fof(f16052,plain,
! [X0,X1] :
( leq(multiplication(multiplication(c(X1),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4513,f336]) ).
fof(f16053,plain,
! [X0,X1] :
( leq(multiplication(multiplication(codomain(X1),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4512,f336]) ).
fof(f16054,plain,
! [X0,X1] :
( leq(multiplication(multiplication(divergence(X1),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4511,f336]) ).
fof(f16055,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(omega(X0),forward_diamond(X1,X2)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2491,f336]) ).
fof(f16056,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(omega(X0),backward_box(X1,X2)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2490,f336]) ).
fof(f16057,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(omega(X0),forward_box(X1,X2)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2489,f336]) ).
fof(f16058,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(omega(X0),backward_diamond(X1,X2)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2488,f336]) ).
fof(f16059,plain,
! [X0,X1] :
( leq(multiplication(multiplication(omega(X0),domain(X1)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2497,f336]) ).
fof(f16060,plain,
! [X0,X1] :
( leq(multiplication(multiplication(omega(X0),coantidomain(X1)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2496,f336]) ).
fof(f16061,plain,
! [X0,X1] :
( leq(multiplication(multiplication(omega(X0),antidomain(X1)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2495,f336]) ).
fof(f16062,plain,
! [X0,X1] :
( leq(multiplication(multiplication(omega(X0),c(X1)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2494,f336]) ).
fof(f16063,plain,
! [X0,X1] :
( leq(multiplication(multiplication(omega(X0),codomain(X1)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2493,f336]) ).
fof(f16064,plain,
! [X0,X1] :
( leq(multiplication(multiplication(omega(X0),divergence(X1)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f2492,f336]) ).
fof(f16065,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,omega(X1)),star(omega(X1))),X1)
| ~ leq(multiplication(addition(X0,one),omega(X1)),X1) ),
inference(paramodulation,[status(thm)],[f232,f336]) ).
fof(f16066,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,omega(X1)),star(omega(X1))),X1)
| ~ leq(multiplication(addition(one,X0),omega(X1)),X1) ),
inference(paramodulation,[status(thm)],[f207,f336]) ).
fof(f16067,plain,
! [X0,X1] :
( leq(multiplication(multiplication(omega(X0),X1),star(omega(X0))),X0)
| ~ leq(multiplication(omega(X0),addition(X1,one)),X0) ),
inference(paramodulation,[status(thm)],[f192,f336]) ).
fof(f16068,plain,
! [X0,X1] :
( leq(multiplication(multiplication(omega(X0),X1),star(omega(X0))),X0)
| ~ leq(multiplication(omega(X0),addition(one,X1)),X0) ),
inference(paramodulation,[status(thm)],[f162,f336]) ).
fof(f16069,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,omega(X0)),star(omega(X0))),X0)
| ~ leq(addition(omega(X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f1329,f336]) ).
fof(f16070,plain,
! [X0,X1] :
( leq(multiplication(addition(omega(X1),X0),star(omega(X1))),X1)
| ~ leq(addition(X0,omega(X1)),X1) ),
inference(paramodulation,[status(thm)],[f1026,f336]) ).
fof(f16071,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,omega(X1)),star(omega(X1))),X1)
| ~ leq(addition(X0,omega(X1)),X1) ),
inference(paramodulation,[status(thm)],[f1005,f336]) ).
fof(f16072,plain,
! [X0,X1] :
( leq(multiplication(addition(omega(X0),X1),star(omega(X0))),X0)
| ~ leq(addition(omega(X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f105,f336]) ).
fof(f16073,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,X1),star(omega(X2))),X2)
| ~ leq(addition(X0,addition(X1,omega(X2))),X2) ),
inference(paramodulation,[status(thm)],[f97,f336]) ).
fof(f16074,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X2,X0),star(omega(X1))),X1)
| ~ leq(addition(X0,addition(omega(X1),X2)),X1) ),
inference(paramodulation,[status(thm)],[f97,f336]) ).
fof(f16076,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(X1))),X1)
| ~ leq(addition(X0,omega(X1)),X1) ),
inference(paramodulation,[status(thm)],[f35,f336]) ).
fof(f16077,plain,
! [X0,X1] :
( leq(multiplication(X0,star(omega(X1))),X1)
| ~ leq(addition(X0,omega(X1)),X1) ),
inference(paramodulation,[status(thm)],[f35,f336]) ).
fof(f16078,plain,
! [X0] :
( leq(multiplication(omega(X0),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f38,f336]) ).
fof(f16080,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16049]) ).
fof(f16081,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X1),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16050]) ).
fof(f16082,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X1),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16051]) ).
fof(f16083,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16052]) ).
fof(f16084,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16053]) ).
fof(f16085,plain,
! [X0,X1] :
( leq(multiplication(divergence(X1),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16054]) ).
fof(f16086,plain,
! [X0,X1,X2] :
( leq(multiplication(omega(X0),multiplication(forward_diamond(X1,X2),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16055]) ).
fof(f16087,plain,
! [X0,X1,X2] :
( leq(multiplication(omega(X0),multiplication(backward_box(X1,X2),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16056]) ).
fof(f16088,plain,
! [X0,X1,X2] :
( leq(multiplication(omega(X0),multiplication(forward_box(X1,X2),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16057]) ).
fof(f16089,plain,
! [X0,X1,X2] :
( leq(multiplication(omega(X0),multiplication(backward_diamond(X1,X2),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16058]) ).
fof(f16090,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(domain(X1),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16059]) ).
fof(f16091,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(coantidomain(X1),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16060]) ).
fof(f16092,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(antidomain(X1),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16061]) ).
fof(f16093,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(c(X1),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16062]) ).
fof(f16094,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(codomain(X1),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16063]) ).
fof(f16095,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(divergence(X1),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16064]) ).
fof(f16096,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(omega(X1),star(omega(X1)))),X1)
| ~ leq(multiplication(addition(X0,one),omega(X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f16065]) ).
fof(f16097,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(omega(X1),star(omega(X1)))),X1)
| ~ leq(multiplication(addition(one,X0),omega(X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f16066]) ).
fof(f16098,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(X1,star(omega(X0)))),X0)
| ~ leq(multiplication(omega(X0),addition(X1,one)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16067]) ).
fof(f16099,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),multiplication(X1,star(omega(X0)))),X0)
| ~ leq(multiplication(omega(X0),addition(one,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16068]) ).
fof(f16104,plain,
! [X0,X1] : leq(multiplication(domain_difference(X0,X1),star(coantidomain(antidomain(X1)))),antidomain(X1)),
inference(resolution,[status(thm)],[f346,f6998]) ).
fof(f16105,plain,
! [X0,X1] : leq(multiplication(domain_difference(X0,X1),star(coantidomain(domain(X0)))),domain(X0)),
inference(resolution,[status(thm)],[f346,f3834]) ).
fof(f16106,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(forward_diamond(X0,X1),X2),star(coantidomain(X2))),X2),
inference(resolution,[status(thm)],[f346,f7010]) ).
fof(f16107,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(forward_box(X0,X1),X2),star(coantidomain(X2))),X2),
inference(resolution,[status(thm)],[f346,f6659]) ).
fof(f16108,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(backward_box(X0,X1),X2),star(coantidomain(X2))),X2),
inference(resolution,[status(thm)],[f346,f6658]) ).
fof(f16109,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(backward_diamond(X0,X1),X2),star(coantidomain(X2))),X2),
inference(resolution,[status(thm)],[f346,f6519]) ).
fof(f16110,plain,
! [X0,X1] : leq(multiplication(multiplication(coantidomain(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f346,f7158]) ).
fof(f16111,plain,
! [X0,X1] : leq(multiplication(multiplication(domain(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f346,f6808]) ).
fof(f16112,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f346,f6667]) ).
fof(f16113,plain,
! [X0,X1] : leq(multiplication(multiplication(c(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f346,f6526]) ).
fof(f16114,plain,
! [X0,X1] : leq(multiplication(multiplication(codomain(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f346,f6393]) ).
fof(f16115,plain,
! [X0,X1] : leq(multiplication(multiplication(divergence(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f346,f5965]) ).
fof(f16116,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,forward_diamond(X1,X2)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f4077]) ).
fof(f16117,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,forward_box(X1,X2)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f3741]) ).
fof(f16118,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,backward_box(X1,X2)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f3740]) ).
fof(f16119,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,backward_diamond(X1,X2)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f3497]) ).
fof(f16120,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,coantidomain(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f4627]) ).
fof(f16121,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,domain(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f3841]) ).
fof(f16122,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,antidomain(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f3749]) ).
fof(f16123,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,c(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f3652]) ).
fof(f16124,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,codomain(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f3411]) ).
fof(f16125,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,divergence(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f3330]) ).
fof(f16126,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),star(coantidomain(addition(X2,one)))),addition(X2,one)),
inference(resolution,[status(thm)],[f346,f2078]) ).
fof(f16129,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),star(coantidomain(addition(X2,one)))),addition(X2,one)),
inference(resolution,[status(thm)],[f346,f2052]) ).
fof(f16132,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),star(coantidomain(addition(X2,one)))),addition(X2,one)),
inference(resolution,[status(thm)],[f346,f2028]) ).
fof(f16135,plain,
! [X0] : leq(multiplication(divergence(X0),star(coantidomain(codomain(divergence(X0))))),codomain(divergence(X0))),
inference(resolution,[status(thm)],[f346,f6073]) ).
fof(f16137,plain,
! [X0] : leq(multiplication(divergence(X0),star(coantidomain(domain(divergence(X0))))),domain(divergence(X0))),
inference(resolution,[status(thm)],[f346,f4208]) ).
fof(f16138,plain,
! [X0,X1] : leq(multiplication(divergence(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f346,f2232]) ).
fof(f16139,plain,
! [X0,X1] : leq(multiplication(divergence(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f346,f1779]) ).
fof(f16141,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),star(coantidomain(addition(X2,one)))),addition(X2,one)),
inference(resolution,[status(thm)],[f346,f1907]) ).
fof(f16144,plain,
! [X0] : leq(multiplication(codomain(X0),star(coantidomain(codomain(codomain(X0))))),codomain(codomain(X0))),
inference(resolution,[status(thm)],[f346,f6509]) ).
fof(f16146,plain,
! [X0] : leq(multiplication(codomain(X0),star(coantidomain(domain(codomain(X0))))),domain(codomain(X0))),
inference(resolution,[status(thm)],[f346,f4210]) ).
fof(f16147,plain,
! [X0,X1] : leq(multiplication(codomain(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f346,f2247]) ).
fof(f16148,plain,
! [X0,X1] : leq(multiplication(codomain(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f346,f1780]) ).
fof(f16150,plain,
! [X0] : leq(multiplication(c(X0),star(coantidomain(antidomain(X0)))),antidomain(X0)),
inference(resolution,[status(thm)],[f346,f13625]) ).
fof(f16151,plain,
! [X0] : leq(multiplication(c(X0),star(coantidomain(codomain(c(X0))))),codomain(c(X0))),
inference(resolution,[status(thm)],[f346,f6648]) ).
fof(f16153,plain,
! [X0,X1] : leq(multiplication(c(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f346,f2264]) ).
fof(f16154,plain,
! [X0,X1] : leq(multiplication(c(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f346,f1781]) ).
fof(f16156,plain,
! [X0] : leq(multiplication(antidomain(c(X0)),star(coantidomain(domain(X0)))),domain(X0)),
inference(resolution,[status(thm)],[f346,f13956]) ).
fof(f16157,plain,
! [X0] : leq(multiplication(antidomain(X0),star(coantidomain(codomain(antidomain(X0))))),codomain(antidomain(X0))),
inference(resolution,[status(thm)],[f346,f6796]) ).
fof(f16159,plain,
! [X0] : leq(multiplication(antidomain(X0),star(coantidomain(c(X0)))),c(X0)),
inference(resolution,[status(thm)],[f346,f4241]) ).
fof(f16160,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f346,f2373]) ).
fof(f16161,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f346,f1782]) ).
fof(f16163,plain,
! [X0] : leq(multiplication(coantidomain(X0),star(coantidomain(coantidomain(codomain(X0))))),coantidomain(codomain(X0))),
inference(resolution,[status(thm)],[f346,f7305]) ).
fof(f16164,plain,
! [X0] : leq(multiplication(coantidomain(X0),star(coantidomain(domain(coantidomain(X0))))),domain(coantidomain(X0))),
inference(resolution,[status(thm)],[f346,f4735]) ).
fof(f16166,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f346,f2387]) ).
fof(f16167,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f346,f1783]) ).
fof(f16169,plain,
! [X0] : leq(multiplication(domain(X0),star(coantidomain(codomain(domain(X0))))),codomain(domain(X0))),
inference(resolution,[status(thm)],[f346,f7000]) ).
fof(f16171,plain,
! [X0] : leq(multiplication(domain(X0),star(coantidomain(antidomain(c(X0))))),antidomain(c(X0))),
inference(resolution,[status(thm)],[f346,f4249]) ).
fof(f16172,plain,
! [X0,X1] : leq(multiplication(domain(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f346,f2403]) ).
fof(f16173,plain,
! [X0,X1] : leq(multiplication(domain(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f346,f1784]) ).
fof(f16175,plain,
! [X0,X1] : leq(multiplication(one,star(coantidomain(addition(star(X0),X1)))),addition(star(X0),X1)),
inference(resolution,[status(thm)],[f346,f8413]) ).
fof(f16176,plain,
! [X0,X1] : leq(multiplication(one,star(coantidomain(addition(X0,star(X1))))),addition(X0,star(X1))),
inference(resolution,[status(thm)],[f346,f7532]) ).
fof(f16182,plain,
! [X0,X1] : leq(multiplication(addition(X0,X1),star(coantidomain(addition(X1,X0)))),addition(X1,X0)),
inference(resolution,[status(thm)],[f346,f10439]) ).
fof(f16183,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(multiplication(star(X1),X0)))),multiplication(star(X1),X0)),
inference(resolution,[status(thm)],[f346,f8451]) ).
fof(f16184,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(multiplication(X0,addition(one,X1))))),multiplication(X0,addition(one,X1))),
inference(resolution,[status(thm)],[f346,f2478]) ).
fof(f16185,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(multiplication(X0,star(X1))))),multiplication(X0,star(X1))),
inference(resolution,[status(thm)],[f346,f8449]) ).
fof(f16186,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(coantidomain(addition(X1,addition(X0,X2))))),addition(X1,addition(X0,X2))),
inference(resolution,[status(thm)],[f346,f1421]) ).
fof(f16187,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(coantidomain(addition(X1,addition(X2,X0))))),addition(X1,addition(X2,X0))),
inference(resolution,[status(thm)],[f346,f1420]) ).
fof(f16188,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(addition(X1,X0)))),addition(X1,X0)),
inference(resolution,[status(thm)],[f346,f1423]) ).
fof(f16189,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(addition(X0,X1)))),addition(X0,X1)),
inference(resolution,[status(thm)],[f346,f1324]) ).
fof(f16190,plain,
! [X0] : leq(multiplication(X0,star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f346,f239]) ).
fof(f16191,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),multiplication(X2,star(coantidomain(X2)))),X2),
inference(forward_demodulation,[status(thm)],[f39,f16106]) ).
fof(f16192,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),multiplication(X2,star(coantidomain(X2)))),X2),
inference(forward_demodulation,[status(thm)],[f39,f16107]) ).
fof(f16193,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),multiplication(X2,star(coantidomain(X2)))),X2),
inference(forward_demodulation,[status(thm)],[f39,f16108]) ).
fof(f16194,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),multiplication(X2,star(coantidomain(X2)))),X2),
inference(forward_demodulation,[status(thm)],[f39,f16109]) ).
fof(f16195,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f39,f16110]) ).
fof(f16196,plain,
! [X0,X1] : leq(multiplication(domain(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f39,f16111]) ).
fof(f16197,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f39,f16112]) ).
fof(f16198,plain,
! [X0,X1] : leq(multiplication(c(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f39,f16113]) ).
fof(f16199,plain,
! [X0,X1] : leq(multiplication(codomain(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f39,f16114]) ).
fof(f16200,plain,
! [X0,X1] : leq(multiplication(divergence(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f39,f16115]) ).
fof(f16201,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(forward_diamond(X1,X2),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16116]) ).
fof(f16202,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(forward_box(X1,X2),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16117]) ).
fof(f16203,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(backward_box(X1,X2),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16118]) ).
fof(f16204,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(backward_diamond(X1,X2),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16119]) ).
fof(f16205,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(coantidomain(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16120]) ).
fof(f16206,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(domain(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16121]) ).
fof(f16207,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(antidomain(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16122]) ).
fof(f16208,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(c(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16123]) ).
fof(f16209,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(codomain(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16124]) ).
fof(f16210,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(divergence(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f16125]) ).
fof(f16259,plain,
! [X0] : leq(multiplication(coantidomain(X0),star(codomain(codomain(X0)))),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f66,f16163]) ).
fof(f16272,plain,
! [X0,X1] : leq(star(coantidomain(addition(star(X0),X1))),addition(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f41,f16175]) ).
fof(f16273,plain,
! [X0,X1] : leq(star(coantidomain(addition(X0,star(X1)))),addition(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f41,f16176]) ).
fof(f16295,plain,
! [X0,X1] :
( leq(multiplication(X1,one),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f339]) ).
fof(f16296,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16295]) ).
fof(f16298,plain,
! [X0] :
( leq(multiplication(star(X0),addition(X0,one)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7789,f16296]) ).
fof(f16299,plain,
! [X0] :
( leq(multiplication(addition(X0,one),star(X0)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7510,f16296]) ).
fof(f16300,plain,
! [X0,X1] :
( leq(backward_diamond(X0,X1),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1504,f16296]) ).
fof(f16301,plain,
! [X0,X1] :
( leq(forward_box(X0,X1),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1497,f16296]) ).
fof(f16302,plain,
! [X0,X1] :
( leq(backward_box(X0,X1),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1492,f16296]) ).
fof(f16303,plain,
! [X0,X1] :
( leq(forward_diamond(X0,X1),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1485,f16296]) ).
fof(f16304,plain,
! [X0] :
( leq(divergence(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1488,f16296]) ).
fof(f16305,plain,
! [X0] :
( leq(codomain(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1477,f16296]) ).
fof(f16306,plain,
! [X0] :
( leq(c(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1471,f16296]) ).
fof(f16307,plain,
! [X0] :
( leq(antidomain(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1379,f16296]) ).
fof(f16308,plain,
! [X0] :
( leq(coantidomain(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1377,f16296]) ).
fof(f16309,plain,
! [X0] :
( leq(domain(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1375,f16296]) ).
fof(f16310,plain,
! [X0] :
( leq(c(X0),domain(X0))
| ~ leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f569,f16296]) ).
fof(f16312,plain,
! [X0] :
( leq(codomain(X0),coantidomain(X0))
| ~ leq(one,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f683,f16296]) ).
fof(f16315,plain,
! [X0] :
( leq(domain(X0),antidomain(X0))
| ~ leq(one,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f558,f16296]) ).
fof(f16316,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3)))
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(X0,multiplication(X1,X3))) ),
inference(paramodulation,[status(thm)],[f204,f16296]) ).
fof(f16317,plain,
! [X0,X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),multiplication(X0,X2))
| ~ leq(addition(multiplication(addition(X0,X1),X2),X3),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f219,f16296]) ).
fof(f16318,plain,
! [X0,X1,X2,X3] :
( leq(addition(multiplication(X0,X2),X3),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,addition(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f170,f16296]) ).
fof(f16319,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3))
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f211,f16296]) ).
fof(f16320,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f201,f16296]) ).
fof(f16321,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X0,X2))
| ~ leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f153,f16296]) ).
fof(f16322,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,X2),multiplication(X0,X2))
| ~ leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f43,f16296]) ).
fof(f16323,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X0,X1))
| ~ leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f42,f16296]) ).
fof(f16324,plain,
! [X0,X1,X2] :
( leq(X2,addition(X1,X0))
| ~ leq(addition(X0,addition(X1,X2)),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f103,f16296]) ).
fof(f16325,plain,
! [X0,X1,X2] :
( leq(X2,addition(X0,X1))
| ~ leq(addition(X0,addition(X1,X2)),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f36,f16296]) ).
fof(f16343,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X1)
| ~ leq(multiplication(addition(X0,one),X1),X1) ),
inference(paramodulation,[status(thm)],[f232,f16296]) ).
fof(f16344,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X1)
| ~ leq(multiplication(addition(one,X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f207,f16296]) ).
fof(f16345,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X0)
| ~ leq(multiplication(X0,addition(X1,one)),X0) ),
inference(paramodulation,[status(thm)],[f192,f16296]) ).
fof(f16346,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X0)
| ~ leq(multiplication(X0,addition(one,X1)),X0) ),
inference(paramodulation,[status(thm)],[f162,f16296]) ).
fof(f16347,plain,
! [X0,X1] :
( leq(addition(X1,X0),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f1329,f16296]) ).
fof(f16348,plain,
! [X0,X1] :
( leq(addition(X1,X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f1026,f16296]) ).
fof(f16351,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),X2)
| ~ leq(addition(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f97,f16296]) ).
fof(f16352,plain,
! [X0,X1,X2] :
( leq(addition(X2,X0),X1)
| ~ leq(addition(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f97,f16296]) ).
fof(f16354,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f35,f16296]) ).
fof(f16355,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f35,f16296]) ).
fof(f16357,plain,
( sQ10_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16300,f9301,f2093]) ).
fof(f16358,plain,
( sQ9_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16301,f9301,f2067]) ).
fof(f16359,plain,
( sQ8_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16302,f9301,f2043]) ).
fof(f16360,plain,
( sQ7_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16303,f9301,f1922]) ).
fof(f16361,plain,
( sQ6_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16304,f9301,f1763]) ).
fof(f16362,plain,
( sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16305,f9301,f1743]) ).
fof(f16363,plain,
( sQ4_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16306,f9301,f1720]) ).
fof(f16364,plain,
( sQ3_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16307,f9301,f1618]) ).
fof(f16365,plain,
( sQ2_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16308,f9301,f1550]) ).
fof(f16366,plain,
( sQ0_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f16309,f9301,f1525]) ).
fof(f16406,plain,
! [X0,X1,X2] : domain_difference(X0,addition(X1,addition(X2,one))) = zero,
inference(paramodulation,[status(thm)],[f97,f15344]) ).
fof(f16407,plain,
! [X0,X1,X2] : domain_difference(X0,addition(X1,addition(one,X2))) = zero,
inference(paramodulation,[status(thm)],[f97,f15344]) ).
fof(f16429,plain,
! [X0,X1,X2] : domain_difference(X0,addition(X1,addition(X2,one))) = zero,
inference(paramodulation,[status(thm)],[f103,f15406]) ).
fof(f16430,plain,
! [X0,X1,X2] : domain_difference(X0,addition(X1,addition(X2,one))) = zero,
inference(paramodulation,[status(thm)],[f36,f15406]) ).
fof(f16480,plain,
! [X0,X1,X2] : backward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f97,f15583]) ).
fof(f16481,plain,
! [X0,X1,X2] : backward_box(X0,addition(X1,addition(one,X2))) = one,
inference(paramodulation,[status(thm)],[f97,f15583]) ).
fof(f16534,plain,
! [X0,X1,X2] : forward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f97,f15585]) ).
fof(f16535,plain,
! [X0,X1,X2] : forward_box(X0,addition(X1,addition(one,X2))) = one,
inference(paramodulation,[status(thm)],[f97,f15585]) ).
fof(f16555,plain,
! [X0] : leq(addition(one,X0),addition(omega(one),multiplication(star(one),multiplication(X0,addition(one,X0))))),
inference(resolution,[status(thm)],[f391,f2478]) ).
fof(f16556,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(X1,X0))))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f207,f391]) ).
fof(f16557,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(X1,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f224,f391]) ).
fof(f16558,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(X1),multiplication(star(X1),multiplication(one,omega(X0)))))
| ~ leq(omega(X0),multiplication(addition(X0,X1),omega(X0))) ),
inference(paramodulation,[status(thm)],[f11449,f391]) ).
fof(f16559,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(X1),multiplication(star(X1),multiplication(one,omega(X0)))))
| ~ leq(omega(X0),multiplication(addition(X1,X0),omega(X0))) ),
inference(paramodulation,[status(thm)],[f10882,f391]) ).
fof(f16560,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(one,X0))))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f232,f391]) ).
fof(f16561,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(antidomain(X0),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f230,f391]) ).
fof(f16563,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(X1),multiplication(star(X1),multiplication(X0,omega(X0)))))
| ~ leq(omega(X0),multiplication(addition(X1,one),omega(X0))) ),
inference(paramodulation,[status(thm)],[f10882,f391]) ).
fof(f16564,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X1),multiplication(star(X1),multiplication(X0,coantidomain(X0)))))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f233,f391]) ).
fof(f16565,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),multiplication(X1,coantidomain(X0)))))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f226,f391]) ).
fof(f16566,plain,
! [X0,X1] :
( leq(codomain(addition(X0,X1)),addition(omega(X0),multiplication(star(X0),multiplication(X1,codomain(addition(X0,X1))))))
| ~ leq(codomain(addition(X0,X1)),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2309,f391]) ).
fof(f16567,plain,
! [X0,X1,X2] :
( leq(addition(omega(addition(X0,X1)),X2),addition(omega(X0),multiplication(star(X0),multiplication(X1,addition(omega(addition(X0,X1)),X2)))))
| ~ leq(addition(omega(addition(X0,X1)),X2),addition(omega(addition(X0,X1)),multiplication(addition(X0,X1),X2))) ),
inference(paramodulation,[status(thm)],[f318,f391]) ).
fof(f16568,plain,
! [X0,X1,X2] :
( leq(addition(coantidomain(addition(X0,X1)),X2),addition(omega(X0),multiplication(star(X0),multiplication(X1,addition(coantidomain(addition(X0,X1)),X2)))))
| ~ leq(addition(coantidomain(addition(X0,X1)),X2),multiplication(addition(X0,X1),X2)) ),
inference(paramodulation,[status(thm)],[f181,f391]) ).
fof(f16569,plain,
! [X0,X1,X2] :
( leq(addition(X0,omega(addition(X1,X2))),addition(omega(X1),multiplication(star(X1),multiplication(X2,addition(X0,omega(addition(X1,X2)))))))
| ~ leq(addition(X0,omega(addition(X1,X2))),addition(omega(addition(X1,X2)),multiplication(addition(X1,X2),X0))) ),
inference(paramodulation,[status(thm)],[f321,f391]) ).
fof(f16570,plain,
! [X0,X1,X2] :
( leq(addition(X0,coantidomain(addition(X1,X2))),addition(omega(X1),multiplication(star(X1),multiplication(X2,addition(X0,coantidomain(addition(X1,X2)))))))
| ~ leq(addition(X0,coantidomain(addition(X1,X2))),multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f190,f391]) ).
fof(f16571,plain,
! [X0,X1,X2] :
( leq(multiplication(omega(addition(X0,X1)),X2),addition(omega(X0),multiplication(star(X0),multiplication(X1,multiplication(omega(addition(X0,X1)),X2)))))
| ~ leq(multiplication(omega(addition(X0,X1)),X2),multiplication(omega(addition(X0,X1)),X2)) ),
inference(paramodulation,[status(thm)],[f319,f391]) ).
fof(f16572,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(addition(X0,X1)),X2),addition(omega(X0),multiplication(star(X0),multiplication(X1,multiplication(coantidomain(addition(X0,X1)),X2)))))
| ~ leq(multiplication(coantidomain(addition(X0,X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f151,f391]) ).
fof(f16573,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,omega(multiplication(addition(X1,X2),X0))),addition(omega(X1),multiplication(star(X1),multiplication(X2,multiplication(X0,omega(multiplication(addition(X1,X2),X0)))))))
| ~ leq(multiplication(X0,omega(multiplication(addition(X1,X2),X0))),omega(multiplication(addition(X1,X2),X0))) ),
inference(paramodulation,[status(thm)],[f308,f391]) ).
fof(f16574,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,coantidomain(multiplication(addition(X1,X2),X0))),addition(omega(X1),multiplication(star(X1),multiplication(X2,multiplication(X0,coantidomain(multiplication(addition(X1,X2),X0)))))))
| ~ leq(multiplication(X0,coantidomain(multiplication(addition(X1,X2),X0))),zero) ),
inference(paramodulation,[status(thm)],[f144,f391]) ).
fof(f16575,plain,
! [X0,X1] :
( leq(omega(coantidomain(addition(X0,X1))),addition(omega(X0),multiplication(star(X0),multiplication(X1,omega(coantidomain(addition(X0,X1)))))))
| ~ leq(omega(coantidomain(addition(X0,X1))),zero) ),
inference(paramodulation,[status(thm)],[f1813,f391]) ).
fof(f16576,plain,
! [X0,X1] :
( leq(omega(addition(X0,X1)),addition(omega(X0),multiplication(star(X0),multiplication(X1,omega(addition(X0,X1))))))
| ~ leq(omega(addition(X0,X1)),omega(addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f56,f391]) ).
fof(f16577,plain,
! [X0,X1] :
( leq(coantidomain(addition(X0,X1)),addition(omega(X0),multiplication(star(X0),multiplication(X1,coantidomain(addition(X0,X1))))))
| ~ leq(coantidomain(addition(X0,X1)),zero) ),
inference(paramodulation,[status(thm)],[f63,f391]) ).
fof(f16578,plain,
! [X0,X1] :
( leq(zero,addition(omega(X0),multiplication(star(X0),multiplication(X1,zero))))
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f44,f391]) ).
fof(f16579,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X1,one))))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f40,f391]) ).
fof(f16580,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(star(X1),X0))))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(paramodulation,[status(thm)],[f7563,f391]) ).
fof(f16581,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(multiplication(star(X1),addition(X1,one)),X0))))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(paramodulation,[status(thm)],[f7789,f391]) ).
fof(f16582,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(multiplication(addition(X1,one),star(X1)),X0))))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(paramodulation,[status(thm)],[f7510,f391]) ).
fof(f16583,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(backward_diamond(X1,X2),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1504,f391]) ).
fof(f16584,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(forward_box(X1,X2),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1497,f391]) ).
fof(f16585,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(backward_box(X1,X2),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1492,f391]) ).
fof(f16586,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(forward_diamond(X1,X2),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1485,f391]) ).
fof(f16587,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(divergence(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1488,f391]) ).
fof(f16588,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(codomain(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1477,f391]) ).
fof(f16589,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(c(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1471,f391]) ).
fof(f16590,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(antidomain(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1379,f391]) ).
fof(f16591,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(coantidomain(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1377,f391]) ).
fof(f16592,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(domain(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f1375,f391]) ).
fof(f16593,plain,
! [X0,X1] :
( leq(X0,addition(omega(domain(X1)),multiplication(star(domain(X1)),multiplication(c(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f569,f391]) ).
fof(f16594,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(coantidomain(multiplication(X1,X2))),multiplication(star(coantidomain(multiplication(X1,X2))),multiplication(coantidomain(multiplication(codomain(X1),X2)),X0))))
| ~ leq(X0,multiplication(coantidomain(multiplication(codomain(X1),X2)),X0)) ),
inference(paramodulation,[status(thm)],[f615,f391]) ).
fof(f16595,plain,
! [X0,X1] :
( leq(X0,addition(omega(coantidomain(X1)),multiplication(star(coantidomain(X1)),multiplication(codomain(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f683,f391]) ).
fof(f16596,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(multiplication(X1,X2))),multiplication(star(antidomain(multiplication(X1,X2))),multiplication(antidomain(multiplication(X1,domain(X2))),X0))))
| ~ leq(X0,multiplication(antidomain(multiplication(X1,domain(X2))),X0)) ),
inference(paramodulation,[status(thm)],[f479,f391]) ).
fof(f16597,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),multiplication(c(X1),X0))))
| ~ leq(X0,multiplication(c(X1),X0)) ),
inference(paramodulation,[status(thm)],[f514,f391]) ).
fof(f16598,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),multiplication(domain(X1),X0))))
| ~ leq(X0,multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f558,f391]) ).
fof(f16599,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,multiplication(X2,X4))),multiplication(star(multiplication(X1,multiplication(X2,X4))),multiplication(multiplication(X3,X4),X0))))
| ~ leq(X0,multiplication(multiplication(addition(multiplication(X1,X2),X3),X4),X0)) ),
inference(paramodulation,[status(thm)],[f204,f391]) ).
fof(f16600,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(addition(multiplication(X2,X3),X4),X0))))
| ~ leq(X0,multiplication(addition(multiplication(addition(X1,X2),X3),X4),X0)) ),
inference(paramodulation,[status(thm)],[f219,f391]) ).
fof(f16601,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(addition(multiplication(X1,X3),X4),X0))))
| ~ leq(X0,multiplication(addition(multiplication(X1,addition(X2,X3)),X4),X0)) ),
inference(paramodulation,[status(thm)],[f170,f391]) ).
fof(f16602,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X4)),multiplication(star(multiplication(X1,X4)),multiplication(multiplication(X2,multiplication(X3,X4)),X0))))
| ~ leq(X0,multiplication(multiplication(addition(X1,multiplication(X2,X3)),X4),X0)) ),
inference(paramodulation,[status(thm)],[f211,f391]) ).
fof(f16603,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),multiplication(multiplication(X1,X3),X0))))
| ~ leq(X0,multiplication(multiplication(addition(X1,X2),X3),X0)) ),
inference(paramodulation,[status(thm)],[f201,f391]) ).
fof(f16604,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(multiplication(X1,addition(X2,X3)),X0)) ),
inference(paramodulation,[status(thm)],[f153,f391]) ).
fof(f16605,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(multiplication(X2,X3),X0))))
| ~ leq(X0,multiplication(multiplication(addition(X1,X2),X3),X0)) ),
inference(paramodulation,[status(thm)],[f43,f391]) ).
fof(f16606,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,X3),X0))))
| ~ leq(X0,multiplication(multiplication(X1,addition(X2,X3)),X0)) ),
inference(paramodulation,[status(thm)],[f42,f391]) ).
fof(f16607,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(addition(X2,X1)),multiplication(star(addition(X2,X1)),multiplication(X3,X0))))
| ~ leq(X0,multiplication(addition(X1,addition(X2,X3)),X0)) ),
inference(paramodulation,[status(thm)],[f103,f391]) ).
fof(f16608,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(addition(X1,X2)),multiplication(star(addition(X1,X2)),multiplication(X3,X0))))
| ~ leq(X0,multiplication(addition(X1,addition(X2,X3)),X0)) ),
inference(paramodulation,[status(thm)],[f36,f391]) ).
fof(f16610,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(domain(X2),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4516,f391]) ).
fof(f16611,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(coantidomain(X2),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4515,f391]) ).
fof(f16612,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(antidomain(X2),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4514,f391]) ).
fof(f16613,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(c(X2),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4513,f391]) ).
fof(f16614,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(codomain(X2),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4512,f391]) ).
fof(f16615,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(divergence(X2),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4511,f391]) ).
fof(f16616,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,forward_diamond(X2,X3)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2491,f391]) ).
fof(f16617,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,backward_box(X2,X3)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2490,f391]) ).
fof(f16618,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,forward_box(X2,X3)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2489,f391]) ).
fof(f16619,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,backward_diamond(X2,X3)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2488,f391]) ).
fof(f16620,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,domain(X2)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2497,f391]) ).
fof(f16621,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,coantidomain(X2)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2496,f391]) ).
fof(f16622,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,antidomain(X2)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2495,f391]) ).
fof(f16623,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,c(X2)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2494,f391]) ).
fof(f16624,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,codomain(X2)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2493,f391]) ).
fof(f16625,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,divergence(X2)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2492,f391]) ).
fof(f16626,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(multiplication(addition(X1,one),X2),X0)) ),
inference(paramodulation,[status(thm)],[f232,f391]) ).
fof(f16627,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(multiplication(addition(one,X1),X2),X0)) ),
inference(paramodulation,[status(thm)],[f207,f391]) ).
fof(f16628,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(multiplication(X1,addition(X2,one)),X0)) ),
inference(paramodulation,[status(thm)],[f192,f391]) ).
fof(f16629,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(multiplication(X1,addition(one,X2)),X0)) ),
inference(paramodulation,[status(thm)],[f162,f391]) ).
fof(f16630,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(addition(X2,X1),X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f1329,f391]) ).
fof(f16631,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(addition(X2,X1),X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f1026,f391]) ).
fof(f16632,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(addition(X1,X2),X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f1005,f391]) ).
fof(f16633,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(addition(X1,X2),X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f105,f391]) ).
fof(f16634,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X3),multiplication(star(X3),multiplication(addition(X1,X2),X0))))
| ~ leq(X0,multiplication(addition(X1,addition(X2,X3)),X0)) ),
inference(paramodulation,[status(thm)],[f97,f391]) ).
fof(f16635,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(addition(X3,X1),X0))))
| ~ leq(X0,multiplication(addition(X1,addition(X2,X3)),X0)) ),
inference(paramodulation,[status(thm)],[f97,f391]) ).
fof(f16636,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(zero,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f37,f391]) ).
fof(f16637,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(X1,X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f35,f391]) ).
fof(f16638,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(X1,X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f35,f391]) ).
fof(f16639,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f38,f391]) ).
fof(f16643,plain,
! [X0] : leq(addition(one,X0),addition(omega(one),multiplication(one,multiplication(X0,addition(one,X0))))),
inference(forward_demodulation,[status(thm)],[f9603,f16555]) ).
fof(f16644,plain,
! [X0] : leq(addition(one,X0),addition(omega(one),multiplication(X0,addition(one,X0)))),
inference(forward_demodulation,[status(thm)],[f41,f16643]) ).
fof(f16645,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(X1,X0))))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f9603,f16556]) ).
fof(f16646,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(X1,X0)))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f41,f16645]) ).
fof(f16647,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16646,f1324]) ).
fof(f16648,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(X1),multiplication(star(X1),omega(X0))))
| ~ leq(omega(X0),multiplication(addition(X0,X1),omega(X0))) ),
inference(forward_demodulation,[status(thm)],[f41,f16558]) ).
fof(f16649,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(X1),multiplication(star(X1),omega(X0))))
| ~ leq(omega(X0),multiplication(addition(X1,X0),omega(X0))) ),
inference(forward_demodulation,[status(thm)],[f41,f16559]) ).
fof(f16650,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X0)))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f41,f16560]) ).
fof(f16651,plain,
! [X0,X1] : leq(X0,addition(omega(X1),multiplication(star(X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16650,f1324]) ).
fof(f16652,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),zero)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f59,f16561]) ).
fof(f16653,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),zero))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f44,f16652]) ).
fof(f16654,plain,
! [X0,X1] :
( leq(X0,omega(X1))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f16653]) ).
fof(f16655,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(X1),multiplication(star(X1),omega(X0))))
| ~ leq(omega(X0),multiplication(addition(X1,one),omega(X0))) ),
inference(forward_demodulation,[status(thm)],[f56,f16563]) ).
fof(f16656,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X1),multiplication(star(X1),zero)))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f63,f16564]) ).
fof(f16657,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X1),zero))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f44,f16656]) ).
fof(f16658,plain,
! [X0,X1] :
( leq(coantidomain(X0),omega(X1))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f37,f16657]) ).
fof(f16659,plain,
! [X0,X1,X2] : leq(multiplication(omega(addition(X0,X1)),X2),addition(omega(X0),multiplication(star(X0),multiplication(X1,multiplication(omega(addition(X0,X1)),X2))))),
inference(forward_subsumption_resolution,[status(thm)],[f16571,f239]) ).
fof(f16660,plain,
! [X0,X1] : leq(omega(addition(X0,X1)),addition(omega(X0),multiplication(star(X0),multiplication(X1,omega(addition(X0,X1)))))),
inference(forward_subsumption_resolution,[status(thm)],[f16576,f239]) ).
fof(f16661,definition,
! [X0,X1] :
( sQ43_spl
<=> leq(zero,addition(omega(X0),multiplication(star(X0),multiplication(X1,zero)))) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f16664,plain,
( sQ43_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f16578,f7983,f16661]) ).
fof(f16665,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(one,addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f40,f16579]) ).
fof(f16666,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(star(X1),X0))))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f9603,f16580]) ).
fof(f16667,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(X1),X0)))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f16666]) ).
fof(f16668,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(star(X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16667,f8451]) ).
fof(f16669,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(multiplication(star(X1),addition(X1,one)),X0))))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f9603,f16581]) ).
fof(f16670,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(multiplication(star(X1),addition(X1,one)),X0)))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f16669]) ).
fof(f16671,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(X1),multiplication(addition(X1,one),X0))))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16670]) ).
fof(f16672,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(star(X1),multiplication(addition(X1,one),X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f16671,f8451]) ).
fof(f16673,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(multiplication(addition(X1,one),star(X1)),X0))))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f9603,f16582]) ).
fof(f16674,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(multiplication(addition(X1,one),star(X1)),X0)))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f16673]) ).
fof(f16675,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(addition(X1,one),multiplication(star(X1),X0))))
| ~ leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16674]) ).
fof(f16676,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(addition(X1,one),multiplication(star(X1),X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f16675,f8451]) ).
fof(f16677,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(backward_diamond(X1,X2),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16583]) ).
fof(f16678,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(backward_diamond(X1,X2),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16677]) ).
fof(f16679,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(backward_diamond(X1,X2),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16678]) ).
fof(f16680,plain,
! [X0,X1,X2] : leq(X0,addition(omega(one),multiplication(backward_diamond(X1,X2),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16679,f239]) ).
fof(f16681,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(forward_box(X1,X2),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16584]) ).
fof(f16682,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(forward_box(X1,X2),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16681]) ).
fof(f16683,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(forward_box(X1,X2),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16682]) ).
fof(f16684,plain,
! [X0,X1,X2] : leq(X0,addition(omega(one),multiplication(forward_box(X1,X2),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16683,f239]) ).
fof(f16685,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(backward_box(X1,X2),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16585]) ).
fof(f16686,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(backward_box(X1,X2),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16685]) ).
fof(f16687,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(backward_box(X1,X2),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16686]) ).
fof(f16688,plain,
! [X0,X1,X2] : leq(X0,addition(omega(one),multiplication(backward_box(X1,X2),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16687,f239]) ).
fof(f16689,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(forward_diamond(X1,X2),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16586]) ).
fof(f16690,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(forward_diamond(X1,X2),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16689]) ).
fof(f16691,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(one),multiplication(forward_diamond(X1,X2),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16690]) ).
fof(f16692,plain,
! [X0,X1,X2] : leq(X0,addition(omega(one),multiplication(forward_diamond(X1,X2),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16691,f239]) ).
fof(f16693,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(divergence(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16587]) ).
fof(f16694,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(divergence(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16693]) ).
fof(f16695,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(divergence(X1),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16694]) ).
fof(f16696,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(divergence(X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16695,f239]) ).
fof(f16697,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(codomain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16588]) ).
fof(f16698,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(codomain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16697]) ).
fof(f16699,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(codomain(X1),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16698]) ).
fof(f16700,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(codomain(X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16699,f239]) ).
fof(f16701,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(c(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16589]) ).
fof(f16702,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(c(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16701]) ).
fof(f16703,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(c(X1),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16702]) ).
fof(f16704,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(c(X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16703,f239]) ).
fof(f16705,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(antidomain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16590]) ).
fof(f16706,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(antidomain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16705]) ).
fof(f16707,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(antidomain(X1),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16706]) ).
fof(f16708,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(antidomain(X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16707,f239]) ).
fof(f16709,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(coantidomain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16591]) ).
fof(f16710,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(coantidomain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16709]) ).
fof(f16711,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(coantidomain(X1),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16710]) ).
fof(f16712,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(coantidomain(X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16711,f239]) ).
fof(f16713,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(domain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16592]) ).
fof(f16714,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(domain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f9603,f16713]) ).
fof(f16715,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(domain(X1),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16714]) ).
fof(f16716,plain,
! [X0,X1] : leq(X0,addition(omega(one),multiplication(domain(X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16715,f239]) ).
fof(f16717,plain,
! [X0,X1] :
( leq(X0,addition(omega(domain(X1)),multiplication(star(domain(X1)),multiplication(c(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16593]) ).
fof(f16718,plain,
! [X0,X1] : leq(X0,addition(omega(domain(X1)),multiplication(star(domain(X1)),multiplication(c(X1),X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f16717,f239]) ).
fof(f16719,plain,
! [X0,X1] :
( leq(X0,addition(omega(coantidomain(X1)),multiplication(star(coantidomain(X1)),multiplication(codomain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16595]) ).
fof(f16720,plain,
! [X0,X1] : leq(X0,addition(omega(coantidomain(X1)),multiplication(star(coantidomain(X1)),multiplication(codomain(X1),X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f16719,f239]) ).
fof(f16721,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),multiplication(domain(X1),X0))))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f41,f16598]) ).
fof(f16722,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),multiplication(domain(X1),X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f16721,f239]) ).
fof(f16723,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,multiplication(X2,X4))),multiplication(star(multiplication(X1,multiplication(X2,X4))),multiplication(multiplication(X3,X4),X0))))
| ~ leq(X0,multiplication(addition(multiplication(X1,X2),X3),multiplication(X4,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16599]) ).
fof(f16724,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,multiplication(X2,X4))),multiplication(star(multiplication(X1,multiplication(X2,X4))),multiplication(X3,multiplication(X4,X0)))))
| ~ leq(X0,multiplication(addition(multiplication(X1,X2),X3),multiplication(X4,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16723]) ).
fof(f16725,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X4)),multiplication(star(multiplication(X1,X4)),multiplication(multiplication(X2,multiplication(X3,X4)),X0))))
| ~ leq(X0,multiplication(addition(X1,multiplication(X2,X3)),multiplication(X4,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16602]) ).
fof(f16726,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X4)),multiplication(star(multiplication(X1,X4)),multiplication(X2,multiplication(multiplication(X3,X4),X0)))))
| ~ leq(X0,multiplication(addition(X1,multiplication(X2,X3)),multiplication(X4,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16725]) ).
fof(f16727,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X4)),multiplication(star(multiplication(X1,X4)),multiplication(X2,multiplication(X3,multiplication(X4,X0))))))
| ~ leq(X0,multiplication(addition(X1,multiplication(X2,X3)),multiplication(X4,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16726]) ).
fof(f16728,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),multiplication(multiplication(X1,X3),X0))))
| ~ leq(X0,multiplication(addition(X1,X2),multiplication(X3,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16603]) ).
fof(f16729,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),multiplication(X1,multiplication(X3,X0)))))
| ~ leq(X0,multiplication(addition(X1,X2),multiplication(X3,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16728]) ).
fof(f16730,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(X1,multiplication(addition(X2,X3),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16604]) ).
fof(f16731,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(X1,multiplication(addition(X2,X3),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16730]) ).
fof(f16732,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(multiplication(X2,X3),X0))))
| ~ leq(X0,multiplication(addition(X1,X2),multiplication(X3,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16605]) ).
fof(f16733,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(X2,multiplication(X3,X0)))))
| ~ leq(X0,multiplication(addition(X1,X2),multiplication(X3,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16732]) ).
fof(f16734,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,X3),X0))))
| ~ leq(X0,multiplication(X1,multiplication(addition(X2,X3),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16606]) ).
fof(f16735,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X3,X0)))))
| ~ leq(X0,multiplication(X1,multiplication(addition(X2,X3),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16734]) ).
fof(f16739,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(domain(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16610]) ).
fof(f16740,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(coantidomain(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16611]) ).
fof(f16741,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(antidomain(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16612]) ).
fof(f16742,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(c(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16613]) ).
fof(f16743,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(codomain(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16614]) ).
fof(f16744,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(divergence(X2),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16615]) ).
fof(f16745,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(forward_diamond(X2,X3),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16616]) ).
fof(f16746,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(backward_box(X2,X3),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16617]) ).
fof(f16747,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(forward_box(X2,X3),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16618]) ).
fof(f16748,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(backward_diamond(X2,X3),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16619]) ).
fof(f16749,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(domain(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16620]) ).
fof(f16750,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(coantidomain(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16621]) ).
fof(f16751,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(antidomain(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16622]) ).
fof(f16752,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(c(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16623]) ).
fof(f16753,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(codomain(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16624]) ).
fof(f16754,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(divergence(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f16625]) ).
fof(f16755,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(addition(X1,one),multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16626]) ).
fof(f16756,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(addition(X1,one),multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16755]) ).
fof(f16757,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(addition(one,X1),multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16627]) ).
fof(f16758,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(addition(one,X1),multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16757]) ).
fof(f16759,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(X1,multiplication(addition(X2,one),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16628]) ).
fof(f16760,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(X1,multiplication(addition(X2,one),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16759]) ).
fof(f16761,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(X1,multiplication(addition(one,X2),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16629]) ).
fof(f16762,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(X1,multiplication(addition(one,X2),X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f16761]) ).
fof(f16763,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),zero)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f45,f16636]) ).
fof(f16764,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),zero))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f44,f16763]) ).
fof(f16765,plain,
! [X0,X1] :
( leq(X0,omega(X1))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f16764]) ).
fof(f16771,plain,
! [X0,X1,X2] : backward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f103,f15951]) ).
fof(f16772,plain,
! [X0,X1,X2] : backward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f36,f15951]) ).
fof(f16794,plain,
! [X0,X1,X2] : forward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f103,f15953]) ).
fof(f16795,plain,
! [X0,X1,X2] : forward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f36,f15953]) ).
fof(f16816,plain,
! [X0] : leq(one,addition(omega(one),multiplication(star(one),multiplication(one,X0)))),
inference(resolution,[status(thm)],[f392,f2478]) ).
fof(f16817,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(antidomain(addition(X0,X2)),X1)),multiplication(star(addition(antidomain(addition(X0,X2)),X1)),multiplication(addition(antidomain(addition(X0,X2)),X1),X2))))
| ~ leq(X0,multiplication(X1,addition(X0,X2))) ),
inference(paramodulation,[status(thm)],[f224,f392]) ).
fof(f16818,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(X1,antidomain(addition(X0,X2)))),multiplication(star(addition(X1,antidomain(addition(X0,X2)))),multiplication(addition(X1,antidomain(addition(X0,X2))),X2))))
| ~ leq(X0,multiplication(X1,addition(X0,X2))) ),
inference(paramodulation,[status(thm)],[f230,f392]) ).
fof(f16819,plain,
! [X0,X1] :
( leq(X0,addition(omega(c(addition(X0,X1))),multiplication(star(c(addition(X0,X1))),multiplication(c(addition(X0,X1)),X1))))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f4265,f392]) ).
fof(f16820,plain,
! [X0,X1] :
( leq(X0,addition(omega(domain(addition(X0,X1))),multiplication(star(domain(addition(X0,X1))),multiplication(domain(addition(X0,X1)),X1))))
| ~ leq(X0,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4146,f392]) ).
fof(f16821,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,X2),X3))))
| ~ leq(X0,multiplication(X1,multiplication(X2,addition(X0,X3)))) ),
inference(paramodulation,[status(thm)],[f39,f392]) ).
fof(f16822,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(addition(X0,X1),X2))),multiplication(star(antidomain(addition(addition(X0,X1),X2))),multiplication(antidomain(addition(addition(X0,X1),X2)),X1))))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f2635,f392]) ).
fof(f16823,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),multiplication(antidomain(X1),X1))))
| ~ leq(X0,multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f186,f392]) ).
fof(f16824,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X1))))
| ~ leq(X0,multiplication(antidomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f177,f392]) ).
fof(f16825,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(addition(X0,X1))),multiplication(star(antidomain(addition(X0,X1))),multiplication(antidomain(addition(X0,X1)),X1))))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f59,f392]) ).
fof(f16827,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(star(one),multiplication(one,X1))))
| ~ leq(X0,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f41,f392]) ).
fof(f16829,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,X1))))
| ~ leq(one,addition(X0,multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f162,f392]) ).
fof(f16830,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),multiplication(X0,X1))))
| ~ leq(coantidomain(X0),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f181,f392]) ).
fof(f16831,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,omega(X1)))))
| ~ leq(X0,addition(omega(X1),multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f321,f392]) ).
fof(f16832,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,one))))
| ~ leq(X0,addition(X1,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f192,f392]) ).
fof(f16833,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,coantidomain(X1)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f190,f392]) ).
fof(f16834,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,star(X1)))))
| ~ leq(one,multiplication(X0,star(X1))) ),
inference(paramodulation,[status(thm)],[f7563,f392]) ).
fof(f16835,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,multiplication(star(X1),addition(X1,one))))))
| ~ leq(one,multiplication(X0,star(X1))) ),
inference(paramodulation,[status(thm)],[f7789,f392]) ).
fof(f16836,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,multiplication(addition(X1,one),star(X1))))))
| ~ leq(one,multiplication(X0,star(X1))) ),
inference(paramodulation,[status(thm)],[f7510,f392]) ).
fof(f16837,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1504,f392]) ).
fof(f16838,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,forward_box(X1,X2)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1497,f392]) ).
fof(f16839,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,backward_box(X1,X2)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1492,f392]) ).
fof(f16840,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1485,f392]) ).
fof(f16841,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,divergence(X1)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1488,f392]) ).
fof(f16842,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,codomain(X1)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1477,f392]) ).
fof(f16843,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,c(X1)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1471,f392]) ).
fof(f16844,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,antidomain(X1)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1379,f392]) ).
fof(f16845,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,coantidomain(X1)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1377,f392]) ).
fof(f16846,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,domain(X1)))))
| ~ leq(one,multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f1375,f392]) ).
fof(f16847,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(X1),multiplication(star(X1),multiplication(X1,c(X0)))))
| ~ leq(domain(X0),multiplication(X1,one)) ),
inference(paramodulation,[status(thm)],[f569,f392]) ).
fof(f16848,plain,
! [X0,X1,X2] :
( leq(coantidomain(multiplication(X0,X1)),addition(omega(X2),multiplication(star(X2),multiplication(X2,coantidomain(multiplication(codomain(X0),X1))))))
| ~ leq(coantidomain(multiplication(X0,X1)),multiplication(X2,coantidomain(multiplication(codomain(X0),X1)))) ),
inference(paramodulation,[status(thm)],[f615,f392]) ).
fof(f16849,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X1),multiplication(star(X1),multiplication(X1,codomain(X0)))))
| ~ leq(coantidomain(X0),multiplication(X1,one)) ),
inference(paramodulation,[status(thm)],[f683,f392]) ).
fof(f16850,plain,
! [X0,X1,X2] :
( leq(antidomain(multiplication(X0,X1)),addition(omega(X2),multiplication(star(X2),multiplication(X2,antidomain(multiplication(X0,domain(X1)))))))
| ~ leq(antidomain(multiplication(X0,X1)),multiplication(X2,antidomain(multiplication(X0,domain(X1))))) ),
inference(paramodulation,[status(thm)],[f479,f392]) ).
fof(f16851,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(X1),multiplication(star(X1),multiplication(X1,c(X0)))))
| ~ leq(antidomain(X0),multiplication(X1,c(X0))) ),
inference(paramodulation,[status(thm)],[f514,f392]) ).
fof(f16852,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(X1),multiplication(star(X1),multiplication(X1,domain(X0)))))
| ~ leq(antidomain(X0),multiplication(X1,one)) ),
inference(paramodulation,[status(thm)],[f558,f392]) ).
fof(f16853,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,multiplication(X1,X2)),addition(omega(X3),multiplication(star(X3),multiplication(X3,multiplication(X4,X2)))))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(addition(multiplication(X0,X1),X4),X2))) ),
inference(paramodulation,[status(thm)],[f204,f392]) ).
fof(f16854,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,addition(multiplication(X3,X1),X4)))))
| ~ leq(multiplication(X0,X1),multiplication(X2,addition(multiplication(addition(X0,X3),X1),X4))) ),
inference(paramodulation,[status(thm)],[f219,f392]) ).
fof(f16855,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,addition(multiplication(X0,X3),X4)))))
| ~ leq(multiplication(X0,X1),multiplication(X2,addition(multiplication(X0,addition(X1,X3)),X4))) ),
inference(paramodulation,[status(thm)],[f170,f392]) ).
fof(f16856,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,multiplication(X3,multiplication(X4,X1))))))
| ~ leq(multiplication(X0,X1),multiplication(X2,multiplication(addition(X0,multiplication(X3,X4)),X1))) ),
inference(paramodulation,[status(thm)],[f211,f392]) ).
fof(f16857,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,multiplication(X3,X1)))))
| ~ leq(multiplication(X0,X1),multiplication(X2,multiplication(addition(X3,X0),X1))) ),
inference(paramodulation,[status(thm)],[f201,f392]) ).
fof(f16858,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,multiplication(X0,X3)))))
| ~ leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,addition(X3,X1)))) ),
inference(paramodulation,[status(thm)],[f153,f392]) ).
fof(f16859,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,multiplication(X3,X1)))))
| ~ leq(multiplication(X0,X1),multiplication(X2,multiplication(addition(X0,X3),X1))) ),
inference(paramodulation,[status(thm)],[f43,f392]) ).
fof(f16860,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,multiplication(X0,X3)))))
| ~ leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,addition(X1,X3)))) ),
inference(paramodulation,[status(thm)],[f42,f392]) ).
fof(f16861,plain,
! [X0,X1,X2,X3] :
( leq(addition(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,X3))))
| ~ leq(addition(X0,X1),multiplication(X2,addition(X1,addition(X0,X3)))) ),
inference(paramodulation,[status(thm)],[f103,f392]) ).
fof(f16862,plain,
! [X0,X1,X2,X3] :
( leq(addition(X0,X1),addition(omega(X2),multiplication(star(X2),multiplication(X2,X3))))
| ~ leq(addition(X0,X1),multiplication(X2,addition(X0,addition(X1,X3)))) ),
inference(paramodulation,[status(thm)],[f36,f392]) ).
fof(f16864,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(domain(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4516,f392]) ).
fof(f16865,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(coantidomain(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4515,f392]) ).
fof(f16866,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(antidomain(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4514,f392]) ).
fof(f16867,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(c(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4513,f392]) ).
fof(f16868,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(codomain(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4512,f392]) ).
fof(f16869,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(divergence(X2),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4511,f392]) ).
fof(f16870,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,forward_diamond(X2,X3))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2491,f392]) ).
fof(f16871,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,backward_box(X2,X3))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2490,f392]) ).
fof(f16872,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,forward_box(X2,X3))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2489,f392]) ).
fof(f16873,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,backward_diamond(X2,X3))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2488,f392]) ).
fof(f16874,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,domain(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2497,f392]) ).
fof(f16875,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,coantidomain(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2496,f392]) ).
fof(f16876,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,antidomain(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2495,f392]) ).
fof(f16877,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,c(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2494,f392]) ).
fof(f16878,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,codomain(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2493,f392]) ).
fof(f16879,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,divergence(X2))))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2492,f392]) ).
fof(f16880,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(X1,multiplication(addition(X2,one),X0))) ),
inference(paramodulation,[status(thm)],[f232,f392]) ).
fof(f16881,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(X1,multiplication(addition(one,X2),X0))) ),
inference(paramodulation,[status(thm)],[f207,f392]) ).
fof(f16882,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,X2)))))
| ~ leq(X0,multiplication(X1,multiplication(X0,addition(X2,one)))) ),
inference(paramodulation,[status(thm)],[f192,f392]) ).
fof(f16883,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,X2)))))
| ~ leq(X0,multiplication(X1,multiplication(X0,addition(one,X2)))) ),
inference(paramodulation,[status(thm)],[f162,f392]) ).
fof(f16884,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X2,X0)))))
| ~ leq(X0,multiplication(X1,addition(X0,X2))) ),
inference(paramodulation,[status(thm)],[f1329,f392]) ).
fof(f16885,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X0,X2)))))
| ~ leq(X0,multiplication(X1,addition(X2,X0))) ),
inference(paramodulation,[status(thm)],[f1026,f392]) ).
fof(f16886,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X2,X0)))))
| ~ leq(X0,multiplication(X1,addition(X2,X0))) ),
inference(paramodulation,[status(thm)],[f1005,f392]) ).
fof(f16887,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X0,X2)))))
| ~ leq(X0,multiplication(X1,addition(X0,X2))) ),
inference(paramodulation,[status(thm)],[f105,f392]) ).
fof(f16888,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X2,X3)))))
| ~ leq(X0,multiplication(X1,addition(X2,addition(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f97,f392]) ).
fof(f16889,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X3,X2)))))
| ~ leq(X0,multiplication(X1,addition(X2,addition(X0,X3)))) ),
inference(paramodulation,[status(thm)],[f97,f392]) ).
fof(f16890,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,zero))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f37,f392]) ).
fof(f16891,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X2))))
| ~ leq(X0,multiplication(X1,addition(X2,X0))) ),
inference(paramodulation,[status(thm)],[f35,f392]) ).
fof(f16892,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X2))))
| ~ leq(X0,multiplication(X1,addition(X2,X0))) ),
inference(paramodulation,[status(thm)],[f35,f392]) ).
fof(f16893,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f38,f392]) ).
fof(f16894,plain,
! [X0] : leq(one,addition(omega(one),multiplication(one,multiplication(one,X0)))),
inference(forward_demodulation,[status(thm)],[f9603,f16816]) ).
fof(f16895,plain,
! [X0] : leq(one,addition(omega(one),multiplication(one,X0))),
inference(forward_demodulation,[status(thm)],[f41,f16894]) ).
fof(f16896,plain,
! [X0] : leq(one,addition(omega(one),X0)),
inference(forward_demodulation,[status(thm)],[f41,f16895]) ).
fof(f16897,plain,
! [X0,X1] : leq(X0,addition(omega(domain(addition(X0,X1))),multiplication(star(domain(addition(X0,X1))),multiplication(domain(addition(X0,X1)),X1)))),
inference(forward_subsumption_resolution,[status(thm)],[f16820,f1324]) ).
fof(f16898,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,addition(X0,X3)))) ),
inference(forward_demodulation,[status(thm)],[f39,f16821]) ).
fof(f16899,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X1,addition(X0,X2)))),multiplication(star(antidomain(addition(addition(X0,X1),X2))),multiplication(antidomain(addition(addition(X0,X1),X2)),X1))))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f103,f16822]) ).
fof(f16900,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X1,addition(X0,X2)))),multiplication(star(antidomain(addition(X1,addition(X0,X2)))),multiplication(antidomain(addition(addition(X0,X1),X2)),X1))))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f103,f16899]) ).
fof(f16901,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X1,addition(X0,X2)))),multiplication(star(antidomain(addition(X1,addition(X0,X2)))),multiplication(antidomain(addition(X1,addition(X0,X2))),X1))))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f103,f16900]) ).
fof(f16902,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X1,addition(X0,X2)))),multiplication(star(antidomain(addition(X1,addition(X0,X2)))),zero)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f2635,f16901]) ).
fof(f16903,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X1,addition(X0,X2)))),zero))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f44,f16902]) ).
fof(f16904,plain,
! [X0,X1,X2] :
( leq(X0,omega(antidomain(addition(X1,addition(X0,X2)))))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f16903]) ).
fof(f16905,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),zero)))
| ~ leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f59,f16823]) ).
fof(f16906,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X1)),zero))
| ~ leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f44,f16905]) ).
fof(f16907,plain,
! [X0,X1] :
( leq(X0,omega(antidomain(X1)))
| ~ leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f16906]) ).
fof(f16912,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,multiplication(one,X1))))
| ~ leq(X0,addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f9603,f16827]) ).
fof(f16913,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),multiplication(one,X1)))
| ~ leq(X0,addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f16912]) ).
fof(f16914,plain,
! [X0,X1] :
( leq(X0,addition(omega(one),X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f41,f16913]) ).
fof(f16915,plain,
! [X0,X1] : leq(X0,addition(omega(one),X1)),
inference(forward_subsumption_resolution,[status(thm)],[f16914,f1324]) ).
fof(f16916,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),omega(X1))))
| ~ leq(X0,addition(omega(X1),multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f56,f16831]) ).
fof(f16917,plain,
! [X0,X1] :
( leq(X0,multiplication(addition(star(X1),one),omega(X1)))
| ~ leq(X0,addition(omega(X1),multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f232,f16916]) ).
fof(f16918,plain,
! [X0,X1] :
( leq(X0,multiplication(addition(one,star(X1)),omega(X1)))
| ~ leq(X0,addition(omega(X1),multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f16917]) ).
fof(f16919,plain,
! [X0,X1] :
( leq(X0,multiplication(star(X1),omega(X1)))
| ~ leq(X0,addition(omega(X1),multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f7563,f16918]) ).
fof(f16920,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(X0,addition(X1,multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f40,f16832]) ).
fof(f16921,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),zero)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f63,f16833]) ).
fof(f16922,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),zero))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f44,f16921]) ).
fof(f16923,plain,
! [X0,X1] :
( leq(X0,omega(X1))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f16922]) ).
fof(f16924,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16837]) ).
fof(f16925,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,forward_box(X1,X2)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16838]) ).
fof(f16926,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,backward_box(X1,X2)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16839]) ).
fof(f16927,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16840]) ).
fof(f16928,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,divergence(X1)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16841]) ).
fof(f16929,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,codomain(X1)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16842]) ).
fof(f16930,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,c(X1)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16843]) ).
fof(f16931,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,antidomain(X1)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16844]) ).
fof(f16932,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,coantidomain(X1)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16845]) ).
fof(f16933,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,domain(X1)))))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f16846]) ).
fof(f16934,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(X1),multiplication(star(X1),multiplication(X1,c(X0)))))
| ~ leq(domain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f40,f16847]) ).
fof(f16935,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X1),multiplication(star(X1),multiplication(X1,codomain(X0)))))
| ~ leq(coantidomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f40,f16849]) ).
fof(f16936,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(X1),multiplication(star(X1),multiplication(X1,domain(X0)))))
| ~ leq(antidomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f40,f16852]) ).
fof(f16937,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),zero)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f44,f16890]) ).
fof(f16938,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),zero))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f44,f16937]) ).
fof(f16939,plain,
! [X0,X1] :
( leq(X0,omega(X1))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f16938]) ).
fof(f16941,plain,
! [X0,X1] : leq(X0,omega(star(X1))),
inference(resolution,[status(thm)],[f407,f8451]) ).
fof(f16942,plain,
! [X0] : leq(addition(one,X0),omega(addition(one,X0))),
inference(resolution,[status(thm)],[f407,f2478]) ).
fof(f16944,plain,
! [X0,X1] :
( leq(X0,omega(addition(one,X1)))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f207,f407]) ).
fof(f16945,plain,
! [X0,X1] :
( leq(X0,omega(addition(antidomain(X0),X1)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f224,f407]) ).
fof(f16946,plain,
! [X0,X1] :
( leq(omega(X0),omega(addition(X1,one)))
| ~ leq(omega(X0),multiplication(addition(X0,X1),omega(X0))) ),
inference(paramodulation,[status(thm)],[f11449,f407]) ).
fof(f16947,plain,
! [X0,X1] :
( leq(omega(X0),omega(addition(X1,one)))
| ~ leq(omega(X0),multiplication(addition(X1,X0),omega(X0))) ),
inference(paramodulation,[status(thm)],[f10882,f407]) ).
fof(f16948,plain,
! [X0,X1] :
( leq(X0,omega(addition(X1,one)))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f232,f407]) ).
fof(f16949,plain,
! [X0,X1] :
( leq(X0,omega(addition(X1,antidomain(X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f230,f407]) ).
fof(f16950,plain,
! [X0,X1] :
( leq(omega(X0),omega(addition(X0,X1)))
| ~ leq(omega(X0),multiplication(addition(X1,one),omega(X0))) ),
inference(paramodulation,[status(thm)],[f11449,f407]) ).
fof(f16951,plain,
! [X0,X1] :
( leq(omega(X0),omega(addition(X1,X0)))
| ~ leq(omega(X0),multiplication(addition(X1,one),omega(X0))) ),
inference(paramodulation,[status(thm)],[f10882,f407]) ).
fof(f16952,plain,
! [X0,X1] :
( leq(coantidomain(X0),omega(addition(X1,X0)))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f233,f407]) ).
fof(f16953,plain,
! [X0,X1] :
( leq(coantidomain(X0),omega(addition(X0,X1)))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f226,f407]) ).
fof(f16954,plain,
! [X0] :
( leq(antidomain(X0),omega(c(X0)))
| ~ leq(antidomain(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2633,f407]) ).
fof(f16955,plain,
! [X0] :
( leq(c(X0),omega(c(X0)))
| ~ leq(c(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2211,f407]) ).
fof(f16956,plain,
! [X0,X1] :
( leq(domain_difference(X0,X1),omega(c(X0)))
| ~ leq(domain_difference(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f1585,f407]) ).
fof(f16957,plain,
! [X0] :
( leq(domain(X0),omega(c(X0)))
| ~ leq(domain(X0),zero) ),
inference(paramodulation,[status(thm)],[f197,f407]) ).
fof(f16958,plain,
! [X0] :
( leq(X0,omega(c(X0)))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f4265,f407]) ).
fof(f16959,plain,
! [X0] :
( leq(codomain(X0),omega(coantidomain(X0)))
| ~ leq(codomain(X0),zero) ),
inference(paramodulation,[status(thm)],[f195,f407]) ).
fof(f16960,plain,
! [X0] :
( leq(domain(X0),omega(domain(X0)))
| ~ leq(domain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2215,f407]) ).
fof(f16961,plain,
! [X0,X1] :
( leq(antidomain(X0),omega(domain(X1)))
| ~ leq(antidomain(X0),domain_difference(X1,X0)) ),
inference(paramodulation,[status(thm)],[f68,f407]) ).
fof(f16962,plain,
! [X0] :
( leq(X0,omega(domain(X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4146,f407]) ).
fof(f16963,plain,
! [X0,X1,X2] :
( leq(X0,omega(multiplication(X1,X2)))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f39,f407]) ).
fof(f16964,plain,
! [X0,X1] :
( leq(X0,omega(antidomain(addition(X0,X1))))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f2635,f407]) ).
fof(f16965,plain,
! [X0,X1] :
( leq(addition(X0,X1),omega(antidomain(X1)))
| ~ leq(addition(X0,X1),multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f186,f407]) ).
fof(f16966,plain,
! [X0,X1] :
( leq(addition(X0,X1),omega(antidomain(X0)))
| ~ leq(addition(X0,X1),multiplication(antidomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f177,f407]) ).
fof(f16967,plain,
! [X0] :
( leq(omega(X0),omega(antidomain(X0)))
| ~ leq(omega(X0),zero) ),
inference(paramodulation,[status(thm)],[f1569,f407]) ).
fof(f16968,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),omega(antidomain(X0)))
| ~ leq(multiplication(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f136,f407]) ).
fof(f16969,plain,
! [X0] :
( leq(X0,omega(antidomain(X0)))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f59,f407]) ).
fof(f16971,plain,
! [X0] :
( leq(X0,omega(one))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f41,f407]) ).
fof(f16972,plain,
! [X0] :
( leq(codomain(X0),omega(X0))
| ~ leq(codomain(X0),X0) ),
inference(paramodulation,[status(thm)],[f2309,f407]) ).
fof(f16973,plain,
! [X0,X1] :
( leq(addition(omega(X0),X1),omega(X0))
| ~ leq(addition(omega(X0),X1),addition(omega(X0),multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f318,f407]) ).
fof(f16974,plain,
! [X0,X1] :
( leq(addition(one,X0),omega(X1))
| ~ leq(addition(one,X0),addition(X1,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f162,f407]) ).
fof(f16975,plain,
! [X0,X1] :
( leq(addition(coantidomain(X0),X1),omega(X0))
| ~ leq(addition(coantidomain(X0),X1),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f181,f407]) ).
fof(f16976,plain,
! [X0,X1] :
( leq(addition(X0,omega(X1)),omega(X1))
| ~ leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f321,f407]) ).
fof(f16977,plain,
! [X0,X1] :
( leq(addition(X0,one),omega(X1))
| ~ leq(addition(X0,one),addition(X1,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f192,f407]) ).
fof(f16978,plain,
! [X0,X1] :
( leq(addition(X0,coantidomain(X1)),omega(X1))
| ~ leq(addition(X0,coantidomain(X1)),multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f190,f407]) ).
fof(f16979,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),X1),omega(X0))
| ~ leq(multiplication(omega(X0),X1),multiplication(omega(X0),X1)) ),
inference(paramodulation,[status(thm)],[f319,f407]) ).
fof(f16980,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X0),X1),omega(X0))
| ~ leq(multiplication(coantidomain(X0),X1),zero) ),
inference(paramodulation,[status(thm)],[f151,f407]) ).
fof(f16981,plain,
! [X0,X1] :
( leq(multiplication(X0,omega(multiplication(X1,X0))),omega(X1))
| ~ leq(multiplication(X0,omega(multiplication(X1,X0))),omega(multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f308,f407]) ).
fof(f16982,plain,
! [X0,X1] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),omega(X1))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),zero) ),
inference(paramodulation,[status(thm)],[f144,f407]) ).
fof(f16983,plain,
! [X0] :
( leq(omega(coantidomain(X0)),omega(X0))
| ~ leq(omega(coantidomain(X0)),zero) ),
inference(paramodulation,[status(thm)],[f1813,f407]) ).
fof(f16985,plain,
! [X0] :
( leq(coantidomain(X0),omega(X0))
| ~ leq(coantidomain(X0),zero) ),
inference(paramodulation,[status(thm)],[f63,f407]) ).
fof(f16986,plain,
! [X0] :
( leq(zero,omega(X0))
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f44,f407]) ).
fof(f16987,plain,
! [X0] :
( leq(one,omega(X0))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f40,f407]) ).
fof(f16988,plain,
! [X0,X1] : leq(X0,omega(addition(one,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f16944,f1324]) ).
fof(f16989,plain,
! [X0,X1] : leq(X0,omega(addition(X1,one))),
inference(forward_subsumption_resolution,[status(thm)],[f16948,f1324]) ).
fof(f16990,plain,
! [X0] : leq(antidomain(X0),omega(c(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16954,f4241]) ).
fof(f16991,plain,
! [X0] : leq(c(X0),omega(c(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16955,f239]) ).
fof(f16992,plain,
! [X0] : leq(domain(X0),omega(domain(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16960,f239]) ).
fof(f16993,plain,
! [X0] : leq(X0,omega(domain(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f16962,f239]) ).
fof(f16994,plain,
! [X0] : leq(X0,omega(one)),
inference(forward_subsumption_resolution,[status(thm)],[f16971,f239]) ).
fof(f16995,plain,
! [X0,X1] : leq(multiplication(omega(X0),X1),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f16979,f239]) ).
fof(f16996,definition,
! [X0] :
( sQ44_spl
<=> leq(zero,omega(X0)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f16999,plain,
( sQ44_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f16986,f7983,f16996]) ).
fof(f17016,plain,
! [X0] : addition(X0,omega(one)) = omega(one),
inference(resolution,[status(thm)],[f16994,f48]) ).
fof(f17035,plain,
! [X0,X1] : addition(X0,omega(star(X1))) = omega(star(X1)),
inference(resolution,[status(thm)],[f16941,f48]) ).
fof(f17038,plain,
! [X0] : leq(multiplication(X0,star(coantidomain(omega(domain(X0))))),omega(domain(X0))),
inference(resolution,[status(thm)],[f16993,f346]) ).
fof(f17039,plain,
! [X0] : leq(multiplication(star(antidomain(omega(domain(X0)))),X0),omega(domain(X0))),
inference(resolution,[status(thm)],[f16993,f304]) ).
fof(f17040,plain,
! [X0] : addition(X0,omega(domain(X0))) = omega(domain(X0)),
inference(resolution,[status(thm)],[f16993,f48]) ).
fof(f17043,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13917,f16993]) ).
fof(f17044,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13916,f16993]) ).
fof(f17047,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),omega(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f69,f16993]) ).
fof(f17049,plain,
! [X0] : leq(domain(X0),omega(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f196,f16993]) ).
fof(f17053,plain,
! [X0,X1] : leq(divergence(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f394,f2232]) ).
fof(f17054,plain,
! [X0,X1] : leq(codomain(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f394,f2247]) ).
fof(f17055,plain,
! [X0,X1] : leq(c(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f394,f2264]) ).
fof(f17056,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f394,f2373]) ).
fof(f17057,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f394,f2387]) ).
fof(f17058,plain,
! [X0,X1] : leq(domain(X0),addition(omega(X1),multiplication(star(X1),one))),
inference(resolution,[status(thm)],[f394,f2403]) ).
fof(f17059,plain,
! [X0,X1] : leq(one,addition(omega(X0),multiplication(star(X0),star(X1)))),
inference(resolution,[status(thm)],[f394,f8413]) ).
fof(f17061,plain,
! [X0,X1] : leq(X0,addition(omega(X1),multiplication(star(X1),X0))),
inference(resolution,[status(thm)],[f394,f1324]) ).
fof(f17062,plain,
! [X0] :
( leq(addition(X0,one),addition(omega(star(X0)),multiplication(star(star(X0)),one)))
| ~ leq(addition(X0,one),star(X0)) ),
inference(paramodulation,[status(thm)],[f7789,f394]) ).
fof(f17063,plain,
! [X0] :
( leq(star(X0),addition(omega(addition(X0,one)),multiplication(star(addition(X0,one)),one)))
| ~ leq(star(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f7510,f394]) ).
fof(f17064,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X3),multiplication(star(X3),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(addition(multiplication(X1,X2),X3),X0)) ),
inference(paramodulation,[status(thm)],[f204,f394]) ).
fof(f17065,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(X3),multiplication(star(X3),multiplication(X2,X1))))
| ~ leq(multiplication(X0,X1),multiplication(addition(X2,multiplication(X3,X0)),X1)) ),
inference(paramodulation,[status(thm)],[f211,f394]) ).
fof(f17068,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X2),multiplication(star(X2),multiplication(X1,X0))))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f43,f394]) ).
fof(f17069,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X2))))
| ~ leq(X0,multiplication(X1,addition(X2,X0))) ),
inference(paramodulation,[status(thm)],[f42,f394]) ).
fof(f17070,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X3),multiplication(star(X3),addition(X2,X1))))
| ~ leq(X0,addition(X1,addition(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f103,f394]) ).
fof(f17071,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X3),multiplication(star(X3),addition(X1,X2))))
| ~ leq(X0,addition(X1,addition(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f36,f394]) ).
fof(f17073,plain,
! [X0,X1] :
( leq(X0,addition(omega(domain(X1)),multiplication(star(domain(X1)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4516,f394]) ).
fof(f17074,plain,
! [X0,X1] :
( leq(X0,addition(omega(coantidomain(X1)),multiplication(star(coantidomain(X1)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4515,f394]) ).
fof(f17075,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4514,f394]) ).
fof(f17076,plain,
! [X0,X1] :
( leq(X0,addition(omega(c(X1)),multiplication(star(c(X1)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4513,f394]) ).
fof(f17077,plain,
! [X0,X1] :
( leq(X0,addition(omega(codomain(X1)),multiplication(star(codomain(X1)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4512,f394]) ).
fof(f17078,plain,
! [X0,X1] :
( leq(X0,addition(omega(divergence(X1)),multiplication(star(divergence(X1)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4511,f394]) ).
fof(f17079,plain,
! [X0,X1,X2] :
( leq(forward_diamond(X0,X1),addition(omega(X2),multiplication(star(X2),X2)))
| ~ leq(forward_diamond(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f2491,f394]) ).
fof(f17080,plain,
! [X0,X1,X2] :
( leq(backward_box(X0,X1),addition(omega(X2),multiplication(star(X2),X2)))
| ~ leq(backward_box(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f2490,f394]) ).
fof(f17081,plain,
! [X0,X1,X2] :
( leq(forward_box(X0,X1),addition(omega(X2),multiplication(star(X2),X2)))
| ~ leq(forward_box(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f2489,f394]) ).
fof(f17082,plain,
! [X0,X1,X2] :
( leq(backward_diamond(X0,X1),addition(omega(X2),multiplication(star(X2),X2)))
| ~ leq(backward_diamond(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f2488,f394]) ).
fof(f17083,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(domain(X0),X1) ),
inference(paramodulation,[status(thm)],[f2497,f394]) ).
fof(f17084,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(coantidomain(X0),X1) ),
inference(paramodulation,[status(thm)],[f2496,f394]) ).
fof(f17085,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(antidomain(X0),X1) ),
inference(paramodulation,[status(thm)],[f2495,f394]) ).
fof(f17086,plain,
! [X0,X1] :
( leq(c(X0),addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(c(X0),X1) ),
inference(paramodulation,[status(thm)],[f2494,f394]) ).
fof(f17087,plain,
! [X0,X1] :
( leq(codomain(X0),addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(codomain(X0),X1) ),
inference(paramodulation,[status(thm)],[f2493,f394]) ).
fof(f17088,plain,
! [X0,X1] :
( leq(divergence(X0),addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(divergence(X0),X1) ),
inference(paramodulation,[status(thm)],[f2492,f394]) ).
fof(f17089,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X0)))
| ~ leq(X0,multiplication(addition(X1,one),X0)) ),
inference(paramodulation,[status(thm)],[f232,f394]) ).
fof(f17090,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X0)))
| ~ leq(X0,multiplication(addition(one,X1),X0)) ),
inference(paramodulation,[status(thm)],[f207,f394]) ).
fof(f17091,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(X0,multiplication(X1,addition(X0,one))) ),
inference(paramodulation,[status(thm)],[f192,f394]) ).
fof(f17092,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X1)))
| ~ leq(X0,multiplication(X1,addition(one,X0))) ),
inference(paramodulation,[status(thm)],[f162,f394]) ).
fof(f17095,plain,
! [X0,X1] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f38,f394]) ).
fof(f17096,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(one,X2)),multiplication(star(addition(one,X2)),X1)))
| ~ leq(X0,addition(X1,addition(X0,multiplication(X2,X0)))) ),
inference(paramodulation,[status(thm)],[f207,f394]) ).
fof(f17097,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(antidomain(X0),X2)),multiplication(star(addition(antidomain(X0),X2)),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f224,f394]) ).
fof(f17098,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(addition(X2,one)),multiplication(star(addition(X2,one)),X1)))
| ~ leq(omega(X0),addition(X1,multiplication(addition(X0,X2),omega(X0)))) ),
inference(paramodulation,[status(thm)],[f11449,f394]) ).
fof(f17099,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(addition(X2,one)),multiplication(star(addition(X2,one)),X1)))
| ~ leq(omega(X0),addition(X1,multiplication(addition(X2,X0),omega(X0)))) ),
inference(paramodulation,[status(thm)],[f10882,f394]) ).
fof(f17100,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(X2,one)),multiplication(star(addition(X2,one)),X1)))
| ~ leq(X0,addition(X1,addition(X0,multiplication(X2,X0)))) ),
inference(paramodulation,[status(thm)],[f232,f394]) ).
fof(f17101,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(addition(X2,antidomain(X0))),multiplication(star(addition(X2,antidomain(X0))),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f230,f394]) ).
fof(f17102,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(addition(X0,X2)),multiplication(star(addition(X0,X2)),X1)))
| ~ leq(omega(X0),addition(X1,multiplication(addition(X2,one),omega(X0)))) ),
inference(paramodulation,[status(thm)],[f11449,f394]) ).
fof(f17103,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(addition(X2,X0)),multiplication(star(addition(X2,X0)),X1)))
| ~ leq(omega(X0),addition(X1,multiplication(addition(X2,one),omega(X0)))) ),
inference(paramodulation,[status(thm)],[f10882,f394]) ).
fof(f17104,plain,
! [X0,X1,X2] :
( leq(coantidomain(X0),addition(omega(addition(X2,X0)),multiplication(star(addition(X2,X0)),X1)))
| ~ leq(coantidomain(X0),addition(X1,multiplication(X2,coantidomain(X0)))) ),
inference(paramodulation,[status(thm)],[f233,f394]) ).
fof(f17105,plain,
! [X0,X1,X2] :
( leq(coantidomain(X0),addition(omega(addition(X0,X2)),multiplication(star(addition(X0,X2)),X1)))
| ~ leq(coantidomain(X0),addition(X1,multiplication(X2,coantidomain(X0)))) ),
inference(paramodulation,[status(thm)],[f226,f394]) ).
fof(f17106,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(antidomain(X0),addition(X1,c(X0))) ),
inference(paramodulation,[status(thm)],[f2633,f394]) ).
fof(f17107,plain,
! [X0,X1] :
( leq(c(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(c(X0),addition(X1,c(X0))) ),
inference(paramodulation,[status(thm)],[f2211,f394]) ).
fof(f17108,plain,
! [X0,X1,X2] :
( leq(domain_difference(X0,X1),addition(omega(c(X0)),multiplication(star(c(X0)),X2)))
| ~ leq(domain_difference(X0,X1),addition(X2,zero)) ),
inference(paramodulation,[status(thm)],[f1585,f394]) ).
fof(f17109,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(domain(X0),addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f197,f394]) ).
fof(f17110,plain,
! [X0,X1] :
( leq(X0,addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(X0,addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f4265,f394]) ).
fof(f17111,plain,
! [X0,X1] :
( leq(codomain(X0),addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),X1)))
| ~ leq(codomain(X0),addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f195,f394]) ).
fof(f17112,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),X1)))
| ~ leq(domain(X0),addition(X1,domain(X0))) ),
inference(paramodulation,[status(thm)],[f2215,f394]) ).
fof(f17113,plain,
! [X0,X1,X2] :
( leq(antidomain(X0),addition(omega(domain(X2)),multiplication(star(domain(X2)),X1)))
| ~ leq(antidomain(X0),addition(X1,domain_difference(X2,X0))) ),
inference(paramodulation,[status(thm)],[f68,f394]) ).
fof(f17114,plain,
! [X0,X1] :
( leq(X0,addition(omega(domain(X0)),multiplication(star(domain(X0)),X1)))
| ~ leq(X0,addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4146,f394]) ).
fof(f17115,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f39,f394]) ).
fof(f17116,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X0,X2))),multiplication(star(antidomain(addition(X0,X2))),X1)))
| ~ leq(X0,addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f2635,f394]) ).
fof(f17117,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),X2)))
| ~ leq(addition(X0,X1),addition(X2,multiplication(antidomain(X1),X0))) ),
inference(paramodulation,[status(thm)],[f186,f394]) ).
fof(f17118,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X2)))
| ~ leq(addition(X0,X1),addition(X2,multiplication(antidomain(X0),X1))) ),
inference(paramodulation,[status(thm)],[f177,f394]) ).
fof(f17119,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(omega(X0),addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f1569,f394]) ).
fof(f17120,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X2)))
| ~ leq(multiplication(X0,X1),addition(X2,zero)) ),
inference(paramodulation,[status(thm)],[f136,f394]) ).
fof(f17121,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(X0,addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f59,f394]) ).
fof(f17124,plain,
! [X0,X1] :
( leq(codomain(X0),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(codomain(X0),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2309,f394]) ).
fof(f17125,plain,
! [X0,X1,X2] :
( leq(addition(omega(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(addition(omega(X0),X1),addition(X2,addition(omega(X0),multiplication(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f318,f394]) ).
fof(f17126,plain,
! [X0,X1,X2] :
( leq(addition(one,X0),addition(omega(X2),multiplication(star(X2),X1)))
| ~ leq(addition(one,X0),addition(X1,addition(X2,multiplication(X2,X0)))) ),
inference(paramodulation,[status(thm)],[f162,f394]) ).
fof(f17127,plain,
! [X0,X1,X2] :
( leq(addition(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(addition(coantidomain(X0),X1),addition(X2,multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f181,f394]) ).
fof(f17128,plain,
! [X0,X1,X2] :
( leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,omega(X1)),addition(X2,addition(omega(X1),multiplication(X1,X0)))) ),
inference(paramodulation,[status(thm)],[f321,f394]) ).
fof(f17129,plain,
! [X0,X1,X2] :
( leq(addition(X0,one),addition(omega(X2),multiplication(star(X2),X1)))
| ~ leq(addition(X0,one),addition(X1,addition(X2,multiplication(X2,X0)))) ),
inference(paramodulation,[status(thm)],[f192,f394]) ).
fof(f17130,plain,
! [X0,X1,X2] :
( leq(addition(X0,coantidomain(X1)),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(addition(X0,coantidomain(X1)),addition(X2,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f190,f394]) ).
fof(f17131,plain,
! [X0,X1,X2] :
( leq(multiplication(omega(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(multiplication(omega(X0),X1),addition(X2,multiplication(omega(X0),X1))) ),
inference(paramodulation,[status(thm)],[f319,f394]) ).
fof(f17132,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(multiplication(coantidomain(X0),X1),addition(X2,zero)) ),
inference(paramodulation,[status(thm)],[f151,f394]) ).
fof(f17133,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,omega(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(multiplication(X0,omega(multiplication(X1,X0))),addition(X2,omega(multiplication(X1,X0)))) ),
inference(paramodulation,[status(thm)],[f308,f394]) ).
fof(f17134,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(X2,zero)) ),
inference(paramodulation,[status(thm)],[f144,f394]) ).
fof(f17135,plain,
! [X0,X1] :
( leq(omega(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(omega(coantidomain(X0)),addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f1813,f394]) ).
fof(f17137,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(coantidomain(X0),addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f63,f394]) ).
fof(f17139,plain,
! [X0,X1] :
( leq(one,addition(omega(X1),multiplication(star(X1),X0)))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f40,f394]) ).
fof(f17140,plain,
! [X0,X1] : leq(divergence(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f17053]) ).
fof(f17141,plain,
! [X0,X1] : leq(divergence(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f17140]) ).
fof(f17142,plain,
! [X0,X1] : leq(codomain(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f17054]) ).
fof(f17143,plain,
! [X0,X1] : leq(codomain(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f17142]) ).
fof(f17144,plain,
! [X0,X1] : leq(c(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f17055]) ).
fof(f17145,plain,
! [X0,X1] : leq(c(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f17144]) ).
fof(f17146,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f17056]) ).
fof(f17147,plain,
! [X0,X1] : leq(antidomain(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f17146]) ).
fof(f17148,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f17057]) ).
fof(f17149,plain,
! [X0,X1] : leq(coantidomain(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f17148]) ).
fof(f17150,plain,
! [X0,X1] : leq(domain(X0),addition(omega(X1),star(X1))),
inference(forward_demodulation,[status(thm)],[f40,f17058]) ).
fof(f17151,plain,
! [X0,X1] : leq(domain(X0),addition(star(X1),omega(X1))),
inference(forward_demodulation,[status(thm)],[f35,f17150]) ).
fof(f17152,plain,
! [X0] :
( leq(addition(X0,one),addition(omega(star(X0)),star(star(X0))))
| ~ leq(addition(X0,one),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f40,f17062]) ).
fof(f17153,plain,
! [X0] :
( leq(addition(X0,one),addition(star(star(X0)),omega(star(X0))))
| ~ leq(addition(X0,one),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f17152]) ).
fof(f17154,plain,
! [X0] :
( leq(star(X0),addition(omega(addition(X0,one)),star(addition(X0,one))))
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f40,f17063]) ).
fof(f17155,plain,
! [X0] :
( leq(star(X0),addition(star(addition(X0,one)),omega(addition(X0,one))))
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f17154]) ).
fof(f17156,plain,
! [X0] : leq(star(X0),addition(star(addition(X0,one)),omega(addition(X0,one)))),
inference(forward_subsumption_resolution,[status(thm)],[f17155,f239]) ).
fof(f17159,plain,
! [X0,X1] : leq(X0,addition(omega(domain(X1)),multiplication(star(domain(X1)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f17073,f239]) ).
fof(f17160,plain,
! [X0,X1] : leq(X0,addition(omega(coantidomain(X1)),multiplication(star(coantidomain(X1)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f17074,f239]) ).
fof(f17161,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f17075,f239]) ).
fof(f17162,plain,
! [X0,X1] : leq(X0,addition(omega(c(X1)),multiplication(star(c(X1)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f17076,f239]) ).
fof(f17163,plain,
! [X0,X1] : leq(X0,addition(omega(codomain(X1)),multiplication(star(codomain(X1)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f17077,f239]) ).
fof(f17164,plain,
! [X0,X1] : leq(X0,addition(omega(divergence(X1)),multiplication(star(divergence(X1)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f17078,f239]) ).
fof(f17165,plain,
! [X0,X1,X2] : leq(X0,addition(omega(addition(one,X1)),multiplication(star(addition(one,X1)),X2))),
inference(forward_subsumption_resolution,[status(thm)],[f17096,f1421]) ).
fof(f17166,plain,
! [X0,X1,X2] : leq(X0,addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),X2))),
inference(forward_subsumption_resolution,[status(thm)],[f17100,f1421]) ).
fof(f17167,plain,
! [X0,X1] : leq(c(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f17107,f1423]) ).
fof(f17168,plain,
! [X0,X1,X2] :
( leq(domain_difference(X0,X1),addition(omega(c(X0)),multiplication(star(c(X0)),X2)))
| ~ leq(domain_difference(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f37,f17108]) ).
fof(f17169,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(domain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f17109]) ).
fof(f17170,plain,
! [X0,X1] :
( leq(X0,addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f17110]) ).
fof(f17171,plain,
! [X0,X1] :
( leq(codomain(X0),addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),X1)))
| ~ leq(codomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f17111]) ).
fof(f17172,plain,
! [X0,X1] : leq(domain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f17112,f1423]) ).
fof(f17173,plain,
! [X0,X1] : leq(X0,addition(omega(domain(X0)),multiplication(star(domain(X0)),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f17114,f1423]) ).
fof(f17174,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(antidomain(addition(X0,X2))),multiplication(star(antidomain(addition(X0,X2))),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f17116]) ).
fof(f17175,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(omega(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f17119]) ).
fof(f17176,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X2)))
| ~ leq(multiplication(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f37,f17120]) ).
fof(f17177,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f17121]) ).
fof(f17185,plain,
! [X0,X1,X2] : leq(multiplication(omega(X0),X1),addition(omega(X0),multiplication(star(X0),X2))),
inference(forward_subsumption_resolution,[status(thm)],[f17131,f1423]) ).
fof(f17186,plain,
! [X0,X1,X2] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),X2)))
| ~ leq(multiplication(coantidomain(X0),X1),X2) ),
inference(forward_demodulation,[status(thm)],[f37,f17132]) ).
fof(f17187,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),X2) ),
inference(forward_demodulation,[status(thm)],[f37,f17134]) ).
fof(f17188,plain,
! [X0,X1] :
( leq(omega(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(omega(coantidomain(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f17135]) ).
fof(f17189,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(coantidomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f17137]) ).
fof(f17192,plain,
! [X0,X1] : leq(X0,addition(omega(star(X1)),multiplication(star(star(X1)),multiplication(star(X1),X0)))),
inference(resolution,[status(thm)],[f396,f8451]) ).
fof(f17193,plain,
! [X0] : leq(addition(one,X0),addition(omega(addition(one,X0)),multiplication(star(addition(one,X0)),multiplication(addition(one,X0),addition(one,X0))))),
inference(resolution,[status(thm)],[f396,f2478]) ).
fof(f17194,plain,
! [X0] : leq(star(X0),addition(omega(star(X0)),multiplication(star(star(X0)),multiplication(star(X0),star(X0))))),
inference(resolution,[status(thm)],[f396,f8449]) ).
fof(f17195,plain,
! [X0,X1] :
( leq(X0,addition(omega(addition(one,X1)),multiplication(star(addition(one,X1)),multiplication(addition(one,X1),X0))))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f207,f396]) ).
fof(f17196,plain,
! [X0,X1] :
( leq(X0,addition(omega(addition(antidomain(X0),X1)),multiplication(star(addition(antidomain(X0),X1)),multiplication(addition(antidomain(X0),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f224,f396]) ).
fof(f17197,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),multiplication(addition(X1,one),omega(X0)))))
| ~ leq(omega(X0),multiplication(addition(X0,X1),omega(X0))) ),
inference(paramodulation,[status(thm)],[f11449,f396]) ).
fof(f17198,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),multiplication(addition(X1,one),omega(X0)))))
| ~ leq(omega(X0),multiplication(addition(X1,X0),omega(X0))) ),
inference(paramodulation,[status(thm)],[f10882,f396]) ).
fof(f17199,plain,
! [X0,X1] :
( leq(X0,addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),multiplication(addition(X1,one),X0))))
| ~ leq(X0,addition(X0,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f232,f396]) ).
fof(f17200,plain,
! [X0,X1] :
( leq(X0,addition(omega(addition(X1,antidomain(X0))),multiplication(star(addition(X1,antidomain(X0))),multiplication(addition(X1,antidomain(X0)),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f230,f396]) ).
fof(f17201,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(addition(X0,X1)),multiplication(star(addition(X0,X1)),multiplication(addition(X0,X1),omega(X0)))))
| ~ leq(omega(X0),multiplication(addition(X1,one),omega(X0))) ),
inference(paramodulation,[status(thm)],[f11449,f396]) ).
fof(f17202,plain,
! [X0,X1] :
( leq(omega(X0),addition(omega(addition(X1,X0)),multiplication(star(addition(X1,X0)),multiplication(addition(X1,X0),omega(X0)))))
| ~ leq(omega(X0),multiplication(addition(X1,one),omega(X0))) ),
inference(paramodulation,[status(thm)],[f10882,f396]) ).
fof(f17203,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(addition(X1,X0)),multiplication(star(addition(X1,X0)),multiplication(addition(X1,X0),coantidomain(X0)))))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f233,f396]) ).
fof(f17204,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(addition(X0,X1)),multiplication(star(addition(X0,X1)),multiplication(addition(X0,X1),coantidomain(X0)))))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f226,f396]) ).
fof(f17205,plain,
! [X0] :
( leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),multiplication(c(X0),antidomain(X0)))))
| ~ leq(antidomain(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2633,f396]) ).
fof(f17206,plain,
! [X0] :
( leq(c(X0),addition(omega(c(X0)),multiplication(star(c(X0)),multiplication(c(X0),c(X0)))))
| ~ leq(c(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2211,f396]) ).
fof(f17207,plain,
! [X0,X1] :
( leq(domain_difference(X0,X1),addition(omega(c(X0)),multiplication(star(c(X0)),multiplication(c(X0),domain_difference(X0,X1)))))
| ~ leq(domain_difference(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f1585,f396]) ).
fof(f17208,plain,
! [X0] :
( leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),multiplication(c(X0),domain(X0)))))
| ~ leq(domain(X0),zero) ),
inference(paramodulation,[status(thm)],[f197,f396]) ).
fof(f17209,plain,
! [X0] :
( leq(X0,addition(omega(c(X0)),multiplication(star(c(X0)),multiplication(c(X0),X0))))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f4265,f396]) ).
fof(f17210,plain,
! [X0] :
( leq(codomain(X0),addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),multiplication(coantidomain(X0),codomain(X0)))))
| ~ leq(codomain(X0),zero) ),
inference(paramodulation,[status(thm)],[f195,f396]) ).
fof(f17211,plain,
! [X0] :
( leq(domain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),multiplication(domain(X0),domain(X0)))))
| ~ leq(domain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2215,f396]) ).
fof(f17212,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(domain(X1)),multiplication(star(domain(X1)),multiplication(domain(X1),antidomain(X0)))))
| ~ leq(antidomain(X0),domain_difference(X1,X0)) ),
inference(paramodulation,[status(thm)],[f68,f396]) ).
fof(f17213,plain,
! [X0] :
( leq(X0,addition(omega(domain(X0)),multiplication(star(domain(X0)),multiplication(domain(X0),X0))))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4146,f396]) ).
fof(f17214,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,X2),X0))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f39,f396]) ).
fof(f17215,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(addition(X0,X1))),multiplication(star(antidomain(addition(X0,X1))),multiplication(antidomain(addition(X0,X1)),X0))))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f2635,f396]) ).
fof(f17216,plain,
! [X0,X1] :
( leq(addition(X0,X1),addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),multiplication(antidomain(X1),addition(X0,X1)))))
| ~ leq(addition(X0,X1),multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f186,f396]) ).
fof(f17217,plain,
! [X0,X1] :
( leq(addition(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(antidomain(X0),addition(X0,X1)))))
| ~ leq(addition(X0,X1),multiplication(antidomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f177,f396]) ).
fof(f17218,plain,
! [X0] :
( leq(omega(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(antidomain(X0),omega(X0)))))
| ~ leq(omega(X0),zero) ),
inference(paramodulation,[status(thm)],[f1569,f396]) ).
fof(f17219,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(antidomain(X0),multiplication(X0,X1)))))
| ~ leq(multiplication(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f136,f396]) ).
fof(f17220,plain,
! [X0] :
( leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X0))))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f59,f396]) ).
fof(f17223,plain,
! [X0] :
( leq(codomain(X0),addition(omega(X0),multiplication(star(X0),multiplication(X0,codomain(X0)))))
| ~ leq(codomain(X0),X0) ),
inference(paramodulation,[status(thm)],[f2309,f396]) ).
fof(f17224,plain,
! [X0,X1] :
( leq(addition(omega(X0),X1),addition(omega(X0),multiplication(star(X0),multiplication(X0,addition(omega(X0),X1)))))
| ~ leq(addition(omega(X0),X1),addition(omega(X0),multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f318,f396]) ).
fof(f17225,plain,
! [X0,X1] :
( leq(addition(one,X0),addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(one,X0)))))
| ~ leq(addition(one,X0),addition(X1,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f162,f396]) ).
fof(f17226,plain,
! [X0,X1] :
( leq(addition(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),multiplication(X0,addition(coantidomain(X0),X1)))))
| ~ leq(addition(coantidomain(X0),X1),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f181,f396]) ).
fof(f17227,plain,
! [X0,X1] :
( leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X0,omega(X1))))))
| ~ leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f321,f396]) ).
fof(f17228,plain,
! [X0,X1] :
( leq(addition(X0,one),addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X0,one)))))
| ~ leq(addition(X0,one),addition(X1,multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f192,f396]) ).
fof(f17229,plain,
! [X0,X1] :
( leq(addition(X0,coantidomain(X1)),addition(omega(X1),multiplication(star(X1),multiplication(X1,addition(X0,coantidomain(X1))))))
| ~ leq(addition(X0,coantidomain(X1)),multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f190,f396]) ).
fof(f17230,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),X1),addition(omega(X0),multiplication(star(X0),multiplication(X0,multiplication(omega(X0),X1)))))
| ~ leq(multiplication(omega(X0),X1),multiplication(omega(X0),X1)) ),
inference(paramodulation,[status(thm)],[f319,f396]) ).
fof(f17231,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),multiplication(X0,multiplication(coantidomain(X0),X1)))))
| ~ leq(multiplication(coantidomain(X0),X1),zero) ),
inference(paramodulation,[status(thm)],[f151,f396]) ).
fof(f17232,plain,
! [X0,X1] :
( leq(multiplication(X0,omega(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,omega(multiplication(X1,X0)))))))
| ~ leq(multiplication(X0,omega(multiplication(X1,X0))),omega(multiplication(X1,X0))) ),
inference(paramodulation,[status(thm)],[f308,f396]) ).
fof(f17233,plain,
! [X0,X1] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(X0,coantidomain(multiplication(X1,X0)))))))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),zero) ),
inference(paramodulation,[status(thm)],[f144,f396]) ).
fof(f17234,plain,
! [X0] :
( leq(omega(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),multiplication(X0,omega(coantidomain(X0))))))
| ~ leq(omega(coantidomain(X0)),zero) ),
inference(paramodulation,[status(thm)],[f1813,f396]) ).
fof(f17236,plain,
! [X0] :
( leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),multiplication(X0,coantidomain(X0)))))
| ~ leq(coantidomain(X0),zero) ),
inference(paramodulation,[status(thm)],[f63,f396]) ).
fof(f17237,plain,
! [X0] :
( leq(zero,addition(omega(X0),multiplication(star(X0),multiplication(X0,zero))))
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f44,f396]) ).
fof(f17238,plain,
! [X0] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,one))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f40,f396]) ).
fof(f17242,plain,
! [X0,X1] : leq(X0,addition(omega(addition(one,X1)),multiplication(star(addition(one,X1)),multiplication(addition(one,X1),X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f17195,f1324]) ).
fof(f17243,plain,
! [X0,X1] :
( leq(X0,addition(omega(addition(antidomain(X0),X1)),multiplication(star(addition(antidomain(X0),X1)),multiplication(X1,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f224,f17196]) ).
fof(f17244,plain,
! [X0,X1] : leq(X0,addition(omega(addition(X1,one)),multiplication(star(addition(X1,one)),multiplication(addition(X1,one),X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f17199,f1324]) ).
fof(f17245,plain,
! [X0,X1] :
( leq(X0,addition(omega(addition(X1,antidomain(X0))),multiplication(star(addition(X1,antidomain(X0))),multiplication(X1,X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f230,f17200]) ).
fof(f17246,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(addition(X1,X0)),multiplication(star(addition(X1,X0)),multiplication(X1,coantidomain(X0)))))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f233,f17203]) ).
fof(f17247,plain,
! [X0,X1] :
( leq(coantidomain(X0),addition(omega(addition(X0,X1)),multiplication(star(addition(X0,X1)),multiplication(X1,coantidomain(X0)))))
| ~ leq(coantidomain(X0),multiplication(X1,coantidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f226,f17204]) ).
fof(f17248,plain,
! [X0] :
( leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),c(X0))))
| ~ leq(antidomain(X0),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f2633,f17205]) ).
fof(f17249,plain,
! [X0] : leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),c(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f17248,f4241]) ).
fof(f17250,plain,
! [X0] :
( leq(c(X0),addition(omega(c(X0)),multiplication(star(c(X0)),c(X0))))
| ~ leq(c(X0),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f2211,f17206]) ).
fof(f17251,plain,
! [X0] : leq(c(X0),addition(omega(c(X0)),multiplication(star(c(X0)),c(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f17250,f239]) ).
fof(f17252,plain,
! [X0,X1] :
( leq(domain_difference(X0,X1),addition(omega(c(X0)),multiplication(star(c(X0)),zero)))
| ~ leq(domain_difference(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f1585,f17207]) ).
fof(f17253,plain,
! [X0,X1] :
( leq(domain_difference(X0,X1),addition(omega(c(X0)),zero))
| ~ leq(domain_difference(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17252]) ).
fof(f17254,plain,
! [X0,X1] :
( leq(domain_difference(X0,X1),omega(c(X0)))
| ~ leq(domain_difference(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17253]) ).
fof(f17255,plain,
! [X0] :
( leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),zero)))
| ~ leq(domain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f197,f17208]) ).
fof(f17256,plain,
! [X0] :
( leq(domain(X0),addition(omega(c(X0)),zero))
| ~ leq(domain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17255]) ).
fof(f17257,plain,
! [X0] :
( leq(domain(X0),omega(c(X0)))
| ~ leq(domain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17256]) ).
fof(f17258,plain,
! [X0] :
( leq(X0,addition(omega(c(X0)),multiplication(star(c(X0)),zero)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f4265,f17209]) ).
fof(f17259,plain,
! [X0] :
( leq(X0,addition(omega(c(X0)),zero))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17258]) ).
fof(f17260,plain,
! [X0] :
( leq(X0,omega(c(X0)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17259]) ).
fof(f17261,plain,
! [X0] :
( leq(codomain(X0),addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),zero)))
| ~ leq(codomain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f195,f17210]) ).
fof(f17262,plain,
! [X0] :
( leq(codomain(X0),addition(omega(coantidomain(X0)),zero))
| ~ leq(codomain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17261]) ).
fof(f17263,plain,
! [X0] :
( leq(codomain(X0),omega(coantidomain(X0)))
| ~ leq(codomain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17262]) ).
fof(f17264,plain,
! [X0] :
( leq(domain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),domain(X0))))
| ~ leq(domain(X0),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2215,f17211]) ).
fof(f17265,plain,
! [X0] : leq(domain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),domain(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f17264,f239]) ).
fof(f17266,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(domain(X1)),multiplication(star(domain(X1)),domain_difference(X1,X0))))
| ~ leq(antidomain(X0),domain_difference(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f68,f17212]) ).
fof(f17267,plain,
! [X0] :
( leq(X0,addition(omega(domain(X0)),multiplication(star(domain(X0)),X0)))
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f4146,f17213]) ).
fof(f17268,plain,
! [X0] : leq(X0,addition(omega(domain(X0)),multiplication(star(domain(X0)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f17267,f239]) ).
fof(f17269,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17214]) ).
fof(f17270,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(addition(X0,X1))),multiplication(star(antidomain(addition(X0,X1))),zero)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f2635,f17215]) ).
fof(f17271,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(addition(X0,X1))),zero))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17270]) ).
fof(f17272,plain,
! [X0,X1] :
( leq(X0,omega(antidomain(addition(X0,X1))))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17271]) ).
fof(f17273,plain,
! [X0,X1] :
( leq(addition(X0,X1),addition(omega(antidomain(X1)),multiplication(star(antidomain(X1)),multiplication(antidomain(X1),X0))))
| ~ leq(addition(X0,X1),multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f186,f17216]) ).
fof(f17274,plain,
! [X0,X1] :
( leq(addition(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X1))))
| ~ leq(addition(X0,X1),multiplication(antidomain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f177,f17217]) ).
fof(f17275,plain,
! [X0] :
( leq(omega(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),zero)))
| ~ leq(omega(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f1569,f17218]) ).
fof(f17276,plain,
! [X0] :
( leq(omega(X0),addition(omega(antidomain(X0)),zero))
| ~ leq(omega(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17275]) ).
fof(f17277,plain,
! [X0] :
( leq(omega(X0),omega(antidomain(X0)))
| ~ leq(omega(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17276]) ).
fof(f17278,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),zero)))
| ~ leq(multiplication(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f136,f17219]) ).
fof(f17279,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),addition(omega(antidomain(X0)),zero))
| ~ leq(multiplication(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17278]) ).
fof(f17280,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),omega(antidomain(X0)))
| ~ leq(multiplication(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17279]) ).
fof(f17281,plain,
! [X0] :
( leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),zero)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f59,f17220]) ).
fof(f17282,plain,
! [X0] :
( leq(X0,addition(omega(antidomain(X0)),zero))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17281]) ).
fof(f17283,plain,
! [X0] :
( leq(X0,omega(antidomain(X0)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17282]) ).
fof(f17291,plain,
! [X0] :
( leq(codomain(X0),addition(omega(X0),multiplication(star(X0),X0)))
| ~ leq(codomain(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f2309,f17223]) ).
fof(f17292,plain,
! [X0,X1] :
( leq(addition(omega(X0),X1),addition(omega(X0),multiplication(star(X0),addition(omega(X0),multiplication(X0,X1)))))
| ~ leq(addition(omega(X0),X1),addition(omega(X0),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f318,f17224]) ).
fof(f17293,plain,
! [X0,X1] :
( leq(addition(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),multiplication(X0,X1))))
| ~ leq(addition(coantidomain(X0),X1),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f181,f17226]) ).
fof(f17294,plain,
! [X0,X1] :
( leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(star(X1),addition(omega(X1),multiplication(X1,X0)))))
| ~ leq(addition(X0,omega(X1)),addition(omega(X1),multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f321,f17227]) ).
fof(f17295,plain,
! [X0,X1] :
( leq(addition(X0,coantidomain(X1)),addition(omega(X1),multiplication(star(X1),multiplication(X1,X0))))
| ~ leq(addition(X0,coantidomain(X1)),multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f190,f17229]) ).
fof(f17296,plain,
! [X0,X1] :
( leq(multiplication(omega(X0),X1),addition(omega(X0),multiplication(star(X0),multiplication(omega(X0),X1))))
| ~ leq(multiplication(omega(X0),X1),multiplication(omega(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f319,f17230]) ).
fof(f17297,plain,
! [X0,X1] : leq(multiplication(omega(X0),X1),addition(omega(X0),multiplication(star(X0),multiplication(omega(X0),X1)))),
inference(forward_subsumption_resolution,[status(thm)],[f17296,f239]) ).
fof(f17298,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(X0),multiplication(star(X0),zero)))
| ~ leq(multiplication(coantidomain(X0),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f151,f17231]) ).
fof(f17299,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(X0),zero))
| ~ leq(multiplication(coantidomain(X0),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17298]) ).
fof(f17300,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X0),X1),omega(X0))
| ~ leq(multiplication(coantidomain(X0),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17299]) ).
fof(f17301,plain,
! [X0,X1] :
( leq(multiplication(X0,omega(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),omega(multiplication(X1,X0)))))
| ~ leq(multiplication(X0,omega(multiplication(X1,X0))),omega(multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f308,f17232]) ).
fof(f17302,plain,
! [X0,X1] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(X1),multiplication(star(X1),zero)))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),zero) ),
inference(forward_demodulation,[status(thm)],[f144,f17233]) ).
fof(f17303,plain,
! [X0,X1] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(X1),zero))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17302]) ).
fof(f17304,plain,
! [X0,X1] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),omega(X1))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17303]) ).
fof(f17305,plain,
! [X0] :
( leq(omega(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),zero)))
| ~ leq(omega(coantidomain(X0)),zero) ),
inference(forward_demodulation,[status(thm)],[f1813,f17234]) ).
fof(f17306,plain,
! [X0] :
( leq(omega(coantidomain(X0)),addition(omega(X0),zero))
| ~ leq(omega(coantidomain(X0)),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17305]) ).
fof(f17307,plain,
! [X0] :
( leq(omega(coantidomain(X0)),omega(X0))
| ~ leq(omega(coantidomain(X0)),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17306]) ).
fof(f17312,plain,
! [X0] :
( leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),zero)))
| ~ leq(coantidomain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f63,f17236]) ).
fof(f17313,plain,
! [X0] :
( leq(coantidomain(X0),addition(omega(X0),zero))
| ~ leq(coantidomain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f17312]) ).
fof(f17314,plain,
! [X0] :
( leq(coantidomain(X0),omega(X0))
| ~ leq(coantidomain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f17313]) ).
fof(f17315,definition,
! [X0] :
( sQ45_spl
<=> leq(zero,addition(omega(X0),multiplication(star(X0),multiplication(X0,zero)))) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f17318,plain,
( sQ45_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f17237,f7983,f17315]) ).
fof(f17319,plain,
! [X0] :
( leq(one,addition(omega(X0),multiplication(star(X0),X0)))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f17238]) ).
fof(f17336,plain,
! [X0,X1] : leq(X0,addition(omega(X1),multiplication(star(X1),omega(one)))),
inference(resolution,[status(thm)],[f16915,f394]) ).
fof(f17339,plain,
! [X0,X1] : addition(X0,addition(omega(one),X1)) = addition(omega(one),X1),
inference(resolution,[status(thm)],[f16915,f48]) ).
fof(f17356,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),omega(one))),
inference(paramodulation,[status(thm)],[f232,f16915]) ).
fof(f17357,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),omega(one))),
inference(paramodulation,[status(thm)],[f207,f16915]) ).
fof(f17358,plain,
! [X0,X1] : leq(X0,multiplication(omega(one),addition(X1,one))),
inference(paramodulation,[status(thm)],[f192,f16915]) ).
fof(f17359,plain,
! [X0,X1] : leq(X0,multiplication(omega(one),addition(one,X1))),
inference(paramodulation,[status(thm)],[f162,f16915]) ).
fof(f17361,plain,
! [X0,X1] : leq(X0,addition(X1,omega(one))),
inference(paramodulation,[status(thm)],[f1026,f16915]) ).
fof(f17364,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,omega(one)))),
inference(paramodulation,[status(thm)],[f97,f16915]) ).
fof(f17365,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(omega(one),X2))),
inference(paramodulation,[status(thm)],[f97,f16915]) ).
fof(f17386,plain,
! [X0,X1] : addition(X0,omega(addition(one,X1))) = omega(addition(one,X1)),
inference(resolution,[status(thm)],[f16988,f48]) ).
fof(f17420,plain,
! [X0,X1,X2] : leq(X0,omega(addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f97,f16988]) ).
fof(f17421,plain,
! [X0,X1,X2] : leq(X0,omega(addition(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f97,f16988]) ).
fof(f17426,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),one))),
inference(resolution,[status(thm)],[f398,f2078]) ).
fof(f17427,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),one))),
inference(resolution,[status(thm)],[f398,f2052]) ).
fof(f17428,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),one))),
inference(resolution,[status(thm)],[f398,f2028]) ).
fof(f17429,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),one))),
inference(resolution,[status(thm)],[f398,f1779]) ).
fof(f17430,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),one))),
inference(resolution,[status(thm)],[f398,f1907]) ).
fof(f17431,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),one))),
inference(resolution,[status(thm)],[f398,f1780]) ).
fof(f17432,plain,
! [X0,X1,X2] : leq(c(X0),addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),one))),
inference(resolution,[status(thm)],[f398,f1781]) ).
fof(f17433,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),one))),
inference(resolution,[status(thm)],[f398,f1782]) ).
fof(f17434,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),one))),
inference(resolution,[status(thm)],[f398,f1783]) ).
fof(f17435,plain,
! [X0,X1,X2] : leq(domain(X0),addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),one))),
inference(resolution,[status(thm)],[f398,f1784]) ).
fof(f17436,plain,
! [X0,X1,X2] : leq(one,addition(omega(multiplication(X0,X1)),multiplication(star(multiplication(X0,X1)),star(X2)))),
inference(resolution,[status(thm)],[f398,f7532]) ).
fof(f17438,plain,
! [X0,X1,X2,X3] : leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),addition(X0,X3)))),
inference(resolution,[status(thm)],[f398,f1421]) ).
fof(f17439,plain,
! [X0,X1,X2,X3] : leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),addition(X3,X0)))),
inference(resolution,[status(thm)],[f398,f1420]) ).
fof(f17440,plain,
! [X0,X1,X2] : leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),X0))),
inference(resolution,[status(thm)],[f398,f1423]) ).
fof(f17442,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),addition(multiplication(X2,multiplication(X3,X0)),X4))))
| ~ leq(X0,addition(multiplication(addition(X1,X2),multiplication(X3,X0)),X4)) ),
inference(paramodulation,[status(thm)],[f219,f398]) ).
fof(f17443,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),addition(multiplication(X1,X3),X4))))
| ~ leq(X0,addition(multiplication(X1,addition(multiplication(X2,X0),X3)),X4)) ),
inference(paramodulation,[status(thm)],[f170,f398]) ).
fof(f17444,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X4)),multiplication(star(multiplication(X1,X4)),multiplication(X2,multiplication(X3,multiplication(X4,X0))))))
| ~ leq(X0,multiplication(addition(X1,multiplication(X2,X3)),multiplication(X4,X0))) ),
inference(paramodulation,[status(thm)],[f211,f398]) ).
fof(f17445,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),multiplication(X1,multiplication(X3,X0)))))
| ~ leq(X0,multiplication(addition(X1,X2),multiplication(X3,X0))) ),
inference(paramodulation,[status(thm)],[f201,f398]) ).
fof(f17446,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(X1,X2))))
| ~ leq(X0,multiplication(X1,addition(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f153,f398]) ).
fof(f17447,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X3)),multiplication(star(multiplication(X1,X3)),multiplication(X2,multiplication(X3,X0)))))
| ~ leq(X0,multiplication(addition(X1,X2),multiplication(X3,X0))) ),
inference(paramodulation,[status(thm)],[f43,f398]) ).
fof(f17448,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,X3))))
| ~ leq(X0,multiplication(X1,addition(multiplication(X2,X0),X3))) ),
inference(paramodulation,[status(thm)],[f42,f398]) ).
fof(f17449,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(domain(X3),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4516,f398]) ).
fof(f17450,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(coantidomain(X3),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4515,f398]) ).
fof(f17451,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(antidomain(X3),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4514,f398]) ).
fof(f17452,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(c(X3),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4513,f398]) ).
fof(f17453,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(codomain(X3),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4512,f398]) ).
fof(f17454,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(divergence(X3),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4511,f398]) ).
fof(f17455,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),forward_diamond(X3,X4)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2491,f398]) ).
fof(f17456,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),backward_box(X3,X4)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2490,f398]) ).
fof(f17457,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),forward_box(X3,X4)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2489,f398]) ).
fof(f17458,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),backward_diamond(X3,X4)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2488,f398]) ).
fof(f17459,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),domain(X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2497,f398]) ).
fof(f17460,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),coantidomain(X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2496,f398]) ).
fof(f17461,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),antidomain(X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2495,f398]) ).
fof(f17462,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),c(X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2494,f398]) ).
fof(f17463,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),codomain(X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2493,f398]) ).
fof(f17464,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),divergence(X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f2492,f398]) ).
fof(f17465,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),multiplication(X1,multiplication(X2,multiplication(X3,X0))))))
| ~ leq(X0,multiplication(addition(X1,one),multiplication(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f232,f398]) ).
fof(f17466,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),multiplication(X1,multiplication(X2,multiplication(X3,X0))))))
| ~ leq(X0,multiplication(addition(one,X1),multiplication(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f207,f398]) ).
fof(f17467,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),X3))))
| ~ leq(X0,multiplication(multiplication(X1,multiplication(X2,X0)),addition(X3,one))) ),
inference(paramodulation,[status(thm)],[f192,f398]) ).
fof(f17468,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),X3))))
| ~ leq(X0,multiplication(multiplication(X1,multiplication(X2,X0)),addition(one,X3))) ),
inference(paramodulation,[status(thm)],[f162,f398]) ).
fof(f17469,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),addition(X3,multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f1329,f398]) ).
fof(f17470,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),addition(multiplication(X2,multiplication(X3,X0)),X1))))
| ~ leq(X0,addition(X1,multiplication(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f1026,f398]) ).
fof(f17471,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),addition(X1,multiplication(X2,multiplication(X3,X0))))))
| ~ leq(X0,addition(X1,multiplication(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f1005,f398]) ).
fof(f17472,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),addition(multiplication(X1,multiplication(X2,X0)),X3))))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f105,f398]) ).
fof(f17473,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X3,X4)),multiplication(star(multiplication(X3,X4)),addition(X1,X2))))
| ~ leq(X0,addition(X1,addition(X2,multiplication(X3,multiplication(X4,X0))))) ),
inference(paramodulation,[status(thm)],[f97,f398]) ).
fof(f17474,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),addition(X4,X1))))
| ~ leq(X0,addition(X1,addition(multiplication(X2,multiplication(X3,X0)),X4))) ),
inference(paramodulation,[status(thm)],[f97,f398]) ).
fof(f17475,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),zero)))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f37,f398]) ).
fof(f17476,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f35,f398]) ).
fof(f17477,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,X3)),multiplication(star(multiplication(X2,X3)),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f35,f398]) ).
fof(f17478,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,X0)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f38,f398]) ).
fof(f17479,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(addition(antidomain(multiplication(X2,X0)),X1),X2)),multiplication(star(multiplication(addition(antidomain(multiplication(X2,X0)),X1),X2)),X3)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f224,f398]) ).
fof(f17480,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(addition(X1,antidomain(multiplication(X2,X0))),X2)),multiplication(star(multiplication(addition(X1,antidomain(multiplication(X2,X0))),X2)),X3)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f230,f398]) ).
fof(f17481,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(c(multiplication(X2,X0)),X2)),multiplication(star(multiplication(c(multiplication(X2,X0)),X2)),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f4265,f398]) ).
fof(f17482,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(domain(multiplication(X1,X0)),X1)),multiplication(star(multiplication(domain(multiplication(X1,X0)),X1)),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f4146,f398]) ).
fof(f17483,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(multiplication(X1,X2),X3)),multiplication(star(multiplication(multiplication(X1,X2),X3)),X4)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,X0))),X4)) ),
inference(paramodulation,[status(thm)],[f39,f398]) ).
fof(f17484,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(antidomain(addition(multiplication(X2,X0),X3)),X2)),multiplication(star(multiplication(antidomain(addition(multiplication(X2,X0),X3)),X2)),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f2635,f398]) ).
fof(f17486,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(antidomain(multiplication(X2,X0)),X2)),multiplication(star(multiplication(antidomain(multiplication(X2,X0)),X2)),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f59,f398]) ).
fof(f17492,plain,
! [X0,X1,X2] :
( leq(coantidomain(multiplication(X0,X1)),addition(omega(multiplication(X0,X1)),multiplication(star(multiplication(X0,X1)),X2)))
| ~ leq(coantidomain(multiplication(X0,X1)),addition(zero,X2)) ),
inference(paramodulation,[status(thm)],[f144,f398]) ).
fof(f17493,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,addition(one,X2))),multiplication(star(multiplication(X1,addition(one,X2))),X3)))
| ~ leq(X0,addition(multiplication(X1,addition(X0,multiplication(X2,X0))),X3)) ),
inference(paramodulation,[status(thm)],[f207,f398]) ).
fof(f17494,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,addition(antidomain(X0),X2))),multiplication(star(multiplication(X1,addition(antidomain(X0),X2))),X3)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f224,f398]) ).
fof(f17495,plain,
! [X0,X1,X2,X3] :
( leq(omega(X0),addition(omega(multiplication(X1,addition(X2,one))),multiplication(star(multiplication(X1,addition(X2,one))),X3)))
| ~ leq(omega(X0),addition(multiplication(X1,multiplication(addition(X0,X2),omega(X0))),X3)) ),
inference(paramodulation,[status(thm)],[f11449,f398]) ).
fof(f17496,plain,
! [X0,X1,X2,X3] :
( leq(omega(X0),addition(omega(multiplication(X1,addition(X2,one))),multiplication(star(multiplication(X1,addition(X2,one))),X3)))
| ~ leq(omega(X0),addition(multiplication(X1,multiplication(addition(X2,X0),omega(X0))),X3)) ),
inference(paramodulation,[status(thm)],[f10882,f398]) ).
fof(f17497,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,addition(X2,one))),multiplication(star(multiplication(X1,addition(X2,one))),X3)))
| ~ leq(X0,addition(multiplication(X1,addition(X0,multiplication(X2,X0))),X3)) ),
inference(paramodulation,[status(thm)],[f232,f398]) ).
fof(f17498,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,addition(X2,antidomain(X0)))),multiplication(star(multiplication(X1,addition(X2,antidomain(X0)))),X3)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f230,f398]) ).
fof(f17499,plain,
! [X0,X1,X2,X3] :
( leq(omega(X0),addition(omega(multiplication(X1,addition(X0,X2))),multiplication(star(multiplication(X1,addition(X0,X2))),X3)))
| ~ leq(omega(X0),addition(multiplication(X1,multiplication(addition(X2,one),omega(X0))),X3)) ),
inference(paramodulation,[status(thm)],[f11449,f398]) ).
fof(f17500,plain,
! [X0,X1,X2,X3] :
( leq(omega(X0),addition(omega(multiplication(X1,addition(X2,X0))),multiplication(star(multiplication(X1,addition(X2,X0))),X3)))
| ~ leq(omega(X0),addition(multiplication(X1,multiplication(addition(X2,one),omega(X0))),X3)) ),
inference(paramodulation,[status(thm)],[f10882,f398]) ).
fof(f17501,plain,
! [X0,X1,X2,X3] :
( leq(coantidomain(X0),addition(omega(multiplication(X1,addition(X2,X0))),multiplication(star(multiplication(X1,addition(X2,X0))),X3)))
| ~ leq(coantidomain(X0),addition(multiplication(X1,multiplication(X2,coantidomain(X0))),X3)) ),
inference(paramodulation,[status(thm)],[f233,f398]) ).
fof(f17502,plain,
! [X0,X1,X2,X3] :
( leq(coantidomain(X0),addition(omega(multiplication(X1,addition(X0,X2))),multiplication(star(multiplication(X1,addition(X0,X2))),X3)))
| ~ leq(coantidomain(X0),addition(multiplication(X1,multiplication(X2,coantidomain(X0))),X3)) ),
inference(paramodulation,[status(thm)],[f226,f398]) ).
fof(f17503,plain,
! [X0,X1,X2] :
( leq(antidomain(X0),addition(omega(multiplication(X1,c(X0))),multiplication(star(multiplication(X1,c(X0))),X2)))
| ~ leq(antidomain(X0),addition(multiplication(X1,c(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f2633,f398]) ).
fof(f17504,plain,
! [X0,X1,X2] :
( leq(c(X0),addition(omega(multiplication(X1,c(X0))),multiplication(star(multiplication(X1,c(X0))),X2)))
| ~ leq(c(X0),addition(multiplication(X1,c(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f2211,f398]) ).
fof(f17505,plain,
! [X0,X1,X2,X3] :
( leq(domain_difference(X0,X1),addition(omega(multiplication(X2,c(X0))),multiplication(star(multiplication(X2,c(X0))),X3)))
| ~ leq(domain_difference(X0,X1),addition(multiplication(X2,zero),X3)) ),
inference(paramodulation,[status(thm)],[f1585,f398]) ).
fof(f17506,plain,
! [X0,X1,X2] :
( leq(domain(X0),addition(omega(multiplication(X1,c(X0))),multiplication(star(multiplication(X1,c(X0))),X2)))
| ~ leq(domain(X0),addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f197,f398]) ).
fof(f17507,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X1,c(X0))),multiplication(star(multiplication(X1,c(X0))),X2)))
| ~ leq(X0,addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f4265,f398]) ).
fof(f17508,plain,
! [X0,X1,X2] :
( leq(codomain(X0),addition(omega(multiplication(X1,coantidomain(X0))),multiplication(star(multiplication(X1,coantidomain(X0))),X2)))
| ~ leq(codomain(X0),addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f195,f398]) ).
fof(f17509,plain,
! [X0,X1,X2] :
( leq(domain(X0),addition(omega(multiplication(X1,domain(X0))),multiplication(star(multiplication(X1,domain(X0))),X2)))
| ~ leq(domain(X0),addition(multiplication(X1,domain(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f2215,f398]) ).
fof(f17510,plain,
! [X0,X1,X2,X3] :
( leq(antidomain(X0),addition(omega(multiplication(X1,domain(X2))),multiplication(star(multiplication(X1,domain(X2))),X3)))
| ~ leq(antidomain(X0),addition(multiplication(X1,domain_difference(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f68,f398]) ).
fof(f17511,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X1,domain(X0))),multiplication(star(multiplication(X1,domain(X0))),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f4146,f398]) ).
fof(f17512,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,multiplication(X2,X3))),multiplication(star(multiplication(X1,multiplication(X2,X3))),X4)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,X0))),X4)) ),
inference(paramodulation,[status(thm)],[f39,f398]) ).
fof(f17513,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,antidomain(addition(X0,X3)))),multiplication(star(multiplication(X1,antidomain(addition(X0,X3)))),X2)))
| ~ leq(X0,addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f2635,f398]) ).
fof(f17514,plain,
! [X0,X1,X2,X3] :
( leq(addition(X0,X1),addition(omega(multiplication(X2,antidomain(X1))),multiplication(star(multiplication(X2,antidomain(X1))),X3)))
| ~ leq(addition(X0,X1),addition(multiplication(X2,multiplication(antidomain(X1),X0)),X3)) ),
inference(paramodulation,[status(thm)],[f186,f398]) ).
fof(f17515,plain,
! [X0,X1,X2,X3] :
( leq(addition(X0,X1),addition(omega(multiplication(X2,antidomain(X0))),multiplication(star(multiplication(X2,antidomain(X0))),X3)))
| ~ leq(addition(X0,X1),addition(multiplication(X2,multiplication(antidomain(X0),X1)),X3)) ),
inference(paramodulation,[status(thm)],[f177,f398]) ).
fof(f17516,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(multiplication(X1,antidomain(X0))),multiplication(star(multiplication(X1,antidomain(X0))),X2)))
| ~ leq(omega(X0),addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f1569,f398]) ).
fof(f17517,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(multiplication(X2,antidomain(X0))),multiplication(star(multiplication(X2,antidomain(X0))),X3)))
| ~ leq(multiplication(X0,X1),addition(multiplication(X2,zero),X3)) ),
inference(paramodulation,[status(thm)],[f136,f398]) ).
fof(f17518,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X1,antidomain(X0))),multiplication(star(multiplication(X1,antidomain(X0))),X2)))
| ~ leq(X0,addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f59,f398]) ).
fof(f17521,plain,
! [X0,X1,X2] :
( leq(codomain(X0),addition(omega(multiplication(X1,X0)),multiplication(star(multiplication(X1,X0)),X2)))
| ~ leq(codomain(X0),addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f2309,f398]) ).
fof(f17522,plain,
! [X0,X1,X2,X3] :
( leq(addition(omega(X0),X1),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X3)))
| ~ leq(addition(omega(X0),X1),addition(multiplication(X2,addition(omega(X0),multiplication(X0,X1))),X3)) ),
inference(paramodulation,[status(thm)],[f318,f398]) ).
fof(f17523,plain,
! [X0,X1,X2,X3] :
( leq(addition(one,X0),addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),X3)))
| ~ leq(addition(one,X0),addition(multiplication(X1,addition(X2,multiplication(X2,X0))),X3)) ),
inference(paramodulation,[status(thm)],[f162,f398]) ).
fof(f17524,plain,
! [X0,X1,X2,X3] :
( leq(addition(coantidomain(X0),X1),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X3)))
| ~ leq(addition(coantidomain(X0),X1),addition(multiplication(X2,multiplication(X0,X1)),X3)) ),
inference(paramodulation,[status(thm)],[f181,f398]) ).
fof(f17525,plain,
! [X0,X1,X2,X3] :
( leq(addition(X0,omega(X1)),addition(omega(multiplication(X2,X1)),multiplication(star(multiplication(X2,X1)),X3)))
| ~ leq(addition(X0,omega(X1)),addition(multiplication(X2,addition(omega(X1),multiplication(X1,X0))),X3)) ),
inference(paramodulation,[status(thm)],[f321,f398]) ).
fof(f17526,plain,
! [X0,X1,X2,X3] :
( leq(addition(X0,one),addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),X3)))
| ~ leq(addition(X0,one),addition(multiplication(X1,addition(X2,multiplication(X2,X0))),X3)) ),
inference(paramodulation,[status(thm)],[f192,f398]) ).
fof(f17527,plain,
! [X0,X1,X2,X3] :
( leq(addition(X0,coantidomain(X1)),addition(omega(multiplication(X2,X1)),multiplication(star(multiplication(X2,X1)),X3)))
| ~ leq(addition(X0,coantidomain(X1)),addition(multiplication(X2,multiplication(X1,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f190,f398]) ).
fof(f17528,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(omega(X0),X1),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X3)))
| ~ leq(multiplication(omega(X0),X1),addition(multiplication(X2,multiplication(omega(X0),X1)),X3)) ),
inference(paramodulation,[status(thm)],[f319,f398]) ).
fof(f17529,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X3)))
| ~ leq(multiplication(coantidomain(X0),X1),addition(multiplication(X2,zero),X3)) ),
inference(paramodulation,[status(thm)],[f151,f398]) ).
fof(f17530,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,omega(multiplication(X1,X0))),addition(omega(multiplication(X2,X1)),multiplication(star(multiplication(X2,X1)),X3)))
| ~ leq(multiplication(X0,omega(multiplication(X1,X0))),addition(multiplication(X2,omega(multiplication(X1,X0))),X3)) ),
inference(paramodulation,[status(thm)],[f308,f398]) ).
fof(f17531,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(multiplication(X2,X1)),multiplication(star(multiplication(X2,X1)),X3)))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(multiplication(X2,zero),X3)) ),
inference(paramodulation,[status(thm)],[f144,f398]) ).
fof(f17532,plain,
! [X0,X1,X2] :
( leq(omega(coantidomain(X0)),addition(omega(multiplication(X1,X0)),multiplication(star(multiplication(X1,X0)),X2)))
| ~ leq(omega(coantidomain(X0)),addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f1813,f398]) ).
fof(f17533,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(multiplication(X1,X0)),multiplication(star(multiplication(X1,X0)),X2)))
| ~ leq(omega(X0),addition(multiplication(X1,omega(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f56,f398]) ).
fof(f17534,plain,
! [X0,X1,X2] :
( leq(coantidomain(X0),addition(omega(multiplication(X1,X0)),multiplication(star(multiplication(X1,X0)),X2)))
| ~ leq(coantidomain(X0),addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f63,f398]) ).
fof(f17536,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(multiplication(X0,X1)),multiplication(star(multiplication(X0,X1)),X2)))
| ~ leq(one,addition(multiplication(X0,X1),X2)) ),
inference(paramodulation,[status(thm)],[f40,f398]) ).
fof(f17537,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(omega(multiplication(X2,X3)),star(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f40,f17426]) ).
fof(f17538,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(star(multiplication(X2,X3)),omega(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f35,f17537]) ).
fof(f17539,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(omega(multiplication(X2,X3)),star(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f40,f17427]) ).
fof(f17540,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(star(multiplication(X2,X3)),omega(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f35,f17539]) ).
fof(f17541,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(omega(multiplication(X2,X3)),star(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f40,f17428]) ).
fof(f17542,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(star(multiplication(X2,X3)),omega(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f35,f17541]) ).
fof(f17543,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(omega(multiplication(X1,X2)),star(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f40,f17429]) ).
fof(f17544,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(star(multiplication(X1,X2)),omega(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f35,f17543]) ).
fof(f17545,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(omega(multiplication(X2,X3)),star(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f40,f17430]) ).
fof(f17546,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(star(multiplication(X2,X3)),omega(multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f35,f17545]) ).
fof(f17547,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(omega(multiplication(X1,X2)),star(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f40,f17431]) ).
fof(f17548,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(star(multiplication(X1,X2)),omega(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f35,f17547]) ).
fof(f17549,plain,
! [X0,X1,X2] : leq(c(X0),addition(omega(multiplication(X1,X2)),star(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f40,f17432]) ).
fof(f17550,plain,
! [X0,X1,X2] : leq(c(X0),addition(star(multiplication(X1,X2)),omega(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f35,f17549]) ).
fof(f17551,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(omega(multiplication(X1,X2)),star(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f40,f17433]) ).
fof(f17552,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(star(multiplication(X1,X2)),omega(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f35,f17551]) ).
fof(f17553,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(omega(multiplication(X1,X2)),star(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f40,f17434]) ).
fof(f17554,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(star(multiplication(X1,X2)),omega(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f35,f17553]) ).
fof(f17555,plain,
! [X0,X1,X2] : leq(domain(X0),addition(omega(multiplication(X1,X2)),star(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f40,f17435]) ).
fof(f17556,plain,
! [X0,X1,X2] : leq(domain(X0),addition(star(multiplication(X1,X2)),omega(multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f35,f17555]) ).
fof(f17557,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),forward_diamond(X3,X4))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17455]) ).
fof(f17558,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,forward_diamond(X3,X4)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17557]) ).
fof(f17559,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),backward_box(X3,X4))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17456]) ).
fof(f17560,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,backward_box(X3,X4)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17559]) ).
fof(f17561,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),forward_box(X3,X4))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17457]) ).
fof(f17562,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,forward_box(X3,X4)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17561]) ).
fof(f17563,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),backward_diamond(X3,X4))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17458]) ).
fof(f17564,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,backward_diamond(X3,X4)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17563]) ).
fof(f17565,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),domain(X3))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17459]) ).
fof(f17566,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,domain(X3)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17565]) ).
fof(f17567,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),coantidomain(X3))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17460]) ).
fof(f17568,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,coantidomain(X3)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17567]) ).
fof(f17569,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),antidomain(X3))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17461]) ).
fof(f17570,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,antidomain(X3)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17569]) ).
fof(f17571,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),c(X3))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17462]) ).
fof(f17572,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,c(X3)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17571]) ).
fof(f17573,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),codomain(X3))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17463]) ).
fof(f17574,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,codomain(X3)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17573]) ).
fof(f17575,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),divergence(X3))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17464]) ).
fof(f17576,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,divergence(X3)))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f39,f17575]) ).
fof(f17577,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),X3))))
| ~ leq(X0,multiplication(X1,multiplication(multiplication(X2,X0),addition(X3,one)))) ),
inference(forward_demodulation,[status(thm)],[f39,f17467]) ).
fof(f17578,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),X3))))
| ~ leq(X0,multiplication(X1,multiplication(X2,multiplication(X0,addition(X3,one))))) ),
inference(forward_demodulation,[status(thm)],[f39,f17577]) ).
fof(f17579,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,multiplication(X0,addition(X3,one))))) ),
inference(forward_demodulation,[status(thm)],[f39,f17578]) ).
fof(f17580,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,X3))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,multiplication(X0,addition(X3,one))))) ),
inference(forward_demodulation,[status(thm)],[f39,f17579]) ).
fof(f17581,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),X3))))
| ~ leq(X0,multiplication(X1,multiplication(multiplication(X2,X0),addition(one,X3)))) ),
inference(forward_demodulation,[status(thm)],[f39,f17468]) ).
fof(f17582,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(multiplication(X1,multiplication(X2,X0)),X3))))
| ~ leq(X0,multiplication(X1,multiplication(X2,multiplication(X0,addition(one,X3))))) ),
inference(forward_demodulation,[status(thm)],[f39,f17581]) ).
fof(f17583,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(multiplication(X2,X0),X3)))))
| ~ leq(X0,multiplication(X1,multiplication(X2,multiplication(X0,addition(one,X3))))) ),
inference(forward_demodulation,[status(thm)],[f39,f17582]) ).
fof(f17584,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,multiplication(X0,X3))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,multiplication(X0,addition(one,X3))))) ),
inference(forward_demodulation,[status(thm)],[f39,f17583]) ).
fof(f17585,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X1,X2)),zero))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f44,f17475]) ).
fof(f17586,plain,
! [X0,X1,X2] :
( leq(X0,omega(multiplication(X1,X2)))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f37,f17585]) ).
fof(f17587,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(c(multiplication(X2,X0)),X2)),multiplication(star(multiplication(c(multiplication(X2,X0)),X2)),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17481]) ).
fof(f17588,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,multiplication(X2,X3))),multiplication(star(multiplication(multiplication(X1,X2),X3)),X4)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,X0))),X4)) ),
inference(forward_demodulation,[status(thm)],[f39,f17483]) ).
fof(f17589,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,multiplication(X2,X3))),multiplication(star(multiplication(X1,multiplication(X2,X3))),X4)))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,X0))),X4)) ),
inference(forward_demodulation,[status(thm)],[f39,f17588]) ).
fof(f17590,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(antidomain(addition(multiplication(X2,X0),X3)),X2)),multiplication(star(multiplication(antidomain(addition(multiplication(X2,X0),X3)),X2)),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17484]) ).
fof(f17597,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(antidomain(multiplication(X2,X0)),X2)),multiplication(star(multiplication(antidomain(multiplication(X2,X0)),X2)),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17486]) ).
fof(f17614,plain,
! [X0,X1,X2] :
( leq(coantidomain(multiplication(X0,X1)),addition(omega(multiplication(X0,X1)),multiplication(star(multiplication(X0,X1)),X2)))
| ~ leq(coantidomain(multiplication(X0,X1)),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f17492]) ).
fof(f17615,plain,
! [X0,X1,X2,X3] :
( leq(domain_difference(X0,X1),addition(omega(multiplication(X3,c(X0))),multiplication(star(multiplication(X3,c(X0))),X2)))
| ~ leq(domain_difference(X0,X1),addition(zero,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f17505]) ).
fof(f17616,plain,
! [X0,X1,X2,X3] :
( leq(domain_difference(X0,X1),addition(omega(multiplication(X3,c(X0))),multiplication(star(multiplication(X3,c(X0))),X2)))
| ~ leq(domain_difference(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f17615]) ).
fof(f17617,plain,
! [X0,X1,X2] :
( leq(domain(X0),addition(omega(multiplication(X2,c(X0))),multiplication(star(multiplication(X2,c(X0))),X1)))
| ~ leq(domain(X0),addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f17506]) ).
fof(f17618,plain,
! [X0,X1,X2] :
( leq(domain(X0),addition(omega(multiplication(X2,c(X0))),multiplication(star(multiplication(X2,c(X0))),X1)))
| ~ leq(domain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17617]) ).
fof(f17619,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X2,c(X0))),multiplication(star(multiplication(X2,c(X0))),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f17507]) ).
fof(f17620,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X2,c(X0))),multiplication(star(multiplication(X2,c(X0))),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17619]) ).
fof(f17621,plain,
! [X0,X1,X2] :
( leq(codomain(X0),addition(omega(multiplication(X2,coantidomain(X0))),multiplication(star(multiplication(X2,coantidomain(X0))),X1)))
| ~ leq(codomain(X0),addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f17508]) ).
fof(f17622,plain,
! [X0,X1,X2] :
( leq(codomain(X0),addition(omega(multiplication(X2,coantidomain(X0))),multiplication(star(multiplication(X2,coantidomain(X0))),X1)))
| ~ leq(codomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17621]) ).
fof(f17623,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,antidomain(addition(X0,X3)))),multiplication(star(multiplication(X2,antidomain(addition(X0,X3)))),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f17513]) ).
fof(f17624,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(multiplication(X2,antidomain(addition(X0,X3)))),multiplication(star(multiplication(X2,antidomain(addition(X0,X3)))),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17623]) ).
fof(f17625,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(multiplication(X2,antidomain(X0))),multiplication(star(multiplication(X2,antidomain(X0))),X1)))
| ~ leq(omega(X0),addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f17516]) ).
fof(f17626,plain,
! [X0,X1,X2] :
( leq(omega(X0),addition(omega(multiplication(X2,antidomain(X0))),multiplication(star(multiplication(X2,antidomain(X0))),X1)))
| ~ leq(omega(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17625]) ).
fof(f17627,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(multiplication(X3,antidomain(X0))),multiplication(star(multiplication(X3,antidomain(X0))),X2)))
| ~ leq(multiplication(X0,X1),addition(zero,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f17517]) ).
fof(f17628,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),addition(omega(multiplication(X3,antidomain(X0))),multiplication(star(multiplication(X3,antidomain(X0))),X2)))
| ~ leq(multiplication(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f17627]) ).
fof(f17629,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X2,antidomain(X0))),multiplication(star(multiplication(X2,antidomain(X0))),X1)))
| ~ leq(X0,addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f17518]) ).
fof(f17630,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(multiplication(X2,antidomain(X0))),multiplication(star(multiplication(X2,antidomain(X0))),X1)))
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17629]) ).
fof(f17640,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(multiplication(X3,X0)),multiplication(star(multiplication(X3,X0)),X2)))
| ~ leq(multiplication(coantidomain(X0),X1),addition(zero,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f17529]) ).
fof(f17641,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(coantidomain(X0),X1),addition(omega(multiplication(X3,X0)),multiplication(star(multiplication(X3,X0)),X2)))
| ~ leq(multiplication(coantidomain(X0),X1),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f17640]) ).
fof(f17642,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(multiplication(X3,X1)),multiplication(star(multiplication(X3,X1)),X2)))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(zero,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f17531]) ).
fof(f17643,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,coantidomain(multiplication(X1,X0))),addition(omega(multiplication(X3,X1)),multiplication(star(multiplication(X3,X1)),X2)))
| ~ leq(multiplication(X0,coantidomain(multiplication(X1,X0))),X2) ),
inference(forward_demodulation,[status(thm)],[f80,f17642]) ).
fof(f17644,plain,
! [X0,X1,X2] :
( leq(omega(coantidomain(X0)),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X1)))
| ~ leq(omega(coantidomain(X0)),addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f17532]) ).
fof(f17645,plain,
! [X0,X1,X2] :
( leq(omega(coantidomain(X0)),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X1)))
| ~ leq(omega(coantidomain(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17644]) ).
fof(f17646,plain,
! [X0,X1,X2] :
( leq(coantidomain(X0),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X1)))
| ~ leq(coantidomain(X0),addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f17534]) ).
fof(f17647,plain,
! [X0,X1,X2] :
( leq(coantidomain(X0),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X1)))
| ~ leq(coantidomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f17646]) ).
fof(f17666,plain,
! [X0,X1] : addition(X0,omega(addition(X1,one))) = omega(addition(X1,one)),
inference(resolution,[status(thm)],[f16989,f48]) ).
fof(f17667,plain,
! [X0,X1,X2] : leq(X0,omega(addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f103,f16989]) ).
fof(f17668,plain,
! [X0,X1,X2] : leq(X0,omega(addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f36,f16989]) ).
fof(f17673,plain,
! [X0] : leq(multiplication(antidomain(X0),star(coantidomain(omega(c(X0))))),omega(c(X0))),
inference(resolution,[status(thm)],[f16990,f346]) ).
fof(f17674,plain,
! [X0] : leq(multiplication(star(antidomain(omega(c(X0)))),antidomain(X0)),omega(c(X0))),
inference(resolution,[status(thm)],[f16990,f304]) ).
fof(f17675,plain,
! [X0] : addition(antidomain(X0),omega(c(X0))) = omega(c(X0)),
inference(resolution,[status(thm)],[f16990,f48]) ).
fof(f17681,plain,
! [X0] : leq(domain(X0),omega(c(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f62,f16990]) ).
fof(f17685,plain,
! [X0] : leq(antidomain(c(X0)),omega(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f13920,f16990]) ).
fof(f17688,plain,
! [X0,X1] : leq(antidomain(backward_diamond(X0,c(X1))),omega(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f72,f16990]) ).
fof(f17689,plain,
! [X0,X1] : leq(antidomain(forward_diamond(X0,c(X1))),omega(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f71,f16990]) ).
fof(f17691,plain,
! [X0] : leq(antidomain(antidomain(X0)),omega(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f547,f16990]) ).
fof(f17701,plain,
! [X0] : leq(domain(X0),omega(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f547,f17681]) ).
fof(f17712,plain,
! [X0] : leq(domain(X0),omega(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f17691]) ).
fof(f17715,plain,
! [X0] : leq(multiplication(c(X0),star(coantidomain(omega(c(X0))))),omega(c(X0))),
inference(resolution,[status(thm)],[f16991,f346]) ).
fof(f17716,plain,
! [X0] : leq(multiplication(star(antidomain(omega(c(X0)))),c(X0)),omega(c(X0))),
inference(resolution,[status(thm)],[f16991,f304]) ).
fof(f17717,plain,
! [X0] : addition(c(X0),omega(c(X0))) = omega(c(X0)),
inference(resolution,[status(thm)],[f16991,f48]) ).
fof(f17720,plain,
! [X0] : leq(antidomain(c(X0)),omega(c(c(X0)))),
inference(paramodulation,[status(thm)],[f13920,f16991]) ).
fof(f17723,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(c(backward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f72,f16991]) ).
fof(f17724,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(c(forward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f71,f16991]) ).
fof(f17726,plain,
! [X0] : leq(antidomain(c(X0)),omega(c(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f547,f16991]) ).
fof(f17730,plain,
! [X0] : leq(c(c(X0)),omega(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f13920,f16991]) ).
fof(f17733,plain,
! [X0,X1] : leq(c(backward_diamond(X0,c(X1))),omega(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f72,f16991]) ).
fof(f17734,plain,
! [X0,X1] : leq(c(forward_diamond(X0,c(X1))),omega(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f71,f16991]) ).
fof(f17736,plain,
! [X0] : leq(c(antidomain(X0)),omega(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f547,f16991]) ).
fof(f17742,plain,
! [X0] : leq(antidomain(c(X0)),omega(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f13920,f17720]) ).
fof(f17746,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f72,f17723]) ).
fof(f17747,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f71,f17724]) ).
fof(f17749,plain,
! [X0] : leq(antidomain(c(X0)),omega(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f547,f17726]) ).
fof(f17756,plain,
! [X0] : leq(antidomain(c(X0)),omega(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f13920,f17730]) ).
fof(f17760,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f72,f17733]) ).
fof(f17761,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f71,f17734]) ).
fof(f17763,plain,
! [X0] : leq(antidomain(c(X0)),omega(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f547,f17736]) ).
fof(f17766,plain,
! [X0] : leq(multiplication(domain(X0),star(coantidomain(omega(domain(X0))))),omega(domain(X0))),
inference(resolution,[status(thm)],[f16992,f346]) ).
fof(f17767,plain,
! [X0] : leq(multiplication(star(antidomain(omega(domain(X0)))),domain(X0)),omega(domain(X0))),
inference(resolution,[status(thm)],[f16992,f304]) ).
fof(f17768,plain,
! [X0] : addition(domain(X0),omega(domain(X0))) = omega(domain(X0)),
inference(resolution,[status(thm)],[f16992,f48]) ).
fof(f17771,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(domain(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f13917,f16992]) ).
fof(f17772,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(domain(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f13916,f16992]) ).
fof(f17775,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),omega(domain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f69,f16992]) ).
fof(f17777,plain,
! [X0] : leq(antidomain(c(X0)),omega(domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f196,f16992]) ).
fof(f17782,plain,
! [X0,X1] : leq(domain(forward_box(X0,X1)),omega(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13917,f16992]) ).
fof(f17783,plain,
! [X0,X1] : leq(domain(backward_box(X0,X1)),omega(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f13916,f16992]) ).
fof(f17786,plain,
! [X0,X1] : leq(domain(multiplication(X0,domain(X1))),omega(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f69,f16992]) ).
fof(f17788,plain,
! [X0] : leq(domain(domain(X0)),omega(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f196,f16992]) ).
fof(f17793,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13917,f17771]) ).
fof(f17794,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13916,f17772]) ).
fof(f17797,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),omega(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f69,f17775]) ).
fof(f17800,plain,
! [X0] : leq(antidomain(c(X0)),omega(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f17777]) ).
fof(f17805,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13917,f17782]) ).
fof(f17806,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f13916,f17783]) ).
fof(f17809,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),omega(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f69,f17786]) ).
fof(f17812,plain,
! [X0] : leq(antidomain(c(X0)),omega(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f17788]) ).
fof(f17815,plain,
! [X0,X1] : leq(domain_difference(X0,X1),addition(omega(antidomain(domain_difference(X0,X1))),multiplication(star(antidomain(domain_difference(X0,X1))),antidomain(X1)))),
inference(resolution,[status(thm)],[f409,f6998]) ).
fof(f17816,plain,
! [X0,X1] : leq(domain_difference(X0,X1),addition(omega(antidomain(domain_difference(X0,X1))),multiplication(star(antidomain(domain_difference(X0,X1))),domain(X0)))),
inference(resolution,[status(thm)],[f409,f3834]) ).
fof(f17817,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),addition(omega(antidomain(multiplication(forward_diamond(X0,X1),X2))),multiplication(star(antidomain(multiplication(forward_diamond(X0,X1),X2))),X2))),
inference(resolution,[status(thm)],[f409,f7010]) ).
fof(f17818,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),addition(omega(antidomain(multiplication(forward_box(X0,X1),X2))),multiplication(star(antidomain(multiplication(forward_box(X0,X1),X2))),X2))),
inference(resolution,[status(thm)],[f409,f6659]) ).
fof(f17819,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),addition(omega(antidomain(multiplication(backward_box(X0,X1),X2))),multiplication(star(antidomain(multiplication(backward_box(X0,X1),X2))),X2))),
inference(resolution,[status(thm)],[f409,f6658]) ).
fof(f17820,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),addition(omega(antidomain(multiplication(backward_diamond(X0,X1),X2))),multiplication(star(antidomain(multiplication(backward_diamond(X0,X1),X2))),X2))),
inference(resolution,[status(thm)],[f409,f6519]) ).
fof(f17821,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(omega(antidomain(multiplication(coantidomain(X0),X1))),multiplication(star(antidomain(multiplication(coantidomain(X0),X1))),X1))),
inference(resolution,[status(thm)],[f409,f7158]) ).
fof(f17822,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),addition(omega(antidomain(multiplication(domain(X0),X1))),multiplication(star(antidomain(multiplication(domain(X0),X1))),X1))),
inference(resolution,[status(thm)],[f409,f6808]) ).
fof(f17823,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(omega(antidomain(multiplication(antidomain(X0),X1))),multiplication(star(antidomain(multiplication(antidomain(X0),X1))),X1))),
inference(resolution,[status(thm)],[f409,f6667]) ).
fof(f17824,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),addition(omega(antidomain(multiplication(c(X0),X1))),multiplication(star(antidomain(multiplication(c(X0),X1))),X1))),
inference(resolution,[status(thm)],[f409,f6526]) ).
fof(f17825,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),addition(omega(antidomain(multiplication(codomain(X0),X1))),multiplication(star(antidomain(multiplication(codomain(X0),X1))),X1))),
inference(resolution,[status(thm)],[f409,f6393]) ).
fof(f17826,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),addition(omega(antidomain(multiplication(divergence(X0),X1))),multiplication(star(antidomain(multiplication(divergence(X0),X1))),X1))),
inference(resolution,[status(thm)],[f409,f5965]) ).
fof(f17827,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(omega(antidomain(multiplication(X0,forward_diamond(X1,X2)))),multiplication(star(antidomain(multiplication(X0,forward_diamond(X1,X2)))),X0))),
inference(resolution,[status(thm)],[f409,f4077]) ).
fof(f17828,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),addition(omega(antidomain(multiplication(X0,forward_box(X1,X2)))),multiplication(star(antidomain(multiplication(X0,forward_box(X1,X2)))),X0))),
inference(resolution,[status(thm)],[f409,f3741]) ).
fof(f17829,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),addition(omega(antidomain(multiplication(X0,backward_box(X1,X2)))),multiplication(star(antidomain(multiplication(X0,backward_box(X1,X2)))),X0))),
inference(resolution,[status(thm)],[f409,f3740]) ).
fof(f17830,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(omega(antidomain(multiplication(X0,backward_diamond(X1,X2)))),multiplication(star(antidomain(multiplication(X0,backward_diamond(X1,X2)))),X0))),
inference(resolution,[status(thm)],[f409,f3497]) ).
fof(f17831,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(omega(antidomain(multiplication(X0,coantidomain(X1)))),multiplication(star(antidomain(multiplication(X0,coantidomain(X1)))),X0))),
inference(resolution,[status(thm)],[f409,f4627]) ).
fof(f17832,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(omega(antidomain(multiplication(X0,domain(X1)))),multiplication(star(antidomain(multiplication(X0,domain(X1)))),X0))),
inference(resolution,[status(thm)],[f409,f3841]) ).
fof(f17833,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(omega(antidomain(multiplication(X0,antidomain(X1)))),multiplication(star(antidomain(multiplication(X0,antidomain(X1)))),X0))),
inference(resolution,[status(thm)],[f409,f3749]) ).
fof(f17834,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),addition(omega(antidomain(multiplication(X0,c(X1)))),multiplication(star(antidomain(multiplication(X0,c(X1)))),X0))),
inference(resolution,[status(thm)],[f409,f3652]) ).
fof(f17835,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),addition(omega(antidomain(multiplication(X0,codomain(X1)))),multiplication(star(antidomain(multiplication(X0,codomain(X1)))),X0))),
inference(resolution,[status(thm)],[f409,f3411]) ).
fof(f17836,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),addition(omega(antidomain(multiplication(X0,divergence(X1)))),multiplication(star(antidomain(multiplication(X0,divergence(X1)))),X0))),
inference(resolution,[status(thm)],[f409,f3330]) ).
fof(f17837,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(omega(antidomain(backward_diamond(X0,X1))),multiplication(star(antidomain(backward_diamond(X0,X1))),addition(X2,one)))),
inference(resolution,[status(thm)],[f409,f2078]) ).
fof(f17838,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(omega(antidomain(backward_diamond(X0,X1))),multiplication(star(antidomain(backward_diamond(X0,X1))),star(X2)))),
inference(resolution,[status(thm)],[f409,f7768]) ).
fof(f17839,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),addition(omega(antidomain(backward_diamond(X0,X1))),multiplication(star(antidomain(backward_diamond(X0,X1))),one))),
inference(resolution,[status(thm)],[f409,f1473]) ).
fof(f17840,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(omega(antidomain(forward_box(X0,X1))),multiplication(star(antidomain(forward_box(X0,X1))),addition(X2,one)))),
inference(resolution,[status(thm)],[f409,f2052]) ).
fof(f17841,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(omega(antidomain(forward_box(X0,X1))),multiplication(star(antidomain(forward_box(X0,X1))),star(X2)))),
inference(resolution,[status(thm)],[f409,f7762]) ).
fof(f17842,plain,
! [X0,X1] : leq(forward_box(X0,X1),addition(omega(antidomain(forward_box(X0,X1))),multiplication(star(antidomain(forward_box(X0,X1))),one))),
inference(resolution,[status(thm)],[f409,f1466]) ).
fof(f17843,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(omega(antidomain(backward_box(X0,X1))),multiplication(star(antidomain(backward_box(X0,X1))),addition(X2,one)))),
inference(resolution,[status(thm)],[f409,f2028]) ).
fof(f17844,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(omega(antidomain(backward_box(X0,X1))),multiplication(star(antidomain(backward_box(X0,X1))),star(X2)))),
inference(resolution,[status(thm)],[f409,f7761]) ).
fof(f17845,plain,
! [X0,X1] : leq(backward_box(X0,X1),addition(omega(antidomain(backward_box(X0,X1))),multiplication(star(antidomain(backward_box(X0,X1))),one))),
inference(resolution,[status(thm)],[f409,f1465]) ).
fof(f17846,plain,
! [X0] : leq(divergence(X0),addition(omega(antidomain(divergence(X0))),multiplication(star(antidomain(divergence(X0))),codomain(divergence(X0))))),
inference(resolution,[status(thm)],[f409,f6073]) ).
fof(f17847,plain,
! [X0,X1] : leq(divergence(X0),addition(omega(antidomain(divergence(X0))),multiplication(star(antidomain(divergence(X0))),star(X1)))),
inference(resolution,[status(thm)],[f409,f7523]) ).
fof(f17848,plain,
! [X0] : leq(divergence(X0),addition(omega(antidomain(divergence(X0))),multiplication(star(antidomain(divergence(X0))),domain(divergence(X0))))),
inference(resolution,[status(thm)],[f409,f4208]) ).
fof(f17849,plain,
! [X0,X1] : leq(divergence(X0),addition(omega(antidomain(divergence(X0))),multiplication(star(antidomain(divergence(X0))),addition(one,X1)))),
inference(resolution,[status(thm)],[f409,f2232]) ).
fof(f17850,plain,
! [X0,X1] : leq(divergence(X0),addition(omega(antidomain(divergence(X0))),multiplication(star(antidomain(divergence(X0))),addition(X1,one)))),
inference(resolution,[status(thm)],[f409,f1779]) ).
fof(f17851,plain,
! [X0] : leq(divergence(X0),addition(omega(antidomain(divergence(X0))),multiplication(star(antidomain(divergence(X0))),one))),
inference(resolution,[status(thm)],[f409,f1484]) ).
fof(f17852,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(omega(antidomain(forward_diamond(X0,X1))),multiplication(star(antidomain(forward_diamond(X0,X1))),addition(X2,one)))),
inference(resolution,[status(thm)],[f409,f1907]) ).
fof(f17853,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(omega(antidomain(forward_diamond(X0,X1))),multiplication(star(antidomain(forward_diamond(X0,X1))),star(X2)))),
inference(resolution,[status(thm)],[f409,f7572]) ).
fof(f17854,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),addition(omega(antidomain(forward_diamond(X0,X1))),multiplication(star(antidomain(forward_diamond(X0,X1))),one))),
inference(resolution,[status(thm)],[f409,f1427]) ).
fof(f17855,plain,
! [X0] : leq(codomain(X0),addition(omega(antidomain(codomain(X0))),multiplication(star(antidomain(codomain(X0))),codomain(codomain(X0))))),
inference(resolution,[status(thm)],[f409,f6509]) ).
fof(f17856,plain,
! [X0,X1] : leq(codomain(X0),addition(omega(antidomain(codomain(X0))),multiplication(star(antidomain(codomain(X0))),star(X1)))),
inference(resolution,[status(thm)],[f409,f7522]) ).
fof(f17857,plain,
! [X0] : leq(codomain(X0),addition(omega(antidomain(codomain(X0))),multiplication(star(antidomain(codomain(X0))),domain(codomain(X0))))),
inference(resolution,[status(thm)],[f409,f4210]) ).
fof(f17858,plain,
! [X0,X1] : leq(codomain(X0),addition(omega(antidomain(codomain(X0))),multiplication(star(antidomain(codomain(X0))),addition(one,X1)))),
inference(resolution,[status(thm)],[f409,f2247]) ).
fof(f17859,plain,
! [X0,X1] : leq(codomain(X0),addition(omega(antidomain(codomain(X0))),multiplication(star(antidomain(codomain(X0))),addition(X1,one)))),
inference(resolution,[status(thm)],[f409,f1780]) ).
fof(f17860,plain,
! [X0] : leq(codomain(X0),addition(omega(antidomain(codomain(X0))),multiplication(star(antidomain(codomain(X0))),one))),
inference(resolution,[status(thm)],[f409,f1435]) ).
fof(f17861,plain,
! [X0] : leq(c(X0),addition(omega(antidomain(c(X0))),multiplication(star(antidomain(c(X0))),omega(c(X0))))),
inference(resolution,[status(thm)],[f409,f16991]) ).
fof(f17862,plain,
! [X0] : leq(c(X0),addition(omega(antidomain(c(X0))),multiplication(star(antidomain(c(X0))),antidomain(X0)))),
inference(resolution,[status(thm)],[f409,f13625]) ).
fof(f17863,plain,
! [X0] : leq(c(X0),addition(omega(antidomain(c(X0))),multiplication(star(antidomain(c(X0))),codomain(c(X0))))),
inference(resolution,[status(thm)],[f409,f6648]) ).
fof(f17864,plain,
! [X0,X1] : leq(c(X0),addition(omega(antidomain(c(X0))),multiplication(star(antidomain(c(X0))),star(X1)))),
inference(resolution,[status(thm)],[f409,f7521]) ).
fof(f17865,plain,
! [X0,X1] : leq(c(X0),addition(omega(antidomain(c(X0))),multiplication(star(antidomain(c(X0))),addition(one,X1)))),
inference(resolution,[status(thm)],[f409,f2264]) ).
fof(f17866,plain,
! [X0,X1] : leq(c(X0),addition(omega(antidomain(c(X0))),multiplication(star(antidomain(c(X0))),addition(X1,one)))),
inference(resolution,[status(thm)],[f409,f1781]) ).
fof(f17867,plain,
! [X0] : leq(c(X0),addition(omega(antidomain(c(X0))),multiplication(star(antidomain(c(X0))),one))),
inference(resolution,[status(thm)],[f409,f1430]) ).
fof(f17868,plain,
! [X0] : leq(antidomain(c(X0)),addition(omega(antidomain(antidomain(c(X0)))),multiplication(star(antidomain(antidomain(c(X0)))),domain(X0)))),
inference(resolution,[status(thm)],[f409,f13956]) ).
fof(f17869,plain,
! [X0] : leq(antidomain(X0),addition(omega(antidomain(antidomain(X0))),multiplication(star(antidomain(antidomain(X0))),omega(c(X0))))),
inference(resolution,[status(thm)],[f409,f16990]) ).
fof(f17870,plain,
! [X0] : leq(antidomain(X0),addition(omega(antidomain(antidomain(X0))),multiplication(star(antidomain(antidomain(X0))),codomain(antidomain(X0))))),
inference(resolution,[status(thm)],[f409,f6796]) ).
fof(f17871,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(antidomain(antidomain(X0))),multiplication(star(antidomain(antidomain(X0))),star(X1)))),
inference(resolution,[status(thm)],[f409,f7520]) ).
fof(f17872,plain,
! [X0] : leq(antidomain(X0),addition(omega(antidomain(antidomain(X0))),multiplication(star(antidomain(antidomain(X0))),c(X0)))),
inference(resolution,[status(thm)],[f409,f4241]) ).
fof(f17873,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(antidomain(antidomain(X0))),multiplication(star(antidomain(antidomain(X0))),addition(one,X1)))),
inference(resolution,[status(thm)],[f409,f2373]) ).
fof(f17874,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(antidomain(antidomain(X0))),multiplication(star(antidomain(antidomain(X0))),addition(X1,one)))),
inference(resolution,[status(thm)],[f409,f1782]) ).
fof(f17875,plain,
! [X0] : leq(antidomain(X0),addition(omega(antidomain(antidomain(X0))),multiplication(star(antidomain(antidomain(X0))),one))),
inference(resolution,[status(thm)],[f409,f1412]) ).
fof(f17876,plain,
! [X0] : leq(coantidomain(X0),addition(omega(antidomain(coantidomain(X0))),multiplication(star(antidomain(coantidomain(X0))),coantidomain(codomain(X0))))),
inference(resolution,[status(thm)],[f409,f7305]) ).
fof(f17877,plain,
! [X0] : leq(coantidomain(X0),addition(omega(antidomain(coantidomain(X0))),multiplication(star(antidomain(coantidomain(X0))),domain(coantidomain(X0))))),
inference(resolution,[status(thm)],[f409,f4735]) ).
fof(f17878,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(antidomain(coantidomain(X0))),multiplication(star(antidomain(coantidomain(X0))),star(X1)))),
inference(resolution,[status(thm)],[f409,f7519]) ).
fof(f17879,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(antidomain(coantidomain(X0))),multiplication(star(antidomain(coantidomain(X0))),addition(one,X1)))),
inference(resolution,[status(thm)],[f409,f2387]) ).
fof(f17880,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(antidomain(coantidomain(X0))),multiplication(star(antidomain(coantidomain(X0))),addition(X1,one)))),
inference(resolution,[status(thm)],[f409,f1783]) ).
fof(f17881,plain,
! [X0] : leq(coantidomain(X0),addition(omega(antidomain(coantidomain(X0))),multiplication(star(antidomain(coantidomain(X0))),one))),
inference(resolution,[status(thm)],[f409,f1410]) ).
fof(f17882,plain,
! [X0] : leq(domain(X0),addition(omega(antidomain(domain(X0))),multiplication(star(antidomain(domain(X0))),omega(domain(X0))))),
inference(resolution,[status(thm)],[f409,f16992]) ).
fof(f17883,plain,
! [X0] : leq(domain(X0),addition(omega(antidomain(domain(X0))),multiplication(star(antidomain(domain(X0))),codomain(domain(X0))))),
inference(resolution,[status(thm)],[f409,f7000]) ).
fof(f17884,plain,
! [X0,X1] : leq(domain(X0),addition(omega(antidomain(domain(X0))),multiplication(star(antidomain(domain(X0))),star(X1)))),
inference(resolution,[status(thm)],[f409,f7518]) ).
fof(f17885,plain,
! [X0] : leq(domain(X0),addition(omega(antidomain(domain(X0))),multiplication(star(antidomain(domain(X0))),antidomain(c(X0))))),
inference(resolution,[status(thm)],[f409,f4249]) ).
fof(f17886,plain,
! [X0,X1] : leq(domain(X0),addition(omega(antidomain(domain(X0))),multiplication(star(antidomain(domain(X0))),addition(one,X1)))),
inference(resolution,[status(thm)],[f409,f2403]) ).
fof(f17887,plain,
! [X0,X1] : leq(domain(X0),addition(omega(antidomain(domain(X0))),multiplication(star(antidomain(domain(X0))),addition(X1,one)))),
inference(resolution,[status(thm)],[f409,f1784]) ).
fof(f17888,plain,
! [X0] : leq(domain(X0),addition(omega(antidomain(domain(X0))),multiplication(star(antidomain(domain(X0))),one))),
inference(resolution,[status(thm)],[f409,f1408]) ).
fof(f17896,plain,
! [X0,X1] : leq(addition(X0,X1),addition(omega(antidomain(addition(X0,X1))),multiplication(star(antidomain(addition(X0,X1))),addition(X1,X0)))),
inference(resolution,[status(thm)],[f409,f10439]) ).
fof(f17897,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),omega(addition(one,X1))))),
inference(resolution,[status(thm)],[f409,f16988]) ).
fof(f17898,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),omega(addition(X1,one))))),
inference(resolution,[status(thm)],[f409,f16989]) ).
fof(f17899,plain,
! [X0] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),omega(domain(X0))))),
inference(resolution,[status(thm)],[f409,f16993]) ).
fof(f17900,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),omega(star(X1))))),
inference(resolution,[status(thm)],[f409,f16941]) ).
fof(f17901,plain,
! [X0] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),omega(one)))),
inference(resolution,[status(thm)],[f409,f16994]) ).
fof(f17902,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(star(X1),X0)))),
inference(resolution,[status(thm)],[f409,f8451]) ).
fof(f17903,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(X0,addition(one,X1))))),
inference(resolution,[status(thm)],[f409,f2478]) ).
fof(f17904,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(X0,star(X1))))),
inference(resolution,[status(thm)],[f409,f8449]) ).
fof(f17905,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),addition(omega(one),X1)))),
inference(resolution,[status(thm)],[f409,f16915]) ).
fof(f17906,plain,
! [X0,X1,X2] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),addition(X1,addition(X0,X2))))),
inference(resolution,[status(thm)],[f409,f1421]) ).
fof(f17907,plain,
! [X0,X1,X2] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),addition(X1,addition(X2,X0))))),
inference(resolution,[status(thm)],[f409,f1420]) ).
fof(f17908,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),addition(X1,X0)))),
inference(resolution,[status(thm)],[f409,f1423]) ).
fof(f17909,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),addition(X0,X1)))),
inference(resolution,[status(thm)],[f409,f1324]) ).
fof(f17910,plain,
! [X0] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X0))),
inference(resolution,[status(thm)],[f409,f239]) ).
fof(f17911,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),addition(omega(antidomain(backward_diamond(X0,X1))),star(antidomain(backward_diamond(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f40,f17839]) ).
fof(f17912,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),addition(star(antidomain(backward_diamond(X0,X1))),omega(antidomain(backward_diamond(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f35,f17911]) ).
fof(f17913,plain,
! [X0,X1] : leq(forward_box(X0,X1),addition(omega(antidomain(forward_box(X0,X1))),star(antidomain(forward_box(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f40,f17842]) ).
fof(f17914,plain,
! [X0,X1] : leq(forward_box(X0,X1),addition(star(antidomain(forward_box(X0,X1))),omega(antidomain(forward_box(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f35,f17913]) ).
fof(f17915,plain,
! [X0,X1] : leq(backward_box(X0,X1),addition(omega(antidomain(backward_box(X0,X1))),star(antidomain(backward_box(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f40,f17845]) ).
fof(f17916,plain,
! [X0,X1] : leq(backward_box(X0,X1),addition(star(antidomain(backward_box(X0,X1))),omega(antidomain(backward_box(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f35,f17915]) ).
fof(f17917,plain,
! [X0] : leq(divergence(X0),addition(omega(antidomain(divergence(X0))),star(antidomain(divergence(X0))))),
inference(forward_demodulation,[status(thm)],[f40,f17851]) ).
fof(f17918,plain,
! [X0] : leq(divergence(X0),addition(star(antidomain(divergence(X0))),omega(antidomain(divergence(X0))))),
inference(forward_demodulation,[status(thm)],[f35,f17917]) ).
fof(f17919,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),addition(omega(antidomain(forward_diamond(X0,X1))),star(antidomain(forward_diamond(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f40,f17854]) ).
fof(f17920,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),addition(star(antidomain(forward_diamond(X0,X1))),omega(antidomain(forward_diamond(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f35,f17919]) ).
fof(f17921,plain,
! [X0] : leq(codomain(X0),addition(omega(antidomain(codomain(X0))),star(antidomain(codomain(X0))))),
inference(forward_demodulation,[status(thm)],[f40,f17860]) ).
fof(f17922,plain,
! [X0] : leq(codomain(X0),addition(star(antidomain(codomain(X0))),omega(antidomain(codomain(X0))))),
inference(forward_demodulation,[status(thm)],[f35,f17921]) ).
fof(f17923,plain,
! [X0] : leq(c(X0),addition(omega(antidomain(c(X0))),star(antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f40,f17867]) ).
fof(f17924,plain,
! [X0] : leq(c(X0),addition(star(antidomain(c(X0))),omega(antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f35,f17923]) ).
fof(f17925,plain,
! [X0] : leq(antidomain(c(X0)),addition(omega(domain(c(X0))),multiplication(star(antidomain(antidomain(c(X0)))),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f17868]) ).
fof(f17926,plain,
! [X0] : leq(antidomain(c(X0)),addition(omega(c(X0)),multiplication(star(antidomain(antidomain(c(X0)))),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f13678,f17925]) ).
fof(f17927,plain,
! [X0] : leq(antidomain(c(X0)),addition(omega(c(X0)),multiplication(star(domain(c(X0))),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f17926]) ).
fof(f17928,plain,
! [X0] : leq(antidomain(c(X0)),addition(omega(c(X0)),multiplication(star(c(X0)),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f13678,f17927]) ).
fof(f17929,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(antidomain(antidomain(X0))),omega(c(X0))))),
inference(forward_demodulation,[status(thm)],[f62,f17869]) ).
fof(f17930,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),omega(c(X0))))),
inference(forward_demodulation,[status(thm)],[f62,f17929]) ).
fof(f17931,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(antidomain(antidomain(X0))),codomain(antidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f62,f17870]) ).
fof(f17932,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),codomain(antidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f62,f17931]) ).
fof(f17933,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(antidomain(antidomain(X0))),star(X1)))),
inference(forward_demodulation,[status(thm)],[f62,f17871]) ).
fof(f17934,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),star(X1)))),
inference(forward_demodulation,[status(thm)],[f62,f17933]) ).
fof(f17935,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(antidomain(antidomain(X0))),c(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f17872]) ).
fof(f17936,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),c(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f17935]) ).
fof(f17937,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(antidomain(antidomain(X0))),addition(one,X1)))),
inference(forward_demodulation,[status(thm)],[f62,f17873]) ).
fof(f17938,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),addition(one,X1)))),
inference(forward_demodulation,[status(thm)],[f62,f17937]) ).
fof(f17939,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(antidomain(antidomain(X0))),addition(X1,one)))),
inference(forward_demodulation,[status(thm)],[f62,f17874]) ).
fof(f17940,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),addition(X1,one)))),
inference(forward_demodulation,[status(thm)],[f62,f17939]) ).
fof(f17941,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(antidomain(antidomain(X0))),one))),
inference(forward_demodulation,[status(thm)],[f62,f17875]) ).
fof(f17942,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),star(antidomain(antidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f40,f17941]) ).
fof(f17943,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),star(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f17942]) ).
fof(f17944,plain,
! [X0] : leq(antidomain(X0),addition(star(domain(X0)),omega(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f17943]) ).
fof(f17945,plain,
! [X0] : leq(coantidomain(X0),addition(omega(antidomain(coantidomain(X0))),star(antidomain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f40,f17881]) ).
fof(f17946,plain,
! [X0] : leq(coantidomain(X0),addition(star(antidomain(coantidomain(X0))),omega(antidomain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f35,f17945]) ).
fof(f17947,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(antidomain(domain(X0))),omega(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f67,f17882]) ).
fof(f17948,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),omega(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f67,f17947]) ).
fof(f17949,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(antidomain(domain(X0))),codomain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f67,f17883]) ).
fof(f17950,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),codomain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f67,f17949]) ).
fof(f17951,plain,
! [X0,X1] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(antidomain(domain(X0))),star(X1)))),
inference(forward_demodulation,[status(thm)],[f67,f17884]) ).
fof(f17952,plain,
! [X0,X1] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),star(X1)))),
inference(forward_demodulation,[status(thm)],[f67,f17951]) ).
fof(f17953,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(antidomain(domain(X0))),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f67,f17885]) ).
fof(f17954,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f67,f17953]) ).
fof(f17955,plain,
! [X0,X1] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(antidomain(domain(X0))),addition(one,X1)))),
inference(forward_demodulation,[status(thm)],[f67,f17886]) ).
fof(f17956,plain,
! [X0,X1] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),addition(one,X1)))),
inference(forward_demodulation,[status(thm)],[f67,f17955]) ).
fof(f17957,plain,
! [X0,X1] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(antidomain(domain(X0))),addition(X1,one)))),
inference(forward_demodulation,[status(thm)],[f67,f17887]) ).
fof(f17958,plain,
! [X0,X1] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),addition(X1,one)))),
inference(forward_demodulation,[status(thm)],[f67,f17957]) ).
fof(f17959,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),multiplication(star(antidomain(domain(X0))),one))),
inference(forward_demodulation,[status(thm)],[f67,f17888]) ).
fof(f17960,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),star(antidomain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f40,f17959]) ).
fof(f17961,plain,
! [X0] : leq(domain(X0),addition(omega(c(X0)),star(c(X0)))),
inference(forward_demodulation,[status(thm)],[f67,f17960]) ).
fof(f17962,plain,
! [X0] : leq(domain(X0),addition(star(c(X0)),omega(c(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f17961]) ).
fof(f18016,plain,
! [X0,X1,X2] : leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),omega(one)))),
inference(resolution,[status(thm)],[f17361,f398]) ).
fof(f18017,plain,
! [X0,X1] : leq(X0,addition(omega(X1),multiplication(star(X1),omega(one)))),
inference(resolution,[status(thm)],[f17361,f58]) ).
fof(f18018,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),addition(X1,omega(one))))),
inference(resolution,[status(thm)],[f17361,f409]) ).
fof(f18021,plain,
! [X0,X1] : addition(X0,addition(X1,omega(one))) = addition(X1,omega(one)),
inference(resolution,[status(thm)],[f17361,f48]) ).
fof(f18022,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,omega(one)))),
inference(paramodulation,[status(thm)],[f103,f17361]) ).
fof(f18023,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,omega(one)))),
inference(paramodulation,[status(thm)],[f36,f17361]) ).
fof(f18031,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(omega(X2),multiplication(star(X2),one))),
inference(resolution,[status(thm)],[f2794,f394]) ).
fof(f18032,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(omega(antidomain(backward_diamond(X0,X1))),multiplication(star(antidomain(backward_diamond(X0,X1))),addition(one,X2)))),
inference(resolution,[status(thm)],[f2794,f409]) ).
fof(f18033,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),star(coantidomain(addition(one,X2)))),addition(one,X2)),
inference(resolution,[status(thm)],[f2794,f346]) ).
fof(f18035,plain,
! [X0,X1,X2] : addition(backward_diamond(X0,X1),addition(one,X2)) = addition(one,X2),
inference(resolution,[status(thm)],[f2794,f48]) ).
fof(f18075,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f97,f2794]) ).
fof(f18076,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(X2,addition(one,X3))),
inference(paramodulation,[status(thm)],[f97,f2794]) ).
fof(f18081,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(omega(X2),star(X2))),
inference(forward_demodulation,[status(thm)],[f40,f18031]) ).
fof(f18082,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(star(X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f35,f18081]) ).
fof(f18086,plain,
! [X0,X1,X2] : addition(one,addition(X0,backward_diamond(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f18035]) ).
fof(f18087,plain,
! [X0] : leq(addition(X0,one),addition(omega(X0),multiplication(star(X0),multiplication(one,addition(X0,one))))),
inference(resolution,[status(thm)],[f2886,f391]) ).
fof(f18088,plain,
! [X0] : leq(X0,addition(omega(X0),multiplication(star(X0),multiplication(X0,one)))),
inference(resolution,[status(thm)],[f2886,f392]) ).
fof(f18089,plain,
! [X0] : leq(addition(X0,one),addition(omega(addition(X0,one)),multiplication(star(addition(X0,one)),multiplication(addition(X0,one),addition(X0,one))))),
inference(resolution,[status(thm)],[f2886,f396]) ).
fof(f18091,plain,
! [X0,X1] : leq(X0,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(X0,addition(X1,one))))),
inference(resolution,[status(thm)],[f2886,f409]) ).
fof(f18092,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(multiplication(X0,addition(X1,one))))),multiplication(X0,addition(X1,one))),
inference(resolution,[status(thm)],[f2886,f346]) ).
fof(f18093,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(X0,addition(X1,one)))),X0),multiplication(X0,addition(X1,one))),
inference(resolution,[status(thm)],[f2886,f304]) ).
fof(f18094,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = multiplication(X0,addition(X1,one)),
inference(resolution,[status(thm)],[f2886,f48]) ).
fof(f18099,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f39,f2886]) ).
fof(f18110,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f103,f2886]) ).
fof(f18111,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f36,f2886]) ).
fof(f18116,plain,
! [X0] : leq(addition(X0,one),addition(omega(X0),multiplication(star(X0),addition(X0,one)))),
inference(forward_demodulation,[status(thm)],[f41,f18087]) ).
fof(f18117,plain,
! [X0] : leq(X0,addition(omega(X0),multiplication(star(X0),X0))),
inference(forward_demodulation,[status(thm)],[f40,f18088]) ).
fof(f18138,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(omega(X2),multiplication(star(X2),one))),
inference(resolution,[status(thm)],[f2994,f394]) ).
fof(f18139,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(omega(antidomain(backward_box(X0,X1))),multiplication(star(antidomain(backward_box(X0,X1))),addition(one,X2)))),
inference(resolution,[status(thm)],[f2994,f409]) ).
fof(f18140,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),star(coantidomain(addition(one,X2)))),addition(one,X2)),
inference(resolution,[status(thm)],[f2994,f346]) ).
fof(f18142,plain,
! [X0,X1,X2] : addition(backward_box(X0,X1),addition(one,X2)) = addition(one,X2),
inference(resolution,[status(thm)],[f2994,f48]) ).
fof(f18182,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f97,f2994]) ).
fof(f18183,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(X2,addition(one,X3))),
inference(paramodulation,[status(thm)],[f97,f2994]) ).
fof(f18188,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(omega(X2),star(X2))),
inference(forward_demodulation,[status(thm)],[f40,f18138]) ).
fof(f18189,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(star(X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f35,f18188]) ).
fof(f18193,plain,
! [X0,X1,X2] : addition(one,addition(X0,backward_box(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f18142]) ).
fof(f18194,plain,
! [X0] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),coantidomain(codomain(X0))))),
inference(resolution,[status(thm)],[f413,f7305]) ).
fof(f18195,plain,
! [X0] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),domain(coantidomain(X0))))),
inference(resolution,[status(thm)],[f413,f4735]) ).
fof(f18196,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),star(X1)))),
inference(resolution,[status(thm)],[f413,f7519]) ).
fof(f18197,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),addition(one,X1)))),
inference(resolution,[status(thm)],[f413,f2387]) ).
fof(f18198,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),addition(X1,one)))),
inference(resolution,[status(thm)],[f413,f1783]) ).
fof(f18199,plain,
! [X0] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),one))),
inference(resolution,[status(thm)],[f413,f1410]) ).
fof(f18200,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),omega(addition(one,X1))))),
inference(resolution,[status(thm)],[f413,f16988]) ).
fof(f18201,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),omega(addition(X1,one))))),
inference(resolution,[status(thm)],[f413,f16989]) ).
fof(f18202,plain,
! [X0] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),omega(domain(coantidomain(X0)))))),
inference(resolution,[status(thm)],[f413,f16993]) ).
fof(f18203,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),omega(star(X1))))),
inference(resolution,[status(thm)],[f413,f16941]) ).
fof(f18204,plain,
! [X0] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),omega(one)))),
inference(resolution,[status(thm)],[f413,f16994]) ).
fof(f18205,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),multiplication(star(X1),coantidomain(X0))))),
inference(resolution,[status(thm)],[f413,f8451]) ).
fof(f18206,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),multiplication(coantidomain(X0),addition(one,X1))))),
inference(resolution,[status(thm)],[f413,f2478]) ).
fof(f18207,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),multiplication(coantidomain(X0),addition(X1,one))))),
inference(resolution,[status(thm)],[f413,f2886]) ).
fof(f18208,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),multiplication(coantidomain(X0),star(X1))))),
inference(resolution,[status(thm)],[f413,f8449]) ).
fof(f18209,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),addition(omega(one),X1)))),
inference(resolution,[status(thm)],[f413,f16915]) ).
fof(f18210,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),addition(X1,omega(one))))),
inference(resolution,[status(thm)],[f413,f17361]) ).
fof(f18211,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),addition(X1,addition(coantidomain(X0),X2))))),
inference(resolution,[status(thm)],[f413,f1421]) ).
fof(f18212,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),addition(X1,addition(X2,coantidomain(X0)))))),
inference(resolution,[status(thm)],[f413,f1420]) ).
fof(f18213,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),addition(X1,coantidomain(X0))))),
inference(resolution,[status(thm)],[f413,f1423]) ).
fof(f18214,plain,
! [X0,X1] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),addition(coantidomain(X0),X1)))),
inference(resolution,[status(thm)],[f413,f1324]) ).
fof(f18215,plain,
! [X0] : leq(coantidomain(X0),addition(omega(X0),multiplication(star(X0),coantidomain(X0)))),
inference(resolution,[status(thm)],[f413,f239]) ).
fof(f18218,plain,
! [X0,X1] :
( leq(coantidomain(coantidomain(X0)),addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),X1)))
| ~ leq(codomain(X0),X1) ),
inference(paramodulation,[status(thm)],[f66,f413]) ).
fof(f18220,plain,
! [X0] : leq(coantidomain(X0),addition(omega(X0),star(X0))),
inference(forward_demodulation,[status(thm)],[f40,f18199]) ).
fof(f18221,plain,
! [X0] : leq(coantidomain(X0),addition(star(X0),omega(X0))),
inference(forward_demodulation,[status(thm)],[f35,f18220]) ).
fof(f18227,plain,
! [X0,X1] :
( leq(codomain(X0),addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),X1)))
| ~ leq(codomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f66,f18218]) ).
fof(f18231,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(omega(X2),multiplication(star(X2),one))),
inference(resolution,[status(thm)],[f2995,f394]) ).
fof(f18232,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(omega(antidomain(forward_box(X0,X1))),multiplication(star(antidomain(forward_box(X0,X1))),addition(one,X2)))),
inference(resolution,[status(thm)],[f2995,f409]) ).
fof(f18233,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),star(coantidomain(addition(one,X2)))),addition(one,X2)),
inference(resolution,[status(thm)],[f2995,f346]) ).
fof(f18235,plain,
! [X0,X1,X2] : addition(forward_box(X0,X1),addition(one,X2)) = addition(one,X2),
inference(resolution,[status(thm)],[f2995,f48]) ).
fof(f18278,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f97,f2995]) ).
fof(f18279,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(X2,addition(one,X3))),
inference(paramodulation,[status(thm)],[f97,f2995]) ).
fof(f18284,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(omega(X2),star(X2))),
inference(forward_demodulation,[status(thm)],[f40,f18231]) ).
fof(f18285,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(star(X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f35,f18284]) ).
fof(f18289,plain,
! [X0,X1,X2] : addition(one,addition(X0,forward_box(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f18235]) ).
fof(f18290,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(omega(X2),multiplication(star(X2),one))),
inference(resolution,[status(thm)],[f3306,f394]) ).
fof(f18291,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(omega(antidomain(forward_diamond(X0,X1))),multiplication(star(antidomain(forward_diamond(X0,X1))),addition(one,X2)))),
inference(resolution,[status(thm)],[f3306,f409]) ).
fof(f18292,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),star(coantidomain(addition(one,X2)))),addition(one,X2)),
inference(resolution,[status(thm)],[f3306,f346]) ).
fof(f18294,plain,
! [X0,X1,X2] : addition(forward_diamond(X0,X1),addition(one,X2)) = addition(one,X2),
inference(resolution,[status(thm)],[f3306,f48]) ).
fof(f18336,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f97,f3306]) ).
fof(f18337,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(X2,addition(one,X3))),
inference(paramodulation,[status(thm)],[f97,f3306]) ).
fof(f18342,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(omega(X2),star(X2))),
inference(forward_demodulation,[status(thm)],[f40,f18290]) ).
fof(f18343,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(star(X2),omega(X2))),
inference(forward_demodulation,[status(thm)],[f35,f18342]) ).
fof(f18347,plain,
! [X0,X1,X2] : addition(one,addition(X0,forward_diamond(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f97,f18294]) ).
fof(f18348,plain,
! [X0,X1] : leq(one,addition(omega(star(X0)),multiplication(star(star(X0)),X1))),
inference(resolution,[status(thm)],[f405,f8413]) ).
fof(f18349,plain,
! [X0,X1] : leq(one,addition(omega(X0),multiplication(star(X0),star(X1)))),
inference(resolution,[status(thm)],[f405,f7532]) ).
fof(f18350,plain,
! [X0] : leq(one,addition(omega(omega(one)),multiplication(star(omega(one)),X0))),
inference(resolution,[status(thm)],[f405,f16915]) ).
fof(f18351,plain,
! [X0] : leq(one,addition(omega(X0),multiplication(star(X0),omega(one)))),
inference(resolution,[status(thm)],[f405,f17361]) ).
fof(f18352,plain,
! [X0,X1] : leq(one,addition(omega(X0),multiplication(star(X0),addition(one,X1)))),
inference(resolution,[status(thm)],[f405,f1421]) ).
fof(f18353,plain,
! [X0,X1] : leq(one,addition(omega(X0),multiplication(star(X0),addition(X1,one)))),
inference(resolution,[status(thm)],[f405,f1420]) ).
fof(f18359,plain,
! [X0,X1] :
( leq(one,addition(omega(one),multiplication(star(one),backward_diamond(X0,X1))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1504,f405]) ).
fof(f18360,plain,
! [X0,X1] :
( leq(one,addition(omega(one),multiplication(star(one),forward_box(X0,X1))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1497,f405]) ).
fof(f18361,plain,
! [X0,X1] :
( leq(one,addition(omega(one),multiplication(star(one),backward_box(X0,X1))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1492,f405]) ).
fof(f18362,plain,
! [X0,X1] :
( leq(one,addition(omega(one),multiplication(star(one),forward_diamond(X0,X1))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1485,f405]) ).
fof(f18363,plain,
! [X0] :
( leq(one,addition(omega(one),multiplication(star(one),divergence(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1488,f405]) ).
fof(f18364,plain,
! [X0] :
( leq(one,addition(omega(one),multiplication(star(one),codomain(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1477,f405]) ).
fof(f18365,plain,
! [X0] :
( leq(one,addition(omega(one),multiplication(star(one),c(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1471,f405]) ).
fof(f18366,plain,
! [X0] :
( leq(one,addition(omega(one),multiplication(star(one),antidomain(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1379,f405]) ).
fof(f18367,plain,
! [X0] :
( leq(one,addition(omega(one),multiplication(star(one),coantidomain(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1377,f405]) ).
fof(f18368,plain,
! [X0] :
( leq(one,addition(omega(one),multiplication(star(one),domain(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1375,f405]) ).
fof(f18369,plain,
! [X0] :
( leq(one,addition(omega(domain(X0)),multiplication(star(domain(X0)),c(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f569,f405]) ).
fof(f18370,plain,
! [X0,X1] :
( leq(one,addition(omega(coantidomain(multiplication(X0,X1))),multiplication(star(coantidomain(multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),X1)))))
| ~ leq(one,coantidomain(multiplication(codomain(X0),X1))) ),
inference(paramodulation,[status(thm)],[f615,f405]) ).
fof(f18371,plain,
! [X0] :
( leq(one,addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),codomain(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f683,f405]) ).
fof(f18372,plain,
! [X0,X1] :
( leq(one,addition(omega(antidomain(multiplication(X0,X1))),multiplication(star(antidomain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1))))))
| ~ leq(one,antidomain(multiplication(X0,domain(X1)))) ),
inference(paramodulation,[status(thm)],[f479,f405]) ).
fof(f18373,plain,
! [X0] :
( leq(one,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),c(X0))))
| ~ leq(one,c(X0)) ),
inference(paramodulation,[status(thm)],[f514,f405]) ).
fof(f18374,plain,
! [X0] :
( leq(one,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),domain(X0))))
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f558,f405]) ).
fof(f18375,plain,
! [X0,X1,X2,X3] :
( leq(one,addition(omega(multiplication(X0,multiplication(X1,X3))),multiplication(star(multiplication(X0,multiplication(X1,X3))),multiplication(X2,X3))))
| ~ leq(one,multiplication(addition(multiplication(X0,X1),X2),X3)) ),
inference(paramodulation,[status(thm)],[f204,f405]) ).
fof(f18376,plain,
! [X0,X1,X2,X3] :
( leq(one,addition(omega(multiplication(X0,X2)),multiplication(star(multiplication(X0,X2)),addition(multiplication(X1,X2),X3))))
| ~ leq(one,addition(multiplication(addition(X0,X1),X2),X3)) ),
inference(paramodulation,[status(thm)],[f219,f405]) ).
fof(f18377,plain,
! [X0,X1,X2,X3] :
( leq(one,addition(omega(multiplication(X0,X1)),multiplication(star(multiplication(X0,X1)),addition(multiplication(X0,X2),X3))))
| ~ leq(one,addition(multiplication(X0,addition(X1,X2)),X3)) ),
inference(paramodulation,[status(thm)],[f170,f405]) ).
fof(f18378,plain,
! [X0,X1,X2,X3] :
( leq(one,addition(omega(multiplication(X0,X3)),multiplication(star(multiplication(X0,X3)),multiplication(X1,multiplication(X2,X3)))))
| ~ leq(one,multiplication(addition(X0,multiplication(X1,X2)),X3)) ),
inference(paramodulation,[status(thm)],[f211,f405]) ).
fof(f18379,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(X0,X2))))
| ~ leq(one,multiplication(addition(X0,X1),X2)) ),
inference(paramodulation,[status(thm)],[f201,f405]) ).
fof(f18380,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(multiplication(X0,X2)),multiplication(star(multiplication(X0,X2)),multiplication(X0,X1))))
| ~ leq(one,multiplication(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f153,f405]) ).
fof(f18381,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(multiplication(X0,X2)),multiplication(star(multiplication(X0,X2)),multiplication(X1,X2))))
| ~ leq(one,multiplication(addition(X0,X1),X2)) ),
inference(paramodulation,[status(thm)],[f43,f405]) ).
fof(f18382,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(multiplication(X0,X1)),multiplication(star(multiplication(X0,X1)),multiplication(X0,X2))))
| ~ leq(one,multiplication(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f42,f405]) ).
fof(f18383,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(addition(X1,X0)),multiplication(star(addition(X1,X0)),X2)))
| ~ leq(one,addition(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f103,f405]) ).
fof(f18384,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(addition(X0,X1)),multiplication(star(addition(X0,X1)),X2)))
| ~ leq(one,addition(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f36,f405]) ).
fof(f18386,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(domain(X1),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4516,f405]) ).
fof(f18387,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(coantidomain(X1),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4515,f405]) ).
fof(f18388,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(antidomain(X1),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4514,f405]) ).
fof(f18389,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(c(X1),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4513,f405]) ).
fof(f18390,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(codomain(X1),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4512,f405]) ).
fof(f18391,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(divergence(X1),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4511,f405]) ).
fof(f18392,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2491,f405]) ).
fof(f18393,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,backward_box(X1,X2)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2490,f405]) ).
fof(f18394,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,forward_box(X1,X2)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2489,f405]) ).
fof(f18395,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2488,f405]) ).
fof(f18396,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,domain(X1)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2497,f405]) ).
fof(f18397,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,coantidomain(X1)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2496,f405]) ).
fof(f18398,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,antidomain(X1)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2495,f405]) ).
fof(f18399,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,c(X1)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2494,f405]) ).
fof(f18400,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,codomain(X1)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2493,f405]) ).
fof(f18401,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,divergence(X1)))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f2492,f405]) ).
fof(f18402,plain,
! [X0,X1] :
( leq(one,addition(omega(X1),multiplication(star(X1),multiplication(X0,X1))))
| ~ leq(one,multiplication(addition(X0,one),X1)) ),
inference(paramodulation,[status(thm)],[f232,f405]) ).
fof(f18403,plain,
! [X0,X1] :
( leq(one,addition(omega(X1),multiplication(star(X1),multiplication(X0,X1))))
| ~ leq(one,multiplication(addition(one,X0),X1)) ),
inference(paramodulation,[status(thm)],[f207,f405]) ).
fof(f18404,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(X0,X1))))
| ~ leq(one,multiplication(X0,addition(X1,one))) ),
inference(paramodulation,[status(thm)],[f192,f405]) ).
fof(f18406,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),addition(X1,X0))))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1329,f405]) ).
fof(f18407,plain,
! [X0,X1] :
( leq(one,addition(omega(X1),multiplication(star(X1),addition(X1,X0))))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1026,f405]) ).
fof(f18408,plain,
! [X0,X1] :
( leq(one,addition(omega(X1),multiplication(star(X1),addition(X0,X1))))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1005,f405]) ).
fof(f18409,plain,
! [X0,X1] :
( leq(one,addition(omega(X0),multiplication(star(X0),addition(X0,X1))))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f105,f405]) ).
fof(f18410,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X2),multiplication(star(X2),addition(X0,X1))))
| ~ leq(one,addition(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f97,f405]) ).
fof(f18411,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X1),multiplication(star(X1),addition(X2,X0))))
| ~ leq(one,addition(X0,addition(X1,X2))) ),
inference(paramodulation,[status(thm)],[f97,f405]) ).
fof(f18412,plain,
! [X0] :
( leq(one,addition(omega(X0),multiplication(star(X0),zero)))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f37,f405]) ).
fof(f18413,plain,
! [X0,X1] :
( leq(one,addition(omega(X1),multiplication(star(X1),X0)))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f35,f405]) ).
fof(f18414,plain,
! [X0,X1] :
( leq(one,addition(omega(X1),multiplication(star(X1),X0)))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f35,f405]) ).
fof(f18415,plain,
! [X0] :
( leq(one,addition(omega(X0),multiplication(star(X0),X0)))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f38,f405]) ).
fof(f18426,definition,
! [X0,X1] :
( sQ46_spl
<=> leq(one,addition(omega(one),multiplication(star(one),backward_diamond(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f18429,plain,
( sQ46_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18359,f9301,f18426]) ).
fof(f18430,definition,
! [X0,X1] :
( sQ47_spl
<=> leq(one,addition(omega(one),multiplication(star(one),forward_box(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f18433,plain,
( sQ47_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18360,f9301,f18430]) ).
fof(f18434,definition,
! [X0,X1] :
( sQ48_spl
<=> leq(one,addition(omega(one),multiplication(star(one),backward_box(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f18437,plain,
( sQ48_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18361,f9301,f18434]) ).
fof(f18438,definition,
! [X0,X1] :
( sQ49_spl
<=> leq(one,addition(omega(one),multiplication(star(one),forward_diamond(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f18441,plain,
( sQ49_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18362,f9301,f18438]) ).
fof(f18442,definition,
! [X0] :
( sQ50_spl
<=> leq(one,addition(omega(one),multiplication(star(one),divergence(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f18445,plain,
( sQ50_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18363,f9301,f18442]) ).
fof(f18446,definition,
! [X0] :
( sQ51_spl
<=> leq(one,addition(omega(one),multiplication(star(one),codomain(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f18449,plain,
( sQ51_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18364,f9301,f18446]) ).
fof(f18450,definition,
! [X0] :
( sQ52_spl
<=> leq(one,addition(omega(one),multiplication(star(one),c(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f18453,plain,
( sQ52_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18365,f9301,f18450]) ).
fof(f18454,definition,
! [X0] :
( sQ53_spl
<=> leq(one,addition(omega(one),multiplication(star(one),antidomain(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f18457,plain,
( sQ53_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18366,f9301,f18454]) ).
fof(f18458,definition,
! [X0] :
( sQ54_spl
<=> leq(one,addition(omega(one),multiplication(star(one),coantidomain(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f18461,plain,
( sQ54_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18367,f9301,f18458]) ).
fof(f18462,definition,
! [X0] :
( sQ55_spl
<=> leq(one,addition(omega(one),multiplication(star(one),domain(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f18465,plain,
( sQ55_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18368,f9301,f18462]) ).
fof(f18466,definition,
! [X0] :
( sQ56_spl
<=> leq(one,addition(omega(domain(X0)),multiplication(star(domain(X0)),c(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f18467,plain,
! [X0] :
( ~ sQ56_spl
| leq(one,addition(omega(domain(X0)),multiplication(star(domain(X0)),c(X0)))) ),
inference(component_clause,[status(thm)],[f18466]) ).
fof(f18469,plain,
( sQ56_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18369,f9301,f18466]) ).
fof(f18470,definition,
! [X0] :
( sQ57_spl
<=> leq(one,addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),codomain(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f18471,plain,
! [X0] :
( ~ sQ57_spl
| leq(one,addition(omega(coantidomain(X0)),multiplication(star(coantidomain(X0)),codomain(X0)))) ),
inference(component_clause,[status(thm)],[f18470]) ).
fof(f18473,plain,
( sQ57_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18371,f9301,f18470]) ).
fof(f18474,definition,
! [X0] :
( sQ58_spl
<=> leq(one,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),domain(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f18475,plain,
! [X0] :
( ~ sQ58_spl
| leq(one,addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),domain(X0)))) ),
inference(component_clause,[status(thm)],[f18474]) ).
fof(f18477,plain,
( sQ58_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f18374,f9301,f18474]) ).
fof(f18481,plain,
! [X0] :
( leq(one,addition(omega(X0),zero))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f44,f18412]) ).
fof(f18482,plain,
! [X0] :
( leq(one,omega(X0))
| ~ leq(one,X0) ),
inference(forward_demodulation,[status(thm)],[f37,f18481]) ).
fof(f18504,plain,
! [X0,X1] : leq(multiplication(antidomain(multiplication(X0,X1)),star(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,domain(X1)))),
inference(resolution,[status(thm)],[f480,f344]) ).
fof(f18505,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),addition(omega(antidomain(antidomain(multiplication(X0,X1)))),multiplication(star(antidomain(antidomain(multiplication(X0,X1)))),antidomain(multiplication(X0,domain(X1)))))),
inference(resolution,[status(thm)],[f480,f409]) ).
fof(f18506,plain,
! [X0,X1] : leq(multiplication(antidomain(multiplication(X0,X1)),star(coantidomain(antidomain(multiplication(X0,domain(X1)))))),antidomain(multiplication(X0,domain(X1)))),
inference(resolution,[status(thm)],[f480,f346]) ).
fof(f18507,plain,
! [X0,X1] : leq(multiplication(star(antidomain(antidomain(multiplication(X0,domain(X1))))),antidomain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))),
inference(resolution,[status(thm)],[f480,f304]) ).
fof(f18509,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X1,X0))),antidomain(multiplication(addition(one,X1),domain(X0)))),
inference(paramodulation,[status(thm)],[f207,f480]) ).
fof(f18510,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(addition(antidomain(X1),X0),domain(X1)))),
inference(paramodulation,[status(thm)],[f224,f480]) ).
fof(f18511,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,X1),omega(X0))),antidomain(multiplication(addition(X1,one),domain(omega(X0))))),
inference(paramodulation,[status(thm)],[f11449,f480]) ).
fof(f18512,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,X1),omega(X1))),antidomain(multiplication(addition(X0,one),domain(omega(X1))))),
inference(paramodulation,[status(thm)],[f10882,f480]) ).
fof(f18513,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X1,X0))),antidomain(multiplication(addition(X1,one),domain(X0)))),
inference(paramodulation,[status(thm)],[f232,f480]) ).
fof(f18514,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(addition(X0,antidomain(X1)),domain(X1)))),
inference(paramodulation,[status(thm)],[f230,f480]) ).
fof(f18515,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,one),omega(X1))),antidomain(multiplication(addition(X1,X0),domain(omega(X1))))),
inference(paramodulation,[status(thm)],[f11449,f480]) ).
fof(f18516,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,one),omega(X1))),antidomain(multiplication(addition(X0,X1),domain(omega(X1))))),
inference(paramodulation,[status(thm)],[f10882,f480]) ).
fof(f18517,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,coantidomain(X1))),antidomain(multiplication(addition(X0,X1),domain(coantidomain(X1))))),
inference(paramodulation,[status(thm)],[f233,f480]) ).
fof(f18518,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,coantidomain(X1))),antidomain(multiplication(addition(X1,X0),domain(coantidomain(X1))))),
inference(paramodulation,[status(thm)],[f226,f480]) ).
fof(f18521,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(c(X0),domain(domain_difference(X0,X1))))),
inference(paramodulation,[status(thm)],[f1585,f480]) ).
fof(f18522,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(c(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f197,f480]) ).
fof(f18524,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))),
inference(paramodulation,[status(thm)],[f195,f480]) ).
fof(f18525,plain,
! [X0] : leq(antidomain(domain(X0)),antidomain(multiplication(domain(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f2215,f480]) ).
fof(f18526,plain,
! [X0,X1] : leq(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),domain(antidomain(X1))))),
inference(paramodulation,[status(thm)],[f68,f480]) ).
fof(f18528,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(multiplication(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f39,f480]) ).
fof(f18529,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0)))),
inference(paramodulation,[status(thm)],[f2635,f480]) ).
fof(f18530,plain,
! [X0,X1] : leq(antidomain(multiplication(antidomain(X0),X1)),antidomain(multiplication(antidomain(X0),domain(addition(X1,X0))))),
inference(paramodulation,[status(thm)],[f186,f480]) ).
fof(f18531,plain,
! [X0,X1] : leq(antidomain(multiplication(antidomain(X0),X1)),antidomain(multiplication(antidomain(X0),domain(addition(X0,X1))))),
inference(paramodulation,[status(thm)],[f177,f480]) ).
fof(f18532,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(omega(X0))))),
inference(paramodulation,[status(thm)],[f1569,f480]) ).
fof(f18533,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f136,f480]) ).
fof(f18534,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f59,f480]) ).
fof(f18537,plain,
! [X0] : leq(antidomain(X0),antidomain(multiplication(X0,domain(codomain(X0))))),
inference(paramodulation,[status(thm)],[f2309,f480]) ).
fof(f18538,plain,
! [X0,X1] : leq(antidomain(addition(omega(X0),multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(omega(X0),X1))))),
inference(paramodulation,[status(thm)],[f318,f480]) ).
fof(f18539,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(one,X1))))),
inference(paramodulation,[status(thm)],[f162,f480]) ).
fof(f18540,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(addition(coantidomain(X0),X1))))),
inference(paramodulation,[status(thm)],[f181,f480]) ).
fof(f18541,plain,
! [X0,X1] : leq(antidomain(addition(omega(X0),multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(X1,omega(X0)))))),
inference(paramodulation,[status(thm)],[f321,f480]) ).
fof(f18542,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(X1,one))))),
inference(paramodulation,[status(thm)],[f192,f480]) ).
fof(f18543,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(addition(X1,coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f190,f480]) ).
fof(f18544,plain,
! [X0,X1] : leq(antidomain(multiplication(omega(X0),X1)),antidomain(multiplication(X0,domain(multiplication(omega(X0),X1))))),
inference(paramodulation,[status(thm)],[f319,f480]) ).
fof(f18545,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1))))),
inference(paramodulation,[status(thm)],[f151,f480]) ).
fof(f18546,plain,
! [X0,X1] : leq(antidomain(omega(multiplication(X0,X1))),antidomain(multiplication(X0,domain(multiplication(X1,omega(multiplication(X0,X1))))))),
inference(paramodulation,[status(thm)],[f308,f480]) ).
fof(f18547,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1))))))),
inference(paramodulation,[status(thm)],[f144,f480]) ).
fof(f18548,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(X0,domain(omega(coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f1813,f480]) ).
fof(f18549,plain,
! [X0] : leq(antidomain(omega(X0)),antidomain(multiplication(X0,domain(omega(X0))))),
inference(paramodulation,[status(thm)],[f56,f480]) ).
fof(f18550,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(X0,domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f63,f480]) ).
fof(f18553,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(antidomain(domain(X0)),X1),X0)),antidomain(multiplication(X1,domain(X0)))),
inference(paramodulation,[status(thm)],[f224,f480]) ).
fof(f18554,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,antidomain(domain(X1))),X1)),antidomain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f230,f480]) ).
fof(f18558,plain,
! [X0] : leq(antidomain(multiplication(domain(domain(X0)),X0)),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f4146,f480]) ).
fof(f18559,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(multiplication(X0,X1),X2)),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(paramodulation,[status(thm)],[f39,f480]) ).
fof(f18564,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,addition(one,X1))),antidomain(multiplication(X0,one))),
inference(paramodulation,[status(thm)],[f15345,f480]) ).
fof(f18565,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,addition(X1,one))),antidomain(multiplication(X0,one))),
inference(paramodulation,[status(thm)],[f15407,f480]) ).
fof(f18569,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,star(X1))),antidomain(multiplication(X0,one))),
inference(paramodulation,[status(thm)],[f8543,f480]) ).
fof(f18570,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,forward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f69,f480]) ).
fof(f18572,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,antidomain(c(X1))))),
inference(paramodulation,[status(thm)],[f196,f480]) ).
fof(f18573,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f361,f480]) ).
fof(f18575,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),addition(omega(domain(multiplication(X0,X1))),multiplication(star(antidomain(antidomain(multiplication(X0,X1)))),antidomain(multiplication(X0,domain(X1)))))),
inference(forward_demodulation,[status(thm)],[f62,f18505]) ).
fof(f18576,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),addition(omega(domain(multiplication(X0,X1))),multiplication(star(domain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))))),
inference(forward_demodulation,[status(thm)],[f62,f18575]) ).
fof(f18577,plain,
! [X0,X1] : leq(multiplication(star(domain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f62,f18507]) ).
fof(f18578,plain,
! [X0,X1] : leq(multiplication(star(forward_diamond(X0,X1)),antidomain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f69,f18577]) ).
fof(f18583,plain,
! [X0,X1] : leq(one,antidomain(multiplication(c(X0),domain(domain_difference(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f577,f18521]) ).
fof(f18584,plain,
! [X0] : leq(one,antidomain(multiplication(c(X0),domain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f577,f18522]) ).
fof(f18585,plain,
! [X0] : leq(one,antidomain(multiplication(c(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f196,f18584]) ).
fof(f18589,plain,
! [X0] : leq(one,antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))),
inference(forward_demodulation,[status(thm)],[f577,f18524]) ).
fof(f18590,plain,
! [X0] : leq(c(X0),antidomain(multiplication(domain(X0),domain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f67,f18525]) ).
fof(f18591,plain,
! [X0] : leq(c(X0),antidomain(multiplication(domain(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f196,f18590]) ).
fof(f18592,plain,
! [X0] : leq(c(X0),antidomain(domain_difference(X0,c(X0)))),
inference(forward_demodulation,[status(thm)],[f68,f18591]) ).
fof(f18593,plain,
! [X0,X1] : leq(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),c(X1)))),
inference(forward_demodulation,[status(thm)],[f361,f18526]) ).
fof(f18596,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(forward_demodulation,[status(thm)],[f39,f18528]) ).
fof(f18597,plain,
! [X0,X1] : leq(one,antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f577,f18529]) ).
fof(f18598,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),domain(omega(X0))))),
inference(forward_demodulation,[status(thm)],[f577,f18532]) ).
fof(f18599,plain,
! [X0,X1] : leq(one,antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f577,f18533]) ).
fof(f18600,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f577,f18534]) ).
fof(f18606,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,one))),
inference(forward_demodulation,[status(thm)],[f15345,f18539]) ).
fof(f18607,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f18606]) ).
fof(f18608,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,one))),
inference(forward_demodulation,[status(thm)],[f15407,f18542]) ).
fof(f18609,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f18608]) ).
fof(f18610,plain,
! [X0,X1] : leq(one,antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1))))),
inference(forward_demodulation,[status(thm)],[f577,f18545]) ).
fof(f18611,plain,
! [X0,X1] : leq(one,antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1))))))),
inference(forward_demodulation,[status(thm)],[f577,f18547]) ).
fof(f18612,plain,
! [X0] : leq(one,antidomain(multiplication(X0,domain(omega(coantidomain(X0)))))),
inference(forward_demodulation,[status(thm)],[f577,f18548]) ).
fof(f18613,plain,
! [X0] : leq(one,antidomain(multiplication(X0,domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f577,f18550]) ).
fof(f18620,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(c(X0),X1),X0)),antidomain(multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f67,f18553]) ).
fof(f18621,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,c(X1)),X1)),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f67,f18554]) ).
fof(f18631,plain,
! [X0] : leq(antidomain(multiplication(antidomain(c(X0)),X0)),antidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f196,f18558]) ).
fof(f18632,plain,
! [X0] : leq(antidomain(multiplication(antidomain(c(X0)),X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f67,f18631]) ).
fof(f18633,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(forward_demodulation,[status(thm)],[f39,f18559]) ).
fof(f18644,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,addition(one,X1))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f18564]) ).
fof(f18645,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,addition(X1,one))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f18565]) ).
fof(f18646,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,star(X1))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f40,f18569]) ).
fof(f18653,plain,
! [X0,X1] : leq(domain_difference(antidomain(X0),X1),addition(omega(antidomain(domain_difference(antidomain(X0),X1))),multiplication(star(antidomain(domain_difference(antidomain(X0),X1))),c(X0)))),
inference(resolution,[status(thm)],[f4064,f409]) ).
fof(f18654,plain,
! [X0,X1] : leq(multiplication(domain_difference(antidomain(X0),X1),star(coantidomain(c(X0)))),c(X0)),
inference(resolution,[status(thm)],[f4064,f346]) ).
fof(f18655,plain,
! [X0,X1] : leq(multiplication(star(antidomain(c(X0))),domain_difference(antidomain(X0),X1)),c(X0)),
inference(resolution,[status(thm)],[f4064,f304]) ).
fof(f18656,plain,
! [X0,X1] : addition(domain_difference(antidomain(X0),X1),c(X0)) = c(X0),
inference(resolution,[status(thm)],[f4064,f48]) ).
fof(f18668,plain,
! [X0,X1] : leq(domain_difference(c(X0),X1),c(domain(X0))),
inference(paramodulation,[status(thm)],[f67,f4064]) ).
fof(f18669,plain,
! [X0,X1] : leq(domain_difference(domain(X0),X1),c(antidomain(X0))),
inference(paramodulation,[status(thm)],[f62,f4064]) ).
fof(f18673,plain,
! [X0,X1] : leq(domain_difference(antidomain(c(X0)),X1),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f13920,f4064]) ).
fof(f18674,plain,
! [X0,X1] : leq(domain_difference(antidomain(domain(X0)),X1),c(X0)),
inference(paramodulation,[status(thm)],[f13881,f4064]) ).
fof(f18676,plain,
! [X0,X1,X2] : leq(domain_difference(antidomain(backward_diamond(X0,c(X1))),X2),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f72,f4064]) ).
fof(f18677,plain,
! [X0,X1,X2] : leq(domain_difference(antidomain(forward_diamond(X0,c(X1))),X2),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f71,f4064]) ).
fof(f18679,plain,
! [X0,X1] : leq(domain_difference(antidomain(antidomain(X0)),X1),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f547,f4064]) ).
fof(f18681,plain,
! [X0,X1] : addition(c(X0),domain_difference(antidomain(X0),X1)) = c(X0),
inference(forward_demodulation,[status(thm)],[f35,f18656]) ).
fof(f18691,plain,
! [X0,X1] : leq(domain_difference(c(X0),X1),c(X0)),
inference(forward_demodulation,[status(thm)],[f13881,f18668]) ).
fof(f18692,plain,
! [X0,X1] : leq(domain_difference(domain(X0),X1),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f547,f18669]) ).
fof(f18699,plain,
! [X0,X1] : leq(domain_difference(c(X0),X1),c(X0)),
inference(forward_demodulation,[status(thm)],[f67,f18674]) ).
fof(f18704,plain,
! [X0,X1] : leq(domain_difference(domain(X0),X1),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f62,f18679]) ).
fof(f18707,plain,
! [X0] : c(X0) = antidomain(X0),
inference(backward_demodulation,[status(thm)],[f4201,f2633]) ).
fof(f18710,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f13920,f4201]) ).
fof(f18713,plain,
! [X0,X1] : antidomain(backward_diamond(X0,c(X1))) = multiplication(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f72,f4201]) ).
fof(f18714,plain,
! [X0,X1] : antidomain(forward_diamond(X0,c(X1))) = multiplication(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f71,f4201]) ).
fof(f18716,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(antidomain(c(X0)),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f547,f4201]) ).
fof(f18723,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(c(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f62,f4201]) ).
fof(f18730,plain,
! [X0,X1,X2] :
( leq(antidomain(X0),addition(omega(multiplication(X1,c(X0))),multiplication(star(multiplication(X1,c(X0))),X2)))
| ~ leq(antidomain(X0),addition(multiplication(X1,antidomain(X0)),X2)) ),
inference(paramodulation,[status(thm)],[f4201,f398]) ).
fof(f18731,plain,
! [X0] :
( leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),multiplication(c(X0),antidomain(X0)))))
| ~ leq(antidomain(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f4201,f396]) ).
fof(f18732,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(antidomain(X0),addition(X1,antidomain(X0))) ),
inference(paramodulation,[status(thm)],[f4201,f394]) ).
fof(f18734,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(c(X0),antidomain(X0)))
| ~ leq(addition(multiplication(c(X0),multiplication(antidomain(X0),X1)),X2),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f4201,f332]) ).
fof(f18735,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(antidomain(X1))),multiplication(X0,c(X1)))
| ~ leq(addition(multiplication(X0,antidomain(X1)),X2),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f4201,f332]) ).
fof(f18736,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0)))),c(X0))
| ~ leq(antidomain(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f4201,f343]) ).
fof(f18737,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),c(X1))
| ~ leq(addition(X0,antidomain(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f4201,f329]) ).
fof(f18738,plain,
! [X0] : multiplication(c(X0),multiplication(antidomain(X0),omega(antidomain(X0)))) = omega(multiplication(c(X0),antidomain(X0))),
inference(paramodulation,[status(thm)],[f4201,f308]) ).
fof(f18739,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,c(X1))),X2),antidomain(X1))
| ~ leq(addition(multiplication(X0,antidomain(X1)),X2),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f4201,f296]) ).
fof(f18740,plain,
! [X0] :
( leq(multiplication(star(c(X0)),multiplication(c(X0),antidomain(X0))),antidomain(X0))
| ~ leq(antidomain(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f4201,f295]) ).
fof(f18741,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),antidomain(X1))
| ~ leq(addition(X0,antidomain(X1)),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f4201,f293]) ).
fof(f18742,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(multiplication(c(X0),antidomain(X0)))))),star(antidomain(X0))),
inference(paramodulation,[status(thm)],[f4201,f252]) ).
fof(f18743,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0))))),star(multiplication(c(X0),antidomain(X0)))),
inference(paramodulation,[status(thm)],[f4201,f252]) ).
fof(f18744,plain,
! [X0,X1,X2] : addition(multiplication(X0,antidomain(X1)),addition(antidomain(X1),X2)) = addition(multiplication(addition(X0,c(X1)),antidomain(X1)),X2),
inference(paramodulation,[status(thm)],[f4201,f219]) ).
fof(f18745,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(multiplication(X1,antidomain(X0)),X2)) = addition(multiplication(addition(c(X0),X1),antidomain(X0)),X2),
inference(paramodulation,[status(thm)],[f4201,f219]) ).
fof(f18747,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),antidomain(X2)) = addition(multiplication(X0,antidomain(X2)),multiplication(X1,antidomain(X2))),
inference(paramodulation,[status(thm)],[f4201,f211]) ).
fof(f18748,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),antidomain(X0)) = addition(antidomain(X0),multiplication(X1,multiplication(X2,antidomain(X0)))),
inference(paramodulation,[status(thm)],[f4201,f211]) ).
fof(f18750,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),antidomain(X2)) = addition(multiplication(X0,multiplication(X1,antidomain(X2))),antidomain(X2)),
inference(paramodulation,[status(thm)],[f4201,f204]) ).
fof(f18751,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),antidomain(X1)) = addition(multiplication(X0,antidomain(X1)),multiplication(X2,antidomain(X1))),
inference(paramodulation,[status(thm)],[f4201,f204]) ).
fof(f18752,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(multiplication(X1,antidomain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f4201,f201]) ).
fof(f18753,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(antidomain(X1),multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f4201,f201]) ).
fof(f18754,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(antidomain(X0),X2)) = addition(multiplication(c(X0),addition(X1,antidomain(X0))),X2),
inference(paramodulation,[status(thm)],[f4201,f170]) ).
fof(f18755,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(multiplication(c(X0),X1),X2)) = addition(multiplication(c(X0),addition(antidomain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f4201,f170]) ).
fof(f18758,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(multiplication(c(X0),X1),antidomain(X0)),
inference(paramodulation,[status(thm)],[f4201,f153]) ).
fof(f18759,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(antidomain(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f4201,f153]) ).
fof(f18761,plain,
! [X0] : multiplication(antidomain(c(X0)),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f4201,f136]) ).
fof(f18762,plain,
! [X0] : addition(coantidomain(antidomain(X0)),coantidomain(multiplication(codomain(c(X0)),antidomain(X0)))) = coantidomain(multiplication(codomain(c(X0)),antidomain(X0))),
inference(paramodulation,[status(thm)],[f4201,f615]) ).
fof(f18763,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(multiplication(c(X0),domain(antidomain(X0))))) = antidomain(multiplication(c(X0),domain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f4201,f479]) ).
fof(f18764,plain,
! [X0,X1] :
( leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1)))
| ~ leq(antidomain(X0),addition(antidomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4201,f58]) ).
fof(f18765,plain,
! [X0,X1] :
( leq(multiplication(X1,star(antidomain(X0))),c(X0))
| ~ leq(addition(antidomain(X0),X1),c(X0)) ),
inference(paramodulation,[status(thm)],[f4201,f55]) ).
fof(f18766,plain,
! [X0,X1] :
( leq(multiplication(star(c(X0)),X1),antidomain(X0))
| ~ leq(addition(antidomain(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f4201,f53]) ).
fof(f18767,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(multiplication(X0,antidomain(X1)),antidomain(X1)),
inference(paramodulation,[status(thm)],[f4201,f43]) ).
fof(f18768,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(antidomain(X0),multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f4201,f43]) ).
fof(f18769,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(multiplication(c(X0),X1),antidomain(X0)),
inference(paramodulation,[status(thm)],[f4201,f42]) ).
fof(f18770,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(antidomain(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f4201,f42]) ).
fof(f18771,plain,
! [X0,X1] : multiplication(c(X0),multiplication(antidomain(X0),X1)) = multiplication(antidomain(X0),X1),
inference(paramodulation,[status(thm)],[f4201,f39]) ).
fof(f18779,plain,
! [X0] : domain(X0) = multiplication(antidomain(c(X0)),antidomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f18716]) ).
fof(f18780,plain,
! [X0] : domain(X0) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f18779]) ).
fof(f18789,plain,
! [X0] : domain(X0) = multiplication(c(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f18723]) ).
fof(f18790,plain,
! [X0] : domain(X0) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f547,f18789]) ).
fof(f18796,plain,
! [X0] :
( leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),antidomain(X0))))
| ~ leq(antidomain(X0),antidomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f4201,f18731]) ).
fof(f18797,plain,
! [X0] : leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),antidomain(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f18796,f239]) ).
fof(f18798,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f18732,f1423]) ).
fof(f18799,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),antidomain(X0))
| ~ leq(addition(multiplication(c(X0),multiplication(antidomain(X0),X1)),X2),antidomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f4201,f18734]) ).
fof(f18800,plain,
! [X0] : leq(multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0)))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f18736,f4241]) ).
fof(f18801,plain,
! [X0] : multiplication(c(X0),omega(antidomain(X0))) = omega(multiplication(c(X0),antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f56,f18738]) ).
fof(f18802,plain,
! [X0] : multiplication(c(X0),omega(antidomain(X0))) = omega(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f4201,f18801]) ).
fof(f18803,plain,
! [X0] :
( leq(multiplication(star(c(X0)),antidomain(X0)),antidomain(X0))
| ~ leq(antidomain(X0),antidomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f4201,f18740]) ).
fof(f18804,plain,
! [X0] : leq(multiplication(star(c(X0)),antidomain(X0)),antidomain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f18803,f239]) ).
fof(f18805,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0))))),star(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f4201,f18742]) ).
fof(f18806,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0))))),star(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f4201,f18743]) ).
fof(f18807,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,multiplication(X2,antidomain(X0)))) = addition(multiplication(addition(X2,c(X0)),antidomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f97,f18744]) ).
fof(f18811,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),antidomain(X2)) = multiplication(addition(X1,X0),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f201,f18747]) ).
fof(f18814,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),antidomain(X2)) = addition(antidomain(X2),multiplication(X0,multiplication(X1,antidomain(X2)))),
inference(forward_demodulation,[status(thm)],[f35,f18750]) ).
fof(f18815,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),antidomain(X1)) = multiplication(addition(X2,X0),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f201,f18751]) ).
fof(f18816,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(antidomain(X0),multiplication(X1,antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f18752]) ).
fof(f18817,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = multiplication(addition(X1,one),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f232,f18816]) ).
fof(f18818,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = multiplication(addition(X0,one),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f232,f18753]) ).
fof(f18819,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,multiplication(c(X0),X2))) = addition(multiplication(c(X0),addition(X2,antidomain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f97,f18754]) ).
fof(f18827,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(antidomain(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f18758]) ).
fof(f18829,plain,
! [X0] : addition(domain(X0),antidomain(multiplication(c(X0),domain(antidomain(X0))))) = antidomain(multiplication(c(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f18763]) ).
fof(f18830,plain,
! [X0] : addition(domain(X0),antidomain(multiplication(c(X0),c(X0)))) = antidomain(multiplication(c(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f361,f18829]) ).
fof(f18831,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(multiplication(c(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f2211,f18830]) ).
fof(f18832,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(multiplication(c(X0),c(X0))),
inference(forward_demodulation,[status(thm)],[f361,f18831]) ).
fof(f18833,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f2211,f18832]) ).
fof(f18834,plain,
! [X0,X1] : leq(antidomain(X0),addition(omega(c(X0)),multiplication(star(c(X0)),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f18764,f1324]) ).
fof(f18835,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(antidomain(X1),multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f35,f18767]) ).
fof(f18836,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = multiplication(addition(X0,one),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f232,f18835]) ).
fof(f18837,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = multiplication(addition(X1,one),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f232,f18768]) ).
fof(f18838,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(antidomain(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f18769]) ).
fof(f18841,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(backward_demodulation,[status(thm)],[f18707,f13881]) ).
fof(f18844,plain,
! [X0,X1] : backward_box(X0,X1) = antidomain(backward_diamond(X0,c(X1))),
inference(backward_demodulation,[status(thm)],[f18707,f72]) ).
fof(f18845,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(forward_diamond(X0,c(X1))),
inference(backward_demodulation,[status(thm)],[f18707,f71]) ).
fof(f18849,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(X0),antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f18707,f4201]) ).
fof(f18850,plain,
! [X0,X1] : leq(domain_difference(antidomain(X0),X1),antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f18707,f4064]) ).
fof(f18851,plain,
! [X0] : leq(c(X0),omega(antidomain(X0))),
inference(backward_demodulation,[status(thm)],[f18707,f16991]) ).
fof(f18853,plain,
! [X0] : forward_box(antidomain(X0),antidomain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f18707,f14887]) ).
fof(f18855,plain,
! [X0] : forward_box(antidomain(antidomain(X0)),X0) = one,
inference(backward_demodulation,[status(thm)],[f18707,f14241]) ).
fof(f18856,plain,
! [X0] : forward_diamond(antidomain(X0),domain(X0)) = zero,
inference(backward_demodulation,[status(thm)],[f18707,f13992]) ).
fof(f18859,plain,
! [X0] : domain(c(X0)) = antidomain(X0),
inference(backward_demodulation,[status(thm)],[f18707,f13678]) ).
fof(f18860,plain,
! [X0] : c(X0) = multiplication(c(X0),antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f18707,f2211]) ).
fof(f18861,plain,
! [X0,X1] : multiplication(antidomain(X0),domain_difference(X0,X1)) = zero,
inference(backward_demodulation,[status(thm)],[f18707,f1585]) ).
fof(f18876,plain,
! [X0] : forward_diamond(one,X0) = antidomain(antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f18707,f774]) ).
fof(f18878,plain,
! [X0] : forward_diamond(antidomain(X0),X0) = zero,
inference(backward_demodulation,[status(thm)],[f18707,f770]) ).
fof(f18879,plain,
! [X0] : multiplication(antidomain(X0),domain(X0)) = zero,
inference(backward_demodulation,[status(thm)],[f18707,f197]) ).
fof(f18880,plain,
! [X0] : domain(domain(X0)) = antidomain(antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f18707,f196]) ).
fof(f18883,plain,
! [X0] : antidomain(X0) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f18707,f18841]) ).
fof(f18884,plain,
! [X0,X1] : backward_box(X0,X1) = antidomain(backward_diamond(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f18707,f18844]) ).
fof(f18885,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(forward_diamond(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f18707,f18845]) ).
fof(f18886,plain,
! [X0] : leq(antidomain(X0),omega(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f18707,f18851]) ).
fof(f18888,plain,
! [X0] : forward_box(domain(X0),X0) = one,
inference(forward_demodulation,[status(thm)],[f62,f18855]) ).
fof(f18890,plain,
! [X0] : domain(antidomain(X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f18707,f18859]) ).
fof(f18891,plain,
! [X0] : antidomain(X0) = multiplication(c(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f18707,f18860]) ).
fof(f18892,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f18707,f18891]) ).
fof(f18896,plain,
! [X0] : forward_diamond(one,X0) = domain(X0),
inference(forward_demodulation,[status(thm)],[f62,f18876]) ).
fof(f18898,plain,
! [X0] : domain(domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f62,f18880]) ).
fof(f18904,plain,
! [X0,X1] : antidomain(multiplication(X0,domain(X1))) = antidomain(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f69,f18883]) ).
fof(f18907,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(domain(X1)))
| ~ leq(X0,antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f18883,f344]) ).
fof(f18911,plain,
! [X0,X1] : leq(domain_difference(X0,domain(X1)),antidomain(X1)),
inference(paramodulation,[status(thm)],[f18883,f6998]) ).
fof(f18914,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f18883,f230]) ).
fof(f18915,plain,
! [X0] : antidomain(domain(X0)) = domain_difference(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f18883,f4195]) ).
fof(f18916,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(paramodulation,[status(thm)],[f18883,f224]) ).
fof(f18920,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = multiplication(antidomain(domain(X0)),X1),
inference(paramodulation,[status(thm)],[f18883,f186]) ).
fof(f18922,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = multiplication(antidomain(domain(X0)),X1),
inference(paramodulation,[status(thm)],[f18883,f177]) ).
fof(f18923,plain,
! [X0] : multiplication(antidomain(X0),omega(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f18883,f1569]) ).
fof(f18925,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f18883,f136]) ).
fof(f18927,plain,
! [X0,X1] : domain_difference(X0,domain(X1)) = multiplication(domain(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f18883,f68]) ).
fof(f18928,plain,
! [X0] : addition(antidomain(X0),domain(domain(X0))) = one,
inference(paramodulation,[status(thm)],[f18883,f558]) ).
fof(f18934,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f18883,f18907]) ).
fof(f18937,plain,
! [X0] : antidomain(X0) = domain_difference(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f18883,f18915]) ).
fof(f18938,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f18883,f18920]) ).
fof(f18939,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f18883,f18922]) ).
fof(f18940,plain,
! [X0,X1] : domain_difference(X0,domain(X1)) = domain_difference(X0,X1),
inference(forward_demodulation,[status(thm)],[f68,f18927]) ).
fof(f18942,plain,
! [X0] : backward_box(one,X0) = antidomain(codomain(codomain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f798,f18884]) ).
fof(f18943,plain,
! [X0] : backward_box(coantidomain(codomain(antidomain(X0))),X0) = antidomain(zero),
inference(paramodulation,[status(thm)],[f806,f18884]) ).
fof(f18945,plain,
! [X0,X1,X2] : backward_box(X0,backward_diamond(X1,antidomain(X2))) = antidomain(backward_diamond(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f18884,f18884]) ).
fof(f18950,plain,
! [X0] : backward_box(X0,zero) = antidomain(backward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f577,f18884]) ).
fof(f18951,plain,
! [X0,X1] : backward_box(X0,antidomain(X1)) = antidomain(backward_diamond(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f62,f18884]) ).
fof(f18953,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(backward_diamond(X1,antidomain(X2)))),antidomain(backward_diamond(X1,antidomain(X2))))
| ~ leq(X0,backward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f18884,f344]) ).
fof(f18954,plain,
! [X0,X1] : leq(antidomain(backward_diamond(X0,antidomain(X1))),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f18884,f6796]) ).
fof(f18955,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(antidomain(backward_diamond(X0,antidomain(X1))))),
inference(paramodulation,[status(thm)],[f18884,f6796]) ).
fof(f18957,plain,
! [X0,X1,X2] : leq(domain_difference(X0,backward_diamond(X1,antidomain(X2))),backward_box(X1,X2)),
inference(paramodulation,[status(thm)],[f18884,f6998]) ).
fof(f18959,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f18884,f4514]) ).
fof(f18960,plain,
! [X0,X1,X2] : multiplication(addition(X0,backward_box(X1,X2)),backward_diamond(X1,antidomain(X2))) = multiplication(X0,backward_diamond(X1,antidomain(X2))),
inference(paramodulation,[status(thm)],[f18884,f230]) ).
fof(f18961,plain,
! [X0,X1] : antidomain(backward_diamond(X0,antidomain(X1))) = domain_difference(backward_box(X0,X1),backward_diamond(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f18884,f4195]) ).
fof(f18962,plain,
! [X0,X1,X2] : multiplication(addition(backward_box(X0,X1),X2),backward_diamond(X0,antidomain(X1))) = multiplication(X2,backward_diamond(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f18884,f224]) ).
fof(f18966,plain,
! [X0,X1,X2] : multiplication(backward_box(X0,X1),addition(X2,backward_diamond(X0,antidomain(X1)))) = multiplication(antidomain(backward_diamond(X0,antidomain(X1))),X2),
inference(paramodulation,[status(thm)],[f18884,f186]) ).
fof(f18968,plain,
! [X0,X1,X2] : multiplication(backward_box(X0,X1),addition(backward_diamond(X0,antidomain(X1)),X2)) = multiplication(antidomain(backward_diamond(X0,antidomain(X1))),X2),
inference(paramodulation,[status(thm)],[f18884,f177]) ).
fof(f18969,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),omega(backward_diamond(X0,antidomain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f18884,f1569]) ).
fof(f18971,plain,
! [X0,X1,X2] : multiplication(backward_box(X0,X1),multiplication(backward_diamond(X0,antidomain(X1)),X2)) = zero,
inference(paramodulation,[status(thm)],[f18884,f136]) ).
fof(f18973,plain,
! [X0,X1,X2] : domain_difference(X0,backward_diamond(X1,antidomain(X2))) = multiplication(domain(X0),backward_box(X1,X2)),
inference(paramodulation,[status(thm)],[f18884,f68]) ).
fof(f18974,plain,
! [X0,X1] : addition(backward_box(X0,X1),domain(backward_diamond(X0,antidomain(X1)))) = one,
inference(paramodulation,[status(thm)],[f18884,f558]) ).
fof(f18975,plain,
! [X0,X1] : domain(backward_diamond(X0,antidomain(X1))) = antidomain(backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f18884,f62]) ).
fof(f18976,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),backward_diamond(X0,antidomain(X1))) = zero,
inference(paramodulation,[status(thm)],[f18884,f59]) ).
fof(f18977,plain,
! [X0] : backward_box(coantidomain(codomain(antidomain(X0))),X0) = one,
inference(forward_demodulation,[status(thm)],[f577,f18943]) ).
fof(f18986,plain,
! [X0] : backward_box(X0,zero) = antidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f810,f18950]) ).
fof(f18989,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(backward_diamond(X1,antidomain(X2)))),backward_box(X1,X2))
| ~ leq(X0,backward_box(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f18884,f18953]) ).
fof(f18990,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18884,f18954]) ).
fof(f18991,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18884,f18955]) ).
fof(f18992,plain,
! [X0,X1] : backward_box(X0,X1) = domain_difference(backward_box(X0,X1),backward_diamond(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f18884,f18961]) ).
fof(f18993,plain,
! [X0,X1,X2] : multiplication(backward_box(X0,X1),addition(X2,backward_diamond(X0,antidomain(X1)))) = multiplication(backward_box(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f18884,f18966]) ).
fof(f18994,plain,
! [X0,X1,X2] : multiplication(backward_box(X0,X1),addition(backward_diamond(X0,antidomain(X1)),X2)) = multiplication(backward_box(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f18884,f18968]) ).
fof(f19002,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f13917,f18888]) ).
fof(f19003,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f13916,f18888]) ).
fof(f19005,plain,
! [X0,X1] : forward_box(forward_diamond(X0,X1),multiplication(X0,domain(X1))) = one,
inference(paramodulation,[status(thm)],[f69,f18888]) ).
fof(f19043,plain,
! [X0] : domain(antidomain(X0)) = multiplication(antidomain(X0),domain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f18890,f2215]) ).
fof(f19050,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f18890,f4146]) ).
fof(f19052,plain,
! [X0,X1] : leq(domain_difference(antidomain(X0),X1),antidomain(X0)),
inference(paramodulation,[status(thm)],[f18890,f3834]) ).
fof(f19057,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),antidomain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f18890,f75]) ).
fof(f19058,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(antidomain(X0)),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f18890,f75]) ).
fof(f19059,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(X0),addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2))) != addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f18890,f75]) ).
fof(f19060,plain,
! [X0,X1] : forward_diamond(X0,antidomain(X1)) = domain(multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f18890,f69]) ).
fof(f19061,plain,
! [X0,X1] : domain_difference(antidomain(X0),X1) = multiplication(antidomain(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f18890,f68]) ).
fof(f19076,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(X0),domain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f18890,f19043]) ).
fof(f19077,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f18890,f19076]) ).
fof(f19080,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),antidomain(X2))) != addition(forward_diamond(X1,domain(X0)),antidomain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19057]) ).
fof(f19081,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),antidomain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(antidomain(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),antidomain(X2))) != addition(forward_diamond(X1,domain(X0)),antidomain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19080]) ).
fof(f19082,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),antidomain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),antidomain(X2)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),antidomain(X2))) != addition(forward_diamond(X1,domain(X0)),antidomain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19081]) ).
fof(f19083,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(X0),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19058]) ).
fof(f19084,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(X0),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,antidomain(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19083]) ).
fof(f19085,plain,
! [X0,X1,X2] :
( addition(antidomain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(X0),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,antidomain(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19084]) ).
fof(f19086,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(X0),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(antidomain(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19059]) ).
fof(f19087,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(X0),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,antidomain(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19086]) ).
fof(f19088,plain,
! [X0,X1,X2] :
( addition(antidomain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(antidomain(X0),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,antidomain(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f19087]) ).
fof(f19095,plain,
divergence(one) = domain(divergence(one)),
inference(paramodulation,[status(thm)],[f73,f18896]) ).
fof(f19098,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(domain(domain(X0)),domain(X1))) != addition(forward_diamond(one,domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f18896,f75]) ).
fof(f19111,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(domain(domain(X0)),domain(X1))) != addition(domain(domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f18896,f19098]) ).
fof(f19112,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(one,domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(domain(domain(X0)),domain(X1))) != addition(domain(domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f9603,f19111]) ).
fof(f19113,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),domain(domain(X1)))) = addition(divergence(one),forward_diamond(star(one),domain(X1)))
| addition(domain(X0),addition(domain(domain(X0)),domain(X1))) != addition(domain(domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f18896,f19112]) ).
fof(f19114,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),domain(domain(X1)))) = addition(divergence(one),forward_diamond(one,domain(X1)))
| addition(domain(X0),addition(domain(domain(X0)),domain(X1))) != addition(domain(domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f9603,f19113]) ).
fof(f19115,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),domain(domain(X1)))) = addition(divergence(one),domain(domain(X1)))
| addition(domain(X0),addition(domain(domain(X0)),domain(X1))) != addition(domain(domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f18896,f19114]) ).
fof(f19120,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),backward_diamond(X0,antidomain(X1))) = zero,
inference(paramodulation,[status(thm)],[f18884,f18878]) ).
fof(f19126,plain,
! [X0] : forward_diamond(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f62,f18878]) ).
fof(f19130,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(antidomain(domain(X0))),forward_diamond(star(antidomain(domain(X0))),domain(X1)))) = addition(divergence(antidomain(domain(X0))),forward_diamond(star(antidomain(domain(X0))),domain(X1)))
| addition(domain(X0),addition(zero,domain(X1))) != addition(forward_diamond(antidomain(domain(X0)),domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f18878,f75]) ).
fof(f19146,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))) = addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))
| addition(zero,addition(domain(X0),domain(X1))) != addition(forward_diamond(antidomain(domain(X1)),domain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f19130]) ).
fof(f19147,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))) = addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))
| addition(domain(X0),domain(X1)) != addition(forward_diamond(antidomain(domain(X1)),domain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f19146]) ).
fof(f19148,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))) = addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))
| addition(domain(X0),domain(X1)) != addition(zero,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f18878,f19147]) ).
fof(f19149,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))) = addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f80,f19148]) ).
fof(f19150,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(domain(X1))),domain(X0)))) = addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18883,f19149]) ).
fof(f19151,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))) = addition(divergence(antidomain(domain(X1))),forward_diamond(star(antidomain(domain(X1))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18883,f19150]) ).
fof(f19152,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(domain(X1))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18883,f19151]) ).
fof(f19153,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18883,f19152]) ).
fof(f19158,plain,
! [X0] : forward_box(one,X0) = antidomain(domain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f18896,f18885]) ).
fof(f19160,plain,
! [X0,X1,X2] : forward_box(X0,forward_diamond(X1,antidomain(X2))) = antidomain(forward_diamond(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f18885,f18885]) ).
fof(f19161,plain,
! [X0,X1,X2] : forward_box(X0,backward_diamond(X1,antidomain(X2))) = antidomain(forward_diamond(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f18884,f18885]) ).
fof(f19166,plain,
! [X0] : forward_box(X0,zero) = antidomain(forward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f577,f18885]) ).
fof(f19167,plain,
! [X0,X1] : forward_box(X0,antidomain(X1)) = antidomain(forward_diamond(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f62,f18885]) ).
fof(f19169,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),forward_diamond(X0,antidomain(X1))) = zero,
inference(paramodulation,[status(thm)],[f18885,f18878]) ).
fof(f19171,plain,
! [X0,X1,X2] : backward_box(X0,forward_diamond(X1,antidomain(X2))) = antidomain(backward_diamond(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f18885,f18884]) ).
fof(f19172,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(forward_diamond(X1,antidomain(X2)))),antidomain(forward_diamond(X1,antidomain(X2))))
| ~ leq(X0,forward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f18885,f344]) ).
fof(f19173,plain,
! [X0,X1] : leq(antidomain(forward_diamond(X0,antidomain(X1))),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f18885,f6796]) ).
fof(f19174,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(antidomain(forward_diamond(X0,antidomain(X1))))),
inference(paramodulation,[status(thm)],[f18885,f6796]) ).
fof(f19176,plain,
! [X0,X1,X2] : leq(domain_difference(X0,forward_diamond(X1,antidomain(X2))),forward_box(X1,X2)),
inference(paramodulation,[status(thm)],[f18885,f6998]) ).
fof(f19178,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f18885,f4514]) ).
fof(f19179,plain,
! [X0,X1,X2] : multiplication(addition(X0,forward_box(X1,X2)),forward_diamond(X1,antidomain(X2))) = multiplication(X0,forward_diamond(X1,antidomain(X2))),
inference(paramodulation,[status(thm)],[f18885,f230]) ).
fof(f19180,plain,
! [X0,X1] : antidomain(forward_diamond(X0,antidomain(X1))) = domain_difference(forward_box(X0,X1),forward_diamond(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f18885,f4195]) ).
fof(f19181,plain,
! [X0,X1,X2] : multiplication(addition(forward_box(X0,X1),X2),forward_diamond(X0,antidomain(X1))) = multiplication(X2,forward_diamond(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f18885,f224]) ).
fof(f19185,plain,
! [X0,X1,X2] : multiplication(forward_box(X0,X1),addition(X2,forward_diamond(X0,antidomain(X1)))) = multiplication(antidomain(forward_diamond(X0,antidomain(X1))),X2),
inference(paramodulation,[status(thm)],[f18885,f186]) ).
fof(f19187,plain,
! [X0,X1,X2] : multiplication(forward_box(X0,X1),addition(forward_diamond(X0,antidomain(X1)),X2)) = multiplication(antidomain(forward_diamond(X0,antidomain(X1))),X2),
inference(paramodulation,[status(thm)],[f18885,f177]) ).
fof(f19188,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),omega(forward_diamond(X0,antidomain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f18885,f1569]) ).
fof(f19190,plain,
! [X0,X1,X2] : multiplication(forward_box(X0,X1),multiplication(forward_diamond(X0,antidomain(X1)),X2)) = zero,
inference(paramodulation,[status(thm)],[f18885,f136]) ).
fof(f19192,plain,
! [X0,X1,X2] : domain_difference(X0,forward_diamond(X1,antidomain(X2))) = multiplication(domain(X0),forward_box(X1,X2)),
inference(paramodulation,[status(thm)],[f18885,f68]) ).
fof(f19193,plain,
! [X0,X1] : addition(forward_box(X0,X1),domain(forward_diamond(X0,antidomain(X1)))) = one,
inference(paramodulation,[status(thm)],[f18885,f558]) ).
fof(f19194,plain,
! [X0,X1] : domain(forward_diamond(X0,antidomain(X1))) = antidomain(forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f18885,f62]) ).
fof(f19195,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),forward_diamond(X0,antidomain(X1))) = zero,
inference(paramodulation,[status(thm)],[f18885,f59]) ).
fof(f19198,plain,
! [X0] : forward_box(one,X0) = antidomain(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f18883,f19158]) ).
fof(f19199,plain,
! [X0] : forward_box(one,X0) = domain(X0),
inference(forward_demodulation,[status(thm)],[f62,f19198]) ).
fof(f19208,plain,
! [X0] : forward_box(X0,zero) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f777,f19166]) ).
fof(f19209,plain,
! [X0] : forward_box(X0,zero) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f18883,f19208]) ).
fof(f19213,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(forward_diamond(X1,antidomain(X2)))),forward_box(X1,X2))
| ~ leq(X0,forward_box(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f18885,f19172]) ).
fof(f19214,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18885,f19173]) ).
fof(f19215,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18885,f19174]) ).
fof(f19216,plain,
! [X0,X1] : forward_box(X0,X1) = domain_difference(forward_box(X0,X1),forward_diamond(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f18885,f19180]) ).
fof(f19217,plain,
! [X0,X1,X2] : multiplication(forward_box(X0,X1),addition(X2,forward_diamond(X0,antidomain(X1)))) = multiplication(forward_box(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f18885,f19185]) ).
fof(f19218,plain,
! [X0,X1,X2] : multiplication(forward_box(X0,X1),addition(forward_diamond(X0,antidomain(X1)),X2)) = multiplication(forward_box(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f18885,f19187]) ).
fof(f19226,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f69,f18898]) ).
fof(f19247,plain,
! [X0,X1] : leq(domain_difference(domain(X0),X1),domain(X0)),
inference(paramodulation,[status(thm)],[f18898,f3834]) ).
fof(f19255,plain,
! [X0,X1] : forward_diamond(X0,domain(X1)) = domain(multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f18898,f69]) ).
fof(f19256,plain,
! [X0,X1] : domain_difference(domain(X0),X1) = multiplication(domain(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f18898,f68]) ).
fof(f19262,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = forward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f69,f19226]) ).
fof(f19280,plain,
! [X0,X1] : forward_diamond(X0,domain(X1)) = forward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f69,f19255]) ).
fof(f19281,plain,
! [X0,X1] : domain_difference(domain(X0),X1) = domain_difference(X0,X1),
inference(forward_demodulation,[status(thm)],[f68,f19256]) ).
fof(f19286,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(resolution,[status(thm)],[f508,f49]) ).
fof(f19287,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(addition(antidomain(multiplication(X1,X2)),X0),multiplication(X1,domain(X2))))) = antidomain(multiplication(addition(antidomain(multiplication(X1,X2)),X0),multiplication(X1,domain(X2)))),
inference(paramodulation,[status(thm)],[f224,f508]) ).
fof(f19288,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(addition(X0,antidomain(multiplication(X1,X2))),multiplication(X1,domain(X2))))) = antidomain(multiplication(addition(X0,antidomain(multiplication(X1,X2))),multiplication(X1,domain(X2)))),
inference(paramodulation,[status(thm)],[f230,f508]) ).
fof(f19289,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))))) = antidomain(multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f4146,f508]) ).
fof(f19290,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(multiplication(X0,X1),multiplication(X2,domain(X3))))) = antidomain(multiplication(multiplication(X0,X1),multiplication(X2,domain(X3)))),
inference(paramodulation,[status(thm)],[f39,f508]) ).
fof(f19291,plain,
! [X0,X1,X2] : addition(antidomain(zero),antidomain(multiplication(antidomain(addition(multiplication(X0,X1),X2)),multiplication(X0,domain(X1))))) = antidomain(multiplication(antidomain(addition(multiplication(X0,X1),X2)),multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f2635,f508]) ).
fof(f19293,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1))))) = antidomain(multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f59,f508]) ).
fof(f19298,plain,
! [X0,X1] : addition(antidomain(omega(multiplication(X0,X1))),antidomain(multiplication(X0,multiplication(X1,domain(omega(multiplication(X0,X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(omega(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f308,f508]) ).
fof(f19299,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f144,f508]) ).
fof(f19300,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(X1,multiplication(X2,X1)))),antidomain(multiplication(X0,multiplication(addition(one,X2),domain(X1))))) = antidomain(multiplication(X0,multiplication(addition(one,X2),domain(X1)))),
inference(paramodulation,[status(thm)],[f207,f508]) ).
fof(f19301,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(addition(antidomain(X2),X1),domain(X2))))) = antidomain(multiplication(X0,multiplication(addition(antidomain(X2),X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f224,f508]) ).
fof(f19302,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(addition(X1,X2),omega(X1)))),antidomain(multiplication(X0,multiplication(addition(X2,one),domain(omega(X1)))))) = antidomain(multiplication(X0,multiplication(addition(X2,one),domain(omega(X1))))),
inference(paramodulation,[status(thm)],[f11449,f508]) ).
fof(f19303,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(addition(X1,X2),omega(X2)))),antidomain(multiplication(X0,multiplication(addition(X1,one),domain(omega(X2)))))) = antidomain(multiplication(X0,multiplication(addition(X1,one),domain(omega(X2))))),
inference(paramodulation,[status(thm)],[f10882,f508]) ).
fof(f19304,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(X1,multiplication(X2,X1)))),antidomain(multiplication(X0,multiplication(addition(X2,one),domain(X1))))) = antidomain(multiplication(X0,multiplication(addition(X2,one),domain(X1)))),
inference(paramodulation,[status(thm)],[f232,f508]) ).
fof(f19305,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(addition(X1,antidomain(X2)),domain(X2))))) = antidomain(multiplication(X0,multiplication(addition(X1,antidomain(X2)),domain(X2)))),
inference(paramodulation,[status(thm)],[f230,f508]) ).
fof(f19306,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(addition(X1,one),omega(X2)))),antidomain(multiplication(X0,multiplication(addition(X2,X1),domain(omega(X2)))))) = antidomain(multiplication(X0,multiplication(addition(X2,X1),domain(omega(X2))))),
inference(paramodulation,[status(thm)],[f11449,f508]) ).
fof(f19307,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(addition(X1,one),omega(X2)))),antidomain(multiplication(X0,multiplication(addition(X1,X2),domain(omega(X2)))))) = antidomain(multiplication(X0,multiplication(addition(X1,X2),domain(omega(X2))))),
inference(paramodulation,[status(thm)],[f10882,f508]) ).
fof(f19308,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,coantidomain(X2)))),antidomain(multiplication(X0,multiplication(addition(X1,X2),domain(coantidomain(X2)))))) = antidomain(multiplication(X0,multiplication(addition(X1,X2),domain(coantidomain(X2))))),
inference(paramodulation,[status(thm)],[f233,f508]) ).
fof(f19309,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,coantidomain(X2)))),antidomain(multiplication(X0,multiplication(addition(X2,X1),domain(coantidomain(X2)))))) = antidomain(multiplication(X0,multiplication(addition(X2,X1),domain(coantidomain(X2))))),
inference(paramodulation,[status(thm)],[f226,f508]) ).
fof(f19310,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1)))))) = antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1))))),
inference(paramodulation,[status(thm)],[f195,f508]) ).
fof(f19314,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(multiplication(X1,X2),domain(X3))))) = antidomain(multiplication(X0,multiplication(multiplication(X1,X2),domain(X3)))),
inference(paramodulation,[status(thm)],[f39,f508]) ).
fof(f19315,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(antidomain(addition(X1,X2)),domain(X1))))) = antidomain(multiplication(X0,multiplication(antidomain(addition(X1,X2)),domain(X1)))),
inference(paramodulation,[status(thm)],[f2635,f508]) ).
fof(f19316,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(antidomain(X1),X2))),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(addition(X2,X1)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(addition(X2,X1))))),
inference(paramodulation,[status(thm)],[f186,f508]) ).
fof(f19317,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(antidomain(X1),X2))),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(addition(X1,X2)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(addition(X1,X2))))),
inference(paramodulation,[status(thm)],[f177,f508]) ).
fof(f19318,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(omega(X1)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(omega(X1))))),
inference(paramodulation,[status(thm)],[f1569,f508]) ).
fof(f19319,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2))))),
inference(paramodulation,[status(thm)],[f136,f508]) ).
fof(f19320,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1)))),
inference(paramodulation,[status(thm)],[f59,f508]) ).
fof(f19323,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,domain(codomain(X1)))))) = antidomain(multiplication(X0,multiplication(X1,domain(codomain(X1))))),
inference(paramodulation,[status(thm)],[f2309,f508]) ).
fof(f19324,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(omega(X1),multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,domain(addition(omega(X1),X2)))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(omega(X1),X2))))),
inference(paramodulation,[status(thm)],[f318,f508]) ).
fof(f19325,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(X1,multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,domain(addition(one,X2)))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(one,X2))))),
inference(paramodulation,[status(thm)],[f162,f508]) ).
fof(f19326,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(addition(coantidomain(X1),X2)))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(coantidomain(X1),X2))))),
inference(paramodulation,[status(thm)],[f181,f508]) ).
fof(f19327,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(omega(X1),multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,omega(X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,omega(X1)))))),
inference(paramodulation,[status(thm)],[f321,f508]) ).
fof(f19328,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(X1,multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,one)))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,one))))),
inference(paramodulation,[status(thm)],[f192,f508]) ).
fof(f19329,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,coantidomain(X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,coantidomain(X1)))))),
inference(paramodulation,[status(thm)],[f190,f508]) ).
fof(f19330,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(omega(X1),X2))),antidomain(multiplication(X0,multiplication(X1,domain(multiplication(omega(X1),X2)))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(omega(X1),X2))))),
inference(paramodulation,[status(thm)],[f319,f508]) ).
fof(f19331,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2)))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2))))),
inference(paramodulation,[status(thm)],[f151,f508]) ).
fof(f19332,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,omega(multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,omega(multiplication(X1,X2)))))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,omega(multiplication(X1,X2))))))),
inference(paramodulation,[status(thm)],[f308,f508]) ).
fof(f19333,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2)))))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2))))))),
inference(paramodulation,[status(thm)],[f144,f508]) ).
fof(f19334,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(X1,domain(omega(coantidomain(X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(omega(coantidomain(X1)))))),
inference(paramodulation,[status(thm)],[f1813,f508]) ).
fof(f19335,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,omega(X1))),antidomain(multiplication(X0,multiplication(X1,domain(omega(X1)))))) = antidomain(multiplication(X0,multiplication(X1,domain(omega(X1))))),
inference(paramodulation,[status(thm)],[f56,f508]) ).
fof(f19336,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1)))))) = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1))))),
inference(paramodulation,[status(thm)],[f63,f508]) ).
fof(f19339,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),multiplication(X0,X1))),antidomain(multiplication(X2,multiplication(X0,domain(X1))))) = antidomain(multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f224,f508]) ).
fof(f19340,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(addition(X0,antidomain(multiplication(X1,domain(X2)))),multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))) = antidomain(multiplication(addition(X0,antidomain(multiplication(X1,domain(X2)))),multiplication(X1,domain(X2)))),
inference(paramodulation,[status(thm)],[f230,f508]) ).
fof(f19341,plain,
! [X0,X1] : addition(antidomain(multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f4146,f508]) ).
fof(f19342,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(multiplication(X0,X1),multiplication(X2,X3))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(multiplication(X0,X1),multiplication(X2,domain(X3)))),
inference(paramodulation,[status(thm)],[f39,f508]) ).
fof(f19354,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(multiplication(X1,X2),X3))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(multiplication(X1,X2),domain(X3)))),
inference(paramodulation,[status(thm)],[f39,f508]) ).
fof(f19361,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,addition(one,X2)))),antidomain(multiplication(X0,multiplication(X1,one)))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(one,X2))))),
inference(paramodulation,[status(thm)],[f15345,f508]) ).
fof(f19362,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,addition(X2,one)))),antidomain(multiplication(X0,multiplication(X1,one)))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,one))))),
inference(paramodulation,[status(thm)],[f15407,f508]) ).
fof(f19365,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,star(X2)))),antidomain(multiplication(X0,multiplication(X1,one)))) = antidomain(multiplication(X0,multiplication(X1,domain(star(X2))))),
inference(paramodulation,[status(thm)],[f8543,f508]) ).
fof(f19366,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3))))),antidomain(multiplication(X0,multiplication(X1,forward_diamond(X2,X3))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,domain(X3)))))),
inference(paramodulation,[status(thm)],[f69,f508]) ).
fof(f19370,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),multiplication(X0,multiplication(X1,domain(X2)))) = multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(X0,multiplication(X1,domain(X2)))),
inference(paramodulation,[status(thm)],[f508,f230]) ).
fof(f19371,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(antidomain(multiplication(X0,multiplication(X1,X2)))),multiplication(star(antidomain(multiplication(X0,multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,domain(X2)))))))
| ~ leq(one,antidomain(multiplication(X0,multiplication(X1,domain(X2))))) ),
inference(paramodulation,[status(thm)],[f508,f405]) ).
fof(f19372,plain,
! [X0,X1,X2,X3] :
( leq(antidomain(multiplication(X0,multiplication(X1,X2))),addition(omega(X3),multiplication(star(X3),multiplication(X3,antidomain(multiplication(X0,multiplication(X1,domain(X2))))))))
| ~ leq(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(X3,antidomain(multiplication(X0,multiplication(X1,domain(X2)))))) ),
inference(paramodulation,[status(thm)],[f508,f392]) ).
fof(f19373,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(antidomain(multiplication(X1,multiplication(X2,X3)))),multiplication(star(antidomain(multiplication(X1,multiplication(X2,X3)))),multiplication(antidomain(multiplication(X1,multiplication(X2,domain(X3)))),X0))))
| ~ leq(X0,multiplication(antidomain(multiplication(X1,multiplication(X2,domain(X3)))),X0)) ),
inference(paramodulation,[status(thm)],[f508,f391]) ).
fof(f19375,plain,
! [X0,X1,X2] :
( leq(multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),star(antidomain(multiplication(X0,multiplication(X1,X2))))),one)
| ~ leq(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),one) ),
inference(paramodulation,[status(thm)],[f508,f335]) ).
fof(f19376,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(antidomain(multiplication(X0,multiplication(X1,domain(X2))))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f508,f2635]) ).
fof(f19377,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(antidomain(multiplication(X1,multiplication(X2,domain(X3)))),star(antidomain(multiplication(X1,multiplication(X2,X3)))))),X0)
| ~ leq(multiplication(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3))))),X0) ),
inference(paramodulation,[status(thm)],[f508,f341]) ).
fof(f19378,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),multiplication(X3,star(X3))),antidomain(multiplication(X0,multiplication(X1,X2))))
| ~ leq(multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3),antidomain(multiplication(X0,multiplication(X1,X2)))) ),
inference(paramodulation,[status(thm)],[f508,f340]) ).
fof(f19379,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),omega(antidomain(multiplication(X0,multiplication(X1,X2))))) = multiplication(addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),one),omega(antidomain(multiplication(X0,multiplication(X1,X2))))),
inference(paramodulation,[status(thm)],[f508,f11449]) ).
fof(f19386,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(multiplication(X0,multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),one)
| ~ leq(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),one) ),
inference(paramodulation,[status(thm)],[f508,f302]) ).
fof(f19387,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3)))))),antidomain(multiplication(X1,multiplication(X2,X3))))
| ~ leq(multiplication(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3))))),antidomain(multiplication(X1,multiplication(X2,X3)))) ),
inference(paramodulation,[status(thm)],[f508,f291]) ).
fof(f19388,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(antidomain(multiplication(X0,multiplication(X1,X2)))),multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)),X3)
| ~ leq(multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3),X3) ),
inference(paramodulation,[status(thm)],[f508,f290]) ).
fof(f19389,plain,
! [X0,X1,X2,X3] :
( addition(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3))))) != antidomain(multiplication(X1,multiplication(X2,domain(X3))))
| leq(addition(X0,antidomain(multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X1,multiplication(X2,domain(X3))))) ),
inference(paramodulation,[status(thm)],[f508,f243]) ).
fof(f19390,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3))))) != multiplication(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3)))))
| leq(multiplication(X0,antidomain(multiplication(X1,multiplication(X2,X3)))),multiplication(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3)))))) ),
inference(paramodulation,[status(thm)],[f508,f242]) ).
fof(f19391,plain,
! [X0,X1,X2,X3] :
( multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3) != multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)
| leq(multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),X3),multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)) ),
inference(paramodulation,[status(thm)],[f508,f241]) ).
fof(f19392,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),coantidomain(antidomain(multiplication(X0,multiplication(X1,domain(X2)))))) = multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),coantidomain(antidomain(multiplication(X0,multiplication(X1,domain(X2)))))),
inference(paramodulation,[status(thm)],[f508,f233]) ).
fof(f19394,plain,
! [X0,X1,X2] : multiplication(antidomain(antidomain(multiplication(X0,multiplication(X1,domain(X2))))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))) = multiplication(antidomain(antidomain(multiplication(X0,multiplication(X1,domain(X2))))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f508,f186]) ).
fof(f19396,plain,
! [X0,X1,X2,X3] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),addition(X3,antidomain(multiplication(X0,multiplication(X1,domain(X2)))))),
inference(paramodulation,[status(thm)],[f508,f1421]) ).
fof(f19399,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(paramodulation,[status(thm)],[f508,f1324]) ).
fof(f19401,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),addition(antidomain(multiplication(X0,multiplication(X1,X2))),X3)) = addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3),
inference(paramodulation,[status(thm)],[f508,f103]) ).
fof(f19402,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)) = addition(X3,antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(paramodulation,[status(thm)],[f508,f97]) ).
fof(f19403,plain,
! [X0,X1,X2,X3] : addition(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3))))) = addition(antidomain(multiplication(X1,multiplication(X2,domain(X3)))),addition(X0,antidomain(multiplication(X1,multiplication(X2,X3))))),
inference(paramodulation,[status(thm)],[f508,f97]) ).
fof(f19404,plain,
! [X0,X1,X2] :
( antidomain(multiplication(X0,multiplication(X1,domain(X2)))) != antidomain(multiplication(X0,multiplication(X1,X2)))
| leq(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(X1,X2)))) ),
inference(paramodulation,[status(thm)],[f508,f246]) ).
fof(f19405,plain,
! [X0,X1,X2] :
( antidomain(multiplication(X0,multiplication(X1,domain(X2)))) != antidomain(multiplication(X0,multiplication(X1,domain(X2))))
| leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))) ),
inference(paramodulation,[status(thm)],[f508,f49]) ).
fof(f19406,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)) = addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3),
inference(paramodulation,[status(thm)],[f508,f36]) ).
fof(f19407,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(multiplication(X0,X1),multiplication(X2,domain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f19290]) ).
fof(f19408,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3))))),
inference(forward_demodulation,[status(thm)],[f39,f19407]) ).
fof(f19409,plain,
! [X0,X1,X2] : addition(one,antidomain(multiplication(antidomain(addition(multiplication(X0,X1),X2)),multiplication(X0,domain(X1))))) = antidomain(multiplication(antidomain(addition(multiplication(X0,X1),X2)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f577,f19291]) ).
fof(f19410,plain,
! [X0,X1,X2] : one = antidomain(multiplication(antidomain(addition(multiplication(X0,X1),X2)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1379,f19409]) ).
fof(f19414,plain,
! [X0,X1] : addition(one,antidomain(multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1))))) = antidomain(multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f577,f19293]) ).
fof(f19415,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1379,f19414]) ).
fof(f19426,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f577,f19299]) ).
fof(f19427,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f1379,f19426]) ).
fof(f19428,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1)))))) = antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1))))),
inference(forward_demodulation,[status(thm)],[f44,f19310]) ).
fof(f19429,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1)))))) = antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1))))),
inference(forward_demodulation,[status(thm)],[f577,f19428]) ).
fof(f19430,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1))))),
inference(forward_demodulation,[status(thm)],[f1379,f19429]) ).
fof(f19441,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(multiplication(X1,X2),domain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f19314]) ).
fof(f19442,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3))))),
inference(forward_demodulation,[status(thm)],[f39,f19441]) ).
fof(f19443,plain,
! [X0,X1,X2] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(antidomain(addition(X1,X2)),domain(X1))))) = antidomain(multiplication(X0,multiplication(antidomain(addition(X1,X2)),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f44,f19315]) ).
fof(f19444,plain,
! [X0,X1,X2] : addition(one,antidomain(multiplication(X0,multiplication(antidomain(addition(X1,X2)),domain(X1))))) = antidomain(multiplication(X0,multiplication(antidomain(addition(X1,X2)),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f577,f19443]) ).
fof(f19445,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(antidomain(addition(X1,X2)),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1379,f19444]) ).
fof(f19446,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(omega(X1)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(omega(X1))))),
inference(forward_demodulation,[status(thm)],[f44,f19318]) ).
fof(f19447,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(antidomain(X1),domain(omega(X1)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(omega(X1))))),
inference(forward_demodulation,[status(thm)],[f577,f19446]) ).
fof(f19448,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(omega(X1))))),
inference(forward_demodulation,[status(thm)],[f1379,f19447]) ).
fof(f19449,plain,
! [X0,X1,X2] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f44,f19319]) ).
fof(f19450,plain,
! [X0,X1,X2] : addition(one,antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f577,f19449]) ).
fof(f19451,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f1379,f19450]) ).
fof(f19452,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f44,f19320]) ).
fof(f19453,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f577,f19452]) ).
fof(f19454,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1379,f19453]) ).
fof(f19462,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(X1,multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,one)))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(one,X2))))),
inference(forward_demodulation,[status(thm)],[f15345,f19325]) ).
fof(f19463,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,one))),antidomain(multiplication(X0,addition(X1,multiplication(X1,X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(one,X2))))),
inference(forward_demodulation,[status(thm)],[f35,f19462]) ).
fof(f19464,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,addition(X1,multiplication(X1,X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(one,X2))))),
inference(forward_demodulation,[status(thm)],[f40,f19463]) ).
fof(f19465,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,addition(X1,multiplication(X1,X2))))) = antidomain(multiplication(X0,multiplication(X1,one))),
inference(forward_demodulation,[status(thm)],[f15345,f19464]) ).
fof(f19466,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,addition(X1,multiplication(X1,X2))))) = antidomain(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f40,f19465]) ).
fof(f19467,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(X1,multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,one)))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,one))))),
inference(forward_demodulation,[status(thm)],[f15407,f19328]) ).
fof(f19468,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,one))),antidomain(multiplication(X0,addition(X1,multiplication(X1,X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,one))))),
inference(forward_demodulation,[status(thm)],[f35,f19467]) ).
fof(f19469,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,addition(X1,multiplication(X1,X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,one))))),
inference(forward_demodulation,[status(thm)],[f40,f19468]) ).
fof(f19470,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,addition(X1,multiplication(X1,X2))))) = antidomain(multiplication(X0,multiplication(X1,one))),
inference(forward_demodulation,[status(thm)],[f15407,f19469]) ).
fof(f19471,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,addition(X1,multiplication(X1,X2))))) = antidomain(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f40,f19470]) ).
fof(f19472,plain,
! [X0,X1,X2] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2)))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2))))),
inference(forward_demodulation,[status(thm)],[f44,f19331]) ).
fof(f19473,plain,
! [X0,X1,X2] : addition(one,antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2)))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2))))),
inference(forward_demodulation,[status(thm)],[f577,f19472]) ).
fof(f19474,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2))))),
inference(forward_demodulation,[status(thm)],[f1379,f19473]) ).
fof(f19475,plain,
! [X0,X1,X2] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2)))))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2))))))),
inference(forward_demodulation,[status(thm)],[f44,f19333]) ).
fof(f19476,plain,
! [X0,X1,X2] : addition(one,antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2)))))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2))))))),
inference(forward_demodulation,[status(thm)],[f577,f19475]) ).
fof(f19477,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2))))))),
inference(forward_demodulation,[status(thm)],[f1379,f19476]) ).
fof(f19478,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(X1,domain(omega(coantidomain(X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(omega(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f44,f19334]) ).
fof(f19479,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(X1,domain(omega(coantidomain(X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(omega(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f577,f19478]) ).
fof(f19480,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(omega(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f1379,f19479]) ).
fof(f19481,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1)))))) = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1))))),
inference(forward_demodulation,[status(thm)],[f44,f19336]) ).
fof(f19482,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1)))))) = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1))))),
inference(forward_demodulation,[status(thm)],[f577,f19481]) ).
fof(f19483,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1))))),
inference(forward_demodulation,[status(thm)],[f1379,f19482]) ).
fof(f19494,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(addition(antidomain(multiplication(X1,domain(X2))),X0),multiplication(X1,X2)))) = antidomain(multiplication(addition(antidomain(multiplication(X1,domain(X2))),X0),multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f35,f19339]) ).
fof(f19495,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(addition(antidomain(multiplication(X1,domain(X2))),X0),multiplication(X1,X2)))) = antidomain(multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f224,f19494]) ).
fof(f19496,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(addition(X0,antidomain(multiplication(X1,domain(X2)))),multiplication(X1,X2)))) = antidomain(multiplication(addition(X0,antidomain(multiplication(X1,domain(X2)))),multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f35,f19340]) ).
fof(f19497,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(addition(X0,antidomain(multiplication(X1,domain(X2)))),multiplication(X1,X2)))) = antidomain(multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f230,f19496]) ).
fof(f19498,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,X1)))) = antidomain(multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f35,f19341]) ).
fof(f19499,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(forward_diamond(X0,X1),multiplication(X0,X1)))) = antidomain(multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f69,f19498]) ).
fof(f19500,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(forward_diamond(X0,X1),multiplication(X0,X1)))) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f4146,f19499]) ).
fof(f19501,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(multiplication(X0,X1),multiplication(X2,domain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f19342]) ).
fof(f19502,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3))))),
inference(forward_demodulation,[status(thm)],[f39,f19501]) ).
fof(f19550,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(multiplication(X1,X2),domain(X3)))),
inference(forward_demodulation,[status(thm)],[f39,f19354]) ).
fof(f19551,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,multiplication(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3))))),
inference(forward_demodulation,[status(thm)],[f39,f19550]) ).
fof(f19576,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,one))),antidomain(multiplication(X0,multiplication(X1,addition(one,X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(one,X2))))),
inference(forward_demodulation,[status(thm)],[f35,f19361]) ).
fof(f19577,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,addition(one,X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(one,X2))))),
inference(forward_demodulation,[status(thm)],[f40,f19576]) ).
fof(f19578,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,addition(one,X2))))) = antidomain(multiplication(X0,multiplication(X1,one))),
inference(forward_demodulation,[status(thm)],[f15345,f19577]) ).
fof(f19579,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,addition(one,X2))))) = antidomain(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f40,f19578]) ).
fof(f19580,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,one))),antidomain(multiplication(X0,multiplication(X1,addition(X2,one))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,one))))),
inference(forward_demodulation,[status(thm)],[f35,f19362]) ).
fof(f19581,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,addition(X2,one))))) = antidomain(multiplication(X0,multiplication(X1,domain(addition(X2,one))))),
inference(forward_demodulation,[status(thm)],[f40,f19580]) ).
fof(f19582,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,addition(X2,one))))) = antidomain(multiplication(X0,multiplication(X1,one))),
inference(forward_demodulation,[status(thm)],[f15407,f19581]) ).
fof(f19583,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,addition(X2,one))))) = antidomain(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f40,f19582]) ).
fof(f19586,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,one))),antidomain(multiplication(X0,multiplication(X1,star(X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(star(X2))))),
inference(forward_demodulation,[status(thm)],[f35,f19365]) ).
fof(f19587,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,star(X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(star(X2))))),
inference(forward_demodulation,[status(thm)],[f40,f19586]) ).
fof(f19588,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,star(X2))))) = antidomain(multiplication(X0,multiplication(X1,one))),
inference(forward_demodulation,[status(thm)],[f8543,f19587]) ).
fof(f19589,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,star(X2))))) = antidomain(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f40,f19588]) ).
fof(f19590,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,forward_diamond(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,domain(X3)))))),
inference(forward_demodulation,[status(thm)],[f35,f19366]) ).
fof(f19591,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,forward_diamond(X2,X3)))),antidomain(multiplication(X0,multiplication(X1,multiplication(X2,domain(X3)))))) = antidomain(multiplication(X0,multiplication(X1,forward_diamond(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f69,f19590]) ).
fof(f19602,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f59,f19370]) ).
fof(f19603,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),star(antidomain(multiplication(X0,multiplication(X1,X2))))),one),
inference(forward_subsumption_resolution,[status(thm)],[f19375,f1412]) ).
fof(f19604,plain,
! [X0,X1,X2] : zero = multiplication(domain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f62,f19376]) ).
fof(f19605,plain,
! [X0,X1,X2] : zero = domain_difference(multiplication(X0,multiplication(X1,domain(X2))),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f68,f19604]) ).
fof(f19606,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(antidomain(multiplication(X1,multiplication(X2,domain(X3)))),star(antidomain(multiplication(X1,multiplication(X2,X3)))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f19377,f3749]) ).
fof(f19607,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),omega(antidomain(multiplication(X0,multiplication(X1,X2))))) = multiplication(addition(one,antidomain(multiplication(X0,multiplication(X1,domain(X2))))),omega(antidomain(multiplication(X0,multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f35,f19379]) ).
fof(f19608,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),omega(antidomain(multiplication(X0,multiplication(X1,X2))))) = multiplication(one,omega(antidomain(multiplication(X0,multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f1379,f19607]) ).
fof(f19609,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),omega(antidomain(multiplication(X0,multiplication(X1,X2))))) = omega(antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f41,f19608]) ).
fof(f19622,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(multiplication(X0,multiplication(X1,X2)))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),one),
inference(forward_subsumption_resolution,[status(thm)],[f19386,f1412]) ).
fof(f19623,plain,
! [X0,X1,X2,X3] : leq(multiplication(star(antidomain(multiplication(X0,multiplication(X1,X2)))),multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)),X3),
inference(forward_subsumption_resolution,[status(thm)],[f19388,f6667]) ).
fof(f19624,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,antidomain(multiplication(X1,multiplication(X2,X3)))),multiplication(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3)))))),
inference(trivial_equality_resolution,[status(thm)],[f19390]) ).
fof(f19625,plain,
! [X0,X1,X2,X3] : leq(multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),X3),multiplication(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)),
inference(trivial_equality_resolution,[status(thm)],[f19391]) ).
fof(f19626,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),coantidomain(antidomain(multiplication(X0,multiplication(X1,domain(X2)))))),
inference(forward_demodulation,[status(thm)],[f63,f19392]) ).
fof(f19627,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(antidomain(multiplication(X0,multiplication(X1,domain(X2))))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f59,f19394]) ).
fof(f19628,plain,
! [X0,X1,X2] : zero = multiplication(domain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f62,f19627]) ).
fof(f19629,plain,
! [X0,X1,X2] : zero = domain_difference(multiplication(X0,multiplication(X1,domain(X2))),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f68,f19628]) ).
fof(f19630,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),addition(X3,antidomain(multiplication(X0,multiplication(X1,domain(X2)))))) = addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3),
inference(forward_demodulation,[status(thm)],[f97,f19401]) ).
fof(f19631,plain,
! [X0,X1,X2,X3] : addition(X0,antidomain(multiplication(X1,multiplication(X2,domain(X3))))) = addition(antidomain(multiplication(X1,multiplication(X2,X3))),addition(antidomain(multiplication(X1,multiplication(X2,domain(X3)))),X0)),
inference(forward_demodulation,[status(thm)],[f97,f19403]) ).
fof(f19632,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(trivial_equality_resolution,[status(thm)],[f19405]) ).
fof(f19675,plain,
! [X0] : leq(antidomain(X0),addition(omega(antidomain(antidomain(X0))),multiplication(star(antidomain(antidomain(X0))),omega(antidomain(X0))))),
inference(resolution,[status(thm)],[f18886,f409]) ).
fof(f19676,plain,
! [X0] : leq(multiplication(antidomain(X0),star(coantidomain(omega(antidomain(X0))))),omega(antidomain(X0))),
inference(resolution,[status(thm)],[f18886,f346]) ).
fof(f19677,plain,
! [X0] : leq(multiplication(star(antidomain(omega(antidomain(X0)))),antidomain(X0)),omega(antidomain(X0))),
inference(resolution,[status(thm)],[f18886,f304]) ).
fof(f19678,plain,
! [X0] : addition(antidomain(X0),omega(antidomain(X0))) = omega(antidomain(X0)),
inference(resolution,[status(thm)],[f18886,f48]) ).
fof(f19679,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(antidomain(forward_diamond(X0,antidomain(X1))))),
inference(paramodulation,[status(thm)],[f18885,f18886]) ).
fof(f19680,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(antidomain(backward_diamond(X0,antidomain(X1))))),
inference(paramodulation,[status(thm)],[f18884,f18886]) ).
fof(f19688,plain,
! [X0,X1] : leq(antidomain(forward_diamond(X0,antidomain(X1))),omega(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f18885,f18886]) ).
fof(f19689,plain,
! [X0,X1] : leq(antidomain(backward_diamond(X0,antidomain(X1))),omega(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f18884,f18886]) ).
fof(f19697,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(antidomain(antidomain(X0))),omega(antidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f62,f19675]) ).
fof(f19698,plain,
! [X0] : leq(antidomain(X0),addition(omega(domain(X0)),multiplication(star(domain(X0)),omega(antidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f62,f19697]) ).
fof(f19699,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18885,f19679]) ).
fof(f19700,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18884,f19680]) ).
fof(f19712,plain,
! [X0,X1] : leq(forward_box(X0,X1),omega(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18885,f19688]) ).
fof(f19713,plain,
! [X0,X1] : leq(backward_box(X0,X1),omega(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18884,f19689]) ).
fof(f19725,plain,
! [X0] : addition(one,antidomain(multiplication(antidomain(X0),domain(X0)))) = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f577,f485]) ).
fof(f19726,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1379,f19725]) ).
fof(f19728,plain,
! [X0,X1] : one = antidomain(multiplication(forward_box(X0,X1),domain(forward_diamond(X0,antidomain(X1))))),
inference(paramodulation,[status(thm)],[f18885,f19726]) ).
fof(f19729,plain,
! [X0,X1] : one = antidomain(multiplication(backward_box(X0,X1),domain(backward_diamond(X0,antidomain(X1))))),
inference(paramodulation,[status(thm)],[f18884,f19726]) ).
fof(f19744,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f69,f19726]) ).
fof(f19753,plain,
! [X0,X1] : forward_box(X0,multiplication(antidomain(X1),domain(X1))) = antidomain(forward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f19726,f18885]) ).
fof(f19756,plain,
! [X0,X1] : backward_box(X0,multiplication(antidomain(X1),domain(X1))) = antidomain(backward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f19726,f18884]) ).
fof(f19757,plain,
! [X0,X1] :
( leq(multiplication(X0,star(multiplication(antidomain(X1),domain(X1)))),antidomain(multiplication(antidomain(X1),domain(X1))))
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f19726,f344]) ).
fof(f19761,plain,
! [X0,X1] : leq(domain_difference(X0,multiplication(antidomain(X1),domain(X1))),one),
inference(paramodulation,[status(thm)],[f19726,f6998]) ).
fof(f19764,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(antidomain(X1),domain(X1))) = multiplication(X0,multiplication(antidomain(X1),domain(X1))),
inference(paramodulation,[status(thm)],[f19726,f230]) ).
fof(f19766,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(antidomain(X1),domain(X1))) = multiplication(X0,multiplication(antidomain(X1),domain(X1))),
inference(paramodulation,[status(thm)],[f19726,f224]) ).
fof(f19770,plain,
! [X0,X1] : multiplication(one,addition(X0,multiplication(antidomain(X1),domain(X1)))) = multiplication(antidomain(multiplication(antidomain(X1),domain(X1))),X0),
inference(paramodulation,[status(thm)],[f19726,f186]) ).
fof(f19772,plain,
! [X0,X1] : multiplication(one,addition(multiplication(antidomain(X0),domain(X0)),X1)) = multiplication(antidomain(multiplication(antidomain(X0),domain(X0))),X1),
inference(paramodulation,[status(thm)],[f19726,f177]) ).
fof(f19773,plain,
! [X0] : multiplication(one,omega(multiplication(antidomain(X0),domain(X0)))) = zero,
inference(paramodulation,[status(thm)],[f19726,f1569]) ).
fof(f19775,plain,
! [X0,X1] : multiplication(one,multiplication(multiplication(antidomain(X0),domain(X0)),X1)) = zero,
inference(paramodulation,[status(thm)],[f19726,f136]) ).
fof(f19777,plain,
! [X0,X1] : domain_difference(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f19726,f68]) ).
fof(f19814,plain,
! [X0,X1] : forward_box(X0,multiplication(antidomain(X1),domain(X1))) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f777,f19753]) ).
fof(f19815,plain,
! [X0,X1] : forward_box(X0,multiplication(antidomain(X1),domain(X1))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f18883,f19814]) ).
fof(f19819,plain,
! [X0,X1] : backward_box(X0,multiplication(antidomain(X1),domain(X1))) = antidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f810,f19756]) ).
fof(f19820,plain,
! [X0,X1] :
( leq(multiplication(X0,star(multiplication(antidomain(X1),domain(X1)))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f19726,f19757]) ).
fof(f19831,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(antidomain(multiplication(antidomain(X1),domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f41,f19770]) ).
fof(f19832,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(one,X0),
inference(forward_demodulation,[status(thm)],[f19726,f19831]) ).
fof(f19833,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f41,f19832]) ).
fof(f19834,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = multiplication(antidomain(multiplication(antidomain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f41,f19772]) ).
fof(f19835,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = multiplication(one,X1),
inference(forward_demodulation,[status(thm)],[f19726,f19834]) ).
fof(f19836,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f41,f19835]) ).
fof(f19837,plain,
! [X0] : omega(multiplication(antidomain(X0),domain(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f41,f19773]) ).
fof(f19838,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),domain(X0)),X1) = zero,
inference(forward_demodulation,[status(thm)],[f41,f19775]) ).
fof(f19839,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f19838]) ).
fof(f19840,plain,
! [X0,X1] : domain_difference(X0,multiplication(antidomain(X1),domain(X1))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f40,f19777]) ).
fof(f19845,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),antidomain(forward_diamond(X0,antidomain(X1)))) = one,
inference(paramodulation,[status(thm)],[f18885,f18853]) ).
fof(f19846,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),antidomain(backward_diamond(X0,antidomain(X1)))) = one,
inference(paramodulation,[status(thm)],[f18884,f18853]) ).
fof(f19855,plain,
! [X0,X1] : forward_box(antidomain(forward_diamond(X0,antidomain(X1))),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f18885,f18853]) ).
fof(f19856,plain,
! [X0,X1] : forward_box(antidomain(backward_diamond(X0,antidomain(X1))),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f18884,f18853]) ).
fof(f19875,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f18885,f19845]) ).
fof(f19876,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f18884,f19846]) ).
fof(f19882,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f18885,f19855]) ).
fof(f19883,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f18884,f19856]) ).
fof(f19901,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),domain(forward_diamond(X0,antidomain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f18885,f18856]) ).
fof(f19902,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),domain(backward_diamond(X0,antidomain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f18884,f18856]) ).
fof(f19917,plain,
! [X0,X1] : forward_diamond(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f69,f18856]) ).
fof(f19920,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(antidomain(X0)),forward_diamond(star(antidomain(X0)),domain(X1)))) = addition(divergence(antidomain(X0)),forward_diamond(star(antidomain(X0)),domain(X1)))
| addition(domain(X0),addition(zero,domain(X1))) != addition(forward_diamond(antidomain(X0),domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f18856,f75]) ).
fof(f19943,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))
| addition(zero,addition(domain(X0),domain(X1))) != addition(forward_diamond(antidomain(X1),domain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f19920]) ).
fof(f19944,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))
| addition(domain(X0),domain(X1)) != addition(forward_diamond(antidomain(X1),domain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f19943]) ).
fof(f19945,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))
| addition(domain(X0),domain(X1)) != addition(zero,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f18856,f19944]) ).
fof(f19946,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f80,f19945]) ).
fof(f19950,plain,
! [X0] : leq(antidomain(omega(X0)),antidomain(multiplication(X0,domain(omega(X0))))),
inference(resolution,[status(thm)],[f488,f49]) ).
fof(f19952,plain,
! [X0,X1] : addition(antidomain(omega(multiplication(X0,X1))),antidomain(multiplication(X0,multiplication(X1,domain(omega(multiplication(X0,X1))))))) = antidomain(multiplication(multiplication(X0,X1),domain(omega(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f39,f488]) ).
fof(f19957,plain,
! [X0] : multiplication(antidomain(multiplication(X0,domain(omega(X0)))),multiplication(X0,domain(omega(X0)))) = multiplication(antidomain(omega(X0)),multiplication(X0,domain(omega(X0)))),
inference(paramodulation,[status(thm)],[f488,f230]) ).
fof(f19958,plain,
! [X0] :
( leq(one,addition(omega(antidomain(omega(X0))),multiplication(star(antidomain(omega(X0))),antidomain(multiplication(X0,domain(omega(X0)))))))
| ~ leq(one,antidomain(multiplication(X0,domain(omega(X0))))) ),
inference(paramodulation,[status(thm)],[f488,f405]) ).
fof(f19959,plain,
! [X0,X1] :
( leq(antidomain(omega(X0)),addition(omega(X1),multiplication(star(X1),multiplication(X1,antidomain(multiplication(X0,domain(omega(X0))))))))
| ~ leq(antidomain(omega(X0)),multiplication(X1,antidomain(multiplication(X0,domain(omega(X0)))))) ),
inference(paramodulation,[status(thm)],[f488,f392]) ).
fof(f19960,plain,
! [X0,X1] :
( leq(X0,addition(omega(antidomain(omega(X1))),multiplication(star(antidomain(omega(X1))),multiplication(antidomain(multiplication(X1,domain(omega(X1)))),X0))))
| ~ leq(X0,multiplication(antidomain(multiplication(X1,domain(omega(X1)))),X0)) ),
inference(paramodulation,[status(thm)],[f488,f391]) ).
fof(f19962,plain,
! [X0] :
( leq(multiplication(antidomain(multiplication(X0,domain(omega(X0)))),star(antidomain(omega(X0)))),one)
| ~ leq(antidomain(multiplication(X0,domain(omega(X0)))),one) ),
inference(paramodulation,[status(thm)],[f488,f335]) ).
fof(f19963,plain,
! [X0] : zero = multiplication(antidomain(antidomain(multiplication(X0,domain(omega(X0))))),antidomain(omega(X0))),
inference(paramodulation,[status(thm)],[f488,f2635]) ).
fof(f19964,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(antidomain(multiplication(X1,domain(omega(X1)))),star(antidomain(omega(X1))))),X0)
| ~ leq(multiplication(X0,antidomain(multiplication(X1,domain(omega(X1))))),X0) ),
inference(paramodulation,[status(thm)],[f488,f341]) ).
fof(f19965,plain,
! [X0,X1] :
( leq(multiplication(antidomain(multiplication(X0,domain(omega(X0)))),multiplication(X1,star(X1))),antidomain(omega(X0)))
| ~ leq(multiplication(antidomain(multiplication(X0,domain(omega(X0)))),X1),antidomain(omega(X0))) ),
inference(paramodulation,[status(thm)],[f488,f340]) ).
fof(f19966,plain,
! [X0] : multiplication(antidomain(multiplication(X0,domain(omega(X0)))),omega(antidomain(omega(X0)))) = multiplication(addition(antidomain(multiplication(X0,domain(omega(X0)))),one),omega(antidomain(omega(X0)))),
inference(paramodulation,[status(thm)],[f488,f11449]) ).
fof(f19973,plain,
! [X0] :
( leq(multiplication(star(antidomain(omega(X0))),antidomain(multiplication(X0,domain(omega(X0))))),one)
| ~ leq(antidomain(multiplication(X0,domain(omega(X0)))),one) ),
inference(paramodulation,[status(thm)],[f488,f302]) ).
fof(f19974,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(multiplication(X1,domain(omega(X1)))))),antidomain(omega(X1)))
| ~ leq(multiplication(X0,antidomain(multiplication(X1,domain(omega(X1))))),antidomain(omega(X1))) ),
inference(paramodulation,[status(thm)],[f488,f291]) ).
fof(f19975,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(omega(X0))),multiplication(antidomain(multiplication(X0,domain(omega(X0)))),X1)),X1)
| ~ leq(multiplication(antidomain(multiplication(X0,domain(omega(X0)))),X1),X1) ),
inference(paramodulation,[status(thm)],[f488,f290]) ).
fof(f19976,plain,
! [X0,X1] :
( addition(X0,antidomain(multiplication(X1,domain(omega(X1))))) != antidomain(multiplication(X1,domain(omega(X1))))
| leq(addition(X0,antidomain(omega(X1))),antidomain(multiplication(X1,domain(omega(X1))))) ),
inference(paramodulation,[status(thm)],[f488,f243]) ).
fof(f19977,plain,
! [X0,X1] :
( multiplication(X0,antidomain(multiplication(X1,domain(omega(X1))))) != multiplication(X0,antidomain(multiplication(X1,domain(omega(X1)))))
| leq(multiplication(X0,antidomain(omega(X1))),multiplication(X0,antidomain(multiplication(X1,domain(omega(X1)))))) ),
inference(paramodulation,[status(thm)],[f488,f242]) ).
fof(f19978,plain,
! [X0,X1] :
( multiplication(antidomain(multiplication(X0,domain(omega(X0)))),X1) != multiplication(antidomain(multiplication(X0,domain(omega(X0)))),X1)
| leq(multiplication(antidomain(omega(X0)),X1),multiplication(antidomain(multiplication(X0,domain(omega(X0)))),X1)) ),
inference(paramodulation,[status(thm)],[f488,f241]) ).
fof(f19979,plain,
! [X0] : multiplication(antidomain(multiplication(X0,domain(omega(X0)))),coantidomain(antidomain(multiplication(X0,domain(omega(X0)))))) = multiplication(antidomain(omega(X0)),coantidomain(antidomain(multiplication(X0,domain(omega(X0)))))),
inference(paramodulation,[status(thm)],[f488,f233]) ).
fof(f19981,plain,
! [X0] : multiplication(antidomain(antidomain(multiplication(X0,domain(omega(X0))))),antidomain(multiplication(X0,domain(omega(X0))))) = multiplication(antidomain(antidomain(multiplication(X0,domain(omega(X0))))),antidomain(omega(X0))),
inference(paramodulation,[status(thm)],[f488,f186]) ).
fof(f19983,plain,
! [X0,X1] : leq(antidomain(omega(X0)),addition(X1,antidomain(multiplication(X0,domain(omega(X0)))))),
inference(paramodulation,[status(thm)],[f488,f1421]) ).
fof(f19986,plain,
! [X0] : leq(antidomain(omega(X0)),antidomain(multiplication(X0,domain(omega(X0))))),
inference(paramodulation,[status(thm)],[f488,f1324]) ).
fof(f19988,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(omega(X0)))),addition(antidomain(omega(X0)),X1)) = addition(antidomain(multiplication(X0,domain(omega(X0)))),X1),
inference(paramodulation,[status(thm)],[f488,f103]) ).
fof(f19989,plain,
! [X0,X1] : addition(antidomain(omega(X0)),addition(antidomain(multiplication(X0,domain(omega(X0)))),X1)) = addition(X1,antidomain(multiplication(X0,domain(omega(X0))))),
inference(paramodulation,[status(thm)],[f488,f97]) ).
fof(f19990,plain,
! [X0,X1] : addition(X0,antidomain(multiplication(X1,domain(omega(X1))))) = addition(antidomain(multiplication(X1,domain(omega(X1)))),addition(X0,antidomain(omega(X1)))),
inference(paramodulation,[status(thm)],[f488,f97]) ).
fof(f19991,plain,
! [X0] :
( antidomain(multiplication(X0,domain(omega(X0)))) != antidomain(omega(X0))
| leq(antidomain(multiplication(X0,domain(omega(X0)))),antidomain(omega(X0))) ),
inference(paramodulation,[status(thm)],[f488,f246]) ).
fof(f19992,plain,
! [X0] :
( antidomain(multiplication(X0,domain(omega(X0)))) != antidomain(multiplication(X0,domain(omega(X0))))
| leq(antidomain(omega(X0)),antidomain(multiplication(X0,domain(omega(X0))))) ),
inference(paramodulation,[status(thm)],[f488,f49]) ).
fof(f19993,plain,
! [X0,X1] : addition(antidomain(omega(X0)),addition(antidomain(multiplication(X0,domain(omega(X0)))),X1)) = addition(antidomain(multiplication(X0,domain(omega(X0)))),X1),
inference(paramodulation,[status(thm)],[f488,f36]) ).
fof(f19997,plain,
! [X0,X1] : addition(antidomain(omega(multiplication(X0,X1))),antidomain(multiplication(X0,multiplication(X1,domain(omega(multiplication(X0,X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(omega(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f39,f19952]) ).
fof(f20009,plain,
! [X0] : zero = multiplication(antidomain(omega(X0)),multiplication(X0,domain(omega(X0)))),
inference(forward_demodulation,[status(thm)],[f59,f19957]) ).
fof(f20010,plain,
! [X0] : leq(multiplication(antidomain(multiplication(X0,domain(omega(X0)))),star(antidomain(omega(X0)))),one),
inference(forward_subsumption_resolution,[status(thm)],[f19962,f1412]) ).
fof(f20011,plain,
! [X0] : zero = multiplication(domain(multiplication(X0,domain(omega(X0)))),antidomain(omega(X0))),
inference(forward_demodulation,[status(thm)],[f62,f19963]) ).
fof(f20012,plain,
! [X0] : zero = domain_difference(multiplication(X0,domain(omega(X0))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f68,f20011]) ).
fof(f20013,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(antidomain(multiplication(X1,domain(omega(X1)))),star(antidomain(omega(X1))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f19964,f3749]) ).
fof(f20014,plain,
! [X0] : multiplication(antidomain(multiplication(X0,domain(omega(X0)))),omega(antidomain(omega(X0)))) = multiplication(addition(one,antidomain(multiplication(X0,domain(omega(X0))))),omega(antidomain(omega(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f19966]) ).
fof(f20015,plain,
! [X0] : multiplication(antidomain(multiplication(X0,domain(omega(X0)))),omega(antidomain(omega(X0)))) = multiplication(one,omega(antidomain(omega(X0)))),
inference(forward_demodulation,[status(thm)],[f1379,f20014]) ).
fof(f20016,plain,
! [X0] : multiplication(antidomain(multiplication(X0,domain(omega(X0)))),omega(antidomain(omega(X0)))) = omega(antidomain(omega(X0))),
inference(forward_demodulation,[status(thm)],[f41,f20015]) ).
fof(f20029,plain,
! [X0] : leq(multiplication(star(antidomain(omega(X0))),antidomain(multiplication(X0,domain(omega(X0))))),one),
inference(forward_subsumption_resolution,[status(thm)],[f19973,f1412]) ).
fof(f20030,plain,
! [X0,X1] : leq(multiplication(star(antidomain(omega(X0))),multiplication(antidomain(multiplication(X0,domain(omega(X0)))),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f19975,f6667]) ).
fof(f20031,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(omega(X1))),multiplication(X0,antidomain(multiplication(X1,domain(omega(X1)))))),
inference(trivial_equality_resolution,[status(thm)],[f19977]) ).
fof(f20032,plain,
! [X0,X1] : leq(multiplication(antidomain(omega(X0)),X1),multiplication(antidomain(multiplication(X0,domain(omega(X0)))),X1)),
inference(trivial_equality_resolution,[status(thm)],[f19978]) ).
fof(f20033,plain,
! [X0] : zero = multiplication(antidomain(omega(X0)),coantidomain(antidomain(multiplication(X0,domain(omega(X0)))))),
inference(forward_demodulation,[status(thm)],[f63,f19979]) ).
fof(f20034,plain,
! [X0] : zero = multiplication(antidomain(antidomain(multiplication(X0,domain(omega(X0))))),antidomain(omega(X0))),
inference(forward_demodulation,[status(thm)],[f59,f19981]) ).
fof(f20035,plain,
! [X0] : zero = multiplication(domain(multiplication(X0,domain(omega(X0)))),antidomain(omega(X0))),
inference(forward_demodulation,[status(thm)],[f62,f20034]) ).
fof(f20036,plain,
! [X0] : zero = domain_difference(multiplication(X0,domain(omega(X0))),omega(X0)),
inference(forward_demodulation,[status(thm)],[f68,f20035]) ).
fof(f20037,plain,
! [X0,X1] : addition(antidomain(omega(X0)),addition(X1,antidomain(multiplication(X0,domain(omega(X0)))))) = addition(antidomain(multiplication(X0,domain(omega(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f97,f19988]) ).
fof(f20038,plain,
! [X0,X1] : addition(X0,antidomain(multiplication(X1,domain(omega(X1))))) = addition(antidomain(omega(X1)),addition(antidomain(multiplication(X1,domain(omega(X1)))),X0)),
inference(forward_demodulation,[status(thm)],[f97,f19990]) ).
fof(f20039,plain,
! [X0] : leq(antidomain(omega(X0)),antidomain(multiplication(X0,domain(omega(X0))))),
inference(trivial_equality_resolution,[status(thm)],[f19992]) ).
fof(f20042,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),domain(forward_diamond(X0,antidomain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f18885,f18879]) ).
fof(f20043,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),domain(backward_diamond(X0,antidomain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f18884,f18879]) ).
fof(f20058,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f69,f18879]) ).
fof(f20071,plain,
! [X0,X1,X2] :
( leq(domain(X0),addition(omega(multiplication(X1,antidomain(X0))),multiplication(star(multiplication(X1,antidomain(X0))),X2)))
| ~ leq(domain(X0),addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f18879,f398]) ).
fof(f20072,plain,
! [X0] :
( leq(domain(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),multiplication(antidomain(X0),domain(X0)))))
| ~ leq(domain(X0),zero) ),
inference(paramodulation,[status(thm)],[f18879,f396]) ).
fof(f20073,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(domain(X0),addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f18879,f394]) ).
fof(f20074,plain,
! [X0] :
( leq(domain(X0),omega(antidomain(X0)))
| ~ leq(domain(X0),zero) ),
inference(paramodulation,[status(thm)],[f18879,f407]) ).
fof(f20075,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(antidomain(X0),domain(X0)))
| ~ leq(addition(multiplication(antidomain(X0),multiplication(domain(X0),X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f18879,f332]) ).
fof(f20076,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(domain(X2))),multiplication(X0,antidomain(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f18879,f332]) ).
fof(f20077,plain,
! [X0] :
( leq(multiplication(antidomain(X0),multiplication(domain(X0),star(domain(X0)))),antidomain(X0))
| ~ leq(zero,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f18879,f343]) ).
fof(f20078,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(addition(X0,zero),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f18879,f329]) ).
fof(f20080,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,antidomain(X2))),X1),domain(X2))
| ~ leq(addition(multiplication(X0,zero),X1),domain(X2)) ),
inference(paramodulation,[status(thm)],[f18879,f296]) ).
fof(f20082,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),domain(X1))
| ~ leq(addition(X0,zero),domain(X1)) ),
inference(paramodulation,[status(thm)],[f18879,f293]) ).
fof(f20085,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),addition(zero,X2)) = addition(multiplication(addition(X0,antidomain(X1)),domain(X1)),X2),
inference(paramodulation,[status(thm)],[f18879,f219]) ).
fof(f20086,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,domain(X1)),X2)) = addition(multiplication(addition(antidomain(X1),X0),domain(X1)),X2),
inference(paramodulation,[status(thm)],[f18879,f219]) ).
fof(f20088,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f18879,f211]) ).
fof(f20089,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),domain(X0)) = addition(zero,multiplication(X1,multiplication(X2,domain(X0)))),
inference(paramodulation,[status(thm)],[f18879,f211]) ).
fof(f20091,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),domain(X2)) = addition(multiplication(X0,multiplication(X1,domain(X2))),zero),
inference(paramodulation,[status(thm)],[f18879,f204]) ).
fof(f20092,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),domain(X1)) = addition(multiplication(X0,zero),multiplication(X2,domain(X1))),
inference(paramodulation,[status(thm)],[f18879,f204]) ).
fof(f20093,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = addition(multiplication(X1,domain(X0)),zero),
inference(paramodulation,[status(thm)],[f18879,f201]) ).
fof(f20094,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = addition(zero,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f18879,f201]) ).
fof(f20095,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),addition(zero,X2)) = addition(multiplication(antidomain(X0),addition(X1,domain(X0))),X2),
inference(paramodulation,[status(thm)],[f18879,f170]) ).
fof(f20096,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(antidomain(X0),X1),X2)) = addition(multiplication(antidomain(X0),addition(domain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f18879,f170]) ).
fof(f20099,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f18879,f153]) ).
fof(f20100,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f18879,f153]) ).
fof(f20103,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),domain(X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f18879,f615]) ).
fof(f20105,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(domain(X0),addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f18879,f58]) ).
fof(f20106,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f18879,f55]) ).
fof(f20107,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),domain(X1))
| ~ leq(addition(zero,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f18879,f53]) ).
fof(f20108,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = addition(multiplication(X0,domain(X1)),zero),
inference(paramodulation,[status(thm)],[f18879,f43]) ).
fof(f20109,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = addition(zero,multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f18879,f43]) ).
fof(f20110,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f18879,f42]) ).
fof(f20111,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f18879,f42]) ).
fof(f20112,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f18879,f39]) ).
fof(f20144,plain,
! [X0,X1,X2] :
( leq(domain(X0),addition(omega(multiplication(X2,antidomain(X0))),multiplication(star(multiplication(X2,antidomain(X0))),X1)))
| ~ leq(domain(X0),addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f20071]) ).
fof(f20145,plain,
! [X0,X1,X2] :
( leq(domain(X0),addition(omega(multiplication(X2,antidomain(X0))),multiplication(star(multiplication(X2,antidomain(X0))),X1)))
| ~ leq(domain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f20144]) ).
fof(f20146,plain,
! [X0] :
( leq(domain(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),zero)))
| ~ leq(domain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f18879,f20072]) ).
fof(f20147,plain,
! [X0] :
( leq(domain(X0),addition(omega(antidomain(X0)),zero))
| ~ leq(domain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f20146]) ).
fof(f20148,plain,
! [X0] :
( leq(domain(X0),omega(antidomain(X0)))
| ~ leq(domain(X0),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f20147]) ).
fof(f20149,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(domain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f20073]) ).
fof(f20150,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),zero)
| ~ leq(addition(multiplication(antidomain(X0),multiplication(domain(X0),X1)),X2),zero) ),
inference(forward_demodulation,[status(thm)],[f18879,f20075]) ).
fof(f20151,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain(X2))),multiplication(X1,antidomain(X2)))
| ~ leq(addition(zero,X0),multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f44,f20076]) ).
fof(f20152,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain(X2))),multiplication(X1,antidomain(X2)))
| ~ leq(X0,multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f80,f20151]) ).
fof(f20153,plain,
! [X0] : leq(multiplication(antidomain(X0),multiplication(domain(X0),star(domain(X0)))),antidomain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f20077,f240]) ).
fof(f20154,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f20078]) ).
fof(f20159,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),domain(X1))
| ~ leq(addition(zero,X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f20080]) ).
fof(f20160,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f20159]) ).
fof(f20162,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f37,f20082]) ).
fof(f20175,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,domain(X2)))) = addition(multiplication(addition(X1,antidomain(X2)),domain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f97,f20085]) ).
fof(f20176,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,domain(X2))) = addition(multiplication(addition(X1,antidomain(X2)),domain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f80,f20175]) ).
fof(f20177,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),X2) = addition(multiplication(addition(antidomain(X1),X0),domain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f20086]) ).
fof(f20181,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f44,f20088]) ).
fof(f20182,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),domain(X2)) = multiplication(X0,domain(X2)),
inference(forward_demodulation,[status(thm)],[f37,f20181]) ).
fof(f20183,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),domain(X0)) = multiplication(X1,multiplication(X2,domain(X0))),
inference(forward_demodulation,[status(thm)],[f80,f20089]) ).
fof(f20186,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),domain(X2)) = multiplication(X0,multiplication(X1,domain(X2))),
inference(forward_demodulation,[status(thm)],[f37,f20091]) ).
fof(f20187,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),domain(X1)) = addition(zero,multiplication(X2,domain(X1))),
inference(forward_demodulation,[status(thm)],[f44,f20092]) ).
fof(f20188,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),domain(X1)) = multiplication(X2,domain(X1)),
inference(forward_demodulation,[status(thm)],[f80,f20187]) ).
fof(f20189,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f20093]) ).
fof(f20190,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f80,f20094]) ).
fof(f20191,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(antidomain(X1),X2))) = addition(multiplication(antidomain(X1),addition(X2,domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f97,f20095]) ).
fof(f20192,plain,
! [X0,X1,X2] : addition(X0,multiplication(antidomain(X1),X2)) = addition(multiplication(antidomain(X1),addition(X2,domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f80,f20191]) ).
fof(f20193,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),X2) = addition(multiplication(antidomain(X0),addition(domain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f20096]) ).
fof(f20199,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f20099]) ).
fof(f20200,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f20100]) ).
fof(f20203,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(antidomain(X0)),domain(X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f696,f20103]) ).
fof(f20204,plain,
! [X0] : one = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1377,f20203]) ).
fof(f20209,plain,
! [X0,X1] :
( leq(domain(X0),addition(omega(antidomain(X0)),multiplication(star(antidomain(X0)),X1)))
| ~ leq(domain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f20105]) ).
fof(f20210,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f20106]) ).
fof(f20211,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f80,f20107]) ).
fof(f20212,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f20108]) ).
fof(f20213,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f80,f20109]) ).
fof(f20214,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f20110]) ).
fof(f20215,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f80,f20111]) ).
fof(f20216,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f20112]) ).
fof(f20221,plain,
! [X0] : zero = domain_difference(domain(X0),X0),
inference(paramodulation,[status(thm)],[f707,f18940]) ).
fof(f20229,plain,
! [X0,X1,X2] : domain_difference(X0,forward_diamond(X1,X2)) = domain_difference(X0,multiplication(X1,domain(X2))),
inference(paramodulation,[status(thm)],[f69,f18940]) ).
fof(f20265,plain,
! [X0,X1] : zero = domain_difference(forward_diamond(X0,X1),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f69,f20221]) ).
fof(f20287,plain,
! [X0] : addition(one,antidomain(multiplication(X0,domain(coantidomain(X0))))) = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f577,f489]) ).
fof(f20288,plain,
! [X0] : one = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1379,f20287]) ).
fof(f20289,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f39,f20288]) ).
fof(f20294,plain,
! [X0] : one = antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f66,f20288]) ).
fof(f20300,plain,
! [X0] : multiplication(one,domain(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(paramodulation,[status(thm)],[f20288,f18879]) ).
fof(f20306,plain,
! [X0,X1] : forward_box(X0,multiplication(X1,domain(coantidomain(X1)))) = antidomain(forward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f20288,f18885]) ).
fof(f20309,plain,
! [X0,X1] : backward_box(X0,multiplication(X1,domain(coantidomain(X1)))) = antidomain(backward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f20288,f18884]) ).
fof(f20310,plain,
! [X0,X1] :
( leq(multiplication(X0,star(multiplication(X1,domain(coantidomain(X1))))),antidomain(multiplication(X1,domain(coantidomain(X1)))))
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f20288,f344]) ).
fof(f20314,plain,
! [X0,X1] : leq(domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))),one),
inference(paramodulation,[status(thm)],[f20288,f6998]) ).
fof(f20317,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,domain(coantidomain(X1)))) = multiplication(X0,multiplication(X1,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f20288,f230]) ).
fof(f20319,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,domain(coantidomain(X1)))) = multiplication(X0,multiplication(X1,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f20288,f224]) ).
fof(f20323,plain,
! [X0,X1] : multiplication(one,addition(X0,multiplication(X1,domain(coantidomain(X1))))) = multiplication(antidomain(multiplication(X1,domain(coantidomain(X1)))),X0),
inference(paramodulation,[status(thm)],[f20288,f186]) ).
fof(f20325,plain,
! [X0,X1] : multiplication(one,addition(multiplication(X0,domain(coantidomain(X0))),X1)) = multiplication(antidomain(multiplication(X0,domain(coantidomain(X0)))),X1),
inference(paramodulation,[status(thm)],[f20288,f177]) ).
fof(f20326,plain,
! [X0] : multiplication(one,omega(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(paramodulation,[status(thm)],[f20288,f1569]) ).
fof(f20328,plain,
! [X0,X1] : multiplication(one,multiplication(multiplication(X0,domain(coantidomain(X0))),X1)) = zero,
inference(paramodulation,[status(thm)],[f20288,f136]) ).
fof(f20330,plain,
! [X0,X1] : domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f20288,f68]) ).
fof(f20333,plain,
! [X0] : multiplication(one,multiplication(X0,domain(coantidomain(X0)))) = zero,
inference(paramodulation,[status(thm)],[f20288,f59]) ).
fof(f20349,plain,
! [X0] : domain(multiplication(X0,domain(coantidomain(X0)))) = zero,
inference(forward_demodulation,[status(thm)],[f41,f20300]) ).
fof(f20350,plain,
! [X0] : forward_diamond(X0,coantidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f69,f20349]) ).
fof(f20358,plain,
! [X0,X1] : forward_box(X0,multiplication(X1,domain(coantidomain(X1)))) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f777,f20306]) ).
fof(f20359,plain,
! [X0,X1] : forward_box(X0,multiplication(X1,domain(coantidomain(X1)))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f18883,f20358]) ).
fof(f20363,plain,
! [X0,X1] : backward_box(X0,multiplication(X1,domain(coantidomain(X1)))) = antidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f810,f20309]) ).
fof(f20364,plain,
! [X0,X1] :
( leq(multiplication(X0,star(multiplication(X1,domain(coantidomain(X1))))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f20288,f20310]) ).
fof(f20375,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(antidomain(multiplication(X1,domain(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f41,f20323]) ).
fof(f20376,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(one,X0),
inference(forward_demodulation,[status(thm)],[f20288,f20375]) ).
fof(f20377,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f41,f20376]) ).
fof(f20378,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = multiplication(antidomain(multiplication(X0,domain(coantidomain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f41,f20325]) ).
fof(f20379,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = multiplication(one,X1),
inference(forward_demodulation,[status(thm)],[f20288,f20378]) ).
fof(f20380,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = X1,
inference(forward_demodulation,[status(thm)],[f41,f20379]) ).
fof(f20381,plain,
! [X0] : omega(multiplication(X0,domain(coantidomain(X0)))) = zero,
inference(forward_demodulation,[status(thm)],[f41,f20326]) ).
fof(f20382,plain,
! [X0,X1] : multiplication(multiplication(X0,domain(coantidomain(X0))),X1) = zero,
inference(forward_demodulation,[status(thm)],[f41,f20328]) ).
fof(f20383,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f20382]) ).
fof(f20384,plain,
! [X0,X1] : domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f40,f20330]) ).
fof(f20387,plain,
! [X0] : multiplication(X0,domain(coantidomain(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f41,f20333]) ).
fof(f20393,plain,
! [X0] : forward_diamond(coantidomain(X0),codomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f66,f20350]) ).
fof(f20443,plain,
forward_box(divergence(one),divergence(one)) = one,
inference(paramodulation,[status(thm)],[f19095,f18888]) ).
fof(f20446,plain,
leq(domain(divergence(one)),omega(divergence(one))),
inference(paramodulation,[status(thm)],[f19095,f16992]) ).
fof(f20447,plain,
leq(divergence(one),omega(domain(divergence(one)))),
inference(paramodulation,[status(thm)],[f19095,f16992]) ).
fof(f20448,plain,
leq(divergence(one),omega(divergence(one))),
inference(paramodulation,[status(thm)],[f19095,f16993]) ).
fof(f20452,plain,
domain(divergence(one)) = multiplication(divergence(one),domain(divergence(one))),
inference(paramodulation,[status(thm)],[f19095,f2215]) ).
fof(f20459,plain,
divergence(one) = multiplication(divergence(one),divergence(one)),
inference(paramodulation,[status(thm)],[f19095,f4146]) ).
fof(f20461,plain,
! [X0] : leq(domain_difference(divergence(one),X0),divergence(one)),
inference(paramodulation,[status(thm)],[f19095,f3834]) ).
fof(f20466,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),divergence(one))) != addition(forward_diamond(X1,domain(X0)),domain(divergence(one))) ),
inference(paramodulation,[status(thm)],[f19095,f75]) ).
fof(f20467,plain,
! [X0,X1] :
( addition(domain(divergence(one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(domain(divergence(one)),addition(forward_diamond(X0,divergence(one)),domain(X1))) != addition(forward_diamond(X0,domain(divergence(one))),domain(X1)) ),
inference(paramodulation,[status(thm)],[f19095,f75]) ).
fof(f20468,plain,
! [X0,X1] :
( addition(domain(divergence(one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(divergence(one),addition(forward_diamond(X0,domain(divergence(one))),domain(X1))) != addition(forward_diamond(X0,domain(divergence(one))),domain(X1)) ),
inference(paramodulation,[status(thm)],[f19095,f75]) ).
fof(f20469,plain,
! [X0] : forward_diamond(X0,divergence(one)) = domain(multiplication(X0,divergence(one))),
inference(paramodulation,[status(thm)],[f19095,f69]) ).
fof(f20470,plain,
! [X0] : domain_difference(divergence(one),X0) = multiplication(divergence(one),antidomain(X0)),
inference(paramodulation,[status(thm)],[f19095,f68]) ).
fof(f20471,plain,
addition(antidomain(divergence(one)),divergence(one)) = one,
inference(paramodulation,[status(thm)],[f19095,f558]) ).
fof(f20474,plain,
leq(divergence(one),omega(divergence(one))),
inference(forward_demodulation,[status(thm)],[f19095,f20446]) ).
fof(f20475,plain,
leq(divergence(one),omega(divergence(one))),
inference(forward_demodulation,[status(thm)],[f19095,f20447]) ).
fof(f20477,plain,
divergence(one) = multiplication(divergence(one),domain(divergence(one))),
inference(forward_demodulation,[status(thm)],[f19095,f20452]) ).
fof(f20478,plain,
divergence(one) = multiplication(divergence(one),divergence(one)),
inference(forward_demodulation,[status(thm)],[f19095,f20477]) ).
fof(f20481,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))
| addition(domain(X0),addition(divergence(one),forward_diamond(X1,domain(X0)))) != addition(forward_diamond(X1,domain(X0)),domain(divergence(one))) ),
inference(forward_demodulation,[status(thm)],[f35,f20466]) ).
fof(f20482,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))
| addition(domain(X0),addition(divergence(one),forward_diamond(X1,domain(X0)))) != addition(domain(divergence(one)),forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f20481]) ).
fof(f20483,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))) = addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))
| addition(domain(X0),addition(divergence(one),forward_diamond(X1,domain(X0)))) != addition(divergence(one),forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f19095,f20482]) ).
fof(f20484,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),divergence(one)))) = addition(divergence(X1),forward_diamond(star(X1),domain(divergence(one))))
| addition(domain(X0),addition(divergence(one),forward_diamond(X1,domain(X0)))) != addition(divergence(one),forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f19095,f20483]) ).
fof(f20485,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),divergence(one)))) = addition(divergence(X1),forward_diamond(star(X1),divergence(one)))
| addition(domain(X0),addition(divergence(one),forward_diamond(X1,domain(X0)))) != addition(divergence(one),forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f19095,f20484]) ).
fof(f20486,plain,
! [X0,X1] :
( addition(domain(divergence(one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(divergence(one),addition(forward_diamond(X0,divergence(one)),domain(X1))) != addition(forward_diamond(X0,domain(divergence(one))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f19095,f20467]) ).
fof(f20487,plain,
! [X0,X1] :
( addition(domain(divergence(one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(divergence(one),addition(forward_diamond(X0,divergence(one)),domain(X1))) != addition(forward_diamond(X0,divergence(one)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f19095,f20486]) ).
fof(f20488,plain,
! [X0,X1] :
( addition(divergence(one),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(divergence(one),addition(forward_diamond(X0,divergence(one)),domain(X1))) != addition(forward_diamond(X0,divergence(one)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f19095,f20487]) ).
fof(f20489,plain,
! [X0,X1] :
( addition(domain(divergence(one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(divergence(one),addition(forward_diamond(X0,divergence(one)),domain(X1))) != addition(forward_diamond(X0,domain(divergence(one))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f19095,f20468]) ).
fof(f20490,plain,
! [X0,X1] :
( addition(domain(divergence(one)),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(divergence(one),addition(forward_diamond(X0,divergence(one)),domain(X1))) != addition(forward_diamond(X0,divergence(one)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f19095,f20489]) ).
fof(f20491,plain,
! [X0,X1] :
( addition(divergence(one),addition(divergence(X0),forward_diamond(star(X0),domain(X1)))) = addition(divergence(X0),forward_diamond(star(X0),domain(X1)))
| addition(divergence(one),addition(forward_diamond(X0,divergence(one)),domain(X1))) != addition(forward_diamond(X0,divergence(one)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f19095,f20490]) ).
fof(f20492,plain,
addition(divergence(one),antidomain(divergence(one))) = one,
inference(forward_demodulation,[status(thm)],[f35,f20471]) ).
fof(f20495,plain,
forward_diamond(divergence(one),antidomain(divergence(one))) = zero,
inference(paramodulation,[status(thm)],[f19095,f19126]) ).
fof(f20500,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f13917,f19126]) ).
fof(f20501,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f13916,f19126]) ).
fof(f20503,plain,
! [X0,X1] : forward_diamond(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f69,f19126]) ).
fof(f20507,plain,
! [X0,X1] : forward_diamond(domain(forward_diamond(X0,antidomain(X1))),forward_box(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f18885,f19126]) ).
fof(f20508,plain,
! [X0,X1] : forward_diamond(domain(backward_diamond(X0,antidomain(X1))),backward_box(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f18884,f19126]) ).
fof(f20558,plain,
! [X0] : domain(divergence(X0)) = forward_diamond(X0,divergence(X0)),
inference(paramodulation,[status(thm)],[f73,f19262]) ).
fof(f20559,plain,
! [X0,X1] : forward_diamond(forward_diamond(X0,X1),antidomain(forward_diamond(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f19262,f19126]) ).
fof(f20566,plain,
! [X0,X1] : forward_box(forward_diamond(X0,X1),forward_diamond(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f19262,f18888]) ).
fof(f20569,plain,
! [X0,X1] : leq(domain(forward_diamond(X0,X1)),omega(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f19262,f16992]) ).
fof(f20570,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),omega(domain(forward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f19262,f16992]) ).
fof(f20571,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),omega(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f19262,f16993]) ).
fof(f20575,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = multiplication(forward_diamond(X0,X1),domain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f19262,f2215]) ).
fof(f20576,plain,
! [X0,X1] : leq(domain(forward_diamond(X0,X1)),codomain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f19262,f7000]) ).
fof(f20577,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(domain(forward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f19262,f7000]) ).
fof(f20579,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f19262,f4516]) ).
fof(f20582,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f19262,f4146]) ).
fof(f20584,plain,
! [X0,X1,X2] : leq(domain_difference(forward_diamond(X0,X1),X2),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f19262,f3834]) ).
fof(f20589,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(forward_diamond(X2,X3))))) = addition(divergence(X1),forward_diamond(star(X1),domain(forward_diamond(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3))) != addition(forward_diamond(X1,domain(X0)),domain(forward_diamond(X2,X3))) ),
inference(paramodulation,[status(thm)],[f19262,f75]) ).
fof(f20590,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_diamond(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(domain(forward_diamond(X0,X1)),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(forward_diamond(X0,X1))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f19262,f75]) ).
fof(f20591,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_diamond(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,domain(forward_diamond(X0,X1))),domain(X3))) != addition(forward_diamond(X2,domain(forward_diamond(X0,X1))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f19262,f75]) ).
fof(f20592,plain,
! [X0,X1,X2] : forward_diamond(X0,forward_diamond(X1,X2)) = domain(multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f19262,f69]) ).
fof(f20593,plain,
! [X0,X1,X2] : domain_difference(forward_diamond(X0,X1),X2) = multiplication(forward_diamond(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f19262,f68]) ).
fof(f20594,plain,
! [X0,X1] : addition(antidomain(forward_diamond(X0,X1)),forward_diamond(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f19262,f558]) ).
fof(f20605,plain,
! [X0] : domain(divergence(X0)) = divergence(X0),
inference(forward_demodulation,[status(thm)],[f73,f20558]) ).
fof(f20607,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),omega(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f19262,f20569]) ).
fof(f20608,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),omega(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f19262,f20570]) ).
fof(f20610,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),domain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f19262,f20575]) ).
fof(f20611,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),forward_diamond(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19262,f20610]) ).
fof(f20612,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f19262,f20576]) ).
fof(f20613,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f19262,f20577]) ).
fof(f20614,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(forward_diamond(X2,X3))))) = addition(divergence(X1),forward_diamond(star(X1),domain(forward_diamond(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20589]) ).
fof(f20615,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),domain(forward_diamond(X2,X3))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20614]) ).
fof(f20616,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3))) != addition(forward_diamond(X1,domain(X0)),forward_diamond(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20615]) ).
fof(f20617,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_diamond(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(forward_diamond(X0,X1))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20590]) ).
fof(f20618,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_diamond(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20617]) ).
fof(f20619,plain,
! [X0,X1,X2,X3] :
( addition(forward_diamond(X0,X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20618]) ).
fof(f20620,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_diamond(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,domain(forward_diamond(X0,X1))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20591]) ).
fof(f20621,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_diamond(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20620]) ).
fof(f20622,plain,
! [X0,X1,X2,X3] :
( addition(forward_diamond(X0,X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3)))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20621]) ).
fof(f20623,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),antidomain(forward_diamond(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f35,f20594]) ).
fof(f20628,plain,
! [X0] : forward_diamond(divergence(X0),antidomain(divergence(X0))) = zero,
inference(paramodulation,[status(thm)],[f20605,f19126]) ).
fof(f20635,plain,
! [X0] : forward_box(divergence(X0),divergence(X0)) = one,
inference(paramodulation,[status(thm)],[f20605,f18888]) ).
fof(f20638,plain,
! [X0] : leq(domain(divergence(X0)),omega(divergence(X0))),
inference(paramodulation,[status(thm)],[f20605,f16992]) ).
fof(f20644,plain,
! [X0] : domain(divergence(X0)) = multiplication(divergence(X0),domain(divergence(X0))),
inference(paramodulation,[status(thm)],[f20605,f2215]) ).
fof(f20651,plain,
! [X0] : divergence(X0) = multiplication(divergence(X0),divergence(X0)),
inference(paramodulation,[status(thm)],[f20605,f4146]) ).
fof(f20653,plain,
! [X0,X1] : leq(domain_difference(divergence(X0),X1),divergence(X0)),
inference(paramodulation,[status(thm)],[f20605,f3834]) ).
fof(f20658,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(divergence(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(divergence(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),divergence(X2))) != addition(forward_diamond(X1,domain(X0)),domain(divergence(X2))) ),
inference(paramodulation,[status(thm)],[f20605,f75]) ).
fof(f20659,plain,
! [X0,X1,X2] :
( addition(domain(divergence(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(divergence(X0)),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,domain(divergence(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f20605,f75]) ).
fof(f20660,plain,
! [X0,X1,X2] :
( addition(domain(divergence(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(divergence(X0),addition(forward_diamond(X1,domain(divergence(X0))),domain(X2))) != addition(forward_diamond(X1,domain(divergence(X0))),domain(X2)) ),
inference(paramodulation,[status(thm)],[f20605,f75]) ).
fof(f20661,plain,
! [X0,X1] : forward_diamond(X0,divergence(X1)) = domain(multiplication(X0,divergence(X1))),
inference(paramodulation,[status(thm)],[f20605,f69]) ).
fof(f20662,plain,
! [X0,X1] : domain_difference(divergence(X0),X1) = multiplication(divergence(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f20605,f68]) ).
fof(f20663,plain,
! [X0] : addition(antidomain(divergence(X0)),divergence(X0)) = one,
inference(paramodulation,[status(thm)],[f20605,f558]) ).
fof(f20667,plain,
! [X0] : leq(divergence(X0),omega(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f20605,f20638]) ).
fof(f20670,plain,
! [X0] : divergence(X0) = multiplication(divergence(X0),domain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f20605,f20644]) ).
fof(f20671,plain,
! [X0] : divergence(X0) = multiplication(divergence(X0),divergence(X0)),
inference(forward_demodulation,[status(thm)],[f20605,f20670]) ).
fof(f20674,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(divergence(X2))))) = addition(divergence(X1),forward_diamond(star(X1),domain(divergence(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),divergence(X2))) != addition(forward_diamond(X1,domain(X0)),divergence(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20658]) ).
fof(f20675,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),divergence(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(divergence(X2))))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),divergence(X2))) != addition(forward_diamond(X1,domain(X0)),divergence(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20674]) ).
fof(f20676,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),divergence(X2)))) = addition(divergence(X1),forward_diamond(star(X1),divergence(X2)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),divergence(X2))) != addition(forward_diamond(X1,domain(X0)),divergence(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20675]) ).
fof(f20677,plain,
! [X0,X1,X2] :
( addition(domain(divergence(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(divergence(X0),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,domain(divergence(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20659]) ).
fof(f20678,plain,
! [X0,X1,X2] :
( addition(domain(divergence(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(divergence(X0),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,divergence(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20677]) ).
fof(f20679,plain,
! [X0,X1,X2] :
( addition(divergence(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(divergence(X0),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,divergence(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20678]) ).
fof(f20680,plain,
! [X0,X1,X2] :
( addition(domain(divergence(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(divergence(X0),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,domain(divergence(X0))),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20660]) ).
fof(f20681,plain,
! [X0,X1,X2] :
( addition(domain(divergence(X0)),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(divergence(X0),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,divergence(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20680]) ).
fof(f20682,plain,
! [X0,X1,X2] :
( addition(divergence(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(divergence(X0),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,divergence(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20681]) ).
fof(f20683,plain,
! [X0] : addition(divergence(X0),antidomain(divergence(X0))) = one,
inference(forward_demodulation,[status(thm)],[f35,f20663]) ).
fof(f20686,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(X2)) ),
inference(backward_demodulation,[status(thm)],[f19280,f75]) ).
fof(f20694,plain,
! [X0,X1] : forward_diamond(X0,one) = forward_diamond(X0,addition(one,X1)),
inference(paramodulation,[status(thm)],[f15345,f19280]) ).
fof(f20695,plain,
! [X0,X1] : forward_diamond(X0,one) = forward_diamond(X0,addition(X1,one)),
inference(paramodulation,[status(thm)],[f15407,f19280]) ).
fof(f20699,plain,
! [X0,X1,X2] : forward_diamond(X0,forward_diamond(X1,X2)) = forward_diamond(X0,multiplication(X1,domain(X2))),
inference(paramodulation,[status(thm)],[f69,f19280]) ).
fof(f20714,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(domain(X0),addition(forward_diamond(X1,X0),domain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f19280,f20686]) ).
fof(f20715,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(domain(X0),addition(forward_diamond(X1,X0),domain(X2))) != addition(forward_diamond(X1,X0),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f19280,f20714]) ).
fof(f20716,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),X2))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(domain(X0),addition(forward_diamond(X1,X0),domain(X2))) != addition(forward_diamond(X1,X0),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f19280,f20715]) ).
fof(f20719,plain,
! [X0,X1] : domain(X0) = forward_diamond(X0,addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f777,f20694]) ).
fof(f20720,plain,
! [X0,X1] : domain(X0) = forward_diamond(X0,addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f777,f20695]) ).
fof(f20737,plain,
! [X0,X1] : domain_difference(one,X0) = domain_difference(addition(one,X1),X0),
inference(paramodulation,[status(thm)],[f15345,f19281]) ).
fof(f20738,plain,
! [X0,X1] : domain_difference(one,X0) = domain_difference(addition(X1,one),X0),
inference(paramodulation,[status(thm)],[f15407,f19281]) ).
fof(f20742,plain,
! [X0,X1,X2] : domain_difference(forward_diamond(X0,X1),X2) = domain_difference(multiplication(X0,domain(X1)),X2),
inference(paramodulation,[status(thm)],[f69,f19281]) ).
fof(f20757,plain,
! [X0,X1] : antidomain(X0) = domain_difference(addition(one,X1),X0),
inference(forward_demodulation,[status(thm)],[f727,f20737]) ).
fof(f20758,plain,
! [X0,X1] : antidomain(X0) = domain_difference(addition(X1,one),X0),
inference(forward_demodulation,[status(thm)],[f727,f20738]) ).
fof(f20764,plain,
! [X0,X1] : addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0)),
inference(resolution,[status(thm)],[f20716,f1005]) ).
fof(f20765,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),forward_diamond(X1,X0)) != addition(forward_diamond(X1,X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f1329,f20716]) ).
fof(f20766,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(forward_diamond(X0,X1),domain(X1)) != addition(forward_diamond(X0,X1),domain(X1)) ),
inference(paramodulation,[status(thm)],[f1005,f20716]) ).
fof(f20767,plain,
! [X0,X1,X2] :
( addition(domain(X1),addition(divergence(X2),forward_diamond(star(X2),X0))) = addition(divergence(X2),forward_diamond(star(X2),X0))
| addition(domain(X0),addition(domain(X1),forward_diamond(X2,X1))) != addition(forward_diamond(X2,X1),domain(X0)) ),
inference(paramodulation,[status(thm)],[f97,f20716]) ).
fof(f20768,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_diamond(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),X3))) = addition(divergence(X2),forward_diamond(star(X2),X3))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(paramodulation,[status(thm)],[f19262,f20716]) ).
fof(f20769,plain,
! [X0,X1,X2] :
( addition(domain(divergence(X0)),addition(divergence(X1),forward_diamond(star(X1),X2))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(divergence(X0),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,divergence(X0)),domain(X2)) ),
inference(paramodulation,[status(thm)],[f20605,f20716]) ).
fof(f20771,plain,
! [X0,X1,X2] :
( addition(domain(antidomain(X0)),addition(divergence(X1),forward_diamond(star(X1),X2))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(antidomain(X0),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,antidomain(X0)),domain(X2)) ),
inference(paramodulation,[status(thm)],[f18890,f20716]) ).
fof(f20772,plain,
! [X0,X1,X2] :
( addition(domain(addition(one,X1)),addition(divergence(X0),forward_diamond(star(X0),X2))) = addition(divergence(X0),forward_diamond(star(X0),X2))
| addition(one,addition(forward_diamond(X0,addition(one,X1)),domain(X2))) != addition(forward_diamond(X0,addition(one,X1)),domain(X2)) ),
inference(paramodulation,[status(thm)],[f15345,f20716]) ).
fof(f20773,plain,
! [X0,X1,X2] :
( addition(domain(addition(X1,one)),addition(divergence(X0),forward_diamond(star(X0),X2))) = addition(divergence(X0),forward_diamond(star(X0),X2))
| addition(one,addition(forward_diamond(X0,addition(X1,one)),domain(X2))) != addition(forward_diamond(X0,addition(X1,one)),domain(X2)) ),
inference(paramodulation,[status(thm)],[f15407,f20716]) ).
fof(f20774,plain,
! [X0,X1,X2,X3] :
( addition(domain(forward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),X3))) = addition(divergence(X2),forward_diamond(star(X2),X3))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3)) ),
inference(paramodulation,[status(thm)],[f13917,f20716]) ).
fof(f20775,plain,
! [X0,X1,X2,X3] :
( addition(domain(backward_box(X0,X1)),addition(divergence(X2),forward_diamond(star(X2),X3))) = addition(divergence(X2),forward_diamond(star(X2),X3))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3)) ),
inference(paramodulation,[status(thm)],[f13916,f20716]) ).
fof(f20776,plain,
! [X0,X1,X2] :
( addition(domain(star(X1)),addition(divergence(X0),forward_diamond(star(X0),X2))) = addition(divergence(X0),forward_diamond(star(X0),X2))
| addition(one,addition(forward_diamond(X0,star(X1)),domain(X2))) != addition(forward_diamond(X0,star(X1)),domain(X2)) ),
inference(paramodulation,[status(thm)],[f8543,f20716]) ).
fof(f20777,plain,
! [X0,X1,X2,X3] :
( addition(domain(multiplication(X0,domain(X1))),addition(divergence(X2),forward_diamond(star(X2),X3))) = addition(divergence(X2),forward_diamond(star(X2),X3))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,multiplication(X0,domain(X1))),domain(X3))) != addition(forward_diamond(X2,multiplication(X0,domain(X1))),domain(X3)) ),
inference(paramodulation,[status(thm)],[f69,f20716]) ).
fof(f20779,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(forward_diamond(X0,one),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(paramodulation,[status(thm)],[f570,f20716]) ).
fof(f20780,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X2),forward_diamond(star(X2),X1))) = addition(divergence(X2),forward_diamond(star(X2),X1))
| addition(domain(X0),addition(domain(X1),forward_diamond(X2,X0))) != addition(forward_diamond(X2,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f35,f20716]) ).
fof(f20781,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X2),forward_diamond(star(X2),X1))) = addition(divergence(X2),forward_diamond(star(X2),X1))
| addition(domain(X0),addition(domain(X1),forward_diamond(X2,X0))) != addition(forward_diamond(X2,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f35,f20716]) ).
fof(f20782,plain,
! [X0,X1] :
( addition(domain(antidomain(X0)),addition(divergence(domain(X0)),forward_diamond(star(domain(X0)),X1))) = addition(divergence(domain(X0)),forward_diamond(star(domain(X0)),X1))
| addition(domain(antidomain(X0)),addition(zero,domain(X1))) != addition(forward_diamond(domain(X0),antidomain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f19126,f20716]) ).
fof(f20783,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(antidomain(X0)),forward_diamond(star(antidomain(X0)),X1))) = addition(divergence(antidomain(X0)),forward_diamond(star(antidomain(X0)),X1))
| addition(domain(X0),addition(zero,domain(X1))) != addition(forward_diamond(antidomain(X0),X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f18878,f20716]) ).
fof(f20784,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(one),forward_diamond(star(one),X1))) = addition(divergence(one),forward_diamond(star(one),X1))
| addition(domain(X0),addition(domain(X0),domain(X1))) != addition(forward_diamond(one,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f18896,f20716]) ).
fof(f20787,plain,
! [X0,X1] :
( addition(domain(coantidomain(X0)),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(domain(coantidomain(X0)),addition(zero,domain(X1))) != addition(forward_diamond(X0,coantidomain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f20350,f20716]) ).
fof(f20788,plain,
! [X0,X1,X2] :
( addition(domain(star(X0)),addition(divergence(X1),forward_diamond(star(X1),X2))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(domain(star(X0)),addition(domain(X1),domain(X2))) != addition(forward_diamond(X1,star(X0)),domain(X2)) ),
inference(paramodulation,[status(thm)],[f8733,f20716]) ).
fof(f20789,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(domain(one),addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(paramodulation,[status(thm)],[f777,f20716]) ).
fof(f20792,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,X0),forward_diamond(X2,X3))) != addition(forward_diamond(X1,X0),domain(forward_diamond(X2,X3))) ),
inference(paramodulation,[status(thm)],[f19262,f20716]) ).
fof(f20793,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),divergence(X2)))) = addition(divergence(X1),forward_diamond(star(X1),divergence(X2)))
| addition(domain(X0),addition(forward_diamond(X1,X0),divergence(X2))) != addition(forward_diamond(X1,X0),domain(divergence(X2))) ),
inference(paramodulation,[status(thm)],[f20605,f20716]) ).
fof(f20795,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),antidomain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),antidomain(X2)))
| addition(domain(X0),addition(forward_diamond(X1,X0),antidomain(X2))) != addition(forward_diamond(X1,X0),domain(antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f18890,f20716]) ).
fof(f20796,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))) = addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))
| addition(domain(X0),addition(forward_diamond(X1,X0),one)) != addition(forward_diamond(X1,X0),domain(addition(one,X2))) ),
inference(paramodulation,[status(thm)],[f15345,f20716]) ).
fof(f20797,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))) = addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))
| addition(domain(X0),addition(forward_diamond(X1,X0),one)) != addition(forward_diamond(X1,X0),domain(addition(X2,one))) ),
inference(paramodulation,[status(thm)],[f15407,f20716]) ).
fof(f20798,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_box(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),forward_box(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,X0),forward_box(X2,X3))) != addition(forward_diamond(X1,X0),domain(forward_box(X2,X3))) ),
inference(paramodulation,[status(thm)],[f13917,f20716]) ).
fof(f20799,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),backward_box(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),backward_box(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,X0),backward_box(X2,X3))) != addition(forward_diamond(X1,X0),domain(backward_box(X2,X3))) ),
inference(paramodulation,[status(thm)],[f13916,f20716]) ).
fof(f20800,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),star(X2)))) = addition(divergence(X1),forward_diamond(star(X1),star(X2)))
| addition(domain(X0),addition(forward_diamond(X1,X0),one)) != addition(forward_diamond(X1,X0),domain(star(X2))) ),
inference(paramodulation,[status(thm)],[f8543,f20716]) ).
fof(f20801,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),multiplication(X2,domain(X3))))) = addition(divergence(X1),forward_diamond(star(X1),multiplication(X2,domain(X3))))
| addition(domain(X0),addition(forward_diamond(X1,X0),forward_diamond(X2,X3))) != addition(forward_diamond(X1,X0),domain(multiplication(X2,domain(X3)))) ),
inference(paramodulation,[status(thm)],[f69,f20716]) ).
fof(f20802,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),zero))) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),addition(forward_diamond(X1,X0),zero)) != addition(forward_diamond(X1,X0),domain(zero)) ),
inference(paramodulation,[status(thm)],[f607,f20716]) ).
fof(f20803,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(domain(X0),addition(forward_diamond(X1,X0),one)) != addition(forward_diamond(X1,X0),domain(one)) ),
inference(paramodulation,[status(thm)],[f570,f20716]) ).
fof(f20804,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),forward_diamond(X1,X0)) != addition(domain(X0),forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f20765]) ).
fof(f20805,plain,
! [X0,X1] : addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0)),
inference(trivial_equality_resolution,[status(thm)],[f20804]) ).
fof(f20806,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),forward_diamond(X1,X0)) != addition(forward_diamond(X1,X0),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f20766]) ).
fof(f20807,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),forward_diamond(X1,X0)) != addition(domain(X0),forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f20806]) ).
fof(f20808,plain,
! [X0,X1] : addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0)),
inference(trivial_equality_resolution,[status(thm)],[f20807]) ).
fof(f20809,plain,
! [X0,X1,X2,X3] :
( addition(forward_diamond(X0,X1),addition(divergence(X2),forward_diamond(star(X2),X3))) = addition(divergence(X2),forward_diamond(star(X2),X3))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_diamond(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20768]) ).
fof(f20810,plain,
! [X0,X1,X2] :
( addition(divergence(X0),addition(divergence(X1),forward_diamond(star(X1),X2))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(divergence(X0),addition(forward_diamond(X1,divergence(X0)),domain(X2))) != addition(forward_diamond(X1,divergence(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20769]) ).
fof(f20814,plain,
! [X0,X1,X2] :
( addition(antidomain(X0),addition(divergence(X1),forward_diamond(star(X1),X2))) = addition(divergence(X1),forward_diamond(star(X1),X2))
| addition(antidomain(X0),addition(forward_diamond(X1,antidomain(X0)),domain(X2))) != addition(forward_diamond(X1,antidomain(X0)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f20771]) ).
fof(f20815,plain,
! [X0,X1,X2] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),X2))) = addition(divergence(X0),forward_diamond(star(X0),X2))
| addition(one,addition(forward_diamond(X0,addition(one,X1)),domain(X2))) != addition(forward_diamond(X0,addition(one,X1)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f15345,f20772]) ).
fof(f20816,plain,
! [X0,X1,X2] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),X2))) = addition(divergence(X0),forward_diamond(star(X0),X2))
| addition(one,addition(forward_diamond(X0,addition(X1,one)),domain(X2))) != addition(forward_diamond(X0,addition(X1,one)),domain(X2)) ),
inference(forward_demodulation,[status(thm)],[f15407,f20773]) ).
fof(f20817,plain,
! [X0,X1,X2,X3] :
( addition(forward_box(X0,X1),addition(divergence(X2),forward_diamond(star(X2),X3))) = addition(divergence(X2),forward_diamond(star(X2),X3))
| addition(forward_box(X0,X1),addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,forward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f20774]) ).
fof(f20818,plain,
! [X0,X1,X2,X3] :
( addition(backward_box(X0,X1),addition(divergence(X2),forward_diamond(star(X2),X3))) = addition(divergence(X2),forward_diamond(star(X2),X3))
| addition(backward_box(X0,X1),addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3))) != addition(forward_diamond(X2,backward_box(X0,X1)),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f20775]) ).
fof(f20819,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,star(X2)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8733,f20776]) ).
fof(f20820,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8733,f20819]) ).
fof(f20821,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f20820]) ).
fof(f20822,plain,
! [X0,X1,X2,X3] :
( addition(forward_diamond(X0,X1),addition(divergence(X2),forward_diamond(star(X2),X3))) = addition(divergence(X2),forward_diamond(star(X2),X3))
| addition(forward_diamond(X0,X1),addition(forward_diamond(X2,multiplication(X0,domain(X1))),domain(X3))) != addition(forward_diamond(X2,multiplication(X0,domain(X1))),domain(X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f20777]) ).
fof(f20829,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f20779]) ).
fof(f20830,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f20829]) ).
fof(f20831,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f20830]) ).
fof(f20832,plain,
! [X0,X1] :
( addition(domain(antidomain(X1)),addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))) = addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))
| addition(zero,addition(domain(X0),domain(antidomain(X1)))) != addition(forward_diamond(domain(X1),antidomain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f20782]) ).
fof(f20833,plain,
! [X0,X1] :
( addition(domain(antidomain(X1)),addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))) = addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))
| addition(domain(X0),domain(antidomain(X1))) != addition(forward_diamond(domain(X1),antidomain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f20832]) ).
fof(f20834,plain,
! [X0,X1] :
( addition(domain(antidomain(X1)),addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))) = addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))
| addition(domain(X0),antidomain(X1)) != addition(forward_diamond(domain(X1),antidomain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f18890,f20833]) ).
fof(f20835,plain,
! [X0,X1] :
( addition(domain(antidomain(X1)),addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))) = addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))
| addition(domain(X0),antidomain(X1)) != addition(zero,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f19126,f20834]) ).
fof(f20836,plain,
! [X0,X1] :
( addition(domain(antidomain(X1)),addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))) = addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))
| addition(domain(X0),antidomain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f80,f20835]) ).
fof(f20837,plain,
! [X0,X1] :
( addition(antidomain(X1),addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))) = addition(divergence(domain(X1)),forward_diamond(star(domain(X1)),X0))
| addition(domain(X0),antidomain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f18890,f20836]) ).
fof(f20838,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),X0))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),X0))
| addition(zero,addition(domain(X0),domain(X1))) != addition(forward_diamond(antidomain(X1),X1),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f20783]) ).
fof(f20839,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),X0))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),X0))
| addition(domain(X0),domain(X1)) != addition(forward_diamond(antidomain(X1),X1),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f20838]) ).
fof(f20840,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),X0))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),X0))
| addition(domain(X0),domain(X1)) != addition(zero,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f18878,f20839]) ).
fof(f20841,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),X0))) = addition(divergence(antidomain(X1)),forward_diamond(star(antidomain(X1)),X0))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f80,f20840]) ).
fof(f20842,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(one),forward_diamond(star(one),X0))) = addition(divergence(one),forward_diamond(star(one),X0))
| addition(domain(X0),domain(X1)) != addition(forward_diamond(one,X1),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f1026,f20784]) ).
fof(f20843,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(one),forward_diamond(star(one),X0))) = addition(divergence(one),forward_diamond(star(one),X0))
| addition(domain(X0),domain(X1)) != addition(domain(X1),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f18896,f20842]) ).
fof(f20844,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(one),forward_diamond(one,X0))) = addition(divergence(one),forward_diamond(star(one),X0))
| addition(domain(X0),domain(X1)) != addition(domain(X1),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f9603,f20843]) ).
fof(f20845,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(one),domain(X0))) = addition(divergence(one),forward_diamond(star(one),X0))
| addition(domain(X0),domain(X1)) != addition(domain(X1),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f18896,f20844]) ).
fof(f20846,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(one),domain(X0))) = addition(divergence(one),forward_diamond(one,X0))
| addition(domain(X0),domain(X1)) != addition(domain(X1),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f9603,f20845]) ).
fof(f20847,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(one),domain(X0))) = addition(divergence(one),domain(X0))
| addition(domain(X0),domain(X1)) != addition(domain(X1),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f18896,f20846]) ).
fof(f20848,plain,
! [X0,X1] : addition(domain(X0),addition(divergence(one),domain(X1))) = addition(divergence(one),domain(X1)),
inference(forward_subsumption_resolution,[status(thm)],[f20847,f35]) ).
fof(f20864,plain,
! [X0,X1] :
( addition(domain(coantidomain(X1)),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(zero,addition(domain(X0),domain(coantidomain(X1)))) != addition(forward_diamond(X1,coantidomain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f20787]) ).
fof(f20865,plain,
! [X0,X1] :
( addition(domain(coantidomain(X1)),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),domain(coantidomain(X1))) != addition(forward_diamond(X1,coantidomain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f20864]) ).
fof(f20866,plain,
! [X0,X1] :
( addition(domain(coantidomain(X1)),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),domain(coantidomain(X1))) != addition(zero,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f20350,f20865]) ).
fof(f20867,plain,
! [X0,X1] :
( addition(domain(coantidomain(X1)),addition(divergence(X1),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),domain(coantidomain(X1))) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f80,f20866]) ).
fof(f20868,plain,
! [X0,X1] :
( addition(divergence(X1),addition(forward_diamond(star(X1),X0),domain(coantidomain(X1)))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),domain(coantidomain(X1))) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f97,f20867]) ).
fof(f20869,plain,
! [X0,X1] :
( addition(divergence(X1),addition(domain(coantidomain(X1)),forward_diamond(star(X1),X0))) = addition(divergence(X1),forward_diamond(star(X1),X0))
| addition(domain(X0),domain(coantidomain(X1))) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f35,f20868]) ).
fof(f20870,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,star(X2)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f20788]) ).
fof(f20871,plain,
! [X0,X1,X2] :
( addition(domain(star(X2)),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8733,f20870]) ).
fof(f20872,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f8543,f20871]) ).
fof(f20873,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f20789]) ).
fof(f20874,plain,
! [X0,X1] :
( addition(domain(one),addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f777,f20873]) ).
fof(f20875,plain,
! [X0,X1] :
( addition(one,addition(divergence(X0),forward_diamond(star(X0),X1))) = addition(divergence(X0),forward_diamond(star(X0),X1))
| addition(one,addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f570,f20874]) ).
fof(f20891,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),forward_diamond(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,X0),forward_diamond(X2,X3))) != addition(forward_diamond(X1,X0),forward_diamond(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f19262,f20792]) ).
fof(f20892,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),divergence(X2)))) = addition(divergence(X1),forward_diamond(star(X1),divergence(X2)))
| addition(domain(X0),addition(forward_diamond(X1,X0),divergence(X2))) != addition(forward_diamond(X1,X0),divergence(X2)) ),
inference(forward_demodulation,[status(thm)],[f20605,f20793]) ).
fof(f20896,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),antidomain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),antidomain(X2)))
| addition(domain(X0),addition(forward_diamond(X1,X0),antidomain(X2))) != addition(forward_diamond(X1,X0),antidomain(X2)) ),
inference(forward_demodulation,[status(thm)],[f18890,f20795]) ).
fof(f20897,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))) = addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(forward_diamond(X1,X0),domain(addition(one,X2))) ),
inference(forward_demodulation,[status(thm)],[f97,f20796]) ).
fof(f20898,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))) = addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(forward_diamond(X1,X0),one) ),
inference(forward_demodulation,[status(thm)],[f15345,f20897]) ).
fof(f20899,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))) = addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(one,forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f20898]) ).
fof(f20900,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))) = addition(divergence(X1),forward_diamond(star(X1),addition(one,X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f1485,f20899]) ).
fof(f20901,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))) = addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(forward_diamond(X1,X0),domain(addition(X2,one))) ),
inference(forward_demodulation,[status(thm)],[f97,f20797]) ).
fof(f20902,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))) = addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(forward_diamond(X1,X0),one) ),
inference(forward_demodulation,[status(thm)],[f15407,f20901]) ).
fof(f20903,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))) = addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(one,forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f20902]) ).
fof(f20904,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))) = addition(divergence(X1),forward_diamond(star(X1),addition(X2,one)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f1485,f20903]) ).
fof(f20905,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),forward_box(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),forward_box(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,X0),forward_box(X2,X3))) != addition(forward_diamond(X1,X0),forward_box(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f13917,f20798]) ).
fof(f20906,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),backward_box(X2,X3)))) = addition(divergence(X1),forward_diamond(star(X1),backward_box(X2,X3)))
| addition(domain(X0),addition(forward_diamond(X1,X0),backward_box(X2,X3))) != addition(forward_diamond(X1,X0),backward_box(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f13916,f20799]) ).
fof(f20907,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),star(X2)))) = addition(divergence(X1),forward_diamond(star(X1),star(X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(forward_diamond(X1,X0),domain(star(X2))) ),
inference(forward_demodulation,[status(thm)],[f97,f20800]) ).
fof(f20908,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),star(X2)))) = addition(divergence(X1),forward_diamond(star(X1),star(X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(forward_diamond(X1,X0),one) ),
inference(forward_demodulation,[status(thm)],[f8543,f20907]) ).
fof(f20909,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),star(X2)))) = addition(divergence(X1),forward_diamond(star(X1),star(X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(one,forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f20908]) ).
fof(f20910,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),star(X2)))) = addition(divergence(X1),forward_diamond(star(X1),star(X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f1485,f20909]) ).
fof(f20911,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),domain(star(X1)))) = addition(divergence(X1),forward_diamond(star(X1),star(X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f8733,f20910]) ).
fof(f20912,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),one)) = addition(divergence(X1),forward_diamond(star(X1),star(X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f20911]) ).
fof(f20913,plain,
! [X0,X1,X2] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),star(X2)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f97,f20912]) ).
fof(f20914,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),domain(star(X1)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f8733,f20913]) ).
fof(f20915,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),one)
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f20914]) ).
fof(f20916,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(one,divergence(X1))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f35,f20915]) ).
fof(f20917,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = one
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f1488,f20916]) ).
fof(f20918,plain,
! [X0,X1,X2,X3] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),multiplication(X2,domain(X3))))) = addition(divergence(X1),forward_diamond(star(X1),multiplication(X2,domain(X3))))
| addition(domain(X0),addition(forward_diamond(X1,X0),forward_diamond(X2,X3))) != addition(forward_diamond(X1,X0),forward_diamond(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f69,f20801]) ).
fof(f20919,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),zero))) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(zero,addition(domain(X0),forward_diamond(X1,X0))) != addition(forward_diamond(X1,X0),domain(zero)) ),
inference(forward_demodulation,[status(thm)],[f97,f20802]) ).
fof(f20920,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),zero))) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),forward_diamond(X1,X0)) != addition(forward_diamond(X1,X0),domain(zero)) ),
inference(forward_demodulation,[status(thm)],[f80,f20919]) ).
fof(f20921,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),zero))) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),forward_diamond(X1,X0)) != addition(domain(zero),forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f20920]) ).
fof(f20922,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),zero))) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),forward_diamond(X1,X0)) != addition(zero,forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f607,f20921]) ).
fof(f20923,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),zero))) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),forward_diamond(X1,X0)) != forward_diamond(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f80,f20922]) ).
fof(f20924,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),zero)) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),forward_diamond(X1,X0)) != forward_diamond(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f776,f20923]) ).
fof(f20925,plain,
! [X0,X1] :
( addition(zero,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),forward_diamond(X1,X0)) != forward_diamond(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f97,f20924]) ).
fof(f20926,plain,
! [X0,X1] :
( addition(domain(X0),divergence(X1)) = addition(divergence(X1),forward_diamond(star(X1),zero))
| addition(domain(X0),forward_diamond(X1,X0)) != forward_diamond(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f80,f20925]) ).
fof(f20927,plain,
! [X0,X1] :
( addition(domain(X0),divergence(X1)) = addition(divergence(X1),zero)
| addition(domain(X0),forward_diamond(X1,X0)) != forward_diamond(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f776,f20926]) ).
fof(f20928,plain,
! [X0,X1] :
( addition(domain(X0),divergence(X1)) = divergence(X1)
| addition(domain(X0),forward_diamond(X1,X0)) != forward_diamond(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f37,f20927]) ).
fof(f20929,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(forward_diamond(X1,X0),domain(one)) ),
inference(forward_demodulation,[status(thm)],[f97,f20803]) ).
fof(f20930,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(domain(one),forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f20929]) ).
fof(f20931,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != addition(one,forward_diamond(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f570,f20930]) ).
fof(f20932,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),one))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f1485,f20931]) ).
fof(f20933,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),domain(star(X1)))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f777,f20932]) ).
fof(f20934,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),one)) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f20933]) ).
fof(f20935,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),forward_diamond(star(X1),one))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f97,f20934]) ).
fof(f20936,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),domain(star(X1)))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f777,f20935]) ).
fof(f20937,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(divergence(X1),one)
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f8543,f20936]) ).
fof(f20938,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = addition(one,divergence(X1))
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f35,f20937]) ).
fof(f20939,plain,
! [X0,X1] :
( addition(one,addition(domain(X0),divergence(X1))) = one
| addition(one,addition(domain(X0),forward_diamond(X1,X0))) != one ),
inference(forward_demodulation,[status(thm)],[f1488,f20938]) ).
fof(f20942,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f39,f20387]) ).
fof(f20947,plain,
! [X0] : multiplication(coantidomain(X0),domain(codomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f66,f20387]) ).
fof(f20956,plain,
! [X0,X1] :
( leq(domain(coantidomain(addition(X0,X1))),addition(omega(X0),multiplication(star(X0),multiplication(X1,domain(coantidomain(addition(X0,X1)))))))
| ~ leq(domain(coantidomain(addition(X0,X1))),zero) ),
inference(paramodulation,[status(thm)],[f20387,f391]) ).
fof(f20957,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(domain(coantidomain(addition(X0,X1))),star(domain(coantidomain(addition(X0,X1)))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f20387,f340]) ).
fof(f20958,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,domain(coantidomain(addition(X0,X1))))),domain(coantidomain(addition(X0,X1))))
| ~ leq(zero,domain(coantidomain(addition(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f20387,f290]) ).
fof(f20959,plain,
! [X0,X1] :
( zero != multiplication(X1,domain(coantidomain(addition(X0,X1))))
| leq(multiplication(X0,domain(coantidomain(addition(X0,X1)))),multiplication(X1,domain(coantidomain(addition(X0,X1))))) ),
inference(paramodulation,[status(thm)],[f20387,f241]) ).
fof(f20962,plain,
! [X0] : backward_diamond(domain(coantidomain(codomain(X0))),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f20387,f70]) ).
fof(f20970,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f20387,f39]) ).
fof(f20983,plain,
! [X0,X1,X2] :
( leq(domain(coantidomain(X0)),addition(omega(multiplication(X1,X0)),multiplication(star(multiplication(X1,X0)),X2)))
| ~ leq(domain(coantidomain(X0)),addition(multiplication(X1,zero),X2)) ),
inference(paramodulation,[status(thm)],[f20387,f398]) ).
fof(f20984,plain,
! [X0] :
( leq(domain(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),multiplication(X0,domain(coantidomain(X0))))))
| ~ leq(domain(coantidomain(X0)),zero) ),
inference(paramodulation,[status(thm)],[f20387,f396]) ).
fof(f20985,plain,
! [X0,X1] :
( leq(domain(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(domain(coantidomain(X0)),addition(X1,zero)) ),
inference(paramodulation,[status(thm)],[f20387,f394]) ).
fof(f20986,plain,
! [X0] :
( leq(domain(coantidomain(X0)),omega(X0))
| ~ leq(domain(coantidomain(X0)),zero) ),
inference(paramodulation,[status(thm)],[f20387,f407]) ).
fof(f20987,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),multiplication(X0,domain(coantidomain(X0))))
| ~ leq(addition(multiplication(X0,multiplication(domain(coantidomain(X0)),X1)),X2),zero) ),
inference(paramodulation,[status(thm)],[f20387,f332]) ).
fof(f20988,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(domain(coantidomain(X2)))),multiplication(X0,X2))
| ~ leq(addition(multiplication(X0,zero),X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f20387,f332]) ).
fof(f20989,plain,
! [X0] :
( leq(multiplication(X0,multiplication(domain(coantidomain(X0)),star(domain(coantidomain(X0))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f20387,f343]) ).
fof(f20990,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(coantidomain(X1)))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f20387,f329]) ).
fof(f20992,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X2)),X1),domain(coantidomain(X2)))
| ~ leq(addition(multiplication(X0,zero),X1),domain(coantidomain(X2))) ),
inference(paramodulation,[status(thm)],[f20387,f296]) ).
fof(f20994,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),domain(coantidomain(X1)))
| ~ leq(addition(X0,zero),domain(coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f20387,f293]) ).
fof(f20997,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(coantidomain(X1))),addition(zero,X2)) = addition(multiplication(addition(X0,X1),domain(coantidomain(X1))),X2),
inference(paramodulation,[status(thm)],[f20387,f219]) ).
fof(f20998,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,domain(coantidomain(X1))),X2)) = addition(multiplication(addition(X1,X0),domain(coantidomain(X1))),X2),
inference(paramodulation,[status(thm)],[f20387,f219]) ).
fof(f20999,plain,
! [X0] : multiplication(addition(X0,one),domain(coantidomain(X0))) = addition(domain(coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f20387,f232]) ).
fof(f21000,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),domain(coantidomain(X2))) = addition(multiplication(X0,domain(coantidomain(X2))),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f20387,f211]) ).
fof(f21001,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),domain(coantidomain(X0))) = addition(zero,multiplication(X1,multiplication(X2,domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f20387,f211]) ).
fof(f21002,plain,
! [X0] : multiplication(addition(one,X0),domain(coantidomain(X0))) = addition(domain(coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f20387,f207]) ).
fof(f21003,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),domain(coantidomain(X2))) = addition(multiplication(X0,multiplication(X1,domain(coantidomain(X2)))),zero),
inference(paramodulation,[status(thm)],[f20387,f204]) ).
fof(f21004,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),domain(coantidomain(X1))) = addition(multiplication(X0,zero),multiplication(X2,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f20387,f204]) ).
fof(f21005,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = addition(multiplication(X1,domain(coantidomain(X0))),zero),
inference(paramodulation,[status(thm)],[f20387,f201]) ).
fof(f21006,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = addition(zero,multiplication(X0,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f20387,f201]) ).
fof(f21007,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(X0,addition(X1,domain(coantidomain(X0)))),X2),
inference(paramodulation,[status(thm)],[f20387,f170]) ).
fof(f21008,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(domain(coantidomain(X0)),X1)),X2),
inference(paramodulation,[status(thm)],[f20387,f170]) ).
fof(f21011,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f20387,f153]) ).
fof(f21012,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f20387,f153]) ).
fof(f21015,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),domain(coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f20387,f615]) ).
fof(f21017,plain,
! [X0,X1] :
( leq(domain(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(domain(coantidomain(X0)),addition(zero,X1)) ),
inference(paramodulation,[status(thm)],[f20387,f58]) ).
fof(f21018,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(coantidomain(X1)))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f20387,f55]) ).
fof(f21019,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),domain(coantidomain(X1)))
| ~ leq(addition(zero,X0),domain(coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f20387,f53]) ).
fof(f21020,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = addition(multiplication(X0,domain(coantidomain(X1))),zero),
inference(paramodulation,[status(thm)],[f20387,f43]) ).
fof(f21021,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = addition(zero,multiplication(X1,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f20387,f43]) ).
fof(f21022,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f20387,f42]) ).
fof(f21023,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f20387,f42]) ).
fof(f21024,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f20387,f39]) ).
fof(f21030,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(domain(coantidomain(addition(X1,X0))),star(domain(coantidomain(addition(X1,X0)))))),X1),
inference(forward_subsumption_resolution,[status(thm)],[f20957,f240]) ).
fof(f21031,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(X1,domain(coantidomain(addition(X0,X1))))),domain(coantidomain(addition(X0,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[f20958,f240]) ).
fof(f21032,plain,
! [X0] : backward_diamond(domain(coantidomain(codomain(X0))),X0) = zero,
inference(forward_demodulation,[status(thm)],[f737,f20962]) ).
fof(f21067,plain,
! [X0,X1,X2] :
( leq(domain(coantidomain(X0)),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X1)))
| ~ leq(domain(coantidomain(X0)),addition(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f44,f20983]) ).
fof(f21068,plain,
! [X0,X1,X2] :
( leq(domain(coantidomain(X0)),addition(omega(multiplication(X2,X0)),multiplication(star(multiplication(X2,X0)),X1)))
| ~ leq(domain(coantidomain(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f21067]) ).
fof(f21069,plain,
! [X0] :
( leq(domain(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),zero)))
| ~ leq(domain(coantidomain(X0)),zero) ),
inference(forward_demodulation,[status(thm)],[f20387,f20984]) ).
fof(f21070,plain,
! [X0] :
( leq(domain(coantidomain(X0)),addition(omega(X0),zero))
| ~ leq(domain(coantidomain(X0)),zero) ),
inference(forward_demodulation,[status(thm)],[f44,f21069]) ).
fof(f21071,plain,
! [X0] :
( leq(domain(coantidomain(X0)),omega(X0))
| ~ leq(domain(coantidomain(X0)),zero) ),
inference(forward_demodulation,[status(thm)],[f37,f21070]) ).
fof(f21072,plain,
! [X0,X1] :
( leq(domain(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(domain(coantidomain(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f20985]) ).
fof(f21073,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),zero)
| ~ leq(addition(multiplication(X0,multiplication(domain(coantidomain(X0)),X1)),X2),zero) ),
inference(forward_demodulation,[status(thm)],[f20387,f20987]) ).
fof(f21074,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain(coantidomain(X2)))),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f44,f20988]) ).
fof(f21075,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain(coantidomain(X2)))),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f80,f21074]) ).
fof(f21076,plain,
! [X0] : leq(multiplication(X0,multiplication(domain(coantidomain(X0)),star(domain(coantidomain(X0))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f20989,f240]) ).
fof(f21077,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(coantidomain(X1)))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f20990]) ).
fof(f21082,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),domain(coantidomain(X1)))
| ~ leq(addition(zero,X0),domain(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f44,f20992]) ).
fof(f21083,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),domain(coantidomain(X1)))
| ~ leq(X0,domain(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f80,f21082]) ).
fof(f21085,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),domain(coantidomain(X1)))
| ~ leq(X0,domain(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f37,f20994]) ).
fof(f21098,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,domain(coantidomain(X2))))) = addition(multiplication(addition(X1,X2),domain(coantidomain(X2))),X0),
inference(forward_demodulation,[status(thm)],[f97,f20997]) ).
fof(f21099,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,domain(coantidomain(X2)))) = addition(multiplication(addition(X1,X2),domain(coantidomain(X2))),X0),
inference(forward_demodulation,[status(thm)],[f80,f21098]) ).
fof(f21100,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(coantidomain(X1))),X2) = addition(multiplication(addition(X1,X0),domain(coantidomain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f80,f20998]) ).
fof(f21101,plain,
! [X0] : multiplication(addition(X0,one),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f20999]) ).
fof(f21102,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),domain(coantidomain(X2))) = addition(multiplication(X0,domain(coantidomain(X2))),zero),
inference(forward_demodulation,[status(thm)],[f44,f21000]) ).
fof(f21103,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),domain(coantidomain(X2))) = multiplication(X0,domain(coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f37,f21102]) ).
fof(f21104,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),domain(coantidomain(X0))) = multiplication(X1,multiplication(X2,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f80,f21001]) ).
fof(f21105,plain,
! [X0] : multiplication(addition(one,X0),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f21002]) ).
fof(f21106,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),domain(coantidomain(X2))) = multiplication(X0,multiplication(X1,domain(coantidomain(X2)))),
inference(forward_demodulation,[status(thm)],[f37,f21003]) ).
fof(f21107,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),domain(coantidomain(X1))) = addition(zero,multiplication(X2,domain(coantidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f44,f21004]) ).
fof(f21108,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),domain(coantidomain(X1))) = multiplication(X2,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f80,f21107]) ).
fof(f21109,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = multiplication(X1,domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f21005]) ).
fof(f21110,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = multiplication(X0,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f80,f21006]) ).
fof(f21111,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,X2))) = addition(multiplication(X1,addition(X2,domain(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f97,f21007]) ).
fof(f21112,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,X2)) = addition(multiplication(X1,addition(X2,domain(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f80,f21111]) ).
fof(f21113,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),X2) = addition(multiplication(X0,addition(domain(coantidomain(X0)),X1)),X2),
inference(forward_demodulation,[status(thm)],[f80,f21008]) ).
fof(f21119,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f21011]) ).
fof(f21120,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f21012]) ).
fof(f21123,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(X0),domain(coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f696,f21015]) ).
fof(f21124,plain,
! [X0] : one = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1377,f21123]) ).
fof(f21129,plain,
! [X0,X1] :
( leq(domain(coantidomain(X0)),addition(omega(X0),multiplication(star(X0),X1)))
| ~ leq(domain(coantidomain(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f80,f21017]) ).
fof(f21130,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(coantidomain(X1)))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f80,f21018]) ).
fof(f21131,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),domain(coantidomain(X1)))
| ~ leq(X0,domain(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f80,f21019]) ).
fof(f21132,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = multiplication(X0,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f37,f21020]) ).
fof(f21133,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = multiplication(X1,domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f80,f21021]) ).
fof(f21134,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f37,f21022]) ).
fof(f21135,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f80,f21023]) ).
fof(f21136,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f45,f21024]) ).
fof(f21143,plain,
! [X0,X1] : forward_diamond(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f70,f20393]) ).
fof(f21147,plain,
! [X0,X1] :
( addition(domain(codomain(X0)),addition(divergence(coantidomain(X0)),forward_diamond(star(coantidomain(X0)),X1))) = addition(divergence(coantidomain(X0)),forward_diamond(star(coantidomain(X0)),X1))
| addition(domain(codomain(X0)),addition(zero,domain(X1))) != addition(forward_diamond(coantidomain(X0),codomain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f20393,f20716]) ).
fof(f21166,plain,
! [X0,X1] :
( addition(domain(codomain(X1)),addition(divergence(coantidomain(X1)),forward_diamond(star(coantidomain(X1)),X0))) = addition(divergence(coantidomain(X1)),forward_diamond(star(coantidomain(X1)),X0))
| addition(zero,addition(domain(X0),domain(codomain(X1)))) != addition(forward_diamond(coantidomain(X1),codomain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f21147]) ).
fof(f21167,plain,
! [X0,X1] :
( addition(domain(codomain(X1)),addition(divergence(coantidomain(X1)),forward_diamond(star(coantidomain(X1)),X0))) = addition(divergence(coantidomain(X1)),forward_diamond(star(coantidomain(X1)),X0))
| addition(domain(X0),domain(codomain(X1))) != addition(forward_diamond(coantidomain(X1),codomain(X1)),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f80,f21166]) ).
fof(f21168,plain,
! [X0,X1] :
( addition(domain(codomain(X1)),addition(divergence(coantidomain(X1)),forward_diamond(star(coantidomain(X1)),X0))) = addition(divergence(coantidomain(X1)),forward_diamond(star(coantidomain(X1)),X0))
| addition(domain(X0),domain(codomain(X1))) != addition(zero,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f20393,f21167]) ).
fof(f21169,plain,
! [X0,X1] :
( addition(domain(codomain(X1)),addition(divergence(coantidomain(X1)),forward_diamond(star(coantidomain(X1)),X0))) = addition(divergence(coantidomain(X1)),forward_diamond(star(coantidomain(X1)),X0))
| addition(domain(X0),domain(codomain(X1))) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f80,f21168]) ).
fof(f21191,plain,
! [X0] : leq(divergence(X0),addition(omega(antidomain(divergence(X0))),multiplication(star(antidomain(divergence(X0))),omega(divergence(X0))))),
inference(resolution,[status(thm)],[f20667,f409]) ).
fof(f21192,plain,
! [X0] : leq(multiplication(divergence(X0),star(coantidomain(omega(divergence(X0))))),omega(divergence(X0))),
inference(resolution,[status(thm)],[f20667,f346]) ).
fof(f21193,plain,
! [X0] : leq(multiplication(star(antidomain(omega(divergence(X0)))),divergence(X0)),omega(divergence(X0))),
inference(resolution,[status(thm)],[f20667,f304]) ).
fof(f21194,plain,
! [X0] : addition(divergence(X0),omega(divergence(X0))) = omega(divergence(X0)),
inference(resolution,[status(thm)],[f20667,f48]) ).
fof(f21201,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(resolution,[status(thm)],[f502,f49]) ).
fof(f21205,plain,
! [X0,X1,X2] : addition(antidomain(addition(X0,multiplication(X1,X0))),addition(antidomain(multiplication(addition(one,X1),domain(X0))),X2)) = addition(antidomain(multiplication(addition(one,X1),domain(X0))),X2),
inference(paramodulation,[status(thm)],[f207,f502]) ).
fof(f21206,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(addition(antidomain(X1),X0),domain(X1))),X2)) = addition(antidomain(multiplication(addition(antidomain(X1),X0),domain(X1))),X2),
inference(paramodulation,[status(thm)],[f224,f502]) ).
fof(f21207,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(addition(X0,X1),omega(X0))),addition(antidomain(multiplication(addition(X1,one),domain(omega(X0)))),X2)) = addition(antidomain(multiplication(addition(X1,one),domain(omega(X0)))),X2),
inference(paramodulation,[status(thm)],[f11449,f502]) ).
fof(f21208,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(addition(X0,X1),omega(X1))),addition(antidomain(multiplication(addition(X0,one),domain(omega(X1)))),X2)) = addition(antidomain(multiplication(addition(X0,one),domain(omega(X1)))),X2),
inference(paramodulation,[status(thm)],[f10882,f502]) ).
fof(f21209,plain,
! [X0,X1,X2] : addition(antidomain(addition(X0,multiplication(X1,X0))),addition(antidomain(multiplication(addition(X1,one),domain(X0))),X2)) = addition(antidomain(multiplication(addition(X1,one),domain(X0))),X2),
inference(paramodulation,[status(thm)],[f232,f502]) ).
fof(f21210,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(addition(X0,antidomain(X1)),domain(X1))),X2)) = addition(antidomain(multiplication(addition(X0,antidomain(X1)),domain(X1))),X2),
inference(paramodulation,[status(thm)],[f230,f502]) ).
fof(f21211,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(addition(X0,one),omega(X1))),addition(antidomain(multiplication(addition(X1,X0),domain(omega(X1)))),X2)) = addition(antidomain(multiplication(addition(X1,X0),domain(omega(X1)))),X2),
inference(paramodulation,[status(thm)],[f11449,f502]) ).
fof(f21212,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(addition(X0,one),omega(X1))),addition(antidomain(multiplication(addition(X0,X1),domain(omega(X1)))),X2)) = addition(antidomain(multiplication(addition(X0,X1),domain(omega(X1)))),X2),
inference(paramodulation,[status(thm)],[f10882,f502]) ).
fof(f21213,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,coantidomain(X1))),addition(antidomain(multiplication(addition(X0,X1),domain(coantidomain(X1)))),X2)) = addition(antidomain(multiplication(addition(X0,X1),domain(coantidomain(X1)))),X2),
inference(paramodulation,[status(thm)],[f233,f502]) ).
fof(f21214,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,coantidomain(X1))),addition(antidomain(multiplication(addition(X1,X0),domain(coantidomain(X1)))),X2)) = addition(antidomain(multiplication(addition(X1,X0),domain(coantidomain(X1)))),X2),
inference(paramodulation,[status(thm)],[f226,f502]) ).
fof(f21215,plain,
! [X0,X1] : addition(antidomain(zero),addition(antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),X1)) = addition(antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),X1),
inference(paramodulation,[status(thm)],[f195,f502]) ).
fof(f21219,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),addition(antidomain(multiplication(multiplication(X0,X1),domain(X2))),X3)) = addition(antidomain(multiplication(multiplication(X0,X1),domain(X2))),X3),
inference(paramodulation,[status(thm)],[f39,f502]) ).
fof(f21220,plain,
! [X0,X1,X2] : addition(antidomain(zero),addition(antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0))),X2)) = addition(antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0))),X2),
inference(paramodulation,[status(thm)],[f2635,f502]) ).
fof(f21222,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(antidomain(X0),X1)),addition(antidomain(multiplication(antidomain(X0),domain(addition(X1,X0)))),X2)) = addition(antidomain(multiplication(antidomain(X0),domain(addition(X1,X0)))),X2),
inference(paramodulation,[status(thm)],[f186,f502]) ).
fof(f21223,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(antidomain(X0),X1)),addition(antidomain(multiplication(antidomain(X0),domain(addition(X0,X1)))),X2)) = addition(antidomain(multiplication(antidomain(X0),domain(addition(X0,X1)))),X2),
inference(paramodulation,[status(thm)],[f177,f502]) ).
fof(f21224,plain,
! [X0,X1] : addition(antidomain(zero),addition(antidomain(multiplication(antidomain(X0),domain(omega(X0)))),X1)) = addition(antidomain(multiplication(antidomain(X0),domain(omega(X0)))),X1),
inference(paramodulation,[status(thm)],[f1569,f502]) ).
fof(f21225,plain,
! [X0,X1,X2] : addition(antidomain(zero),addition(antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1)))),X2)) = addition(antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1)))),X2),
inference(paramodulation,[status(thm)],[f136,f502]) ).
fof(f21230,plain,
! [X0,X1] : addition(antidomain(X0),addition(antidomain(multiplication(X0,domain(codomain(X0)))),X1)) = addition(antidomain(multiplication(X0,domain(codomain(X0)))),X1),
inference(paramodulation,[status(thm)],[f2309,f502]) ).
fof(f21231,plain,
! [X0,X1,X2] : addition(antidomain(addition(omega(X0),multiplication(X0,X1))),addition(antidomain(multiplication(X0,domain(addition(omega(X0),X1)))),X2)) = addition(antidomain(multiplication(X0,domain(addition(omega(X0),X1)))),X2),
inference(paramodulation,[status(thm)],[f318,f502]) ).
fof(f21232,plain,
! [X0,X1,X2] : addition(antidomain(addition(X0,multiplication(X0,X1))),addition(antidomain(multiplication(X0,domain(addition(one,X1)))),X2)) = addition(antidomain(multiplication(X0,domain(addition(one,X1)))),X2),
inference(paramodulation,[status(thm)],[f162,f502]) ).
fof(f21233,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(addition(coantidomain(X0),X1)))),X2)) = addition(antidomain(multiplication(X0,domain(addition(coantidomain(X0),X1)))),X2),
inference(paramodulation,[status(thm)],[f181,f502]) ).
fof(f21234,plain,
! [X0,X1,X2] : addition(antidomain(addition(omega(X0),multiplication(X0,X1))),addition(antidomain(multiplication(X0,domain(addition(X1,omega(X0))))),X2)) = addition(antidomain(multiplication(X0,domain(addition(X1,omega(X0))))),X2),
inference(paramodulation,[status(thm)],[f321,f502]) ).
fof(f21235,plain,
! [X0,X1,X2] : addition(antidomain(addition(X0,multiplication(X0,X1))),addition(antidomain(multiplication(X0,domain(addition(X1,one)))),X2)) = addition(antidomain(multiplication(X0,domain(addition(X1,one)))),X2),
inference(paramodulation,[status(thm)],[f192,f502]) ).
fof(f21236,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(addition(X1,coantidomain(X0))))),X2)) = addition(antidomain(multiplication(X0,domain(addition(X1,coantidomain(X0))))),X2),
inference(paramodulation,[status(thm)],[f190,f502]) ).
fof(f21237,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(omega(X0),X1)),addition(antidomain(multiplication(X0,domain(multiplication(omega(X0),X1)))),X2)) = addition(antidomain(multiplication(X0,domain(multiplication(omega(X0),X1)))),X2),
inference(paramodulation,[status(thm)],[f319,f502]) ).
fof(f21238,plain,
! [X0,X1,X2] : addition(antidomain(zero),addition(antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),X2)) = addition(antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),X2),
inference(paramodulation,[status(thm)],[f151,f502]) ).
fof(f21239,plain,
! [X0,X1,X2] : addition(antidomain(omega(multiplication(X0,X1))),addition(antidomain(multiplication(X0,domain(multiplication(X1,omega(multiplication(X0,X1)))))),X2)) = addition(antidomain(multiplication(X0,domain(multiplication(X1,omega(multiplication(X0,X1)))))),X2),
inference(paramodulation,[status(thm)],[f308,f502]) ).
fof(f21240,plain,
! [X0,X1,X2] : addition(antidomain(zero),addition(antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1)))))),X2)) = addition(antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1)))))),X2),
inference(paramodulation,[status(thm)],[f144,f502]) ).
fof(f21241,plain,
! [X0,X1] : addition(antidomain(zero),addition(antidomain(multiplication(X0,domain(omega(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,domain(omega(coantidomain(X0))))),X1),
inference(paramodulation,[status(thm)],[f1813,f502]) ).
fof(f21242,plain,
! [X0,X1] : addition(antidomain(omega(X0)),addition(antidomain(multiplication(X0,domain(omega(X0)))),X1)) = addition(antidomain(multiplication(X0,domain(omega(X0)))),X1),
inference(paramodulation,[status(thm)],[f56,f502]) ).
fof(f21263,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),multiplication(addition(X2,one),antidomain(multiplication(X0,domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),multiplication(X2,antidomain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f232,f502]) ).
fof(f21264,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),multiplication(addition(one,X2),antidomain(multiplication(X0,domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),multiplication(X2,antidomain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f207,f502]) ).
fof(f21265,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),multiplication(antidomain(multiplication(X0,domain(X1))),addition(X2,one))) = addition(antidomain(multiplication(X0,domain(X1))),multiplication(antidomain(multiplication(X0,domain(X1))),X2)),
inference(paramodulation,[status(thm)],[f192,f502]) ).
fof(f21266,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),multiplication(antidomain(multiplication(X0,domain(X1))),addition(one,X2))) = addition(antidomain(multiplication(X0,domain(X1))),multiplication(antidomain(multiplication(X0,domain(X1))),X2)),
inference(paramodulation,[status(thm)],[f162,f502]) ).
fof(f21268,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(paramodulation,[status(thm)],[f1026,f502]) ).
fof(f21269,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),addition(X2,antidomain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f1005,f502]) ).
fof(f21271,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,X1)),addition(X2,addition(X3,antidomain(multiplication(X0,domain(X1)))))) = addition(antidomain(multiplication(X0,domain(X1))),addition(X2,X3)),
inference(paramodulation,[status(thm)],[f97,f502]) ).
fof(f21272,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,X1)),addition(X2,addition(antidomain(multiplication(X0,domain(X1))),X3))) = addition(antidomain(multiplication(X0,domain(X1))),addition(X3,X2)),
inference(paramodulation,[status(thm)],[f97,f502]) ).
fof(f21274,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),X2),
inference(paramodulation,[status(thm)],[f35,f502]) ).
fof(f21275,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),X2),
inference(paramodulation,[status(thm)],[f35,f502]) ).
fof(f21281,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(multiplication(X0,X1),X2)),addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)) = addition(antidomain(multiplication(multiplication(X0,X1),domain(X2))),X3),
inference(paramodulation,[status(thm)],[f39,f502]) ).
fof(f21282,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(antidomain(addition(domain(X0),X1)),X0)),addition(antidomain(zero),X2)) = addition(antidomain(multiplication(antidomain(addition(domain(X0),X1)),domain(X0))),X2),
inference(paramodulation,[status(thm)],[f2635,f502]) ).
fof(f21292,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(one,X1))),addition(antidomain(multiplication(X0,one)),X2)) = addition(antidomain(multiplication(X0,domain(addition(one,X1)))),X2),
inference(paramodulation,[status(thm)],[f15345,f502]) ).
fof(f21293,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,addition(X1,one))),addition(antidomain(multiplication(X0,one)),X2)) = addition(antidomain(multiplication(X0,domain(addition(X1,one)))),X2),
inference(paramodulation,[status(thm)],[f15407,f502]) ).
fof(f21296,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,star(X1))),addition(antidomain(multiplication(X0,one)),X2)) = addition(antidomain(multiplication(X0,domain(star(X1)))),X2),
inference(paramodulation,[status(thm)],[f8543,f502]) ).
fof(f21297,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),addition(antidomain(multiplication(X0,forward_diamond(X1,X2))),X3)) = addition(antidomain(multiplication(X0,domain(multiplication(X1,domain(X2))))),X3),
inference(paramodulation,[status(thm)],[f69,f502]) ).
fof(f21307,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(antidomain(multiplication(X0,X1))),multiplication(star(antidomain(multiplication(X0,X1))),addition(antidomain(multiplication(X0,domain(X1))),X2))))
| ~ leq(one,addition(antidomain(multiplication(X0,domain(X1))),X2)) ),
inference(paramodulation,[status(thm)],[f502,f405]) ).
fof(f21308,plain,
! [X0,X1,X2,X3] :
( leq(antidomain(multiplication(X0,X1)),addition(omega(X2),multiplication(star(X2),multiplication(X2,addition(antidomain(multiplication(X0,domain(X1))),X3)))))
| ~ leq(antidomain(multiplication(X0,X1)),multiplication(X2,addition(antidomain(multiplication(X0,domain(X1))),X3))) ),
inference(paramodulation,[status(thm)],[f502,f392]) ).
fof(f21309,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(antidomain(multiplication(X1,X2))),multiplication(star(antidomain(multiplication(X1,X2))),multiplication(addition(antidomain(multiplication(X1,domain(X2))),X3),X0))))
| ~ leq(X0,multiplication(addition(antidomain(multiplication(X1,domain(X2))),X3),X0)) ),
inference(paramodulation,[status(thm)],[f502,f391]) ).
fof(f21311,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),star(antidomain(multiplication(X0,X1)))),one)
| ~ leq(addition(antidomain(multiplication(X0,domain(X1))),X2),one) ),
inference(paramodulation,[status(thm)],[f502,f335]) ).
fof(f21312,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(antidomain(multiplication(X0,domain(X1))),X2)),antidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f502,f2635]) ).
fof(f21313,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(addition(antidomain(multiplication(X1,domain(X2))),X3),star(antidomain(multiplication(X1,X2))))),X0)
| ~ leq(multiplication(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)),X0) ),
inference(paramodulation,[status(thm)],[f502,f341]) ).
fof(f21314,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),multiplication(X3,star(X3))),antidomain(multiplication(X0,X1)))
| ~ leq(multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),X3),antidomain(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f502,f340]) ).
fof(f21315,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),omega(antidomain(multiplication(X0,X1)))) = multiplication(addition(addition(antidomain(multiplication(X0,domain(X1))),X2),one),omega(antidomain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f502,f11449]) ).
fof(f21322,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(multiplication(X0,X1))),addition(antidomain(multiplication(X0,domain(X1))),X2)),one)
| ~ leq(addition(antidomain(multiplication(X0,domain(X1))),X2),one) ),
inference(paramodulation,[status(thm)],[f502,f302]) ).
fof(f21323,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,addition(antidomain(multiplication(X1,domain(X2))),X3))),antidomain(multiplication(X1,X2)))
| ~ leq(multiplication(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)),antidomain(multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f502,f291]) ).
fof(f21324,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(antidomain(multiplication(X0,X1))),multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),X3)),X3)
| ~ leq(multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),X3),X3) ),
inference(paramodulation,[status(thm)],[f502,f290]) ).
fof(f21325,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)) != addition(antidomain(multiplication(X1,domain(X2))),X3)
| leq(addition(X0,antidomain(multiplication(X1,X2))),addition(antidomain(multiplication(X1,domain(X2))),X3)) ),
inference(paramodulation,[status(thm)],[f502,f243]) ).
fof(f21326,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)) != multiplication(X0,addition(antidomain(multiplication(X1,domain(X2))),X3))
| leq(multiplication(X0,antidomain(multiplication(X1,X2))),multiplication(X0,addition(antidomain(multiplication(X1,domain(X2))),X3))) ),
inference(paramodulation,[status(thm)],[f502,f242]) ).
fof(f21327,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(antidomain(multiplication(X0,domain(X1))),X3),X2) != multiplication(addition(antidomain(multiplication(X0,domain(X1))),X3),X2)
| leq(multiplication(antidomain(multiplication(X0,X1)),X2),multiplication(addition(antidomain(multiplication(X0,domain(X1))),X3),X2)) ),
inference(paramodulation,[status(thm)],[f502,f241]) ).
fof(f21328,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),coantidomain(addition(antidomain(multiplication(X0,domain(X1))),X2))) = multiplication(antidomain(multiplication(X0,X1)),coantidomain(addition(antidomain(multiplication(X0,domain(X1))),X2))),
inference(paramodulation,[status(thm)],[f502,f233]) ).
fof(f21330,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(antidomain(multiplication(X0,domain(X1))),X2)),addition(antidomain(multiplication(X0,domain(X1))),X2)) = multiplication(antidomain(addition(antidomain(multiplication(X0,domain(X1))),X2)),antidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f502,f186]) ).
fof(f21332,plain,
! [X0,X1,X2,X3] : leq(antidomain(multiplication(X0,X1)),addition(X2,addition(antidomain(multiplication(X0,domain(X1))),X3))),
inference(paramodulation,[status(thm)],[f502,f1421]) ).
fof(f21335,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(paramodulation,[status(thm)],[f502,f1324]) ).
fof(f21337,plain,
! [X0,X1,X2,X3] : addition(addition(antidomain(multiplication(X0,domain(X1))),X2),addition(antidomain(multiplication(X0,X1)),X3)) = addition(addition(antidomain(multiplication(X0,domain(X1))),X2),X3),
inference(paramodulation,[status(thm)],[f502,f103]) ).
fof(f21338,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,X1)),addition(addition(antidomain(multiplication(X0,domain(X1))),X2),X3)) = addition(X3,addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(paramodulation,[status(thm)],[f502,f97]) ).
fof(f21339,plain,
! [X0,X1,X2,X3] : addition(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)) = addition(addition(antidomain(multiplication(X1,domain(X2))),X3),addition(X0,antidomain(multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f502,f97]) ).
fof(f21340,plain,
! [X0,X1,X2] :
( addition(antidomain(multiplication(X0,domain(X1))),X2) != antidomain(multiplication(X0,X1))
| leq(addition(antidomain(multiplication(X0,domain(X1))),X2),antidomain(multiplication(X0,X1))) ),
inference(paramodulation,[status(thm)],[f502,f246]) ).
fof(f21341,plain,
! [X0,X1,X2] :
( addition(antidomain(multiplication(X0,domain(X1))),X2) != addition(antidomain(multiplication(X0,domain(X1))),X2)
| leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)) ),
inference(paramodulation,[status(thm)],[f502,f49]) ).
fof(f21342,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,X1)),addition(addition(antidomain(multiplication(X0,domain(X1))),X2),X3)) = addition(addition(antidomain(multiplication(X0,domain(X1))),X2),X3),
inference(paramodulation,[status(thm)],[f502,f36]) ).
fof(f21346,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),X1)) = addition(antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f577,f21215]) ).
fof(f21365,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)) = addition(antidomain(multiplication(multiplication(X0,X1),domain(X2))),X3),
inference(forward_demodulation,[status(thm)],[f39,f21219]) ).
fof(f21366,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)) = addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3),
inference(forward_demodulation,[status(thm)],[f39,f21365]) ).
fof(f21367,plain,
! [X0,X1,X2] : addition(one,addition(antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0))),X2)) = addition(antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0))),X2),
inference(forward_demodulation,[status(thm)],[f577,f21220]) ).
fof(f21376,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(antidomain(X0),domain(omega(X0)))),X1)) = addition(antidomain(multiplication(antidomain(X0),domain(omega(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f577,f21224]) ).
fof(f21377,plain,
! [X0,X1,X2] : addition(one,addition(antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1)))),X2)) = addition(antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1)))),X2),
inference(forward_demodulation,[status(thm)],[f577,f21225]) ).
fof(f21403,plain,
! [X0,X1,X2] : addition(antidomain(addition(X0,multiplication(X0,X1))),addition(antidomain(multiplication(X0,one)),X2)) = addition(antidomain(multiplication(X0,domain(addition(one,X1)))),X2),
inference(forward_demodulation,[status(thm)],[f15345,f21232]) ).
fof(f21404,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,one)),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(multiplication(X0,domain(addition(one,X2)))),X1),
inference(forward_demodulation,[status(thm)],[f97,f21403]) ).
fof(f21405,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(multiplication(X0,domain(addition(one,X2)))),X1),
inference(forward_demodulation,[status(thm)],[f40,f21404]) ).
fof(f21406,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(multiplication(X0,one)),X1),
inference(forward_demodulation,[status(thm)],[f15345,f21405]) ).
fof(f21407,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f40,f21406]) ).
fof(f21408,plain,
! [X0,X1,X2] : addition(antidomain(addition(X0,multiplication(X0,X1))),addition(antidomain(multiplication(X0,one)),X2)) = addition(antidomain(multiplication(X0,domain(addition(X1,one)))),X2),
inference(forward_demodulation,[status(thm)],[f15407,f21235]) ).
fof(f21409,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,one)),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(multiplication(X0,domain(addition(X2,one)))),X1),
inference(forward_demodulation,[status(thm)],[f97,f21408]) ).
fof(f21410,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(multiplication(X0,domain(addition(X2,one)))),X1),
inference(forward_demodulation,[status(thm)],[f40,f21409]) ).
fof(f21411,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(multiplication(X0,one)),X1),
inference(forward_demodulation,[status(thm)],[f15407,f21410]) ).
fof(f21412,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f40,f21411]) ).
fof(f21413,plain,
! [X0,X1,X2] : addition(one,addition(antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),X2)) = addition(antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),X2),
inference(forward_demodulation,[status(thm)],[f577,f21238]) ).
fof(f21414,plain,
! [X0,X1,X2] : addition(one,addition(antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1)))))),X2)) = addition(antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1)))))),X2),
inference(forward_demodulation,[status(thm)],[f577,f21240]) ).
fof(f21415,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(X0,domain(omega(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,domain(omega(coantidomain(X0))))),X1),
inference(forward_demodulation,[status(thm)],[f577,f21241]) ).
fof(f21457,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),multiplication(addition(X2,one),antidomain(multiplication(X0,domain(X1))))) = multiplication(addition(X2,one),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f232,f21263]) ).
fof(f21458,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),multiplication(addition(one,X2),antidomain(multiplication(X0,domain(X1))))) = multiplication(addition(X2,one),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f232,f21264]) ).
fof(f21459,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),multiplication(antidomain(multiplication(X0,domain(X1))),addition(X2,one))) = multiplication(antidomain(multiplication(X0,domain(X1))),addition(X2,one)),
inference(forward_demodulation,[status(thm)],[f192,f21265]) ).
fof(f21460,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),multiplication(antidomain(multiplication(X0,domain(X1))),addition(one,X2))) = multiplication(antidomain(multiplication(X0,domain(X1))),addition(X2,one)),
inference(forward_demodulation,[status(thm)],[f192,f21266]) ).
fof(f21462,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))) = addition(X2,antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1026,f21268]) ).
fof(f21463,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f1329,f21269]) ).
fof(f21489,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)) = addition(antidomain(multiplication(multiplication(X0,X1),domain(X2))),X3),
inference(forward_demodulation,[status(thm)],[f39,f21281]) ).
fof(f21490,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3)) = addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),X3),
inference(forward_demodulation,[status(thm)],[f39,f21489]) ).
fof(f21491,plain,
! [X0,X1,X2] : addition(antidomain(zero),addition(X0,antidomain(multiplication(antidomain(addition(domain(X1),X2)),X1)))) = addition(antidomain(multiplication(antidomain(addition(domain(X1),X2)),domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f97,f21282]) ).
fof(f21492,plain,
! [X0,X1,X2] : addition(one,addition(X0,antidomain(multiplication(antidomain(addition(domain(X1),X2)),X1)))) = addition(antidomain(multiplication(antidomain(addition(domain(X1),X2)),domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f577,f21491]) ).
fof(f21493,plain,
! [X0,X1,X2] : addition(one,addition(X0,antidomain(multiplication(antidomain(addition(domain(X1),X2)),X1)))) = addition(antidomain(zero),X0),
inference(forward_demodulation,[status(thm)],[f2635,f21492]) ).
fof(f21494,plain,
! [X0,X1,X2] : addition(one,addition(X0,antidomain(multiplication(antidomain(addition(domain(X1),X2)),X1)))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f577,f21493]) ).
fof(f21533,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,one)),addition(X1,antidomain(multiplication(X0,addition(one,X2))))) = addition(antidomain(multiplication(X0,domain(addition(one,X2)))),X1),
inference(forward_demodulation,[status(thm)],[f97,f21292]) ).
fof(f21534,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,addition(one,X2))))) = addition(antidomain(multiplication(X0,domain(addition(one,X2)))),X1),
inference(forward_demodulation,[status(thm)],[f40,f21533]) ).
fof(f21535,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,addition(one,X2))))) = addition(antidomain(multiplication(X0,one)),X1),
inference(forward_demodulation,[status(thm)],[f15345,f21534]) ).
fof(f21536,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,addition(one,X2))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f40,f21535]) ).
fof(f21537,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,one)),addition(X1,antidomain(multiplication(X0,addition(X2,one))))) = addition(antidomain(multiplication(X0,domain(addition(X2,one)))),X1),
inference(forward_demodulation,[status(thm)],[f97,f21293]) ).
fof(f21538,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,addition(X2,one))))) = addition(antidomain(multiplication(X0,domain(addition(X2,one)))),X1),
inference(forward_demodulation,[status(thm)],[f40,f21537]) ).
fof(f21539,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,addition(X2,one))))) = addition(antidomain(multiplication(X0,one)),X1),
inference(forward_demodulation,[status(thm)],[f15407,f21538]) ).
fof(f21540,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,addition(X2,one))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f40,f21539]) ).
fof(f21545,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,one)),addition(X1,antidomain(multiplication(X0,star(X2))))) = addition(antidomain(multiplication(X0,domain(star(X2)))),X1),
inference(forward_demodulation,[status(thm)],[f97,f21296]) ).
fof(f21546,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,star(X2))))) = addition(antidomain(multiplication(X0,domain(star(X2)))),X1),
inference(forward_demodulation,[status(thm)],[f40,f21545]) ).
fof(f21547,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,star(X2))))) = addition(antidomain(multiplication(X0,one)),X1),
inference(forward_demodulation,[status(thm)],[f8543,f21546]) ).
fof(f21548,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,star(X2))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f40,f21547]) ).
fof(f21549,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,forward_diamond(X1,X2))),addition(X3,antidomain(multiplication(X0,multiplication(X1,domain(X2)))))) = addition(antidomain(multiplication(X0,domain(multiplication(X1,domain(X2))))),X3),
inference(forward_demodulation,[status(thm)],[f97,f21297]) ).
fof(f21550,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,forward_diamond(X1,X2))),addition(X3,antidomain(multiplication(X0,multiplication(X1,domain(X2)))))) = addition(antidomain(multiplication(X0,forward_diamond(X1,X2))),X3),
inference(forward_demodulation,[status(thm)],[f69,f21549]) ).
fof(f21563,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),omega(antidomain(multiplication(X0,X1)))) = multiplication(addition(X2,addition(antidomain(multiplication(X0,domain(X1))),one)),omega(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f103,f21315]) ).
fof(f21564,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),omega(antidomain(multiplication(X0,X1)))) = multiplication(addition(X2,addition(one,antidomain(multiplication(X0,domain(X1))))),omega(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f35,f21563]) ).
fof(f21565,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(multiplication(X0,domain(X1))),X2),omega(antidomain(multiplication(X0,X1)))) = multiplication(addition(X2,one),omega(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1379,f21564]) ).
fof(f21588,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,antidomain(multiplication(X1,X2))),multiplication(X0,addition(antidomain(multiplication(X1,domain(X2))),X3))),
inference(trivial_equality_resolution,[status(thm)],[f21326]) ).
fof(f21589,plain,
! [X0,X1,X2,X3] : leq(multiplication(antidomain(multiplication(X0,X1)),X2),multiplication(addition(antidomain(multiplication(X0,domain(X1))),X3),X2)),
inference(trivial_equality_resolution,[status(thm)],[f21327]) ).
fof(f21590,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,X1)),coantidomain(addition(antidomain(multiplication(X0,domain(X1))),X2))),
inference(forward_demodulation,[status(thm)],[f63,f21328]) ).
fof(f21591,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(antidomain(multiplication(X0,domain(X1))),X2)),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f59,f21330]) ).
fof(f21592,plain,
! [X0,X1,X2,X3] : addition(X0,addition(antidomain(multiplication(X1,domain(X2))),addition(antidomain(multiplication(X1,X2)),X3))) = addition(addition(antidomain(multiplication(X1,domain(X2))),X0),X3),
inference(forward_demodulation,[status(thm)],[f103,f21337]) ).
fof(f21593,plain,
! [X0,X1,X2,X3] : addition(X0,addition(antidomain(multiplication(X1,X2)),addition(X3,antidomain(multiplication(X1,domain(X2)))))) = addition(addition(antidomain(multiplication(X1,domain(X2))),X0),X3),
inference(forward_demodulation,[status(thm)],[f97,f21592]) ).
fof(f21594,plain,
! [X0,X1,X2,X3] : addition(X0,addition(antidomain(multiplication(X1,X2)),addition(X3,antidomain(multiplication(X1,domain(X2)))))) = addition(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)),
inference(forward_demodulation,[status(thm)],[f103,f21593]) ).
fof(f21595,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,X1)),addition(X2,addition(antidomain(multiplication(X0,domain(X1))),X3))) = addition(X3,addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(forward_demodulation,[status(thm)],[f103,f21338]) ).
fof(f21596,plain,
! [X0,X1,X2,X3] : addition(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)) = addition(X3,addition(antidomain(multiplication(X1,domain(X2))),addition(X0,antidomain(multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f103,f21339]) ).
fof(f21597,plain,
! [X0,X1,X2,X3] : addition(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)) = addition(X3,addition(antidomain(multiplication(X1,X2)),addition(antidomain(multiplication(X1,domain(X2))),X0))),
inference(forward_demodulation,[status(thm)],[f97,f21596]) ).
fof(f21598,plain,
! [X0,X1,X2,X3] : addition(X0,addition(antidomain(multiplication(X1,domain(X2))),X3)) = addition(X3,addition(antidomain(multiplication(X1,domain(X2))),X0)),
inference(forward_demodulation,[status(thm)],[f502,f21597]) ).
fof(f21599,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(trivial_equality_resolution,[status(thm)],[f21341]) ).
fof(f21600,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,X1)),addition(X2,addition(antidomain(multiplication(X0,domain(X1))),X3))) = addition(addition(antidomain(multiplication(X0,domain(X1))),X2),X3),
inference(forward_demodulation,[status(thm)],[f103,f21342]) ).
fof(f21601,plain,
! [X0,X1,X2,X3] : addition(antidomain(multiplication(X0,X1)),addition(X2,addition(antidomain(multiplication(X0,domain(X1))),X3))) = addition(X2,addition(antidomain(multiplication(X0,domain(X1))),X3)),
inference(forward_demodulation,[status(thm)],[f103,f21600]) ).
fof(f21613,plain,
! [X0] : domain(X0) = domain_difference(X0,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f19281,f4386]) ).
fof(f21618,plain,
! [X0,X1] : domain(forward_diamond(X0,antidomain(X1))) = domain_difference(forward_diamond(X0,antidomain(X1)),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f18885,f21613]) ).
fof(f21619,plain,
! [X0,X1] : domain(backward_diamond(X0,antidomain(X1))) = domain_difference(backward_diamond(X0,antidomain(X1)),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f18884,f21613]) ).
fof(f21639,plain,
! [X0,X1] : forward_diamond(X0,antidomain(X1)) = domain_difference(forward_diamond(X0,antidomain(X1)),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19262,f21618]) ).
fof(f21665,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(backward_diamond(X2,X3),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4507]) ).
fof(f21666,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(backward_diamond(X2,X3),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4507]) ).
fof(f21674,plain,
! [X0,X1] : codomain(backward_diamond(X0,X1)) = addition(codomain(backward_diamond(X0,X1)),backward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f2309,f4507]) ).
fof(f21675,plain,
! [X0,X1,X2] : addition(omega(backward_diamond(X0,X1)),X2) = addition(addition(omega(backward_diamond(X0,X1)),X2),addition(omega(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f318,f4507]) ).
fof(f21676,plain,
! [X0,X1,X2] : addition(coantidomain(backward_diamond(X0,X1)),X2) = addition(addition(coantidomain(backward_diamond(X0,X1)),X2),multiplication(backward_diamond(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f181,f4507]) ).
fof(f21677,plain,
! [X0,X1,X2] : addition(X0,omega(backward_diamond(X1,X2))) = addition(addition(X0,omega(backward_diamond(X1,X2))),addition(omega(backward_diamond(X1,X2)),multiplication(backward_diamond(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f321,f4507]) ).
fof(f21681,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(backward_diamond(X1,X2),X0))) = addition(multiplication(X0,omega(multiplication(backward_diamond(X1,X2),X0))),omega(multiplication(backward_diamond(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f308,f4507]) ).
fof(f21695,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(backward_diamond(X1,X2),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4507,f336]) ).
fof(f21696,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(backward_diamond(X1,X2),omega(X0)))),
inference(paramodulation,[status(thm)],[f4507,f318]) ).
fof(f21697,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(backward_diamond(X1,X2),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4507,f314]) ).
fof(f21699,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(backward_diamond(X1,X2),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4507,f181]) ).
fof(f21720,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(backward_diamond(X3,X4),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4507,f398]) ).
fof(f21721,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(backward_diamond(X3,X4),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4507,f332]) ).
fof(f21722,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(backward_diamond(X3,X4),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4507,f296]) ).
fof(f21726,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(backward_diamond(X3,X4),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4507,f219]) ).
fof(f21727,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(backward_diamond(X3,X4),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4507,f170]) ).
fof(f21728,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(backward_diamond(X2,X3),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4507,f58]) ).
fof(f21729,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(backward_diamond(X2,X3),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4507,f55]) ).
fof(f21730,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(backward_diamond(X2,X3),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4507,f53]) ).
fof(f21731,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(backward_diamond(X2,X3),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4507,f103]) ).
fof(f21732,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(backward_diamond(X2,X3),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4507,f36]) ).
fof(f21735,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(backward_diamond(X1,X2)),multiplication(star(backward_diamond(X1,X2)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4507,f394]) ).
fof(f21736,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X0)),backward_diamond(X1,X2))
| ~ leq(X0,backward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f4507,f329]) ).
fof(f21737,plain,
! [X0,X1,X2] :
( leq(multiplication(star(backward_diamond(X1,X2)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4507,f293]) ).
fof(f21742,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(backward_diamond(X1,X2),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4507,f405]) ).
fof(f21743,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(backward_diamond(X2,X3),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4507,f392]) ).
fof(f21744,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(backward_diamond(X2,X3),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4507,f391]) ).
fof(f21746,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(backward_diamond(X1,X2),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4507,f335]) ).
fof(f21748,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(backward_diamond(X2,X3),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4507,f341]) ).
fof(f21749,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(backward_diamond(X2,X3),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4507,f340]) ).
fof(f21750,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(backward_diamond(X1,X2),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4507,f11449]) ).
fof(f21752,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(backward_diamond(X1,X2),X0))) = multiplication(addition(X0,one),omega(multiplication(backward_diamond(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f4507,f10882]) ).
fof(f21757,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(backward_diamond(X1,X2),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4507,f302]) ).
fof(f21758,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(backward_diamond(X2,X3),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4507,f291]) ).
fof(f21759,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(backward_diamond(X2,X3),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4507,f290]) ).
fof(f21760,plain,
! [X0,X1,X2,X3] :
( addition(X0,X1) != multiplication(backward_diamond(X2,X3),X1)
| leq(addition(X0,X1),multiplication(backward_diamond(X2,X3),X1)) ),
inference(paramodulation,[status(thm)],[f4507,f243]) ).
fof(f21761,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(backward_diamond(X2,X3),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(backward_diamond(X2,X3),X1))) ),
inference(paramodulation,[status(thm)],[f4507,f242]) ).
fof(f21762,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(backward_diamond(X2,X3),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(backward_diamond(X2,X3),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4507,f241]) ).
fof(f21766,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(backward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f4507,f177]) ).
fof(f21768,plain,
! [X0,X1,X2,X3] : leq(multiplication(backward_diamond(X0,X1),X2),addition(X3,X2)),
inference(paramodulation,[status(thm)],[f4507,f1420]) ).
fof(f21772,plain,
! [X0,X1,X2,X3] : addition(multiplication(backward_diamond(X0,X1),X2),addition(X2,X3)) = addition(X2,X3),
inference(paramodulation,[status(thm)],[f4507,f103]) ).
fof(f21773,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(backward_diamond(X1,X2),X0),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f4507,f97]) ).
fof(f21774,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(backward_diamond(X2,X3),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4507,f97]) ).
fof(f21776,plain,
! [X0,X1,X2] :
( X0 != multiplication(backward_diamond(X1,X2),X0)
| leq(X0,multiplication(backward_diamond(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f4507,f49]) ).
fof(f21777,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(backward_diamond(X1,X2),X0),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f4507,f36]) ).
fof(f21787,plain,
! [X0,X1] : codomain(backward_diamond(X0,X1)) = addition(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f21674]) ).
fof(f21788,plain,
! [X0,X1,X2] : addition(omega(backward_diamond(X0,X1)),X2) = addition(X2,addition(omega(backward_diamond(X0,X1)),addition(omega(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),X2)))),
inference(forward_demodulation,[status(thm)],[f103,f21675]) ).
fof(f21789,plain,
! [X0,X1,X2] : addition(omega(backward_diamond(X0,X1)),X2) = addition(X2,addition(multiplication(backward_diamond(X0,X1),X2),omega(backward_diamond(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1026,f21788]) ).
fof(f21790,plain,
! [X0,X1,X2] : addition(omega(backward_diamond(X0,X1)),X2) = addition(X2,addition(omega(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f35,f21789]) ).
fof(f21791,plain,
! [X0,X1,X2] : addition(coantidomain(backward_diamond(X0,X1)),X2) = addition(X2,addition(coantidomain(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f103,f21676]) ).
fof(f21792,plain,
! [X0,X1,X2] : addition(X0,omega(backward_diamond(X1,X2))) = addition(omega(backward_diamond(X1,X2)),addition(X0,addition(omega(backward_diamond(X1,X2)),multiplication(backward_diamond(X1,X2),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f21677]) ).
fof(f21796,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(backward_diamond(X1,X2),X0))) = addition(omega(multiplication(backward_diamond(X1,X2),X0)),multiplication(X0,omega(multiplication(backward_diamond(X1,X2),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f21681]) ).
fof(f21797,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(backward_diamond(X1,X2),X0))) = multiplication(addition(X0,one),omega(multiplication(backward_diamond(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f232,f21796]) ).
fof(f21801,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_diamond(X1,X2),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21695]) ).
fof(f21802,plain,
! [X0,X1,X2] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(backward_diamond(X1,X2),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f21696]) ).
fof(f21803,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(backward_diamond(X1,X2),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f21697,f239]) ).
fof(f21804,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(backward_diamond(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f21699]) ).
fof(f21815,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(backward_diamond(X3,X4),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f21721]) ).
fof(f21816,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(backward_diamond(X3,X4),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f21815]) ).
fof(f21817,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(backward_diamond(X3,X4),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f21816]) ).
fof(f21819,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(backward_diamond(X3,X4),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f21726]) ).
fof(f21820,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(backward_diamond(X3,X4),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f21819]) ).
fof(f21821,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(backward_diamond(X3,X4),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f21820]) ).
fof(f21822,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(backward_diamond(X3,X4),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f21727]) ).
fof(f21823,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(backward_diamond(X2,X3),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21729]) ).
fof(f21824,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(backward_diamond(X2,X3),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21823]) ).
fof(f21825,plain,
! [X0,X1,X2] : leq(X0,addition(omega(backward_diamond(X1,X2)),multiplication(star(backward_diamond(X1,X2)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f21735,f239]) ).
fof(f21826,plain,
! [X0,X1,X2] : leq(multiplication(star(backward_diamond(X0,X1)),X2),X2),
inference(forward_subsumption_resolution,[status(thm)],[f21737,f239]) ).
fof(f21833,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(backward_diamond(X2,X3),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f21744]) ).
fof(f21834,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f21746]) ).
fof(f21835,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(backward_diamond(X2,X3),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21748]) ).
fof(f21836,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(backward_diamond(X2,X3),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21749]) ).
fof(f21837,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(multiplication(backward_diamond(X1,X2),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f21750]) ).
fof(f21838,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(one,multiplication(backward_diamond(X1,X2),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f21837]) ).
fof(f21847,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(backward_diamond(X2,X3),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f21759]) ).
fof(f21848,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(backward_diamond(X2,X3),X0),X1)
| leq(multiplication(X0,X1),multiplication(backward_diamond(X2,X3),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f21762]) ).
fof(f21849,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(backward_diamond(X2,X3),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(backward_diamond(X2,X3),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f21848]) ).
fof(f21853,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f59,f21766]) ).
fof(f21855,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(backward_diamond(X2,X3),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f21772]) ).
fof(f21856,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(backward_diamond(X2,X3),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f21774]) ).
fof(f21863,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(forward_box(X2,X3),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4508]) ).
fof(f21864,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(forward_box(X2,X3),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4508]) ).
fof(f21872,plain,
! [X0,X1] : codomain(forward_box(X0,X1)) = addition(codomain(forward_box(X0,X1)),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f2309,f4508]) ).
fof(f21873,plain,
! [X0,X1,X2] : addition(omega(forward_box(X0,X1)),X2) = addition(addition(omega(forward_box(X0,X1)),X2),addition(omega(forward_box(X0,X1)),multiplication(forward_box(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f318,f4508]) ).
fof(f21874,plain,
! [X0,X1,X2] : addition(coantidomain(forward_box(X0,X1)),X2) = addition(addition(coantidomain(forward_box(X0,X1)),X2),multiplication(forward_box(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f181,f4508]) ).
fof(f21875,plain,
! [X0,X1,X2] : addition(X0,omega(forward_box(X1,X2))) = addition(addition(X0,omega(forward_box(X1,X2))),addition(omega(forward_box(X1,X2)),multiplication(forward_box(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f321,f4508]) ).
fof(f21879,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(forward_box(X1,X2),X0))) = addition(multiplication(X0,omega(multiplication(forward_box(X1,X2),X0))),omega(multiplication(forward_box(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f308,f4508]) ).
fof(f21898,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(forward_box(X1,X2),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4508,f336]) ).
fof(f21899,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(forward_box(X1,X2),omega(X0)))),
inference(paramodulation,[status(thm)],[f4508,f318]) ).
fof(f21900,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(forward_box(X1,X2),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4508,f314]) ).
fof(f21902,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(forward_box(X1,X2),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4508,f181]) ).
fof(f21923,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(forward_box(X3,X4),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4508,f398]) ).
fof(f21924,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(forward_box(X3,X4),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4508,f332]) ).
fof(f21925,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(forward_box(X3,X4),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4508,f296]) ).
fof(f21929,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(forward_box(X3,X4),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4508,f219]) ).
fof(f21930,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(forward_box(X3,X4),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4508,f170]) ).
fof(f21931,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(forward_box(X2,X3),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4508,f58]) ).
fof(f21932,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(forward_box(X2,X3),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4508,f55]) ).
fof(f21933,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(forward_box(X2,X3),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4508,f53]) ).
fof(f21934,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(forward_box(X2,X3),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4508,f103]) ).
fof(f21935,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(forward_box(X2,X3),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4508,f36]) ).
fof(f21938,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(forward_box(X1,X2)),multiplication(star(forward_box(X1,X2)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4508,f394]) ).
fof(f21939,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X0)),forward_box(X1,X2))
| ~ leq(X0,forward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f4508,f329]) ).
fof(f21940,plain,
! [X0,X1,X2] :
( leq(multiplication(star(forward_box(X1,X2)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4508,f293]) ).
fof(f21945,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(forward_box(X1,X2),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4508,f405]) ).
fof(f21946,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(forward_box(X2,X3),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4508,f392]) ).
fof(f21947,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(forward_box(X2,X3),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4508,f391]) ).
fof(f21949,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(forward_box(X1,X2),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4508,f335]) ).
fof(f21951,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(forward_box(X2,X3),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4508,f341]) ).
fof(f21952,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(forward_box(X2,X3),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4508,f340]) ).
fof(f21953,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(forward_box(X1,X2),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4508,f11449]) ).
fof(f21955,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(forward_box(X1,X2),X0))) = multiplication(addition(X0,one),omega(multiplication(forward_box(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f4508,f10882]) ).
fof(f21960,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(forward_box(X1,X2),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4508,f302]) ).
fof(f21961,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(forward_box(X2,X3),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4508,f291]) ).
fof(f21962,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(forward_box(X2,X3),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4508,f290]) ).
fof(f21963,plain,
! [X0,X1,X2,X3] :
( addition(X0,X1) != multiplication(forward_box(X2,X3),X1)
| leq(addition(X0,X1),multiplication(forward_box(X2,X3),X1)) ),
inference(paramodulation,[status(thm)],[f4508,f243]) ).
fof(f21964,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(forward_box(X2,X3),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(forward_box(X2,X3),X1))) ),
inference(paramodulation,[status(thm)],[f4508,f242]) ).
fof(f21965,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(forward_box(X2,X3),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(forward_box(X2,X3),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4508,f241]) ).
fof(f21969,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f4508,f177]) ).
fof(f21971,plain,
! [X0,X1,X2,X3] : leq(multiplication(forward_box(X0,X1),X2),addition(X3,X2)),
inference(paramodulation,[status(thm)],[f4508,f1420]) ).
fof(f21975,plain,
! [X0,X1,X2,X3] : addition(multiplication(forward_box(X0,X1),X2),addition(X2,X3)) = addition(X2,X3),
inference(paramodulation,[status(thm)],[f4508,f103]) ).
fof(f21976,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(forward_box(X1,X2),X0),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f4508,f97]) ).
fof(f21977,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(forward_box(X2,X3),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4508,f97]) ).
fof(f21979,plain,
! [X0,X1,X2] :
( X0 != multiplication(forward_box(X1,X2),X0)
| leq(X0,multiplication(forward_box(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f4508,f49]) ).
fof(f21980,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(forward_box(X1,X2),X0),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f4508,f36]) ).
fof(f21990,plain,
! [X0,X1] : codomain(forward_box(X0,X1)) = addition(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f21872]) ).
fof(f21991,plain,
! [X0,X1,X2] : addition(omega(forward_box(X0,X1)),X2) = addition(X2,addition(omega(forward_box(X0,X1)),addition(omega(forward_box(X0,X1)),multiplication(forward_box(X0,X1),X2)))),
inference(forward_demodulation,[status(thm)],[f103,f21873]) ).
fof(f21992,plain,
! [X0,X1,X2] : addition(omega(forward_box(X0,X1)),X2) = addition(X2,addition(multiplication(forward_box(X0,X1),X2),omega(forward_box(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1026,f21991]) ).
fof(f21993,plain,
! [X0,X1,X2] : addition(omega(forward_box(X0,X1)),X2) = addition(X2,addition(omega(forward_box(X0,X1)),multiplication(forward_box(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f35,f21992]) ).
fof(f21994,plain,
! [X0,X1,X2] : addition(coantidomain(forward_box(X0,X1)),X2) = addition(X2,addition(coantidomain(forward_box(X0,X1)),multiplication(forward_box(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f103,f21874]) ).
fof(f21995,plain,
! [X0,X1,X2] : addition(X0,omega(forward_box(X1,X2))) = addition(omega(forward_box(X1,X2)),addition(X0,addition(omega(forward_box(X1,X2)),multiplication(forward_box(X1,X2),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f21875]) ).
fof(f21999,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(forward_box(X1,X2),X0))) = addition(omega(multiplication(forward_box(X1,X2),X0)),multiplication(X0,omega(multiplication(forward_box(X1,X2),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f21879]) ).
fof(f22000,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(forward_box(X1,X2),X0))) = multiplication(addition(X0,one),omega(multiplication(forward_box(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f232,f21999]) ).
fof(f22009,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_box(X1,X2),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21898]) ).
fof(f22010,plain,
! [X0,X1,X2] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(forward_box(X1,X2),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f21899]) ).
fof(f22011,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(forward_box(X1,X2),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f21900,f239]) ).
fof(f22012,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(forward_box(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f21902]) ).
fof(f22023,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(forward_box(X3,X4),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f21924]) ).
fof(f22024,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(forward_box(X3,X4),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f22023]) ).
fof(f22025,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(forward_box(X3,X4),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f22024]) ).
fof(f22027,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(forward_box(X3,X4),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f21929]) ).
fof(f22028,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(forward_box(X3,X4),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f22027]) ).
fof(f22029,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(forward_box(X3,X4),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f22028]) ).
fof(f22030,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(forward_box(X3,X4),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f21930]) ).
fof(f22031,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(forward_box(X2,X3),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21932]) ).
fof(f22032,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(forward_box(X2,X3),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f22031]) ).
fof(f22033,plain,
! [X0,X1,X2] : leq(X0,addition(omega(forward_box(X1,X2)),multiplication(star(forward_box(X1,X2)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f21938,f239]) ).
fof(f22034,plain,
! [X0,X1,X2] : leq(multiplication(star(forward_box(X0,X1)),X2),X2),
inference(forward_subsumption_resolution,[status(thm)],[f21940,f239]) ).
fof(f22041,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(forward_box(X2,X3),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f21947]) ).
fof(f22042,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f21949]) ).
fof(f22043,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(forward_box(X2,X3),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21951]) ).
fof(f22044,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(forward_box(X2,X3),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f21952]) ).
fof(f22045,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(multiplication(forward_box(X1,X2),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f21953]) ).
fof(f22046,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(one,multiplication(forward_box(X1,X2),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f22045]) ).
fof(f22055,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(forward_box(X2,X3),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f21962]) ).
fof(f22056,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(forward_box(X2,X3),X0),X1)
| leq(multiplication(X0,X1),multiplication(forward_box(X2,X3),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f21965]) ).
fof(f22057,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(forward_box(X2,X3),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(forward_box(X2,X3),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f22056]) ).
fof(f22061,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f59,f21969]) ).
fof(f22063,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(forward_box(X2,X3),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f21975]) ).
fof(f22064,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(forward_box(X2,X3),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f21977]) ).
fof(f22071,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(backward_box(X2,X3),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f103,f4509]) ).
fof(f22072,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(backward_box(X2,X3),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4509]) ).
fof(f22080,plain,
! [X0,X1] : codomain(backward_box(X0,X1)) = addition(codomain(backward_box(X0,X1)),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f2309,f4509]) ).
fof(f22081,plain,
! [X0,X1,X2] : addition(omega(backward_box(X0,X1)),X2) = addition(addition(omega(backward_box(X0,X1)),X2),addition(omega(backward_box(X0,X1)),multiplication(backward_box(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f318,f4509]) ).
fof(f22082,plain,
! [X0,X1,X2] : addition(coantidomain(backward_box(X0,X1)),X2) = addition(addition(coantidomain(backward_box(X0,X1)),X2),multiplication(backward_box(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f181,f4509]) ).
fof(f22083,plain,
! [X0,X1,X2] : addition(X0,omega(backward_box(X1,X2))) = addition(addition(X0,omega(backward_box(X1,X2))),addition(omega(backward_box(X1,X2)),multiplication(backward_box(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f321,f4509]) ).
fof(f22087,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(backward_box(X1,X2),X0))) = addition(multiplication(X0,omega(multiplication(backward_box(X1,X2),X0))),omega(multiplication(backward_box(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f308,f4509]) ).
fof(f22102,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(backward_box(X1,X2),omega(X0)),star(omega(X0))),X0)
| ~ leq(omega(X0),X0) ),
inference(paramodulation,[status(thm)],[f4509,f336]) ).
fof(f22103,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = addition(omega(X0),multiplication(X0,multiplication(backward_box(X1,X2),omega(X0)))),
inference(paramodulation,[status(thm)],[f4509,f318]) ).
fof(f22104,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(backward_box(X1,X2),omega(X0))),omega(X0))
| ~ leq(omega(X0),omega(X0)) ),
inference(paramodulation,[status(thm)],[f4509,f314]) ).
fof(f22106,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(backward_box(X1,X2),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4509,f181]) ).
fof(f22127,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,addition(omega(multiplication(X1,X2)),multiplication(star(multiplication(X1,X2)),multiplication(backward_box(X3,X4),multiplication(X1,multiplication(X2,X0))))))
| ~ leq(X0,multiplication(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f4509,f398]) ).
fof(f22128,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(multiplication(backward_box(X3,X4),multiplication(X0,multiplication(X1,X2))),star(X2)),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4509,f332]) ).
fof(f22129,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(star(multiplication(X0,X1)),multiplication(backward_box(X3,X4),multiplication(X0,multiplication(X1,X2)))),X2)
| ~ leq(multiplication(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f4509,f296]) ).
fof(f22133,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(backward_box(X3,X4),multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f4509,f219]) ).
fof(f22134,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(backward_box(X3,X4),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f4509,f170]) ).
fof(f22135,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(backward_box(X2,X3),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4509,f58]) ).
fof(f22136,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(backward_box(X2,X3),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4509,f55]) ).
fof(f22137,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(backward_box(X2,X3),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4509,f53]) ).
fof(f22138,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(backward_box(X2,X3),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4509,f103]) ).
fof(f22139,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(backward_box(X2,X3),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4509,f36]) ).
fof(f22142,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(backward_box(X1,X2)),multiplication(star(backward_box(X1,X2)),X0)))
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4509,f394]) ).
fof(f22143,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X0)),backward_box(X1,X2))
| ~ leq(X0,backward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f4509,f329]) ).
fof(f22144,plain,
! [X0,X1,X2] :
( leq(multiplication(star(backward_box(X1,X2)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4509,f293]) ).
fof(f22149,plain,
! [X0,X1,X2] :
( leq(one,addition(omega(X0),multiplication(star(X0),multiplication(backward_box(X1,X2),X0))))
| ~ leq(one,X0) ),
inference(paramodulation,[status(thm)],[f4509,f405]) ).
fof(f22150,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(X1,multiplication(backward_box(X2,X3),X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4509,f392]) ).
fof(f22151,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(multiplication(backward_box(X2,X3),X1),X0))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f4509,f391]) ).
fof(f22153,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(backward_box(X1,X2),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4509,f335]) ).
fof(f22155,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(multiplication(backward_box(X2,X3),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4509,f341]) ).
fof(f22156,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(backward_box(X2,X3),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4509,f340]) ).
fof(f22157,plain,
! [X0,X1,X2] : multiplication(X0,omega(X0)) = multiplication(addition(multiplication(backward_box(X1,X2),X0),one),omega(X0)),
inference(paramodulation,[status(thm)],[f4509,f11449]) ).
fof(f22159,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(backward_box(X1,X2),X0))) = multiplication(addition(X0,one),omega(multiplication(backward_box(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f4509,f10882]) ).
fof(f22164,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(backward_box(X1,X2),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4509,f302]) ).
fof(f22165,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(backward_box(X2,X3),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4509,f291]) ).
fof(f22166,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(multiplication(backward_box(X2,X3),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4509,f290]) ).
fof(f22167,plain,
! [X0,X1,X2,X3] :
( addition(X0,X1) != multiplication(backward_box(X2,X3),X1)
| leq(addition(X0,X1),multiplication(backward_box(X2,X3),X1)) ),
inference(paramodulation,[status(thm)],[f4509,f243]) ).
fof(f22168,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(X0,multiplication(backward_box(X2,X3),X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(backward_box(X2,X3),X1))) ),
inference(paramodulation,[status(thm)],[f4509,f242]) ).
fof(f22169,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(backward_box(X2,X3),X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(backward_box(X2,X3),X0),X1)) ),
inference(paramodulation,[status(thm)],[f4509,f241]) ).
fof(f22173,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f4509,f177]) ).
fof(f22175,plain,
! [X0,X1,X2,X3] : leq(multiplication(backward_box(X0,X1),X2),addition(X3,X2)),
inference(paramodulation,[status(thm)],[f4509,f1420]) ).
fof(f22179,plain,
! [X0,X1,X2,X3] : addition(multiplication(backward_box(X0,X1),X2),addition(X2,X3)) = addition(X2,X3),
inference(paramodulation,[status(thm)],[f4509,f103]) ).
fof(f22180,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(backward_box(X1,X2),X0),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f4509,f97]) ).
fof(f22181,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(backward_box(X2,X3),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4509,f97]) ).
fof(f22183,plain,
! [X0,X1,X2] :
( X0 != multiplication(backward_box(X1,X2),X0)
| leq(X0,multiplication(backward_box(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f4509,f49]) ).
fof(f22184,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(backward_box(X1,X2),X0),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f4509,f36]) ).
fof(f22194,plain,
! [X0,X1] : codomain(backward_box(X0,X1)) = addition(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f22080]) ).
fof(f22195,plain,
! [X0,X1,X2] : addition(omega(backward_box(X0,X1)),X2) = addition(X2,addition(omega(backward_box(X0,X1)),addition(omega(backward_box(X0,X1)),multiplication(backward_box(X0,X1),X2)))),
inference(forward_demodulation,[status(thm)],[f103,f22081]) ).
fof(f22196,plain,
! [X0,X1,X2] : addition(omega(backward_box(X0,X1)),X2) = addition(X2,addition(multiplication(backward_box(X0,X1),X2),omega(backward_box(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1026,f22195]) ).
fof(f22197,plain,
! [X0,X1,X2] : addition(omega(backward_box(X0,X1)),X2) = addition(X2,addition(omega(backward_box(X0,X1)),multiplication(backward_box(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f35,f22196]) ).
fof(f22198,plain,
! [X0,X1,X2] : addition(coantidomain(backward_box(X0,X1)),X2) = addition(X2,addition(coantidomain(backward_box(X0,X1)),multiplication(backward_box(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f103,f22082]) ).
fof(f22199,plain,
! [X0,X1,X2] : addition(X0,omega(backward_box(X1,X2))) = addition(omega(backward_box(X1,X2)),addition(X0,addition(omega(backward_box(X1,X2)),multiplication(backward_box(X1,X2),X0)))),
inference(forward_demodulation,[status(thm)],[f103,f22083]) ).
fof(f22203,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(backward_box(X1,X2),X0))) = addition(omega(multiplication(backward_box(X1,X2),X0)),multiplication(X0,omega(multiplication(backward_box(X1,X2),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f22087]) ).
fof(f22204,plain,
! [X0,X1,X2] : multiplication(X0,omega(multiplication(backward_box(X1,X2),X0))) = multiplication(addition(X0,one),omega(multiplication(backward_box(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f232,f22203]) ).
fof(f22210,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_box(X1,X2),multiplication(omega(X0),star(omega(X0)))),X0)
| ~ leq(omega(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f22102]) ).
fof(f22211,plain,
! [X0,X1,X2] : omega(X0) = addition(omega(X0),multiplication(X0,multiplication(backward_box(X1,X2),omega(X0)))),
inference(forward_demodulation,[status(thm)],[f56,f22103]) ).
fof(f22212,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(backward_box(X1,X2),omega(X0))),omega(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f22104,f239]) ).
fof(f22213,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(backward_box(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f63,f22106]) ).
fof(f22224,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(backward_box(X3,X4),multiplication(multiplication(X0,multiplication(X1,X2)),star(X2))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f22128]) ).
fof(f22225,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(backward_box(X3,X4),multiplication(X0,multiplication(multiplication(X1,X2),star(X2)))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f22224]) ).
fof(f22226,plain,
! [X0,X1,X2,X3,X4] :
( leq(multiplication(backward_box(X3,X4),multiplication(X0,multiplication(X1,multiplication(X2,star(X2))))),multiplication(X0,X1))
| ~ leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f22225]) ).
fof(f22228,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(backward_box(X3,X4),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f201,f22133]) ).
fof(f22229,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),multiplication(backward_box(X3,X4),X0)),X2),
inference(forward_demodulation,[status(thm)],[f211,f22228]) ).
fof(f22230,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,multiplication(backward_box(X3,X4),X0))),X2),
inference(forward_demodulation,[status(thm)],[f103,f22229]) ).
fof(f22231,plain,
! [X0,X1,X2,X3,X4] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(backward_box(X3,X4),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f153,f22134]) ).
fof(f22232,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(backward_box(X2,X3),multiplication(multiplication(X0,X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f22136]) ).
fof(f22233,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(backward_box(X2,X3),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f22232]) ).
fof(f22234,plain,
! [X0,X1,X2] : leq(X0,addition(omega(backward_box(X1,X2)),multiplication(star(backward_box(X1,X2)),X0))),
inference(forward_subsumption_resolution,[status(thm)],[f22142,f239]) ).
fof(f22235,plain,
! [X0,X1,X2] : leq(multiplication(star(backward_box(X0,X1)),X2),X2),
inference(forward_subsumption_resolution,[status(thm)],[f22144,f239]) ).
fof(f22242,plain,
! [X0,X1,X2,X3] :
( leq(X0,addition(omega(X1),multiplication(star(X1),multiplication(backward_box(X2,X3),multiplication(X1,X0)))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f22151]) ).
fof(f22243,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f22153]) ).
fof(f22244,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,multiplication(backward_box(X2,X3),multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f22155]) ).
fof(f22245,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(backward_box(X2,X3),multiplication(X0,multiplication(X1,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f22156]) ).
fof(f22246,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(multiplication(backward_box(X1,X2),X0),one),omega(X0)),
inference(forward_demodulation,[status(thm)],[f56,f22157]) ).
fof(f22247,plain,
! [X0,X1,X2] : omega(X0) = multiplication(addition(one,multiplication(backward_box(X1,X2),X0)),omega(X0)),
inference(forward_demodulation,[status(thm)],[f35,f22246]) ).
fof(f22256,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(backward_box(X2,X3),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f22166]) ).
fof(f22257,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(multiplication(backward_box(X2,X3),X0),X1)
| leq(multiplication(X0,X1),multiplication(backward_box(X2,X3),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f22169]) ).
fof(f22258,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,X1) != multiplication(backward_box(X2,X3),multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(backward_box(X2,X3),multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f39,f22257]) ).
fof(f22262,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f59,f22173]) ).
fof(f22264,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(backward_box(X2,X3),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f97,f22179]) ).
fof(f22265,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(backward_box(X2,X3),X1),X0)),
inference(forward_demodulation,[status(thm)],[f97,f22181]) ).
fof(f22271,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(antidomain(forward_diamond(X0,X1)),domain(forward_diamond(X0,X1))) ),
inference(paramodulation,[status(thm)],[f19262,f566]) ).
fof(f22272,plain,
! [X0] :
( one != divergence(X0)
| leq(antidomain(divergence(X0)),domain(divergence(X0))) ),
inference(paramodulation,[status(thm)],[f20605,f566]) ).
fof(f22274,plain,
! [X0] :
( one != antidomain(X0)
| leq(antidomain(antidomain(X0)),domain(antidomain(X0))) ),
inference(paramodulation,[status(thm)],[f18890,f566]) ).
fof(f22275,plain,
! [X0] :
( one != one
| leq(antidomain(addition(one,X0)),domain(addition(one,X0))) ),
inference(paramodulation,[status(thm)],[f15345,f566]) ).
fof(f22276,plain,
! [X0] :
( one != one
| leq(antidomain(addition(X0,one)),domain(addition(X0,one))) ),
inference(paramodulation,[status(thm)],[f15407,f566]) ).
fof(f22277,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(antidomain(forward_box(X0,X1)),domain(forward_box(X0,X1))) ),
inference(paramodulation,[status(thm)],[f13917,f566]) ).
fof(f22278,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(antidomain(backward_box(X0,X1)),domain(backward_box(X0,X1))) ),
inference(paramodulation,[status(thm)],[f13916,f566]) ).
fof(f22279,plain,
! [X0] :
( one != one
| leq(antidomain(star(X0)),domain(star(X0))) ),
inference(paramodulation,[status(thm)],[f8543,f566]) ).
fof(f22280,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(antidomain(multiplication(X0,domain(X1))),domain(multiplication(X0,domain(X1)))) ),
inference(paramodulation,[status(thm)],[f69,f566]) ).
fof(f22281,plain,
( one != zero
| leq(antidomain(zero),domain(zero)) ),
inference(paramodulation,[status(thm)],[f607,f566]) ).
fof(f22282,plain,
( one != one
| leq(antidomain(one),domain(one)) ),
inference(paramodulation,[status(thm)],[f570,f566]) ).
fof(f22291,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(antidomain(forward_diamond(X0,X1)),forward_diamond(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f19262,f22271]) ).
fof(f22292,plain,
! [X0] :
( one != divergence(X0)
| leq(antidomain(divergence(X0)),divergence(X0)) ),
inference(forward_demodulation,[status(thm)],[f20605,f22272]) ).
fof(f22295,plain,
! [X0] :
( one != antidomain(X0)
| leq(domain(X0),domain(antidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f62,f22274]) ).
fof(f22296,plain,
! [X0] :
( one != antidomain(X0)
| leq(domain(X0),antidomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f18890,f22295]) ).
fof(f22297,definition,
! [X0] :
( sQ59_spl
<=> leq(antidomain(addition(one,X0)),domain(addition(one,X0))) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f22300,plain,
( ~ sQ1_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f22275,f22297,f1528]) ).
fof(f22301,definition,
! [X0] :
( sQ60_spl
<=> leq(antidomain(addition(X0,one)),domain(addition(X0,one))) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f22304,plain,
( ~ sQ1_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f22276,f22301,f1528]) ).
fof(f22305,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(antidomain(forward_box(X0,X1)),forward_box(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f13917,f22277]) ).
fof(f22306,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(antidomain(backward_box(X0,X1)),backward_box(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f13916,f22278]) ).
fof(f22307,definition,
! [X0] :
( sQ61_spl
<=> leq(antidomain(star(X0)),domain(star(X0))) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f22310,plain,
( ~ sQ1_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f22279,f22307,f1528]) ).
fof(f22311,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f69,f22280]) ).
fof(f22312,definition,
( sQ62_spl
<=> leq(antidomain(zero),domain(zero)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f22313,plain,
( ~ sQ62_spl
| leq(antidomain(zero),domain(zero)) ),
inference(component_clause,[status(thm)],[f22312]) ).
fof(f22315,definition,
( sQ63_spl
<=> one = zero ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f22318,plain,
( ~ sQ63_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f22281,f22312,f22315]) ).
fof(f22319,definition,
( sQ64_spl
<=> leq(antidomain(one),domain(one)) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f22322,plain,
( ~ sQ1_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f22282,f22319,f1528]) ).
fof(f22331,plain,
( ~ sQ62_spl
| leq(one,domain(zero)) ),
inference(forward_demodulation,[status(thm)],[f577,f22313]) ).
fof(f22332,plain,
( ~ sQ62_spl
| leq(one,zero) ),
inference(forward_demodulation,[status(thm)],[f607,f22331]) ).
fof(f22338,plain,
( ~ sQ62_spl
| addition(one,zero) = zero ),
inference(resolution,[status(thm)],[f22332,f48]) ).
fof(f22351,plain,
( ~ sQ62_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f37,f22338]) ).
fof(f22365,plain,
! [X0,X1] :
( ~ sQ62_spl
| leq(X0,addition(X1,omega(zero))) ),
inference(backward_demodulation,[status(thm)],[f22351,f17361]) ).
fof(f22463,plain,
! [X0,X1] :
( ~ sQ62_spl
| leq(X0,addition(X1,zero)) ),
inference(forward_demodulation,[status(thm)],[f309,f22365]) ).
fof(f22464,plain,
! [X0,X1] :
( ~ sQ62_spl
| leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f37,f22463]) ).
fof(f22546,plain,
! [X0,X1] :
( ~ sQ62_spl
| addition(X0,X1) = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[f48,f22464]) ).
fof(f22758,plain,
! [X0] :
( ~ sQ62_spl
| zero = X0 ),
inference(backward_demodulation,[status(thm)],[f22546,f37]) ).
fof(f22774,plain,
! [X0,X1] :
( ~ sQ62_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f22758,f22758]) ).
fof(model,axiom,
( sQ0_spl
| sQ1_spl
| sQ2_spl
| sQ3_spl
| sQ4_spl
| sQ5_spl
| sQ6_spl
| sQ7_spl
| sQ8_spl
| sQ9_spl
| sQ10_spl
| sQ11_spl
| sQ12_spl
| sQ13_spl
| sQ14_spl
| sQ15_spl
| sQ16_spl
| sQ17_spl
| sQ18_spl
| sQ19_spl
| sQ20_spl
| sQ21_spl
| sQ22_spl
| sQ23_spl
| sQ24_spl
| sQ25_spl
| sQ26_spl
| sQ27_spl
| sQ28_spl
| sQ29_spl
| sQ30_spl
| sQ31_spl
| sQ32_spl
| sQ33_spl
| sQ34_spl
| sQ35_spl
| sQ36_spl
| sQ37_spl
| sQ38_spl
| sQ39_spl
| sQ40_spl
| sQ41_spl
| sQ42_spl
| sQ43_spl
| sQ44_spl
| sQ45_spl
| sQ46_spl
| sQ47_spl
| sQ48_spl
| sQ49_spl
| sQ50_spl
| sQ51_spl
| sQ52_spl
| sQ53_spl
| sQ54_spl
| sQ55_spl
| sQ56_spl
| sQ57_spl
| sQ58_spl
| sQ59_spl
| sQ60_spl
| sQ61_spl
| sQ62_spl
| sQ64_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE180+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:52:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 1.45/1.84 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 1.45/1.84 % SZS output start Saturation for theBenchmark
% See solution above
% 0.75/2.01 % Elapsed time: 1.619032 seconds
% 0.75/2.01 % CPU time: 10.876302 seconds
% 0.75/2.01 % Total memory used: 123.835 MB
% 0.75/2.01 % Net memory used: 118.135 MB
%------------------------------------------------------------------------------