%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE177+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 : n019.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 12:58:28 PM UTC 2026
% Result : Satisfiable 0.94s 1.51s
% Output : Saturation 0.69s
% 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,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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(f19,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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(f23,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,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(f33,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f35,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f38,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f39,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f40,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f41,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f45,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f49,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f50,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(f51,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,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(f53,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f55,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)],[f18]) ).
fof(f56,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f57,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f58,plain,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f59,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)],[f22]) ).
fof(f60,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f62,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f63,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f64,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f65,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f66,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f67,plain,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f68,plain,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f69,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)],[f32]) ).
fof(f70,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)],[f69]) ).
fof(f75,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f35,f33]) ).
fof(f92,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f34]) ).
fof(f94,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f36,f34]) ).
fof(f98,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f33,f34]) ).
fof(f100,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f36,f34]) ).
fof(f114,plain,
antidomain(one) = zero,
inference(paramodulation,[status(thm)],[f38,f54]) ).
fof(f121,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f54,f37]) ).
fof(f131,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f121]) ).
fof(f136,plain,
! [X0] : domain(antidomain(X0)) = antidomain(domain(X0)),
inference(paramodulation,[status(thm)],[f57,f57]) ).
fof(f137,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f114,f57]) ).
fof(f138,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f57,f54]) ).
fof(f139,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f37,f58]) ).
fof(f141,plain,
coantidomain(one) = zero,
inference(paramodulation,[status(thm)],[f39,f58]) ).
fof(f145,plain,
! [X0,X1] : multiplication(X0,multiplication(coantidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f58,f37]) ).
fof(f146,plain,
! [X0,X1] : multiplication(X0,multiplication(coantidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f145]) ).
fof(f148,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f40]) ).
fof(f152,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f54,f40]) ).
fof(f155,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f58,f40]) ).
fof(f157,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f38,f40]) ).
fof(f159,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f54,f40]) ).
fof(f162,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f58,f40]) ).
fof(f164,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f38,f40]) ).
fof(f165,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)],[f40,f34]) ).
fof(f172,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f152]) ).
fof(f176,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f155]) ).
fof(f181,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f159]) ).
fof(f185,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f162]) ).
fof(f187,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f164]) ).
fof(f188,plain,
! [X0] : codomain(coantidomain(X0)) = coantidomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f61,f61]) ).
fof(f189,plain,
codomain(one) = coantidomain(zero),
inference(paramodulation,[status(thm)],[f141,f61]) ).
fof(f190,plain,
! [X0] : multiplication(coantidomain(X0),codomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f61,f58]) ).
fof(f191,plain,
! [X0] : domain(domain(X0)) = antidomain(c(X0)),
inference(paramodulation,[status(thm)],[f62,f57]) ).
fof(f192,plain,
! [X0] : multiplication(c(X0),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f62,f54]) ).
fof(f193,plain,
c(one) = antidomain(antidomain(zero)),
inference(paramodulation,[status(thm)],[f137,f62]) ).
fof(f194,plain,
c(one) = domain(zero),
inference(forward_demodulation,[status(thm)],[f57,f193]) ).
fof(f196,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f33,f41]) ).
fof(f199,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)],[f37,f41]) ).
fof(f200,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f54,f41]) ).
fof(f202,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f41]) ).
fof(f203,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(zero,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f58,f41]) ).
fof(f206,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)],[f37,f41]) ).
fof(f207,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f54,f41]) ).
fof(f209,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f39,f41]) ).
fof(f210,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),zero),
inference(paramodulation,[status(thm)],[f58,f41]) ).
fof(f214,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)],[f41,f34]) ).
fof(f219,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f75,f200]) ).
fof(f221,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f75,f203]) ).
fof(f225,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f207]) ).
fof(f227,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f209]) ).
fof(f228,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f35,f210]) ).
fof(f234,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f47,f36]) ).
fof(f235,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f47,f75]) ).
fof(f236,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f41,f47]) ).
fof(f237,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f40,f47]) ).
fof(f238,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f34,f47]) ).
fof(f240,plain,
! [X0] :
( X0 != zero
| leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f35,f47]) ).
fof(f241,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f33,f47]) ).
fof(f246,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f48,f46]) ).
fof(f247,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f37,f48]) ).
fof(f248,plain,
leq(addition(one,zero),star(zero)),
inference(paramodulation,[status(thm)],[f43,f48]) ).
fof(f249,plain,
leq(addition(one,star(one)),star(one)),
inference(paramodulation,[status(thm)],[f39,f48]) ).
fof(f250,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f34,f246]) ).
fof(f251,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f33,f250]) ).
fof(f252,plain,
leq(one,star(zero)),
inference(forward_demodulation,[status(thm)],[f35,f248]) ).
fof(f255,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f49,f46]) ).
fof(f258,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f34,f255]) ).
fof(f259,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f33,f258]) ).
fof(f284,plain,
addition(one,star(zero)) = star(zero),
inference(resolution,[status(thm)],[f252,f46]) ).
fof(f285,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f41,f51]) ).
fof(f286,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f40,f51]) ).
fof(f288,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f33,f51]) ).
fof(f290,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f36,f51]) ).
fof(f291,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)],[f37,f51]) ).
fof(f292,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f54,f51]) ).
fof(f293,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f43,f51]) ).
fof(f294,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f39,f51]) ).
fof(f295,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),coantidomain(X1))
| ~ leq(addition(zero,X0),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f58,f51]) ).
fof(f296,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f42,f51]) ).
fof(f297,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f38,f51]) ).
fof(f299,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f292]) ).
fof(f300,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f293]) ).
fof(f301,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f295]) ).
fof(f302,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f296]) ).
fof(f306,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f41,f241]) ).
fof(f307,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f40,f241]) ).
fof(f308,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f34,f241]) ).
fof(f316,plain,
! [X0] : domain(antidomain(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f62,f136]) ).
fof(f317,plain,
! [X0] : domain(c(X0)) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f62,f316]) ).
fof(f318,plain,
! [X0] : domain(domain(X0)) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f57,f316]) ).
fof(f321,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X1,X2),star(X2)),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f41,f53]) ).
fof(f322,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f40,f53]) ).
fof(f324,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f33,f53]) ).
fof(f326,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f36,f53]) ).
fof(f327,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)],[f37,f53]) ).
fof(f328,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f54,f53]) ).
fof(f329,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f43,f53]) ).
fof(f330,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f39,f53]) ).
fof(f331,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f58,f53]) ).
fof(f333,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f38,f53]) ).
fof(f334,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f37,f321]) ).
fof(f335,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f37,f322]) ).
fof(f337,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f37,f326]) ).
fof(f338,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f328]) ).
fof(f339,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f329]) ).
fof(f340,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f331]) ).
fof(f345,plain,
! [X0] : multiplication(domain(domain(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f62,f138]) ).
fof(f348,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),domain(X1))
| ~ leq(addition(zero,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f138,f53]) ).
fof(f349,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f138,f51]) ).
fof(f350,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = addition(multiplication(X0,antidomain(X1)),zero),
inference(paramodulation,[status(thm)],[f138,f41]) ).
fof(f351,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = addition(zero,multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f138,f41]) ).
fof(f352,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = addition(multiplication(domain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f138,f40]) ).
fof(f353,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = addition(zero,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f138,f40]) ).
fof(f354,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f138,f37]) ).
fof(f359,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f348]) ).
fof(f360,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f349]) ).
fof(f361,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = multiplication(X0,antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f35,f350]) ).
fof(f362,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f75,f351]) ).
fof(f363,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f352]) ).
fof(f364,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f353]) ).
fof(f365,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f354]) ).
fof(f375,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),coantidomain(X1))
| ~ leq(addition(zero,X0),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f190,f53]) ).
fof(f376,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(addition(zero,X0),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f190,f51]) ).
fof(f377,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = addition(multiplication(X0,codomain(X1)),zero),
inference(paramodulation,[status(thm)],[f190,f41]) ).
fof(f378,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = addition(zero,multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f190,f41]) ).
fof(f379,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f190,f40]) ).
fof(f380,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = addition(zero,multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f190,f40]) ).
fof(f381,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f190,f37]) ).
fof(f386,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f375]) ).
fof(f387,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f376]) ).
fof(f388,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f35,f377]) ).
fof(f389,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f75,f378]) ).
fof(f390,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f379]) ).
fof(f391,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f380]) ).
fof(f392,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f381]) ).
fof(f393,plain,
! [X0] : domain(antidomain(c(X0))) = antidomain(c(domain(X0))),
inference(paramodulation,[status(thm)],[f191,f191]) ).
fof(f394,plain,
! [X0] : domain(c(X0)) = antidomain(c(antidomain(X0))),
inference(paramodulation,[status(thm)],[f316,f191]) ).
fof(f398,plain,
! [X0] : c(c(X0)) = antidomain(c(domain(X0))),
inference(forward_demodulation,[status(thm)],[f316,f393]) ).
fof(f403,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f57,f55]) ).
fof(f404,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f57,f403]) ).
fof(f405,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(resolution,[status(thm)],[f404,f47]) ).
fof(f406,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))) = antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f190,f404]) ).
fof(f407,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(domain(X0),domain(antidomain(X0))))) = antidomain(multiplication(domain(X0),domain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f138,f404]) ).
fof(f408,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)],[f37,f404]) ).
fof(f409,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(X0)))) = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f54,f404]) ).
fof(f411,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(one,domain(X0)))) = antidomain(multiplication(one,domain(X0))),
inference(paramodulation,[status(thm)],[f39,f404]) ).
fof(f412,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(X0,domain(coantidomain(X0))))) = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f58,f404]) ).
fof(f419,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)],[f191,f404]) ).
fof(f420,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))) = antidomain(multiplication(X0,domain(antidomain(X1)))),
inference(paramodulation,[status(thm)],[f316,f404]) ).
fof(f421,plain,
! [X0] : addition(antidomain(multiplication(X0,one)),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,domain(one))),
inference(paramodulation,[status(thm)],[f137,f404]) ).
fof(f422,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)],[f404,f241]) ).
fof(f424,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)],[f404,f34]) ).
fof(f425,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(domain(X0),c(X0)))) = antidomain(multiplication(domain(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f316,f407]) ).
fof(f426,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(domain(X0),c(X0)))) = antidomain(multiplication(domain(X0),c(X0))),
inference(forward_demodulation,[status(thm)],[f316,f425]) ).
fof(f427,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)],[f37,f408]) ).
fof(f428,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)],[f37,f427]) ).
fof(f431,plain,
! [X0] : addition(antidomain(X0),antidomain(domain(X0))) = antidomain(multiplication(one,domain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f411]) ).
fof(f432,plain,
! [X0] : addition(antidomain(X0),c(X0)) = antidomain(multiplication(one,domain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f431]) ).
fof(f433,plain,
! [X0] : addition(antidomain(X0),c(X0)) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f39,f432]) ).
fof(f434,plain,
! [X0] : addition(antidomain(X0),c(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f62,f433]) ).
fof(f451,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)],[f191,f419]) ).
fof(f452,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))) = antidomain(multiplication(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f316,f420]) ).
fof(f453,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,domain(one))),
inference(forward_demodulation,[status(thm)],[f38,f421]) ).
fof(f454,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,antidomain(zero))),
inference(forward_demodulation,[status(thm)],[f137,f453]) ).
fof(f458,plain,
! [X0] : multiplication(c(domain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f191,f192]) ).
fof(f459,plain,
! [X0] : multiplication(c(antidomain(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f316,f192]) ).
fof(f461,plain,
! [X0] : addition(antidomain(multiplication(c(X0),X0)),antidomain(zero)) = antidomain(multiplication(c(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f192,f404]) ).
fof(f462,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),domain(domain(X0))))) = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f192,f404]) ).
fof(f463,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(addition(zero,X0),c(X1)) ),
inference(paramodulation,[status(thm)],[f192,f53]) ).
fof(f464,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),domain(X1))
| ~ leq(addition(zero,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f192,f51]) ).
fof(f465,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = addition(multiplication(X0,domain(X1)),zero),
inference(paramodulation,[status(thm)],[f192,f41]) ).
fof(f466,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = addition(zero,multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f192,f41]) ).
fof(f467,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f192,f40]) ).
fof(f468,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f192,f40]) ).
fof(f469,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f192,f37]) ).
fof(f473,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),X0))) = antidomain(multiplication(c(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f461]) ).
fof(f474,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),X0))) = antidomain(zero),
inference(forward_demodulation,[status(thm)],[f192,f473]) ).
fof(f475,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),antidomain(c(X0))))) = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f462]) ).
fof(f476,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),antidomain(c(X0))))) = antidomain(multiplication(c(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f475]) ).
fof(f477,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f463]) ).
fof(f478,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f464]) ).
fof(f479,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f35,f465]) ).
fof(f480,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f75,f466]) ).
fof(f481,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f467]) ).
fof(f482,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f468]) ).
fof(f483,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f469]) ).
fof(f484,plain,
! [X0] : domain(c(domain(X0))) = c(antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f191,f317]) ).
fof(f485,plain,
! [X0] : domain(c(antidomain(X0))) = c(c(X0)),
inference(paramodulation,[status(thm)],[f316,f317]) ).
fof(f486,plain,
domain(c(one)) = c(antidomain(zero)),
inference(paramodulation,[status(thm)],[f137,f317]) ).
fof(f488,plain,
! [X0] : domain(domain(c(X0))) = c(antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f317,f484]) ).
fof(f489,plain,
! [X0] : antidomain(c(c(X0))) = c(antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f191,f488]) ).
fof(f490,plain,
domain(domain(zero)) = c(antidomain(zero)),
inference(forward_demodulation,[status(thm)],[f194,f486]) ).
fof(f491,plain,
antidomain(c(zero)) = c(antidomain(zero)),
inference(forward_demodulation,[status(thm)],[f191,f490]) ).
fof(f493,plain,
! [X0] : antidomain(c(X0)) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f191,f318]) ).
fof(f503,plain,
! [X0] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f33,f56]) ).
fof(f504,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f57,f503]) ).
fof(f505,plain,
! [X0] : addition(c(X0),domain(domain(X0))) = one,
inference(paramodulation,[status(thm)],[f62,f504]) ).
fof(f506,plain,
! [X0] : addition(domain(X0),domain(antidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f57,f504]) ).
fof(f507,plain,
addition(zero,domain(one)) = one,
inference(paramodulation,[status(thm)],[f114,f504]) ).
fof(f508,plain,
! [X0] : addition(antidomain(domain(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f191,f504]) ).
fof(f510,plain,
addition(antidomain(one),antidomain(zero)) = one,
inference(paramodulation,[status(thm)],[f137,f504]) ).
fof(f511,plain,
! [X0] :
( one != antidomain(X0)
| leq(domain(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f504,f241]) ).
fof(f512,plain,
! [X0] :
( one != domain(X0)
| leq(antidomain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f504,f47]) ).
fof(f513,plain,
! [X0,X1] : addition(antidomain(X0),addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f504,f34]) ).
fof(f514,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f191,f505]) ).
fof(f515,plain,
! [X0] : addition(domain(X0),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f316,f506]) ).
fof(f516,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f75,f507]) ).
fof(f517,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f62,f508]) ).
fof(f521,plain,
addition(antidomain(zero),antidomain(one)) = one,
inference(forward_demodulation,[status(thm)],[f33,f510]) ).
fof(f522,plain,
addition(antidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f114,f521]) ).
fof(f523,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f35,f522]) ).
fof(f527,plain,
multiplication(c(one),one) = zero,
inference(paramodulation,[status(thm)],[f516,f192]) ).
fof(f529,plain,
domain(one) = antidomain(c(one)),
inference(paramodulation,[status(thm)],[f516,f191]) ).
fof(f537,plain,
c(one) = zero,
inference(forward_demodulation,[status(thm)],[f38,f527]) ).
fof(f541,plain,
one = antidomain(c(one)),
inference(forward_demodulation,[status(thm)],[f516,f529]) ).
fof(f542,plain,
one = antidomain(domain(zero)),
inference(forward_demodulation,[status(thm)],[f194,f541]) ).
fof(f543,plain,
one = c(zero),
inference(forward_demodulation,[status(thm)],[f62,f542]) ).
fof(f548,plain,
multiplication(domain(zero),one) = zero,
inference(paramodulation,[status(thm)],[f523,f138]) ).
fof(f553,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f38,f548]) ).
fof(f560,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(forward_demodulation,[status(thm)],[f61,f59]) ).
fof(f561,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(codomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f61,f560]) ).
fof(f562,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(resolution,[status(thm)],[f561,f47]) ).
fof(f563,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(c(X0)),domain(X0)))) = coantidomain(multiplication(codomain(c(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f192,f561]) ).
fof(f564,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0)))) = coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0))),
inference(paramodulation,[status(thm)],[f190,f561]) ).
fof(f565,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(domain(X0)),antidomain(X0)))) = coantidomain(multiplication(codomain(domain(X0)),antidomain(X0))),
inference(paramodulation,[status(thm)],[f138,f561]) ).
fof(f566,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)],[f37,f561]) ).
fof(f567,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),X0))) = coantidomain(multiplication(codomain(antidomain(X0)),X0)),
inference(paramodulation,[status(thm)],[f54,f561]) ).
fof(f568,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(zero),X0))) = coantidomain(multiplication(codomain(zero),X0)),
inference(paramodulation,[status(thm)],[f43,f561]) ).
fof(f569,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(one),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(paramodulation,[status(thm)],[f39,f561]) ).
fof(f570,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),coantidomain(X0)))) = coantidomain(multiplication(codomain(X0),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f58,f561]) ).
fof(f572,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(X0),one))) = coantidomain(multiplication(codomain(X0),one)),
inference(paramodulation,[status(thm)],[f38,f561]) ).
fof(f573,plain,
! [X0] : addition(coantidomain(multiplication(X0,coantidomain(codomain(X0)))),coantidomain(zero)) = coantidomain(multiplication(codomain(X0),coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f58,f561]) ).
fof(f575,plain,
! [X0] : addition(coantidomain(multiplication(X0,one)),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(paramodulation,[status(thm)],[f38,f561]) ).
fof(f576,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)],[f188,f561]) ).
fof(f577,plain,
! [X0] : addition(coantidomain(multiplication(one,X0)),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(paramodulation,[status(thm)],[f189,f561]) ).
fof(f578,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)],[f561,f241]) ).
fof(f579,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)],[f561,f47]) ).
fof(f580,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)],[f561,f34]) ).
fof(f581,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0)))) = coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0))),
inference(forward_demodulation,[status(thm)],[f188,f564]) ).
fof(f582,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0)))) = coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0))),
inference(forward_demodulation,[status(thm)],[f188,f581]) ).
fof(f583,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(forward_demodulation,[status(thm)],[f189,f569]) ).
fof(f584,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(coantidomain(zero),X0)),
inference(forward_demodulation,[status(thm)],[f189,f583]) ).
fof(f587,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f38,f572]) ).
fof(f588,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f587]) ).
fof(f589,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(X0,coantidomain(codomain(X0))))) = coantidomain(multiplication(codomain(X0),coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f33,f573]) ).
fof(f590,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(X0,coantidomain(codomain(X0))))) = coantidomain(zero),
inference(forward_demodulation,[status(thm)],[f58,f589]) ).
fof(f594,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,one))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f33,f575]) ).
fof(f595,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(X0)) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f38,f594]) ).
fof(f596,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f33,f595]) ).
fof(f597,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f596]) ).
fof(f598,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)],[f188,f576]) ).
fof(f599,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(forward_demodulation,[status(thm)],[f39,f577]) ).
fof(f600,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(coantidomain(zero),X0)),
inference(forward_demodulation,[status(thm)],[f189,f599]) ).
fof(f601,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(trivial_equality_resolution,[status(thm)],[f579]) ).
fof(f624,plain,
! [X0] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f33,f60]) ).
fof(f625,plain,
! [X0] : addition(coantidomain(X0),codomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f61,f624]) ).
fof(f626,plain,
! [X0] : addition(codomain(X0),codomain(coantidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f61,f625]) ).
fof(f627,plain,
addition(zero,codomain(one)) = one,
inference(paramodulation,[status(thm)],[f141,f625]) ).
fof(f628,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(codomain(X0))) = one,
inference(paramodulation,[status(thm)],[f188,f625]) ).
fof(f629,plain,
addition(coantidomain(one),coantidomain(zero)) = one,
inference(paramodulation,[status(thm)],[f189,f625]) ).
fof(f630,plain,
! [X0] :
( one != coantidomain(X0)
| leq(codomain(X0),coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f625,f241]) ).
fof(f631,plain,
! [X0] :
( one != codomain(X0)
| leq(coantidomain(X0),codomain(X0)) ),
inference(paramodulation,[status(thm)],[f625,f47]) ).
fof(f632,plain,
! [X0,X1] : addition(coantidomain(X0),addition(codomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f625,f34]) ).
fof(f633,plain,
! [X0] : addition(codomain(X0),coantidomain(codomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f188,f626]) ).
fof(f634,plain,
codomain(one) = one,
inference(forward_demodulation,[status(thm)],[f75,f627]) ).
fof(f635,plain,
! [X0] : addition(codomain(X0),coantidomain(codomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f61,f628]) ).
fof(f636,plain,
addition(coantidomain(zero),coantidomain(one)) = one,
inference(forward_demodulation,[status(thm)],[f33,f629]) ).
fof(f637,plain,
addition(coantidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f141,f636]) ).
fof(f638,plain,
coantidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f35,f637]) ).
fof(f649,plain,
! [X0] : domain_difference(X0,X0) = zero,
inference(backward_demodulation,[status(thm)],[f63,f138]) ).
fof(f650,plain,
! [X0] : domain_difference(zero,X0) = multiplication(zero,antidomain(X0)),
inference(paramodulation,[status(thm)],[f553,f63]) ).
fof(f651,plain,
! [X0,X1] : domain_difference(domain(X0),X1) = multiplication(antidomain(c(X0)),antidomain(X1)),
inference(paramodulation,[status(thm)],[f191,f63]) ).
fof(f652,plain,
! [X0,X1] : domain_difference(antidomain(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f316,f63]) ).
fof(f653,plain,
! [X0] : domain_difference(one,X0) = multiplication(one,antidomain(X0)),
inference(paramodulation,[status(thm)],[f516,f63]) ).
fof(f654,plain,
! [X0] : domain_difference(X0,zero) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f523,f63]) ).
fof(f655,plain,
! [X0,X1] : domain_difference(X0,domain(X1)) = multiplication(domain(X0),c(X1)),
inference(paramodulation,[status(thm)],[f62,f63]) ).
fof(f656,plain,
! [X0,X1] : domain_difference(X0,antidomain(X1)) = multiplication(domain(X0),domain(X1)),
inference(paramodulation,[status(thm)],[f57,f63]) ).
fof(f657,plain,
! [X0] : domain_difference(X0,one) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f114,f63]) ).
fof(f658,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)],[f63,f561]) ).
fof(f659,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)],[f63,f404]) ).
fof(f660,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)],[f63,f53]) ).
fof(f661,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)],[f63,f51]) ).
fof(f662,plain,
! [X0,X1,X2] : multiplication(addition(X0,domain(X1)),antidomain(X2)) = addition(multiplication(X0,antidomain(X2)),domain_difference(X1,X2)),
inference(paramodulation,[status(thm)],[f63,f41]) ).
fof(f663,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),X1),antidomain(X2)) = addition(domain_difference(X0,X2),multiplication(X1,antidomain(X2))),
inference(paramodulation,[status(thm)],[f63,f41]) ).
fof(f664,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(X1,antidomain(X2))) = addition(multiplication(domain(X0),X1),domain_difference(X0,X2)),
inference(paramodulation,[status(thm)],[f63,f40]) ).
fof(f665,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(antidomain(X1),X2)) = addition(domain_difference(X0,X1),multiplication(domain(X0),X2)),
inference(paramodulation,[status(thm)],[f63,f40]) ).
fof(f666,plain,
! [X0,X1,X2] : multiplication(domain(X0),multiplication(antidomain(X1),X2)) = multiplication(domain_difference(X0,X1),X2),
inference(paramodulation,[status(thm)],[f63,f37]) ).
fof(f667,plain,
! [X0] : domain_difference(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f43,f650]) ).
fof(f668,plain,
! [X0] : domain_difference(one,X0) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f39,f653]) ).
fof(f669,plain,
! [X0] : domain_difference(X0,zero) = domain(X0),
inference(forward_demodulation,[status(thm)],[f38,f654]) ).
fof(f670,plain,
! [X0] : domain_difference(X0,one) = zero,
inference(forward_demodulation,[status(thm)],[f42,f657]) ).
fof(f671,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)],[f316,f659]) ).
fof(f672,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)],[f316,f671]) ).
fof(f674,plain,
multiplication(one,codomain(zero)) = zero,
inference(paramodulation,[status(thm)],[f638,f190]) ).
fof(f678,plain,
codomain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f39,f674]) ).
fof(f694,plain,
! [X0] : forward_diamond(c(X0),X0) = domain(zero),
inference(paramodulation,[status(thm)],[f192,f64]) ).
fof(f695,plain,
! [X0,X1,X2] : forward_diamond(multiplication(X0,X1),X2) = domain(multiplication(X0,multiplication(X1,domain(X2)))),
inference(paramodulation,[status(thm)],[f37,f64]) ).
fof(f697,plain,
! [X0] : forward_diamond(zero,X0) = domain(zero),
inference(paramodulation,[status(thm)],[f43,f64]) ).
fof(f698,plain,
! [X0] : forward_diamond(one,X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f39,f64]) ).
fof(f699,plain,
! [X0,X1,X2] : forward_diamond(X0,multiplication(X1,domain(X2))) = domain(multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f64,f64]) ).
fof(f700,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f553,f64]) ).
fof(f701,plain,
! [X0,X1] : forward_diamond(X0,domain(X1)) = domain(multiplication(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f191,f64]) ).
fof(f702,plain,
! [X0,X1] : forward_diamond(X0,antidomain(X1)) = domain(multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f316,f64]) ).
fof(f703,plain,
! [X0] : forward_diamond(X0,one) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f516,f64]) ).
fof(f704,plain,
! [X0,X1,X2] : domain_difference(multiplication(X0,domain(X1)),X2) = multiplication(forward_diamond(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f64,f63]) ).
fof(f705,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f64,f504]) ).
fof(f706,plain,
! [X0,X1] : domain(c(multiplication(X0,domain(X1)))) = c(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f64,f317]) ).
fof(f707,plain,
! [X0,X1] : multiplication(c(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f64,f192]) ).
fof(f708,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)],[f64,f404]) ).
fof(f709,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = antidomain(c(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f64,f191]) ).
fof(f710,plain,
! [X0,X1] : c(multiplication(X0,domain(X1))) = antidomain(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f64,f62]) ).
fof(f711,plain,
! [X0] : forward_diamond(c(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f553,f694]) ).
fof(f714,plain,
! [X0] : forward_diamond(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f553,f697]) ).
fof(f715,plain,
! [X0] : forward_diamond(one,X0) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f191,f698]) ).
fof(f716,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f42,f700]) ).
fof(f717,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f553,f716]) ).
fof(f718,plain,
! [X0] : forward_diamond(X0,one) = domain(X0),
inference(forward_demodulation,[status(thm)],[f38,f703]) ).
fof(f719,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f33,f705]) ).
fof(f720,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)],[f33,f708]) ).
fof(f721,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)],[f64,f720]) ).
fof(f733,plain,
divergence(zero) = zero,
inference(paramodulation,[status(thm)],[f68,f714]) ).
fof(f736,plain,
! [X0] : backward_diamond(coantidomain(codomain(X0)),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f58,f65]) ).
fof(f737,plain,
! [X0] : backward_diamond(zero,X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f42,f65]) ).
fof(f738,plain,
! [X0] : backward_diamond(one,X0) = codomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f38,f65]) ).
fof(f739,plain,
! [X0,X1,X2] : backward_diamond(X0,multiplication(codomain(X1),X2)) = codomain(multiplication(backward_diamond(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f65,f65]) ).
fof(f740,plain,
! [X0] : backward_diamond(X0,zero) = codomain(multiplication(zero,X0)),
inference(paramodulation,[status(thm)],[f678,f65]) ).
fof(f741,plain,
! [X0,X1] : backward_diamond(X0,coantidomain(X1)) = codomain(multiplication(coantidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f188,f65]) ).
fof(f742,plain,
! [X0] : backward_diamond(X0,one) = codomain(multiplication(one,X0)),
inference(paramodulation,[status(thm)],[f634,f65]) ).
fof(f743,plain,
! [X0,X1] : addition(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = one,
inference(paramodulation,[status(thm)],[f65,f625]) ).
fof(f744,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)],[f65,f561]) ).
fof(f745,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f65,f190]) ).
fof(f746,plain,
! [X0] : backward_diamond(coantidomain(codomain(X0)),X0) = zero,
inference(forward_demodulation,[status(thm)],[f678,f736]) ).
fof(f747,plain,
! [X0] : backward_diamond(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f678,f737]) ).
fof(f748,plain,
! [X0] : backward_diamond(X0,zero) = codomain(zero),
inference(forward_demodulation,[status(thm)],[f43,f740]) ).
fof(f749,plain,
! [X0] : backward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f678,f748]) ).
fof(f750,plain,
! [X0] : backward_diamond(X0,one) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f39,f742]) ).
fof(f751,plain,
! [X0,X1] : addition(backward_diamond(X0,X1),coantidomain(multiplication(codomain(X1),X0))) = one,
inference(forward_demodulation,[status(thm)],[f33,f743]) ).
fof(f752,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)],[f33,f744]) ).
fof(f753,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)],[f37,f752]) ).
fof(f754,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)],[f65,f753]) ).
fof(f765,plain,
! [X0] : forward_box(zero,X0) = c(zero),
inference(paramodulation,[status(thm)],[f714,f66]) ).
fof(f766,plain,
! [X0,X1,X2] : forward_box(X0,forward_diamond(X1,c(X2))) = c(forward_diamond(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f66,f66]) ).
fof(f767,plain,
! [X0] : forward_box(X0,zero) = c(forward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f543,f66]) ).
fof(f768,plain,
! [X0,X1] : forward_box(X0,antidomain(X1)) = c(forward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f493,f66]) ).
fof(f769,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = c(forward_diamond(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f317,f66]) ).
fof(f770,plain,
! [X0] : forward_box(X0,one) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f537,f66]) ).
fof(f771,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f66,f192]) ).
fof(f772,plain,
! [X0] : forward_box(zero,X0) = one,
inference(forward_demodulation,[status(thm)],[f543,f765]) ).
fof(f773,plain,
! [X0] : forward_box(X0,one) = c(zero),
inference(forward_demodulation,[status(thm)],[f717,f770]) ).
fof(f774,plain,
! [X0] : forward_box(X0,one) = one,
inference(forward_demodulation,[status(thm)],[f543,f773]) ).
fof(f785,plain,
! [X0] : backward_box(zero,X0) = c(zero),
inference(paramodulation,[status(thm)],[f747,f67]) ).
fof(f786,plain,
! [X0,X1,X2] : backward_box(X0,backward_diamond(X1,c(X2))) = c(backward_diamond(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f67,f67]) ).
fof(f787,plain,
! [X0,X1,X2] : backward_box(X0,forward_diamond(X1,c(X2))) = c(backward_diamond(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f66,f67]) ).
fof(f788,plain,
! [X0] : backward_box(X0,zero) = c(backward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f543,f67]) ).
fof(f789,plain,
! [X0,X1] : backward_box(X0,antidomain(X1)) = c(backward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f493,f67]) ).
fof(f790,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = c(backward_diamond(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f317,f67]) ).
fof(f791,plain,
! [X0] : backward_box(X0,one) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f537,f67]) ).
fof(f792,plain,
! [X0,X1,X2] : forward_box(X0,backward_diamond(X1,c(X2))) = c(forward_diamond(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f67,f66]) ).
fof(f793,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f67,f192]) ).
fof(f794,plain,
! [X0] : backward_box(zero,X0) = one,
inference(forward_demodulation,[status(thm)],[f543,f785]) ).
fof(f795,plain,
! [X0] : backward_box(X0,one) = c(zero),
inference(forward_demodulation,[status(thm)],[f749,f791]) ).
fof(f796,plain,
! [X0] : backward_box(X0,one) = one,
inference(forward_demodulation,[status(thm)],[f543,f795]) ).
fof(f808,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)],[f64,f70]) ).
fof(f810,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)],[f191,f70]) ).
fof(f811,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)],[f316,f70]) ).
fof(f812,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)],[f516,f70]) ).
fof(f813,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)],[f33,f70]) ).
fof(f814,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)],[f33,f70]) ).
fof(f815,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)],[f714,f70]) ).
fof(f816,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)],[f64,f70]) ).
fof(f818,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)],[f191,f70]) ).
fof(f819,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)],[f316,f70]) ).
fof(f820,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)],[f516,f70]) ).
fof(f821,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)],[f64,f70]) ).
fof(f822,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)],[f553,f70]) ).
fof(f823,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)],[f191,f70]) ).
fof(f824,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)],[f316,f70]) ).
fof(f825,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)],[f516,f70]) ).
fof(f826,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)],[f64,f808]) ).
fof(f827,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)],[f64,f826]) ).
fof(f828,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)],[f64,f827]) ).
fof(f837,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)],[f191,f810]) ).
fof(f838,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)],[f191,f837]) ).
fof(f839,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)],[f191,f838]) ).
fof(f840,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)],[f316,f811]) ).
fof(f841,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)],[f316,f840]) ).
fof(f842,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)],[f316,f841]) ).
fof(f843,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)],[f516,f812]) ).
fof(f844,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)],[f516,f843]) ).
fof(f845,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)],[f516,f844]) ).
fof(f846,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)],[f75,f815]) ).
fof(f847,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)],[f714,f846]) ).
fof(f848,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)],[f75,f847]) ).
fof(f849,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)],[f733,f848]) ).
fof(f850,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)],[f75,f849]) ).
fof(f851,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)],[f733,f850]) ).
fof(f852,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)],[f75,f851]) ).
fof(f853,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)],[f64,f816]) ).
fof(f854,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)],[f64,f853]) ).
fof(f855,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)],[f64,f854]) ).
fof(f864,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)],[f191,f818]) ).
fof(f865,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)],[f191,f864]) ).
fof(f866,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)],[f191,f865]) ).
fof(f867,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)],[f316,f819]) ).
fof(f868,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)],[f316,f867]) ).
fof(f869,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)],[f316,f868]) ).
fof(f870,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)],[f516,f820]) ).
fof(f871,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)],[f516,f870]) ).
fof(f872,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)],[f516,f871]) ).
fof(f873,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)],[f64,f821]) ).
fof(f874,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)],[f64,f873]) ).
fof(f875,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)],[f64,f874]) ).
fof(f876,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)],[f35,f822]) ).
fof(f877,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)],[f33,f876]) ).
fof(f878,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)],[f553,f877]) ).
fof(f879,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)],[f75,f878]) ).
fof(f880,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)],[f553,f879]) ).
fof(f881,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)],[f717,f880]) ).
fof(f882,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)],[f35,f881]) ).
fof(f883,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)],[f553,f882]) ).
fof(f884,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)],[f717,f883]) ).
fof(f885,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)],[f35,f884]) ).
fof(f886,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)],[f191,f823]) ).
fof(f887,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)],[f191,f886]) ).
fof(f888,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)],[f191,f887]) ).
fof(f889,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)],[f316,f824]) ).
fof(f890,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)],[f316,f889]) ).
fof(f891,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)],[f316,f890]) ).
fof(f892,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)],[f33,f825]) ).
fof(f893,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)],[f33,f892]) ).
fof(f894,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)],[f516,f893]) ).
fof(f895,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)],[f516,f894]) ).
fof(f896,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)],[f516,f895]) ).
fof(f899,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f67,f711]) ).
fof(f900,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f66,f711]) ).
fof(f902,plain,
! [X0] : forward_diamond(antidomain(c(X0)),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f493,f711]) ).
fof(f903,plain,
! [X0] : forward_diamond(domain(c(X0)),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f317,f711]) ).
fof(f905,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)],[f711,f70]) ).
fof(f906,plain,
! [X0] : forward_box(c(c(X0)),X0) = c(zero),
inference(paramodulation,[status(thm)],[f711,f66]) ).
fof(f909,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)],[f75,f905]) ).
fof(f910,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)],[f711,f909]) ).
fof(f911,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)],[f75,f910]) ).
fof(f912,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)],[f317,f911]) ).
fof(f913,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)],[f317,f912]) ).
fof(f914,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)],[f317,f913]) ).
fof(f915,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)],[f317,f914]) ).
fof(f916,plain,
! [X0] : forward_box(c(c(X0)),X0) = one,
inference(forward_demodulation,[status(thm)],[f543,f906]) ).
fof(f925,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f34,f92]) ).
fof(f929,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f33,f92]) ).
fof(f930,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f33,f92]) ).
fof(f931,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(addition(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f36,f92]) ).
fof(f932,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)],[f561,f92]) ).
fof(f933,plain,
! [X0,X1] : addition(X0,one) = addition(codomain(X1),addition(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f625,f92]) ).
fof(f934,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)],[f404,f92]) ).
fof(f935,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f504,f92]) ).
fof(f936,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)],[f41,f92]) ).
fof(f937,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)],[f40,f92]) ).
fof(f938,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f34,f92]) ).
fof(f940,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X2),addition(X0,X3)),
inference(paramodulation,[status(thm)],[f92,f92]) ).
fof(f941,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X3,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f92,f92]) ).
fof(f943,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f33,f92]) ).
fof(f944,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f33,f92]) ).
fof(f945,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f36,f92]) ).
fof(f946,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f34,f92]) ).
fof(f952,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f36,f92]) ).
fof(f953,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)],[f561,f92]) ).
fof(f954,plain,
! [X0,X1] : addition(coantidomain(X0),addition(codomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f625,f92]) ).
fof(f955,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)],[f404,f92]) ).
fof(f956,plain,
! [X0,X1] : addition(antidomain(X0),addition(domain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f504,f92]) ).
fof(f957,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)],[f41,f92]) ).
fof(f958,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)],[f40,f92]) ).
fof(f959,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(X3,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f34,f92]) ).
fof(f961,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f92,f92]) ).
fof(f962,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f92,f92]) ).
fof(f964,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f33,f92]) ).
fof(f965,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f33,f92]) ).
fof(f966,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f36,f92]) ).
fof(f967,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)],[f92,f70]) ).
fof(f968,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)],[f92,f53]) ).
fof(f969,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)],[f92,f51]) ).
fof(f970,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f92,f34]) ).
fof(f972,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f92,f241]) ).
fof(f973,plain,
! [X0,X1,X2] :
( addition(X2,addition(X0,X1)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f92,f47]) ).
fof(f974,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X2,addition(X0,X1)),X3),
inference(paramodulation,[status(thm)],[f92,f34]) ).
fof(f975,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f92,f33]) ).
fof(f976,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f92,f33]) ).
fof(f977,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f92,f36]) ).
fof(f978,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)],[f92,f53]) ).
fof(f979,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)],[f92,f51]) ).
fof(f980,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f92,f34]) ).
fof(f982,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f92,f241]) ).
fof(f983,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f92,f47]) ).
fof(f984,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X1,addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f92,f34]) ).
fof(f987,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f92,f36]) ).
fof(f988,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f34,f925]) ).
fof(f990,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,addition(X1,X0))),
inference(forward_demodulation,[status(thm)],[f34,f931]) ).
fof(f991,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)],[f92,f932]) ).
fof(f992,plain,
! [X0,X1] : addition(X0,one) = addition(coantidomain(X1),addition(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f933]) ).
fof(f993,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)],[f92,f934]) ).
fof(f994,plain,
! [X0,X1] : addition(X0,one) = addition(antidomain(X1),addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f935]) ).
fof(f996,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f34,f940]) ).
fof(f997,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f34,f941]) ).
fof(f998,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f34,f959]) ).
fof(f1000,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f34,f961]) ).
fof(f1001,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f34,f962]) ).
fof(f1003,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f34,f970]) ).
fof(f1005,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,addition(X0,X1)),X3),
inference(forward_demodulation,[status(thm)],[f34,f974]) ).
fof(f1006,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(addition(X0,X1),X3)),
inference(forward_demodulation,[status(thm)],[f34,f1005]) ).
fof(f1007,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f34,f1006]) ).
fof(f1008,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f34,f977]) ).
fof(f1009,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f34,f984]) ).
fof(f1010,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(addition(X2,X0),X3)),
inference(forward_demodulation,[status(thm)],[f34,f1009]) ).
fof(f1011,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f34,f1010]) ).
fof(f1012,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),c(multiplication(X0,domain(X1)))) = one,
inference(paramodulation,[status(thm)],[f64,f515]) ).
fof(f1015,plain,
! [X0] : addition(c(X0),c(antidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f316,f515]) ).
fof(f1017,plain,
! [X0,X1] : addition(domain(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f67,f515]) ).
fof(f1018,plain,
! [X0,X1] : addition(domain(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f66,f515]) ).
fof(f1020,plain,
! [X0] : addition(domain(antidomain(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f493,f515]) ).
fof(f1023,plain,
! [X0,X1] : addition(domain(X0),addition(c(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f515,f92]) ).
fof(f1024,plain,
! [X0,X1] : addition(X0,one) = addition(c(X1),addition(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f515,f92]) ).
fof(f1025,plain,
! [X0] :
( one != domain(X0)
| leq(c(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f515,f241]) ).
fof(f1026,plain,
! [X0] :
( one != c(X0)
| leq(domain(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f515,f47]) ).
fof(f1027,plain,
! [X0,X1] : addition(domain(X0),addition(c(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f515,f34]) ).
fof(f1030,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f493,f1015]) ).
fof(f1032,plain,
! [X0,X1] : addition(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f33,f1017]) ).
fof(f1033,plain,
! [X0,X1] : addition(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f33,f1018]) ).
fof(f1036,plain,
! [X0] : addition(antidomain(c(X0)),domain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f33,f1020]) ).
fof(f1037,plain,
! [X0] : addition(antidomain(c(X0)),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f316,f1036]) ).
fof(f1038,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f33,f1037]) ).
fof(f1041,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1024]) ).
fof(f1047,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X0,X1),X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f34,f94]) ).
fof(f1049,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f92,f94]) ).
fof(f1050,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f34,f94]) ).
fof(f1053,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f92,f94]) ).
fof(f1061,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X2,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f34,f94]) ).
fof(f1064,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X2),addition(X1,addition(X2,X0)))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f92,f94]) ).
fof(f1065,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X2),addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f92,f94]) ).
fof(f1067,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f33,f94]) ).
fof(f1068,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f33,f94]) ).
fof(f1070,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)],[f94,f53]) ).
fof(f1071,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)],[f94,f51]) ).
fof(f1072,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X0,X1),X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f94,f34]) ).
fof(f1074,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f94,f92]) ).
fof(f1075,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,addition(X0,X1)),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f94,f92]) ).
fof(f1076,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,addition(X1,X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f94,f92]) ).
fof(f1077,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,addition(X1,X0)),X1) ),
inference(paramodulation,[status(thm)],[f94,f241]) ).
fof(f1078,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X1,addition(X0,X1))
| leq(X0,addition(X1,addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f94,f47]) ).
fof(f1079,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,addition(X0,X1)),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f94,f34]) ).
fof(f1080,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)],[f34,f1047]) ).
fof(f1081,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)],[f34,f1080]) ).
fof(f1084,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f34,f1049]) ).
fof(f1103,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)],[f34,f1061]) ).
fof(f1104,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)],[f34,f1103]) ).
fof(f1109,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)],[f34,f1064]) ).
fof(f1110,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)],[f34,f1065]) ).
fof(f1113,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)],[f34,f1072]) ).
fof(f1114,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)],[f34,f1113]) ).
fof(f1117,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f34,f1074]) ).
fof(f1118,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f34,f1075]) ).
fof(f1119,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f34,f1118]) ).
fof(f1120,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(addition(X1,X2),addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f34,f1076]) ).
fof(f1121,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,addition(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f34,f1120]) ).
fof(f1122,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f34,f1079]) ).
fof(f1123,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f34,f1122]) ).
fof(f1124,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f34,f1123]) ).
fof(f1128,plain,
divergence(one) = antidomain(c(divergence(one))),
inference(paramodulation,[status(thm)],[f68,f715]) ).
fof(f1130,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)],[f715,f70]) ).
fof(f1131,plain,
! [X0] : forward_box(one,X0) = c(antidomain(c(c(X0)))),
inference(paramodulation,[status(thm)],[f715,f66]) ).
fof(f1133,plain,
antidomain(c(divergence(one))) = divergence(one),
inference(paramodulation,[status(thm)],[f715,f68]) ).
fof(f1139,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)],[f317,f1130]) ).
fof(f1140,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)],[f62,f1139]) ).
fof(f1141,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)],[f715,f1140]) ).
fof(f1142,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)],[f317,f1141]) ).
fof(f1143,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)],[f62,f1142]) ).
fof(f1144,plain,
! [X0] : forward_box(one,X0) = antidomain(c(c(c(X0)))),
inference(forward_demodulation,[status(thm)],[f493,f1131]) ).
fof(f1149,plain,
! [X0,X1] : backward_diamond(coantidomain(backward_diamond(X0,X1)),multiplication(codomain(X1),X0)) = zero,
inference(paramodulation,[status(thm)],[f65,f746]) ).
fof(f1151,plain,
! [X0] : backward_diamond(coantidomain(coantidomain(codomain(X0))),coantidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f188,f746]) ).
fof(f1154,plain,
! [X0] : backward_box(coantidomain(codomain(c(X0))),X0) = c(zero),
inference(paramodulation,[status(thm)],[f746,f67]) ).
fof(f1160,plain,
! [X0] : backward_diamond(codomain(codomain(X0)),coantidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f61,f1151]) ).
fof(f1167,plain,
! [X0] : backward_box(coantidomain(codomain(c(X0))),X0) = one,
inference(forward_demodulation,[status(thm)],[f543,f1154]) ).
fof(f1171,plain,
! [X0] : backward_box(one,X0) = c(codomain(codomain(c(X0)))),
inference(paramodulation,[status(thm)],[f738,f67]) ).
fof(f1177,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f34,f98]) ).
fof(f1178,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X1,X0),X2)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f94,f98]) ).
fof(f1179,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f92,f98]) ).
fof(f1180,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f92,f98]) ).
fof(f1182,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f33,f98]) ).
fof(f1183,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f33,f98]) ).
fof(f1184,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f36,f98]) ).
fof(f1185,plain,
! [X0,X1] : addition(c(X0),addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f515,f98]) ).
fof(f1186,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)],[f561,f98]) ).
fof(f1187,plain,
! [X0,X1] : addition(codomain(X0),addition(coantidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f625,f98]) ).
fof(f1188,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)],[f404,f98]) ).
fof(f1189,plain,
! [X0,X1] : addition(domain(X0),addition(antidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f504,f98]) ).
fof(f1190,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)],[f41,f98]) ).
fof(f1191,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)],[f40,f98]) ).
fof(f1192,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X2,addition(X1,X0)),X3),
inference(paramodulation,[status(thm)],[f98,f98]) ).
fof(f1195,plain,
! [X0,X1,X2] : addition(addition(X0,addition(X1,X0)),addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f94,f98]) ).
fof(f1196,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f92,f98]) ).
fof(f1197,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X1,addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f92,f98]) ).
fof(f1202,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f98,f34]) ).
fof(f1203,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X1,X0),X2)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f98,f94]) ).
fof(f1204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X2,X1))))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f98,f94]) ).
fof(f1205,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f98,f92]) ).
fof(f1206,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f98,f92]) ).
fof(f1208,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X2,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f98,f94]) ).
fof(f1209,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(X3,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f98,f92]) ).
fof(f1210,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f98,f92]) ).
fof(f1211,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f98,f241]) ).
fof(f1212,plain,
! [X0,X1,X2] :
( addition(X1,addition(X0,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f98,f47]) ).
fof(f1213,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X1,addition(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f98,f34]) ).
fof(f1214,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f98,f33]) ).
fof(f1215,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f98,f33]) ).
fof(f1216,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f98,f36]) ).
fof(f1217,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)],[f98,f1178]) ).
fof(f1218,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)],[f98,f1217]) ).
fof(f1219,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f98,f1180]) ).
fof(f1221,plain,
! [X0,X1] : addition(domain(X0),addition(X1,c(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f92,f1185]) ).
fof(f1222,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)],[f92,f1186]) ).
fof(f1223,plain,
! [X0,X1] : addition(coantidomain(X0),addition(X1,codomain(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f92,f1187]) ).
fof(f1224,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)],[f92,f1188]) ).
fof(f1225,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,domain(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f92,f1189]) ).
fof(f1226,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f98,f1192]) ).
fof(f1227,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,X0),addition(X1,X3)),
inference(forward_demodulation,[status(thm)],[f98,f1226]) ).
fof(f1228,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X0,addition(X2,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f98,f1227]) ).
fof(f1231,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f98,f1195]) ).
fof(f1232,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f1231]) ).
fof(f1233,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1232]) ).
fof(f1234,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f98,f1196]) ).
fof(f1235,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,X2),addition(X1,X3)),
inference(forward_demodulation,[status(thm)],[f98,f1234]) ).
fof(f1236,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f98,f1235]) ).
fof(f1237,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f98,f1197]) ).
fof(f1238,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,X1),addition(X0,X3)),
inference(forward_demodulation,[status(thm)],[f98,f1237]) ).
fof(f1239,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f98,f1238]) ).
fof(f1240,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)],[f98,f1203]) ).
fof(f1241,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)],[f98,f1240]) ).
fof(f1242,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f98,f1206]) ).
fof(f1244,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)],[f98,f1208]) ).
fof(f1245,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)],[f98,f1244]) ).
fof(f1246,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f98,f1209]) ).
fof(f1247,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f98,f1213]) ).
fof(f1248,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X2),addition(X0,X3)),
inference(forward_demodulation,[status(thm)],[f98,f1247]) ).
fof(f1249,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X1,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f98,f1248]) ).
fof(f1251,plain,
! [X0,X1] : forward_box(c(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f67,f916]) ).
fof(f1252,plain,
! [X0,X1] : forward_box(c(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f66,f916]) ).
fof(f1254,plain,
! [X0] : forward_box(c(antidomain(c(X0))),antidomain(X0)) = one,
inference(paramodulation,[status(thm)],[f493,f916]) ).
fof(f1255,plain,
! [X0] : forward_box(c(domain(c(X0))),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f317,f916]) ).
fof(f1259,plain,
! [X0] : forward_box(antidomain(c(c(X0))),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f493,f1254]) ).
fof(f1260,plain,
! [X0] : forward_box(domain(c(c(X0))),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f317,f1255]) ).
fof(f1261,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f100,f47]) ).
fof(f1262,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f98,f100]) ).
fof(f1263,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f34,f100]) ).
fof(f1266,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f92,f100]) ).
fof(f1268,plain,
! [X0] : addition(domain(X0),one) = addition(domain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f515,f100]) ).
fof(f1270,plain,
! [X0] : addition(coantidomain(X0),one) = addition(coantidomain(X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f625,f100]) ).
fof(f1272,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f504,f100]) ).
fof(f1275,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f98,f100]) ).
fof(f1276,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f34,f100]) ).
fof(f1280,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f92,f100]) ).
fof(f1281,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f92,f100]) ).
fof(f1286,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)],[f100,f53]) ).
fof(f1287,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)],[f100,f51]) ).
fof(f1288,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f100,f98]) ).
fof(f1289,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f100,f34]) ).
fof(f1297,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f100,f92]) ).
fof(f1298,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f100,f92]) ).
fof(f1299,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f100,f241]) ).
fof(f1301,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f100,f34]) ).
fof(f1302,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f1262]) ).
fof(f1303,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1302]) ).
fof(f1304,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f98,f1263]) ).
fof(f1305,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f100,f1304]) ).
fof(f1306,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1305]) ).
fof(f1310,plain,
! [X0] : addition(one,domain(X0)) = addition(domain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f33,f1268]) ).
fof(f1311,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f515,f1310]) ).
fof(f1312,plain,
! [X0] : addition(one,coantidomain(X0)) = addition(coantidomain(X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f1270]) ).
fof(f1313,plain,
! [X0] : addition(one,coantidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f625,f1312]) ).
fof(f1314,plain,
! [X0] : addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f1272]) ).
fof(f1315,plain,
! [X0] : addition(one,antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f504,f1314]) ).
fof(f1320,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f1275]) ).
fof(f1321,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1320]) ).
fof(f1322,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f1276]) ).
fof(f1323,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f100,f1322]) ).
fof(f1324,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1323]) ).
fof(f1327,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f1288]) ).
fof(f1328,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1327]) ).
fof(f1329,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f98,f1289]) ).
fof(f1330,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f100,f1329]) ).
fof(f1331,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1330]) ).
fof(f1338,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f98,f1297]) ).
fof(f1339,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f1298]) ).
fof(f1341,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f98,f1301]) ).
fof(f1342,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1341]) ).
fof(f1344,plain,
! [X0] : leq(domain(X0),one),
inference(paramodulation,[status(thm)],[f515,f1261]) ).
fof(f1345,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(paramodulation,[status(thm)],[f561,f1261]) ).
fof(f1346,plain,
! [X0] : leq(coantidomain(X0),one),
inference(paramodulation,[status(thm)],[f625,f1261]) ).
fof(f1347,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f404,f1261]) ).
fof(f1348,plain,
! [X0] : leq(antidomain(X0),one),
inference(paramodulation,[status(thm)],[f504,f1261]) ).
fof(f1349,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f41,f1261]) ).
fof(f1350,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f40,f1261]) ).
fof(f1351,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f98,f1261]) ).
fof(f1352,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f34,f1261]) ).
fof(f1356,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f92,f1261]) ).
fof(f1357,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f92,f1261]) ).
fof(f1359,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f33,f1261]) ).
fof(f1363,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),one),
inference(paramodulation,[status(thm)],[f64,f1344]) ).
fof(f1366,plain,
! [X0] : leq(c(X0),one),
inference(paramodulation,[status(thm)],[f316,f1344]) ).
fof(f1371,plain,
! [X0] : leq(codomain(X0),one),
inference(paramodulation,[status(thm)],[f61,f1346]) ).
fof(f1386,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f41,f1359]) ).
fof(f1387,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f40,f1359]) ).
fof(f1391,plain,
! [X0,X1] : leq(addition(X0,addition(X1,X0)),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f94,f1359]) ).
fof(f1393,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f92,f1359]) ).
fof(f1394,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f92,f1359]) ).
fof(f1399,plain,
! [X0] : addition(c(X0),one) = one,
inference(resolution,[status(thm)],[f1366,f46]) ).
fof(f1400,plain,
! [X0,X1] : leq(backward_box(X0,X1),one),
inference(paramodulation,[status(thm)],[f67,f1366]) ).
fof(f1401,plain,
! [X0,X1] : leq(forward_box(X0,X1),one),
inference(paramodulation,[status(thm)],[f66,f1366]) ).
fof(f1406,plain,
! [X0] : addition(one,c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f33,f1399]) ).
fof(f1407,plain,
! [X0] : addition(codomain(X0),one) = one,
inference(resolution,[status(thm)],[f1371,f46]) ).
fof(f1408,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),one),
inference(paramodulation,[status(thm)],[f65,f1371]) ).
fof(f1412,plain,
! [X0] : addition(one,codomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f33,f1407]) ).
fof(f1413,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1363,f46]) ).
fof(f1419,plain,
! [X0] : leq(divergence(X0),one),
inference(paramodulation,[status(thm)],[f68,f1363]) ).
fof(f1420,plain,
! [X0,X1] : addition(one,forward_diamond(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f33,f1413]) ).
fof(f1421,plain,
! [X0] : addition(divergence(X0),one) = one,
inference(resolution,[status(thm)],[f1419,f46]) ).
fof(f1423,plain,
! [X0] : addition(one,divergence(X0)) = one,
inference(forward_demodulation,[status(thm)],[f33,f1421]) ).
fof(f1424,plain,
! [X0,X1] : addition(backward_box(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1400,f46]) ).
fof(f1427,plain,
! [X0,X1] : addition(one,backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f33,f1424]) ).
fof(f1428,plain,
! [X0,X1] : addition(forward_box(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1401,f46]) ).
fof(f1432,plain,
! [X0,X1] : addition(one,forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f33,f1428]) ).
fof(f1433,plain,
! [X0,X1] : addition(backward_diamond(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1408,f46]) ).
fof(f1439,plain,
! [X0,X1] : addition(one,backward_diamond(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f33,f1433]) ).
fof(f1449,plain,
! [X0,X1] : addition(domain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1311,f98]) ).
fof(f1451,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1311,f92]) ).
fof(f1452,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1311,f92]) ).
fof(f1453,plain,
! [X0] :
( one != one
| leq(domain(X0),one) ),
inference(paramodulation,[status(thm)],[f1311,f241]) ).
fof(f1454,plain,
! [X0] :
( one != domain(X0)
| leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f1311,f47]) ).
fof(f1455,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1311,f34]) ).
fof(f1457,plain,
! [X0,X1] : addition(one,addition(X0,domain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1449]) ).
fof(f1459,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1452]) ).
fof(f1460,definition,
! [X0] :
( sQ0_spl
<=> leq(domain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1463,definition,
( sQ1_spl
<=> one = one ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1465,plain,
( sQ1_spl
| one != one ),
inference(component_clause,[status(thm)],[f1463]) ).
fof(f1466,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1453,f1460,f1463]) ).
fof(f1469,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f62,f131]) ).
fof(f1470,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f57,f131]) ).
fof(f1474,plain,
! [X0,X1] : multiplication(antidomain(domain(X0)),domain_difference(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f63,f131]) ).
fof(f1475,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))) = zero,
inference(paramodulation,[status(thm)],[f37,f131]) ).
fof(f1483,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)],[f131,f561]) ).
fof(f1484,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)],[f131,f404]) ).
fof(f1485,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X1,X2))),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f131,f53]) ).
fof(f1486,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),multiplication(X1,X2))
| ~ leq(addition(zero,X0),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f131,f51]) ).
fof(f1487,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f131,f41]) ).
fof(f1488,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = addition(zero,multiplication(X1,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f131,f41]) ).
fof(f1489,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f131,f40]) ).
fof(f1490,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = addition(zero,multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f131,f40]) ).
fof(f1494,plain,
! [X0,X1] : multiplication(c(X0),domain_difference(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f62,f1474]) ).
fof(f1496,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)],[f638,f1483]) ).
fof(f1497,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)],[f523,f1484]) ).
fof(f1498,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X1,X2))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f1485]) ).
fof(f1499,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f75,f1486]) ).
fof(f1500,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f35,f1487]) ).
fof(f1501,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f75,f1488]) ).
fof(f1502,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f1489]) ).
fof(f1503,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = multiplication(antidomain(X0),X2),
inference(forward_demodulation,[status(thm)],[f75,f1490]) ).
fof(f1513,plain,
! [X0,X1] : addition(coantidomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1313,f98]) ).
fof(f1515,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1313,f92]) ).
fof(f1516,plain,
! [X0,X1] : addition(X0,one) = addition(coantidomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1313,f92]) ).
fof(f1517,plain,
! [X0] :
( one != one
| leq(coantidomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1313,f241]) ).
fof(f1518,plain,
! [X0] :
( one != coantidomain(X0)
| leq(one,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f1313,f47]) ).
fof(f1519,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1313,f34]) ).
fof(f1521,plain,
! [X0,X1] : addition(one,addition(X0,coantidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1513]) ).
fof(f1523,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1516]) ).
fof(f1524,definition,
! [X0] :
( sQ2_spl
<=> leq(coantidomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1527,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1517,f1524,f1463]) ).
fof(f1528,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1465]) ).
fof(f1529,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1528]) ).
fof(f1538,plain,
! [X0,X1] : addition(antidomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1315,f98]) ).
fof(f1540,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1315,f92]) ).
fof(f1541,plain,
! [X0,X1] : addition(X0,one) = addition(antidomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1315,f92]) ).
fof(f1542,plain,
! [X0] :
( one != one
| leq(antidomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1315,f241]) ).
fof(f1543,plain,
! [X0] :
( one != antidomain(X0)
| leq(one,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f1315,f47]) ).
fof(f1544,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1315,f34]) ).
fof(f1546,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1538]) ).
fof(f1548,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1541]) ).
fof(f1549,definition,
! [X0] :
( sQ3_spl
<=> leq(antidomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1552,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f1542,f1549,f1463]) ).
fof(f1554,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(multiplication(X0,X1),X2))))) = zero,
inference(paramodulation,[status(thm)],[f37,f139]) ).
fof(f1558,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(paramodulation,[status(thm)],[f37,f139]) ).
fof(f1563,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),coantidomain(domain_difference(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f63,f139]) ).
fof(f1564,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2))))) = zero,
inference(paramodulation,[status(thm)],[f37,f139]) ).
fof(f1573,plain,
! [X0,X1] : backward_diamond(multiplication(X0,coantidomain(multiplication(codomain(X1),X0))),X1) = codomain(zero),
inference(paramodulation,[status(thm)],[f139,f65]) ).
fof(f1575,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(multiplication(X0,X1),X2))))) = zero,
inference(paramodulation,[status(thm)],[f139,f37]) ).
fof(f1580,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)],[f139,f561]) ).
fof(f1581,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)],[f139,f404]) ).
fof(f1582,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,coantidomain(multiplication(X1,X2))))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f139,f53]) ).
fof(f1583,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)],[f139,f51]) ).
fof(f1584,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)],[f139,f41]) ).
fof(f1585,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)],[f139,f41]) ).
fof(f1586,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f139,f40]) ).
fof(f1587,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = addition(zero,multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f139,f40]) ).
fof(f1588,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(zero,X2),
inference(paramodulation,[status(thm)],[f139,f37]) ).
fof(f1590,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f37,f1554]) ).
fof(f1597,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f37,f1564]) ).
fof(f1607,plain,
! [X0,X1] : backward_diamond(multiplication(X0,coantidomain(multiplication(codomain(X1),X0))),X1) = zero,
inference(forward_demodulation,[status(thm)],[f678,f1573]) ).
fof(f1612,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f37,f1575]) ).
fof(f1614,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)],[f638,f1580]) ).
fof(f1615,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f1313,f1614]) ).
fof(f1616,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)],[f523,f1581]) ).
fof(f1617,plain,
! [X0,X1] : one = antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f1315,f1616]) ).
fof(f1618,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,coantidomain(multiplication(X1,X2))))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f1582]) ).
fof(f1619,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)],[f75,f1583]) ).
fof(f1620,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)],[f35,f1584]) ).
fof(f1621,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)],[f75,f1585]) ).
fof(f1622,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f1586]) ).
fof(f1623,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f75,f1587]) ).
fof(f1624,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = multiplication(zero,X2),
inference(forward_demodulation,[status(thm)],[f37,f1588]) ).
fof(f1625,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(forward_demodulation,[status(thm)],[f43,f1624]) ).
fof(f1636,plain,
! [X0,X1] : addition(c(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1406,f98]) ).
fof(f1638,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1406,f92]) ).
fof(f1639,plain,
! [X0,X1] : addition(X0,one) = addition(c(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1406,f92]) ).
fof(f1640,plain,
! [X0] :
( one != one
| leq(c(X0),one) ),
inference(paramodulation,[status(thm)],[f1406,f241]) ).
fof(f1641,plain,
! [X0] :
( one != c(X0)
| leq(one,c(X0)) ),
inference(paramodulation,[status(thm)],[f1406,f47]) ).
fof(f1642,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1406,f34]) ).
fof(f1644,plain,
! [X0,X1] : addition(one,addition(X0,c(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1636]) ).
fof(f1646,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1639]) ).
fof(f1647,definition,
! [X0] :
( sQ4_spl
<=> leq(c(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1650,plain,
( ~ sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1640,f1647,f1463]) ).
fof(f1659,plain,
! [X0,X1] : addition(codomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1412,f98]) ).
fof(f1661,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1412,f92]) ).
fof(f1662,plain,
! [X0,X1] : addition(X0,one) = addition(codomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1412,f92]) ).
fof(f1663,plain,
! [X0] :
( one != one
| leq(codomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1412,f241]) ).
fof(f1664,plain,
! [X0] :
( one != codomain(X0)
| leq(one,codomain(X0)) ),
inference(paramodulation,[status(thm)],[f1412,f47]) ).
fof(f1665,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1412,f34]) ).
fof(f1667,plain,
! [X0,X1] : addition(one,addition(X0,codomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1659]) ).
fof(f1669,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1662]) ).
fof(f1670,definition,
! [X0] :
( sQ5_spl
<=> leq(codomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1673,plain,
( ~ sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1663,f1670,f1463]) ).
fof(f1679,plain,
! [X0,X1] : addition(divergence(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1423,f98]) ).
fof(f1681,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1423,f92]) ).
fof(f1682,plain,
! [X0,X1] : addition(X0,one) = addition(divergence(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1423,f92]) ).
fof(f1683,plain,
! [X0] :
( one != one
| leq(divergence(X0),one) ),
inference(paramodulation,[status(thm)],[f1423,f241]) ).
fof(f1684,plain,
! [X0] :
( one != divergence(X0)
| leq(one,divergence(X0)) ),
inference(paramodulation,[status(thm)],[f1423,f47]) ).
fof(f1685,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1423,f34]) ).
fof(f1687,plain,
! [X0,X1] : addition(one,addition(X0,divergence(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1679]) ).
fof(f1689,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1682]) ).
fof(f1690,definition,
! [X0] :
( sQ6_spl
<=> leq(divergence(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1693,plain,
( ~ sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1683,f1690,f1463]) ).
fof(f1695,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(paramodulation,[status(thm)],[f37,f146]) ).
fof(f1706,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f61,f146]) ).
fof(f1708,plain,
! [X0,X1] : backward_diamond(multiplication(coantidomain(codomain(X0)),X1),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f146,f65]) ).
fof(f1710,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(paramodulation,[status(thm)],[f146,f37]) ).
fof(f1716,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)],[f146,f561]) ).
fof(f1717,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)],[f146,f404]) ).
fof(f1718,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(coantidomain(X1),X2))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f146,f53]) ).
fof(f1719,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)],[f146,f51]) ).
fof(f1720,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = addition(multiplication(X0,multiplication(coantidomain(X1),X2)),zero),
inference(paramodulation,[status(thm)],[f146,f41]) ).
fof(f1721,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = addition(zero,multiplication(X1,multiplication(coantidomain(X0),X2))),
inference(paramodulation,[status(thm)],[f146,f41]) ).
fof(f1722,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f146,f40]) ).
fof(f1723,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = addition(zero,multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f146,f40]) ).
fof(f1728,plain,
! [X0,X1] : backward_diamond(multiplication(coantidomain(codomain(X0)),X1),X0) = zero,
inference(forward_demodulation,[status(thm)],[f678,f1708]) ).
fof(f1735,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)],[f638,f1716]) ).
fof(f1736,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(X0),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f1313,f1735]) ).
fof(f1737,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)],[f523,f1717]) ).
fof(f1738,plain,
! [X0,X1] : one = antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f1315,f1737]) ).
fof(f1739,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(coantidomain(X1),X2))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f1718]) ).
fof(f1740,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),multiplication(coantidomain(X1),X2))
| ~ leq(X0,multiplication(coantidomain(X1),X2)) ),
inference(forward_demodulation,[status(thm)],[f75,f1719]) ).
fof(f1741,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f35,f1720]) ).
fof(f1742,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f75,f1721]) ).
fof(f1743,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f1722]) ).
fof(f1744,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f75,f1723]) ).
fof(f1747,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f1356,f46]) ).
fof(f1748,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f98,f1356]) ).
fof(f1749,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f34,f1356]) ).
fof(f1758,plain,
! [X0,X1] : leq(divergence(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1423,f1356]) ).
fof(f1759,plain,
! [X0,X1] : leq(codomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1412,f1356]) ).
fof(f1760,plain,
! [X0,X1] : leq(c(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1406,f1356]) ).
fof(f1761,plain,
! [X0,X1] : leq(antidomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1315,f1356]) ).
fof(f1762,plain,
! [X0,X1] : leq(coantidomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1313,f1356]) ).
fof(f1763,plain,
! [X0,X1] : leq(domain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1311,f1356]) ).
fof(f1769,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f41,f1356]) ).
fof(f1770,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f40,f1356]) ).
fof(f1771,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f98,f1356]) ).
fof(f1772,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f34,f1356]) ).
fof(f1774,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X0)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f94,f1356]) ).
fof(f1776,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f92,f1356]) ).
fof(f1777,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X1,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f92,f1356]) ).
fof(f1784,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f1357,f46]) ).
fof(f1785,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f98,f1357]) ).
fof(f1786,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f34,f1357]) ).
fof(f1802,plain,
! [X0,X1,X2] : leq(coantidomain(multiplication(X0,X1)),addition(X2,coantidomain(multiplication(codomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f561,f1357]) ).
fof(f1804,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f404,f1357]) ).
fof(f1806,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f41,f1357]) ).
fof(f1807,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f40,f1357]) ).
fof(f1808,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X1,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f98,f1357]) ).
fof(f1809,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f34,f1357]) ).
fof(f1813,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f92,f1357]) ).
fof(f1814,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f92,f1357]) ).
fof(f1822,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f40,f148]) ).
fof(f1826,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f192,f148]) ).
fof(f1827,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = addition(zero,multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f190,f148]) ).
fof(f1828,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(X1,antidomain(X2))) = addition(domain_difference(X0,X2),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f63,f148]) ).
fof(f1829,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)],[f37,f148]) ).
fof(f1830,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f131,f148]) ).
fof(f1831,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f54,f148]) ).
fof(f1834,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f146,f148]) ).
fof(f1835,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f139,f148]) ).
fof(f1836,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f58,f148]) ).
fof(f1838,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f38,f148]) ).
fof(f1839,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f192,f148]) ).
fof(f1840,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f190,f148]) ).
fof(f1841,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(antidomain(X1),X2)) = addition(multiplication(domain(X0),X2),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f148]) ).
fof(f1842,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)],[f37,f148]) ).
fof(f1843,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = addition(multiplication(antidomain(X0),X2),zero),
inference(paramodulation,[status(thm)],[f131,f148]) ).
fof(f1844,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f54,f148]) ).
fof(f1847,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f146,f148]) ).
fof(f1848,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f139,f148]) ).
fof(f1849,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f58,f148]) ).
fof(f1851,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f38,f148]) ).
fof(f1853,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f148,f40]) ).
fof(f1854,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),star(X2)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f148,f53]) ).
fof(f1855,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f148,f51]) ).
fof(f1856,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f148,f1357]) ).
fof(f1857,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f148,f1356]) ).
fof(f1858,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f148,f1359]) ).
fof(f1859,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f148,f1261]) ).
fof(f1860,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,addition(X2,X1))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f148,f100]) ).
fof(f1861,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)],[f148,f98]) ).
fof(f1863,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)],[f148,f92]) ).
fof(f1864,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)],[f148,f92]) ).
fof(f1865,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f148,f241]) ).
fof(f1866,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f148,f47]) ).
fof(f1867,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)],[f148,f34]) ).
fof(f1872,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f1826]) ).
fof(f1873,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f1827]) ).
fof(f1874,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)],[f37,f1829]) ).
fof(f1875,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)],[f37,f1874]) ).
fof(f1876,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)],[f148,f1875]) ).
fof(f1877,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f148,f1876]) ).
fof(f1878,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f1830]) ).
fof(f1879,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f1831]) ).
fof(f1884,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f1834]) ).
fof(f1885,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f1835]) ).
fof(f1886,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f1836]) ).
fof(f1888,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f1839]) ).
fof(f1889,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f1840]) ).
fof(f1890,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)],[f37,f1842]) ).
fof(f1891,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)],[f37,f1890]) ).
fof(f1892,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)],[f148,f1891]) ).
fof(f1893,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f148,f1892]) ).
fof(f1894,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = multiplication(antidomain(X0),X2),
inference(forward_demodulation,[status(thm)],[f35,f1843]) ).
fof(f1895,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f1844]) ).
fof(f1900,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f35,f1847]) ).
fof(f1901,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f35,f1848]) ).
fof(f1902,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f1849]) ).
fof(f1904,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f1851]) ).
fof(f1906,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f37,f1854]) ).
fof(f1907,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,X2),X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f148,f1860]) ).
fof(f1908,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,X1))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f1907]) ).
fof(f1909,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,X1))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f148,f1908]) ).
fof(f1923,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1420,f1356]) ).
fof(f1927,plain,
! [X0,X1,X2] : addition(forward_diamond(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1420,f98]) ).
fof(f1929,plain,
! [X0,X1,X2] : addition(one,addition(forward_diamond(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1420,f92]) ).
fof(f1930,plain,
! [X0,X1,X2] : addition(X0,one) = addition(forward_diamond(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1420,f92]) ).
fof(f1931,plain,
! [X0,X1] :
( one != one
| leq(forward_diamond(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1420,f241]) ).
fof(f1932,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(one,forward_diamond(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1420,f47]) ).
fof(f1933,plain,
! [X0,X1,X2] : addition(one,addition(forward_diamond(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1420,f34]) ).
fof(f1935,plain,
! [X0,X1,X2] : addition(one,addition(X0,forward_diamond(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1927]) ).
fof(f1937,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1930]) ).
fof(f1938,definition,
! [X0,X1] :
( sQ7_spl
<=> leq(forward_diamond(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1941,plain,
( ~ sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1931,f1938,f1463]) ).
fof(f1946,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1427,f1356]) ).
fof(f1950,plain,
! [X0,X1,X2] : addition(backward_box(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1427,f98]) ).
fof(f1952,plain,
! [X0,X1,X2] : addition(one,addition(backward_box(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1427,f92]) ).
fof(f1953,plain,
! [X0,X1,X2] : addition(X0,one) = addition(backward_box(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1427,f92]) ).
fof(f1954,plain,
! [X0,X1] :
( one != one
| leq(backward_box(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1427,f241]) ).
fof(f1955,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(one,backward_box(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1427,f47]) ).
fof(f1956,plain,
! [X0,X1,X2] : addition(one,addition(backward_box(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1427,f34]) ).
fof(f1958,plain,
! [X0,X1,X2] : addition(one,addition(X0,backward_box(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1950]) ).
fof(f1960,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1953]) ).
fof(f1961,definition,
! [X0,X1] :
( sQ8_spl
<=> leq(backward_box(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1964,plain,
( ~ sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f1954,f1961,f1463]) ).
fof(f1970,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1432,f1356]) ).
fof(f1974,plain,
! [X0,X1,X2] : addition(forward_box(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1432,f98]) ).
fof(f1976,plain,
! [X0,X1,X2] : addition(one,addition(forward_box(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1432,f92]) ).
fof(f1977,plain,
! [X0,X1,X2] : addition(X0,one) = addition(forward_box(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1432,f92]) ).
fof(f1978,plain,
! [X0,X1] :
( one != one
| leq(forward_box(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1432,f241]) ).
fof(f1979,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(one,forward_box(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1432,f47]) ).
fof(f1980,plain,
! [X0,X1,X2] : addition(one,addition(forward_box(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1432,f34]) ).
fof(f1982,plain,
! [X0,X1,X2] : addition(one,addition(X0,forward_box(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f1974]) ).
fof(f1984,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f92,f1977]) ).
fof(f1985,definition,
! [X0,X1] :
( sQ9_spl
<=> leq(forward_box(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1988,plain,
( ~ sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1978,f1985,f1463]) ).
fof(f1996,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1439,f1356]) ).
fof(f2000,plain,
! [X0,X1,X2] : addition(backward_diamond(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1439,f98]) ).
fof(f2002,plain,
! [X0,X1,X2] : addition(one,addition(backward_diamond(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1439,f92]) ).
fof(f2003,plain,
! [X0,X1,X2] : addition(X0,one) = addition(backward_diamond(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1439,f92]) ).
fof(f2004,plain,
! [X0,X1] :
( one != one
| leq(backward_diamond(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1439,f241]) ).
fof(f2005,plain,
! [X0,X1] :
( one != backward_diamond(X0,X1)
| leq(one,backward_diamond(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1439,f47]) ).
fof(f2006,plain,
! [X0,X1,X2] : addition(one,addition(backward_diamond(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1439,f34]) ).
fof(f2008,plain,
! [X0,X1,X2] : addition(one,addition(X0,backward_diamond(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f2000]) ).
fof(f2010,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f92,f2003]) ).
fof(f2011,definition,
! [X0,X1] :
( sQ10_spl
<=> leq(backward_diamond(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f2014,plain,
( ~ sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f2004,f2011,f1463]) ).
fof(f2016,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(antidomain(domain(X0)),X1),
inference(paramodulation,[status(thm)],[f62,f172]) ).
fof(f2017,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(antidomain(antidomain(X0)),X1),
inference(paramodulation,[status(thm)],[f57,f172]) ).
fof(f2029,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f515,f172]) ).
fof(f2031,plain,
! [X0] : multiplication(antidomain(coantidomain(X0)),one) = multiplication(antidomain(coantidomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f625,f172]) ).
fof(f2033,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),one) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f504,f172]) ).
fof(f2034,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)],[f148,f172]) ).
fof(f2035,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)],[f41,f172]) ).
fof(f2036,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)],[f40,f172]) ).
fof(f2037,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X1,addition(X0,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f98,f172]) ).
fof(f2038,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,addition(X1,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f34,f172]) ).
fof(f2040,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),addition(X1,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f94,f172]) ).
fof(f2042,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(paramodulation,[status(thm)],[f92,f172]) ).
fof(f2043,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f92,f172]) ).
fof(f2045,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(paramodulation,[status(thm)],[f33,f172]) ).
fof(f2046,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(paramodulation,[status(thm)],[f33,f172]) ).
fof(f2048,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)],[f172,f148]) ).
fof(f2049,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)],[f172,f148]) ).
fof(f2050,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X0,X1),coantidomain(multiplication(antidomain(X0),X1)))) = zero,
inference(paramodulation,[status(thm)],[f172,f139]) ).
fof(f2052,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)],[f172,f561]) ).
fof(f2053,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)],[f172,f404]) ).
fof(f2054,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)],[f172,f53]) ).
fof(f2055,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)],[f172,f51]) ).
fof(f2056,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)],[f172,f41]) ).
fof(f2057,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)],[f172,f41]) ).
fof(f2058,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)],[f172,f40]) ).
fof(f2059,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)],[f172,f40]) ).
fof(f2060,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X0,X1),X2)) = multiplication(multiplication(antidomain(X0),X1),X2),
inference(paramodulation,[status(thm)],[f172,f37]) ).
fof(f2064,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f2016]) ).
fof(f2065,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f57,f2017]) ).
fof(f2088,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f38,f2029]) ).
fof(f2089,plain,
! [X0] : c(X0) = multiplication(antidomain(domain(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f62,f2088]) ).
fof(f2090,plain,
! [X0] : c(X0) = multiplication(c(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f62,f2089]) ).
fof(f2091,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(antidomain(coantidomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f2031]) ).
fof(f2092,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f2033]) ).
fof(f2093,plain,
! [X0] : domain(X0) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f57,f2092]) ).
fof(f2094,plain,
! [X0] : domain(X0) = multiplication(domain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f57,f2093]) ).
fof(f2095,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f172,f2040]) ).
fof(f2097,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)],[f98,f2048]) ).
fof(f2098,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f148,f2097]) ).
fof(f2099,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f148,f2049]) ).
fof(f2100,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)],[f33,f2056]) ).
fof(f2101,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2058]) ).
fof(f2102,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)],[f98,f2059]) ).
fof(f2103,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2102]) ).
fof(f2104,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X0,X1),X2)) = multiplication(antidomain(X0),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f2060]) ).
fof(f2105,plain,
! [X0,X1] : addition(divergence(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1758,f46]) ).
fof(f2107,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f98,f1758]) ).
fof(f2108,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f34,f1758]) ).
fof(f2110,plain,
! [X0,X1] : leq(divergence(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f33,f1758]) ).
fof(f2113,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f92,f2105]) ).
fof(f2114,plain,
! [X0,X1] : addition(codomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1759,f46]) ).
fof(f2117,plain,
! [X0,X1] : leq(coantidomain(codomain(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f188,f1759]) ).
fof(f2119,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f98,f1759]) ).
fof(f2120,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f34,f1759]) ).
fof(f2122,plain,
! [X0,X1] : leq(codomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f33,f1759]) ).
fof(f2125,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f92,f2114]) ).
fof(f2126,plain,
! [X0,X1] : addition(c(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1760,f46]) ).
fof(f2130,plain,
! [X0,X1] : leq(antidomain(c(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f493,f1760]) ).
fof(f2131,plain,
! [X0,X1] : leq(domain(c(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f317,f1760]) ).
fof(f2133,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f98,f1760]) ).
fof(f2134,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f34,f1760]) ).
fof(f2136,plain,
! [X0,X1] : leq(c(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f33,f1760]) ).
fof(f2139,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f92,f2126]) ).
fof(f2140,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f37,f176]) ).
fof(f2144,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,codomain(X0)),
inference(paramodulation,[status(thm)],[f625,f176]) ).
fof(f2145,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,addition(X1,addition(coantidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f94,f176]) ).
fof(f2147,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f92,f176]) ).
fof(f2148,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f92,f176]) ).
fof(f2150,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f33,f176]) ).
fof(f2151,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f33,f176]) ).
fof(f2154,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(paramodulation,[status(thm)],[f61,f176]) ).
fof(f2156,plain,
! [X0,X1] : backward_diamond(addition(coantidomain(codomain(X0)),X1),X0) = codomain(multiplication(codomain(X0),X1)),
inference(paramodulation,[status(thm)],[f176,f65]) ).
fof(f2157,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)],[f176,f561]) ).
fof(f2159,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f176,f37]) ).
fof(f2162,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f176,f148]) ).
fof(f2163,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f176,f148]) ).
fof(f2164,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f176,f139]) ).
fof(f2166,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)],[f176,f561]) ).
fof(f2167,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)],[f176,f404]) ).
fof(f2168,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(coantidomain(X0),X1))),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f176,f53]) ).
fof(f2169,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)],[f176,f51]) ).
fof(f2170,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)],[f176,f41]) ).
fof(f2171,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)],[f176,f41]) ).
fof(f2172,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f176,f40]) ).
fof(f2173,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f176,f40]) ).
fof(f2174,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f176,f37]) ).
fof(f2175,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f2140]) ).
fof(f2178,plain,
! [X0] : X0 = multiplication(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f2144]) ).
fof(f2179,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,addition(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f176,f2145]) ).
fof(f2184,plain,
! [X0,X1] : backward_diamond(addition(coantidomain(codomain(X0)),X1),X0) = backward_diamond(X1,X0),
inference(forward_demodulation,[status(thm)],[f65,f2156]) ).
fof(f2185,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)],[f33,f2157]) ).
fof(f2186,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)],[f176,f2185]) ).
fof(f2187,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f2159]) ).
fof(f2190,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f98,f2162]) ).
fof(f2191,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f148,f2190]) ).
fof(f2192,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f148,f2163]) ).
fof(f2193,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)],[f33,f2170]) ).
fof(f2194,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2172]) ).
fof(f2195,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f2173]) ).
fof(f2196,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2195]) ).
fof(f2197,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f2174]) ).
fof(f2199,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,multiplication(X1,codomain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f37,f2178]) ).
fof(f2202,plain,
! [X0,X1] : multiplication(codomain(X0),X1) = multiplication(multiplication(codomain(X0),X1),backward_diamond(X1,X0)),
inference(paramodulation,[status(thm)],[f65,f2178]) ).
fof(f2204,plain,
! [X0] : coantidomain(X0) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f188,f2178]) ).
fof(f2206,plain,
! [X0] : backward_diamond(codomain(codomain(X0)),X0) = codomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f2178,f65]) ).
fof(f2207,plain,
! [X0] : addition(coantidomain(multiplication(X0,codomain(codomain(X0)))),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),codomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f2178,f561]) ).
fof(f2209,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,codomain(multiplication(X0,X1)))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f2178,f37]) ).
fof(f2212,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f2178,f148]) ).
fof(f2213,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2178,f148]) ).
fof(f2214,plain,
! [X0] : multiplication(X0,multiplication(codomain(X0),coantidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f2178,f139]) ).
fof(f2216,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(X0),codomain(X0)))) = coantidomain(multiplication(codomain(X0),codomain(X0))),
inference(paramodulation,[status(thm)],[f2178,f561]) ).
fof(f2217,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,domain(codomain(X0))))) = antidomain(multiplication(X0,domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f2178,f404]) ).
fof(f2218,plain,
! [X0,X1] :
( leq(multiplication(X1,star(codomain(X0))),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2178,f53]) ).
fof(f2219,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),codomain(X0))
| ~ leq(addition(X0,X1),codomain(X0)) ),
inference(paramodulation,[status(thm)],[f2178,f51]) ).
fof(f2220,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(multiplication(X0,codomain(X1)),X1),
inference(paramodulation,[status(thm)],[f2178,f41]) ).
fof(f2221,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(X0,multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f2178,f41]) ).
fof(f2222,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f2178,f40]) ).
fof(f2223,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2178,f40]) ).
fof(f2224,plain,
! [X0,X1] : multiplication(X0,multiplication(codomain(X0),X1)) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f2178,f37]) ).
fof(f2226,plain,
! [X0,X1] : multiplication(codomain(X0),X1) = multiplication(codomain(X0),multiplication(X1,backward_diamond(X1,X0))),
inference(forward_demodulation,[status(thm)],[f37,f2202]) ).
fof(f2227,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,codomain(codomain(X0))))) = coantidomain(multiplication(codomain(X0),codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f33,f2207]) ).
fof(f2228,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,codomain(codomain(X0))))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f2178,f2227]) ).
fof(f2229,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f2212]) ).
fof(f2230,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(X1,multiplication(X0,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f33,f2220]) ).
fof(f2231,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f2222]) ).
fof(f2232,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1761,f46]) ).
fof(f2237,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f98,f1761]) ).
fof(f2238,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f34,f1761]) ).
fof(f2240,plain,
! [X0,X1] : leq(antidomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f33,f1761]) ).
fof(f2243,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f92,f2232]) ).
fof(f2244,plain,
! [X0,X1] : addition(coantidomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1762,f46]) ).
fof(f2248,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f98,f1762]) ).
fof(f2249,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f34,f1762]) ).
fof(f2251,plain,
! [X0,X1] : leq(coantidomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f33,f1762]) ).
fof(f2254,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f92,f2244]) ).
fof(f2255,plain,
! [X0,X1] : addition(domain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1763,f46]) ).
fof(f2261,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f98,f1763]) ).
fof(f2262,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f34,f1763]) ).
fof(f2264,plain,
! [X0,X1] : leq(domain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f33,f1763]) ).
fof(f2267,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f92,f2255]) ).
fof(f2271,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,backward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f1439,f157]) ).
fof(f2272,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f1432,f157]) ).
fof(f2273,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f1427,f157]) ).
fof(f2274,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f1420,f157]) ).
fof(f2275,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,divergence(X1))),
inference(paramodulation,[status(thm)],[f1423,f157]) ).
fof(f2276,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f1412,f157]) ).
fof(f2277,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f1406,f157]) ).
fof(f2278,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f1315,f157]) ).
fof(f2279,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f1313,f157]) ).
fof(f2280,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f1311,f157]) ).
fof(f2281,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(X1,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f94,f157]) ).
fof(f2282,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f100,f157]) ).
fof(f2283,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f92,f157]) ).
fof(f2284,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f92,f157]) ).
fof(f2286,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f157]) ).
fof(f2287,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f157]) ).
fof(f2289,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(one,X1)) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f41,f157]) ).
fof(f2290,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X1,addition(X0,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f98,f157]) ).
fof(f2291,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f34,f157]) ).
fof(f2295,plain,
! [X0,X1] : multiplication(domain(X0),addition(one,antidomain(X1))) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f157]) ).
fof(f2296,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(one,X2)) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f37,f157]) ).
fof(f2297,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X0,X1))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f172,f157]) ).
fof(f2298,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f131,f157]) ).
fof(f2299,plain,
! [X0] : multiplication(antidomain(X0),addition(one,X0)) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f54,f157]) ).
fof(f2302,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(coantidomain(X0),X1))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f176,f157]) ).
fof(f2303,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f146,f157]) ).
fof(f2304,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f139,f157]) ).
fof(f2310,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(one,X1),X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f157,f148]) ).
fof(f2311,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(addition(X0,multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f157,f148]) ).
fof(f2312,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(addition(X0,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f157,f139]) ).
fof(f2314,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)],[f157,f561]) ).
fof(f2315,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)],[f157,f404]) ).
fof(f2316,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)],[f157,f53]) ).
fof(f2317,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)],[f157,f51]) ).
fof(f2318,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)],[f157,f41]) ).
fof(f2319,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)],[f157,f41]) ).
fof(f2320,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f157,f40]) ).
fof(f2321,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(one,X1),X2)) = addition(addition(X0,multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f157,f40]) ).
fof(f2322,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(one,X1),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f157,f37]) ).
fof(f2324,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(paramodulation,[status(thm)],[f157,f41]) ).
fof(f2325,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)],[f157,f53]) ).
fof(f2326,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)],[f157,f51]) ).
fof(f2327,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),X2))) = multiplication(addition(X1,X0),addition(one,X2)),
inference(paramodulation,[status(thm)],[f157,f98]) ).
fof(f2328,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),X2))) = multiplication(addition(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f157,f34]) ).
fof(f2330,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f157,f1357]) ).
fof(f2331,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f157,f1356]) ).
fof(f2332,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f157,f1359]) ).
fof(f2333,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f157,f1261]) ).
fof(f2334,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f157,f100]) ).
fof(f2335,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f157,f98]) ).
fof(f2336,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,X1),multiplication(X0,addition(one,X1)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f157,f94]) ).
fof(f2337,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(X2,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f157,f92]) ).
fof(f2338,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(one,X2))) = addition(multiplication(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f157,f92]) ).
fof(f2339,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != X0
| leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f157,f241]) ).
fof(f2340,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != multiplication(X0,X1)
| leq(X0,multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f157,f47]) ).
fof(f2341,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f157,f34]) ).
fof(f2343,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_diamond(X1,X2))),
inference(forward_demodulation,[status(thm)],[f38,f2271]) ).
fof(f2344,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(forward_demodulation,[status(thm)],[f38,f2272]) ).
fof(f2345,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(forward_demodulation,[status(thm)],[f38,f2273]) ).
fof(f2346,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(forward_demodulation,[status(thm)],[f38,f2274]) ).
fof(f2347,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,divergence(X1))),
inference(forward_demodulation,[status(thm)],[f38,f2275]) ).
fof(f2348,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f38,f2276]) ).
fof(f2349,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f38,f2277]) ).
fof(f2350,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f38,f2278]) ).
fof(f2351,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f38,f2279]) ).
fof(f2352,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f38,f2280]) ).
fof(f2357,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f37,f2289]) ).
fof(f2362,plain,
! [X0,X1] : multiplication(domain(X0),one) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1315,f2295]) ).
fof(f2363,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f38,f2362]) ).
fof(f2364,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)],[f37,f2296]) ).
fof(f2365,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = multiplication(X0,addition(multiplication(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f148,f2364]) ).
fof(f2366,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = multiplication(X0,addition(X1,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f33,f2365]) ).
fof(f2367,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X0,X1))) = multiplication(antidomain(X0),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f157,f2297]) ).
fof(f2368,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f2298]) ).
fof(f2369,plain,
! [X0] : multiplication(antidomain(X0),addition(one,X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f2299]) ).
fof(f2374,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f2303]) ).
fof(f2375,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f2304]) ).
fof(f2383,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)],[f98,f2310]) ).
fof(f2384,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)],[f92,f2383]) ).
fof(f2385,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f2384]) ).
fof(f2386,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)],[f98,f2311]) ).
fof(f2387,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)],[f92,f2386]) ).
fof(f2388,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f2387]) ).
fof(f2390,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)],[f98,f2316]) ).
fof(f2391,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)],[f92,f2390]) ).
fof(f2392,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)],[f98,f2317]) ).
fof(f2393,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)],[f92,f2392]) ).
fof(f2394,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)],[f98,f2319]) ).
fof(f2395,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)],[f92,f2394]) ).
fof(f2396,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)],[f92,f2320]) ).
fof(f2397,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f148,f2396]) ).
fof(f2398,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)],[f98,f2321]) ).
fof(f2399,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)],[f98,f2398]) ).
fof(f2400,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)],[f92,f2399]) ).
fof(f2401,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f148,f2400]) ).
fof(f2403,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f37,f2324]) ).
fof(f2404,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)],[f37,f2325]) ).
fof(f2405,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)],[f37,f2404]) ).
fof(f2406,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)],[f37,f2405]) ).
fof(f2407,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)],[f37,f2326]) ).
fof(f2408,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)],[f37,f2407]) ).
fof(f2410,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(one,X2)),X1),
inference(forward_demodulation,[status(thm)],[f92,f2335]) ).
fof(f2411,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(addition(one,X1),X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2336]) ).
fof(f2412,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,addition(one,X1)))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f98,f2411]) ).
fof(f2413,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(one,X2))) = addition(X1,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f92,f2338]) ).
fof(f2417,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(antidomain(domain(X0)),X1),
inference(paramodulation,[status(thm)],[f62,f181]) ).
fof(f2418,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(antidomain(antidomain(X0)),X1),
inference(paramodulation,[status(thm)],[f57,f181]) ).
fof(f2430,plain,
! [X0] : multiplication(antidomain(c(X0)),one) = multiplication(antidomain(c(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f515,f181]) ).
fof(f2431,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)],[f561,f181]) ).
fof(f2432,plain,
! [X0] : multiplication(antidomain(codomain(X0)),one) = multiplication(antidomain(codomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f625,f181]) ).
fof(f2433,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)],[f404,f181]) ).
fof(f2434,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f504,f181]) ).
fof(f2435,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)],[f148,f181]) ).
fof(f2436,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)],[f41,f181]) ).
fof(f2437,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)],[f40,f181]) ).
fof(f2438,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f98,f181]) ).
fof(f2439,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(paramodulation,[status(thm)],[f34,f181]) ).
fof(f2441,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(one,X1))) = multiplication(antidomain(multiplication(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f157,f181]) ).
fof(f2442,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)],[f94,f181]) ).
fof(f2443,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,X1)) = multiplication(antidomain(addition(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f100,f181]) ).
fof(f2444,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,addition(X1,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f92,f181]) ).
fof(f2445,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X1,addition(X2,X0))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f92,f181]) ).
fof(f2452,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X1,X0))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f157]) ).
fof(f2454,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)],[f181,f148]) ).
fof(f2455,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,X0),coantidomain(multiplication(antidomain(X0),X1)))) = zero,
inference(paramodulation,[status(thm)],[f181,f139]) ).
fof(f2457,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)],[f181,f561]) ).
fof(f2458,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)],[f181,f404]) ).
fof(f2459,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)],[f181,f53]) ).
fof(f2460,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)],[f181,f51]) ).
fof(f2461,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)],[f181,f41]) ).
fof(f2462,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)],[f181,f41]) ).
fof(f2463,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)],[f181,f40]) ).
fof(f2464,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)],[f181,f40]) ).
fof(f2465,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X1,X0),X2)) = multiplication(multiplication(antidomain(X0),X1),X2),
inference(paramodulation,[status(thm)],[f181,f37]) ).
fof(f2470,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f2417]) ).
fof(f2471,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f57,f2418]) ).
fof(f2474,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f2430]) ).
fof(f2475,plain,
! [X0,X1] : zero = multiplication(antidomain(coantidomain(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f54,f2431]) ).
fof(f2476,plain,
! [X0] : antidomain(codomain(X0)) = multiplication(antidomain(codomain(X0)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f2432]) ).
fof(f2477,plain,
! [X0,X1] : zero = multiplication(antidomain(antidomain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f54,f2433]) ).
fof(f2478,plain,
! [X0,X1] : zero = multiplication(domain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f57,f2477]) ).
fof(f2479,plain,
! [X0,X1] : zero = domain_difference(multiplication(X0,domain(X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f63,f2478]) ).
fof(f2480,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f2434]) ).
fof(f2481,plain,
! [X0] : c(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f2480]) ).
fof(f2482,plain,
! [X0] : c(X0) = multiplication(c(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f2481]) ).
fof(f2484,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X0),
inference(forward_demodulation,[status(thm)],[f54,f2443]) ).
fof(f2486,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X1,X0))) = multiplication(antidomain(X0),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f157,f2452]) ).
fof(f2489,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f148,f2454]) ).
fof(f2490,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)],[f33,f2461]) ).
fof(f2491,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2463]) ).
fof(f2492,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)],[f98,f2464]) ).
fof(f2493,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,X2)) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f172,f2492]) ).
fof(f2494,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,X2)) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2493]) ).
fof(f2495,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X1,X0),X2)) = multiplication(antidomain(X0),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f2465]) ).
fof(f2496,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f37,f185]) ).
fof(f2503,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)],[f561,f185]) ).
fof(f2504,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f98,f185]) ).
fof(f2505,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f34,f185]) ).
fof(f2511,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(paramodulation,[status(thm)],[f61,f185]) ).
fof(f2513,plain,
! [X0,X1] : backward_diamond(addition(X0,coantidomain(codomain(X1))),X1) = codomain(multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f185,f65]) ).
fof(f2514,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)],[f185,f561]) ).
fof(f2516,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f185,f37]) ).
fof(f2522,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,coantidomain(X0)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f185,f157]) ).
fof(f2524,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f185,f148]) ).
fof(f2525,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f185,f139]) ).
fof(f2527,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)],[f185,f561]) ).
fof(f2528,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)],[f185,f404]) ).
fof(f2529,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,coantidomain(X0)))),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f185,f53]) ).
fof(f2530,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)],[f185,f51]) ).
fof(f2531,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)],[f185,f41]) ).
fof(f2532,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)],[f185,f41]) ).
fof(f2533,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f185,f40]) ).
fof(f2535,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f185,f37]) ).
fof(f2536,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f2496]) ).
fof(f2542,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)],[f37,f2503]) ).
fof(f2543,plain,
! [X0,X1] : zero = multiplication(multiplication(codomain(X0),X1),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f139,f2542]) ).
fof(f2544,plain,
! [X0,X1] : zero = multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f37,f2543]) ).
fof(f2549,plain,
! [X0,X1] : backward_diamond(addition(X0,coantidomain(codomain(X1))),X1) = backward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f2513]) ).
fof(f2550,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)],[f33,f2514]) ).
fof(f2551,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)],[f185,f2550]) ).
fof(f2552,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f2516]) ).
fof(f2560,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f148,f2524]) ).
fof(f2561,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)],[f33,f2531]) ).
fof(f2562,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2533]) ).
fof(f2565,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f2535]) ).
fof(f2566,plain,
! [X0,X1] : addition(divergence(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2110,f46]) ).
fof(f2580,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f92,f2110]) ).
fof(f2581,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f92,f2110]) ).
fof(f2586,plain,
! [X0,X1] : addition(one,addition(X0,divergence(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f2566]) ).
fof(f2587,plain,
! [X0,X1] : addition(codomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2122,f46]) ).
fof(f2588,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f65,f2122]) ).
fof(f2590,plain,
! [X0,X1] : leq(coantidomain(codomain(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f188,f2122]) ).
fof(f2604,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f92,f2122]) ).
fof(f2605,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f92,f2122]) ).
fof(f2610,plain,
! [X0,X1] : addition(one,addition(X0,codomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f2587]) ).
fof(f2616,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f98,f187]) ).
fof(f2617,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f34,f187]) ).
fof(f2622,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(X1,one)) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f41,f187]) ).
fof(f2623,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X1,addition(X0,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f98,f187]) ).
fof(f2624,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f34,f187]) ).
fof(f2626,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = multiplication(X0,addition(one,X1)),
inference(paramodulation,[status(thm)],[f157,f187]) ).
fof(f2629,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X1),one)) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f187]) ).
fof(f2630,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(X2,one)) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f37,f187]) ).
fof(f2632,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(addition(X0,X1),one)) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f172,f187]) ).
fof(f2633,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(multiplication(X0,X1),one)) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f131,f187]) ).
fof(f2638,plain,
! [X0,X1] : multiplication(X0,addition(addition(X1,one),one)) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f187,f187]) ).
fof(f2640,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),one)) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f146,f187]) ).
fof(f2641,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),one)) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f139,f187]) ).
fof(f2649,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f187,f157]) ).
fof(f2650,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,one),X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f187,f148]) ).
fof(f2651,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(addition(X0,multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f187,f148]) ).
fof(f2652,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(addition(X0,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f187,f139]) ).
fof(f2654,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)],[f187,f561]) ).
fof(f2655,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)],[f187,f404]) ).
fof(f2656,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)],[f187,f53]) ).
fof(f2657,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)],[f187,f51]) ).
fof(f2658,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)],[f187,f41]) ).
fof(f2659,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)],[f187,f41]) ).
fof(f2660,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f187,f40]) ).
fof(f2662,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,one),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f187,f37]) ).
fof(f2664,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(paramodulation,[status(thm)],[f187,f41]) ).
fof(f2665,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)],[f187,f53]) ).
fof(f2666,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)],[f187,f51]) ).
fof(f2667,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),X2))) = multiplication(addition(X1,X0),addition(X2,one)),
inference(paramodulation,[status(thm)],[f187,f98]) ).
fof(f2668,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),X2))) = multiplication(addition(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f187,f34]) ).
fof(f2669,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = multiplication(X0,addition(X1,one)),
inference(paramodulation,[status(thm)],[f187,f157]) ).
fof(f2670,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(X1,one))) = multiplication(antidomain(multiplication(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f187,f181]) ).
fof(f2672,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f187,f1357]) ).
fof(f2673,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f187,f1356]) ).
fof(f2674,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f187,f1359]) ).
fof(f2675,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f187,f1261]) ).
fof(f2676,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f187,f100]) ).
fof(f2677,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f187,f98]) ).
fof(f2678,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,X1),multiplication(X0,addition(X1,one)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f187,f94]) ).
fof(f2679,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(X2,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f187,f92]) ).
fof(f2680,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(X2,one))) = addition(multiplication(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f187,f92]) ).
fof(f2681,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != X0
| leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f187,f241]) ).
fof(f2682,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != multiplication(X0,X1)
| leq(X0,multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f187,f47]) ).
fof(f2683,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f187,f34]) ).
fof(f2692,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f37,f2622]) ).
fof(f2699,plain,
! [X0,X1] : multiplication(domain(X0),addition(one,antidomain(X1))) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f2629]) ).
fof(f2700,plain,
! [X0,X1] : multiplication(domain(X0),one) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1315,f2699]) ).
fof(f2701,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f38,f2700]) ).
fof(f2702,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)],[f37,f2630]) ).
fof(f2703,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = multiplication(X0,addition(multiplication(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f148,f2702]) ).
fof(f2704,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = multiplication(X0,addition(X1,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f33,f2703]) ).
fof(f2707,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,addition(X0,one))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f98,f2632]) ).
fof(f2708,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,addition(X0,one))) = multiplication(antidomain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f2707]) ).
fof(f2709,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = addition(antidomain(X0),zero),
inference(forward_demodulation,[status(thm)],[f33,f2633]) ).
fof(f2710,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f2709]) ).
fof(f2722,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f2638]) ).
fof(f2723,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f100,f2722]) ).
fof(f2726,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = addition(X0,zero),
inference(forward_demodulation,[status(thm)],[f33,f2640]) ).
fof(f2727,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f2726]) ).
fof(f2728,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = addition(X0,zero),
inference(forward_demodulation,[status(thm)],[f33,f2641]) ).
fof(f2729,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f2728]) ).
fof(f2740,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f100,f2649]) ).
fof(f2741,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)],[f98,f2650]) ).
fof(f2742,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)],[f92,f2741]) ).
fof(f2743,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f2742]) ).
fof(f2744,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)],[f98,f2651]) ).
fof(f2745,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)],[f92,f2744]) ).
fof(f2746,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f2745]) ).
fof(f2748,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)],[f98,f2656]) ).
fof(f2749,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)],[f92,f2748]) ).
fof(f2750,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)],[f98,f2657]) ).
fof(f2751,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)],[f92,f2750]) ).
fof(f2752,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)],[f98,f2659]) ).
fof(f2753,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)],[f92,f2752]) ).
fof(f2754,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)],[f92,f2660]) ).
fof(f2755,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f148,f2754]) ).
fof(f2761,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f37,f2664]) ).
fof(f2762,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)],[f37,f2665]) ).
fof(f2763,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)],[f37,f2762]) ).
fof(f2764,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)],[f37,f2763]) ).
fof(f2765,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)],[f37,f2666]) ).
fof(f2766,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)],[f37,f2765]) ).
fof(f2768,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,one)),X1),
inference(forward_demodulation,[status(thm)],[f92,f2677]) ).
fof(f2769,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(addition(X1,one),X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2678]) ).
fof(f2770,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,addition(X1,X1)))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f98,f2769]) ).
fof(f2771,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f36,f2770]) ).
fof(f2772,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(X2,one))) = addition(X1,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f92,f2680]) ).
fof(f2773,plain,
! [X0,X1] : addition(c(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2136,f46]) ).
fof(f2774,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f67,f2136]) ).
fof(f2775,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f66,f2136]) ).
fof(f2777,plain,
! [X0,X1] : leq(antidomain(c(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f493,f2136]) ).
fof(f2778,plain,
! [X0,X1] : leq(domain(c(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f317,f2136]) ).
fof(f2792,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f92,f2136]) ).
fof(f2793,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f92,f2136]) ).
fof(f2798,plain,
! [X0,X1] : addition(one,addition(X0,c(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f2773]) ).
fof(f2799,plain,
! [X0,X1] : addition(antidomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2240,f46]) ).
fof(f2816,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f92,f2240]) ).
fof(f2817,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f92,f2240]) ).
fof(f2822,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f2799]) ).
fof(f2825,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)],[f92,f165]) ).
fof(f2826,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)],[f92,f165]) ).
fof(f2829,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)],[f192,f165]) ).
fof(f2830,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)],[f190,f165]) ).
fof(f2831,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)],[f63,f165]) ).
fof(f2832,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)],[f37,f165]) ).
fof(f2834,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)],[f172,f165]) ).
fof(f2835,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)],[f131,f165]) ).
fof(f2839,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(codomain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f2178,f165]) ).
fof(f2840,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)],[f157,f165]) ).
fof(f2841,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)],[f176,f165]) ).
fof(f2842,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)],[f187,f165]) ).
fof(f2844,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)],[f146,f165]) ).
fof(f2845,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)],[f139,f165]) ).
fof(f2848,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f38,f165]) ).
fof(f2849,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)],[f165,f165]) ).
fof(f2850,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)],[f148,f165]) ).
fof(f2851,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)],[f41,f165]) ).
fof(f2852,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)],[f40,f165]) ).
fof(f2853,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)],[f187,f165]) ).
fof(f2854,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)],[f157,f165]) ).
fof(f2855,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)],[f94,f165]) ).
fof(f2856,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)],[f100,f165]) ).
fof(f2857,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)],[f92,f165]) ).
fof(f2858,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)],[f92,f165]) ).
fof(f2859,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f35,f165]) ).
fof(f2860,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)],[f33,f165]) ).
fof(f2861,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)],[f33,f165]) ).
fof(f2862,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f36,f165]) ).
fof(f2863,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)],[f192,f165]) ).
fof(f2864,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)],[f190,f165]) ).
fof(f2865,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)],[f63,f165]) ).
fof(f2866,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)],[f37,f165]) ).
fof(f2867,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)],[f181,f165]) ).
fof(f2868,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)],[f172,f165]) ).
fof(f2869,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)],[f131,f165]) ).
fof(f2873,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,codomain(X0))),X2),
inference(paramodulation,[status(thm)],[f2178,f165]) ).
fof(f2874,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)],[f157,f165]) ).
fof(f2875,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)],[f176,f165]) ).
fof(f2876,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)],[f187,f165]) ).
fof(f2877,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)],[f185,f165]) ).
fof(f2878,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)],[f146,f165]) ).
fof(f2879,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)],[f139,f165]) ).
fof(f2882,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f38,f165]) ).
fof(f2883,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)],[f165,f53]) ).
fof(f2884,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)],[f165,f51]) ).
fof(f2886,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(X0,addition(X2,X1)),X3)),
inference(paramodulation,[status(thm)],[f165,f1357]) ).
fof(f2890,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)],[f165,f92]) ).
fof(f2891,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)],[f165,f92]) ).
fof(f2892,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)],[f165,f181]) ).
fof(f2893,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)],[f165,f172]) ).
fof(f2894,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(X0,addition(X1,X3)),X4))),
inference(paramodulation,[status(thm)],[f165,f1357]) ).
fof(f2895,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)],[f165,f1356]) ).
fof(f2896,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(X0,addition(X3,X1)),X2)),
inference(paramodulation,[status(thm)],[f165,f1359]) ).
fof(f2897,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(X0,addition(X1,X2)),X3)),
inference(paramodulation,[status(thm)],[f165,f1261]) ).
fof(f2899,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)],[f165,f98]) ).
fof(f2900,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)],[f165,f94]) ).
fof(f2901,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)],[f165,f92]) ).
fof(f2902,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)],[f165,f92]) ).
fof(f2903,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)],[f165,f241]) ).
fof(f2904,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)],[f165,f47]) ).
fof(f2905,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)],[f165,f34]) ).
fof(f2913,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,addition(X3,X2)),X0),
inference(forward_demodulation,[status(thm)],[f148,f2826]) ).
fof(f2918,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),X2) = addition(multiplication(c(X0),addition(domain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f2829]) ).
fof(f2919,plain,
! [X0,X1,X2] : addition(multiplication(coantidomain(X0),X1),X2) = addition(multiplication(coantidomain(X0),addition(codomain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f2830]) ).
fof(f2920,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)],[f37,f2832]) ).
fof(f2921,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)],[f165,f2920]) ).
fof(f2922,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)],[f148,f2921]) ).
fof(f2923,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)],[f37,f2922]) ).
fof(f2926,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)],[f165,f2834]) ).
fof(f2927,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)],[f98,f2926]) ).
fof(f2928,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)],[f75,f2835]) ).
fof(f2936,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)],[f98,f2840]) ).
fof(f2937,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)],[f92,f2936]) ).
fof(f2938,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)],[f98,f2937]) ).
fof(f2939,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)],[f148,f2938]) ).
fof(f2940,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)],[f98,f2939]) ).
fof(f2941,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)],[f165,f2841]) ).
fof(f2942,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)],[f98,f2941]) ).
fof(f2943,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)],[f98,f2842]) ).
fof(f2944,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)],[f92,f2943]) ).
fof(f2945,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)],[f98,f2944]) ).
fof(f2946,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)],[f148,f2945]) ).
fof(f2947,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)],[f98,f2946]) ).
fof(f2950,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)],[f75,f2844]) ).
fof(f2951,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)],[f75,f2845]) ).
fof(f2954,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)],[f165,f2849]) ).
fof(f2955,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)],[f165,f2954]) ).
fof(f2956,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)],[f98,f2955]) ).
fof(f2957,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)],[f148,f2850]) ).
fof(f2958,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)],[f98,f2957]) ).
fof(f2959,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = multiplication(X0,addition(X2,addition(X3,X1))),
inference(forward_demodulation,[status(thm)],[f148,f2958]) ).
fof(f2960,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)],[f148,f2852]) ).
fof(f2961,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)],[f98,f2960]) ).
fof(f2962,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = multiplication(X0,addition(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f148,f2961]) ).
fof(f2963,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)],[f37,f2853]) ).
fof(f2964,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)],[f148,f2963]) ).
fof(f2965,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)],[f37,f2964]) ).
fof(f2966,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)],[f148,f2965]) ).
fof(f2967,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)],[f92,f2966]) ).
fof(f2968,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)],[f37,f2854]) ).
fof(f2969,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)],[f148,f2968]) ).
fof(f2970,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)],[f37,f2969]) ).
fof(f2971,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)],[f148,f2970]) ).
fof(f2972,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)],[f92,f2971]) ).
fof(f2973,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)],[f165,f2855]) ).
fof(f2974,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)],[f165,f2856]) ).
fof(f2975,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)],[f165,f2974]) ).
fof(f2976,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)],[f98,f2975]) ).
fof(f2977,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),zero),
inference(forward_demodulation,[status(thm)],[f148,f2859]) ).
fof(f2978,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f35,f2977]) ).
fof(f2979,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f148,f2862]) ).
fof(f2980,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f2979]) ).
fof(f2981,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)],[f92,f2863]) ).
fof(f2982,plain,
! [X0,X1,X2] : addition(X0,multiplication(c(X1),X2)) = addition(multiplication(c(X1),addition(X2,domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f75,f2981]) ).
fof(f2983,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)],[f92,f2864]) ).
fof(f2984,plain,
! [X0,X1,X2] : addition(X0,multiplication(coantidomain(X1),X2)) = addition(multiplication(coantidomain(X1),addition(X2,codomain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f75,f2983]) ).
fof(f2985,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)],[f37,f2866]) ).
fof(f2986,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)],[f165,f2985]) ).
fof(f2987,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)],[f148,f2986]) ).
fof(f2988,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)],[f37,f2987]) ).
fof(f2989,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)],[f165,f2867]) ).
fof(f2990,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)],[f165,f2868]) ).
fof(f2991,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)],[f92,f2869]) ).
fof(f2992,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)],[f75,f2991]) ).
fof(f3003,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,codomain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f92,f2873]) ).
fof(f3004,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)],[f98,f2874]) ).
fof(f3005,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)],[f165,f3004]) ).
fof(f3006,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)],[f92,f3005]) ).
fof(f3007,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)],[f165,f2875]) ).
fof(f3008,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)],[f98,f2876]) ).
fof(f3009,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)],[f165,f3008]) ).
fof(f3010,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)],[f92,f3009]) ).
fof(f3011,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)],[f165,f2877]) ).
fof(f3012,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)],[f92,f2878]) ).
fof(f3013,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)],[f75,f3012]) ).
fof(f3014,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)],[f92,f2879]) ).
fof(f3015,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)],[f75,f3014]) ).
fof(f3022,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,one)),X1),
inference(forward_demodulation,[status(thm)],[f92,f2882]) ).
fof(f3031,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f2891]) ).
fof(f3034,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)],[f98,f2899]) ).
fof(f3035,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)],[f165,f3034]) ).
fof(f3036,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)],[f98,f3035]) ).
fof(f3037,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)],[f98,f2900]) ).
fof(f3038,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)],[f165,f3037]) ).
fof(f3039,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)],[f165,f3038]) ).
fof(f3040,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)],[f98,f2901]) ).
fof(f3041,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)],[f98,f2902]) ).
fof(f3042,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)],[f98,f2905]) ).
fof(f3043,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)],[f98,f3042]) ).
fof(f3048,plain,
! [X0,X1] : addition(coantidomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2251,f46]) ).
fof(f3064,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f92,f2251]) ).
fof(f3065,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f92,f2251]) ).
fof(f3070,plain,
! [X0,X1] : addition(one,addition(X0,coantidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f3048]) ).
fof(f3071,plain,
! [X0,X1] : addition(domain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2264,f46]) ).
fof(f3072,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f64,f2264]) ).
fof(f3089,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f92,f2264]) ).
fof(f3090,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f92,f2264]) ).
fof(f3095,plain,
! [X0,X1] : addition(one,addition(X0,domain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f92,f3071]) ).
fof(f3096,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),X0),
inference(resolution,[status(thm)],[f2347,f241]) ).
fof(f3099,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),divergence(X2)))),
inference(paramodulation,[status(thm)],[f98,f2347]) ).
fof(f3100,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),divergence(X2)))),
inference(paramodulation,[status(thm)],[f34,f2347]) ).
fof(f3118,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)],[f2347,f165]) ).
fof(f3119,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),divergence(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2347,f53]) ).
fof(f3120,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),divergence(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2347,f51]) ).
fof(f3121,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),divergence(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2347,f98]) ).
fof(f3122,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),divergence(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2347,f34]) ).
fof(f3129,plain,
! [X0,X1,X2] : leq(multiplication(X0,divergence(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2347,f1356]) ).
fof(f3133,plain,
! [X0,X1,X2] : addition(multiplication(X0,divergence(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2347,f98]) ).
fof(f3135,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,divergence(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2347,f92]) ).
fof(f3136,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,divergence(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2347,f92]) ).
fof(f3138,plain,
! [X0,X1] :
( X0 != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(paramodulation,[status(thm)],[f2347,f47]) ).
fof(f3139,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,divergence(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2347,f34]) ).
fof(f3151,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)],[f148,f3118]) ).
fof(f3152,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)],[f37,f3151]) ).
fof(f3153,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)],[f148,f3152]) ).
fof(f3154,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)],[f92,f3153]) ).
fof(f3155,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)],[f37,f3119]) ).
fof(f3156,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)],[f37,f3155]) ).
fof(f3157,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)],[f37,f3120]) ).
fof(f3163,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,divergence(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f3133]) ).
fof(f3165,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,divergence(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f3136]) ).
fof(f3168,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,divergence(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3096]) ).
fof(f3175,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),X0),
inference(resolution,[status(thm)],[f2348,f241]) ).
fof(f3178,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),codomain(X2)))),
inference(paramodulation,[status(thm)],[f98,f2348]) ).
fof(f3179,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),codomain(X2)))),
inference(paramodulation,[status(thm)],[f34,f2348]) ).
fof(f3189,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f65,f2348]) ).
fof(f3191,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,coantidomain(codomain(X1)))),
inference(paramodulation,[status(thm)],[f188,f2348]) ).
fof(f3202,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)],[f2348,f165]) ).
fof(f3203,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),codomain(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2348,f53]) ).
fof(f3204,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),codomain(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2348,f51]) ).
fof(f3205,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),codomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2348,f98]) ).
fof(f3206,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),codomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2348,f34]) ).
fof(f3213,plain,
! [X0,X1,X2] : leq(multiplication(X0,codomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2348,f1356]) ).
fof(f3217,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2348,f98]) ).
fof(f3219,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,codomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2348,f92]) ).
fof(f3220,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,codomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2348,f92]) ).
fof(f3222,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f2348,f47]) ).
fof(f3223,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,codomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2348,f34]) ).
fof(f3236,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)],[f148,f3202]) ).
fof(f3237,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)],[f37,f3236]) ).
fof(f3238,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)],[f148,f3237]) ).
fof(f3239,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)],[f92,f3238]) ).
fof(f3240,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)],[f37,f3203]) ).
fof(f3241,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)],[f37,f3240]) ).
fof(f3242,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)],[f37,f3204]) ).
fof(f3248,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,codomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f3217]) ).
fof(f3250,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,codomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f3220]) ).
fof(f3254,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,codomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3175]) ).
fof(f3259,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f65,f3175]) ).
fof(f3261,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(codomain(X1))),X0),
inference(paramodulation,[status(thm)],[f188,f3175]) ).
fof(f3267,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f41,f196]) ).
fof(f3271,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(paramodulation,[status(thm)],[f187,f196]) ).
fof(f3272,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(paramodulation,[status(thm)],[f157,f196]) ).
fof(f3276,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = addition(zero,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f192,f196]) ).
fof(f3277,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = addition(zero,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f190,f196]) ).
fof(f3278,plain,
! [X0,X1,X2] : multiplication(addition(X0,domain(X1)),antidomain(X2)) = addition(domain_difference(X1,X2),multiplication(X0,antidomain(X2))),
inference(paramodulation,[status(thm)],[f63,f196]) ).
fof(f3279,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)],[f37,f196]) ).
fof(f3280,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)],[f181,f196]) ).
fof(f3281,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)],[f172,f196]) ).
fof(f3282,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = addition(zero,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f131,f196]) ).
fof(f3283,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f54,f196]) ).
fof(f3285,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f39,f196]) ).
fof(f3286,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(X1,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f2178,f196]) ).
fof(f3287,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)],[f157,f196]) ).
fof(f3288,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)],[f176,f196]) ).
fof(f3289,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)],[f187,f196]) ).
fof(f3290,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)],[f185,f196]) ).
fof(f3291,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = addition(zero,multiplication(X0,multiplication(coantidomain(X1),X2))),
inference(paramodulation,[status(thm)],[f146,f196]) ).
fof(f3292,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)],[f139,f196]) ).
fof(f3293,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(zero,multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f58,f196]) ).
fof(f3296,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = addition(multiplication(X1,domain(X0)),zero),
inference(paramodulation,[status(thm)],[f192,f196]) ).
fof(f3297,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = addition(multiplication(X1,codomain(X0)),zero),
inference(paramodulation,[status(thm)],[f190,f196]) ).
fof(f3298,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),X1),antidomain(X2)) = addition(multiplication(X1,antidomain(X2)),domain_difference(X0,X2)),
inference(paramodulation,[status(thm)],[f63,f196]) ).
fof(f3299,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)],[f37,f196]) ).
fof(f3300,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)],[f181,f196]) ).
fof(f3301,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)],[f172,f196]) ).
fof(f3302,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = addition(multiplication(X1,multiplication(X0,X2)),zero),
inference(paramodulation,[status(thm)],[f131,f196]) ).
fof(f3303,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(multiplication(X1,X0),zero),
inference(paramodulation,[status(thm)],[f54,f196]) ).
fof(f3305,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f39,f196]) ).
fof(f3306,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(multiplication(X1,codomain(X0)),X0),
inference(paramodulation,[status(thm)],[f2178,f196]) ).
fof(f3307,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)],[f157,f196]) ).
fof(f3308,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)],[f176,f196]) ).
fof(f3309,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)],[f187,f196]) ).
fof(f3310,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)],[f185,f196]) ).
fof(f3311,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = addition(multiplication(X1,multiplication(coantidomain(X0),X2)),zero),
inference(paramodulation,[status(thm)],[f146,f196]) ).
fof(f3312,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)],[f139,f196]) ).
fof(f3313,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(multiplication(X1,coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f58,f196]) ).
fof(f3317,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f196,f41]) ).
fof(f3319,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)],[f196,f165]) ).
fof(f3320,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X2)),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f196,f53]) ).
fof(f3321,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f196,f51]) ).
fof(f3324,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(X1,one)) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f196,f187]) ).
fof(f3325,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(one,X1)) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f196,f157]) ).
fof(f3326,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)],[f196,f181]) ).
fof(f3327,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)],[f196,f172]) ).
fof(f3328,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f196,f1357]) ).
fof(f3329,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f196,f1356]) ).
fof(f3330,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f196,f1359]) ).
fof(f3331,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f196,f1261]) ).
fof(f3332,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(addition(X2,X0),X1)) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f196,f100]) ).
fof(f3333,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)],[f196,f98]) ).
fof(f3335,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)],[f196,f92]) ).
fof(f3336,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)],[f196,f92]) ).
fof(f3337,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f196,f241]) ).
fof(f3338,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f196,f47]) ).
fof(f3339,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)],[f196,f34]) ).
fof(f3347,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f33,f3271]) ).
fof(f3348,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f37,f3347]) ).
fof(f3349,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f33,f3272]) ).
fof(f3350,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f37,f3349]) ).
fof(f3351,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f75,f3276]) ).
fof(f3352,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f75,f3277]) ).
fof(f3353,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f75,f3282]) ).
fof(f3354,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f3283]) ).
fof(f3356,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)],[f98,f3287]) ).
fof(f3357,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)],[f92,f3356]) ).
fof(f3358,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)],[f98,f3289]) ).
fof(f3359,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)],[f92,f3358]) ).
fof(f3360,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f75,f3291]) ).
fof(f3361,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)],[f75,f3292]) ).
fof(f3362,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f75,f3293]) ).
fof(f3367,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f3296]) ).
fof(f3368,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f3297]) ).
fof(f3369,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)],[f33,f3300]) ).
fof(f3370,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)],[f33,f3301]) ).
fof(f3371,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f35,f3302]) ).
fof(f3372,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f35,f3303]) ).
fof(f3374,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f3305]) ).
fof(f3375,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(X0,multiplication(X1,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f3306]) ).
fof(f3376,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)],[f33,f3308]) ).
fof(f3377,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)],[f33,f3310]) ).
fof(f3378,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f35,f3311]) ).
fof(f3379,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)],[f35,f3312]) ).
fof(f3380,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f3313]) ).
fof(f3387,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f3320]) ).
fof(f3390,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f3324]) ).
fof(f3391,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f33,f3390]) ).
fof(f3392,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f37,f3325]) ).
fof(f3393,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f33,f3392]) ).
fof(f3394,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f196,f3332]) ).
fof(f3395,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X0)),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f3394]) ).
fof(f3396,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f196,f3395]) ).
fof(f3402,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),X0),
inference(resolution,[status(thm)],[f2349,f241]) ).
fof(f3406,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),c(X2)))),
inference(paramodulation,[status(thm)],[f98,f2349]) ).
fof(f3407,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),c(X2)))),
inference(paramodulation,[status(thm)],[f34,f2349]) ).
fof(f3415,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f67,f2349]) ).
fof(f3416,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f66,f2349]) ).
fof(f3418,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f493,f2349]) ).
fof(f3419,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f317,f2349]) ).
fof(f3431,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)],[f2349,f165]) ).
fof(f3432,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),c(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2349,f53]) ).
fof(f3433,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),c(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2349,f51]) ).
fof(f3434,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),c(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2349,f98]) ).
fof(f3435,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),c(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2349,f34]) ).
fof(f3442,plain,
! [X0,X1,X2] : leq(multiplication(X0,c(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2349,f1356]) ).
fof(f3446,plain,
! [X0,X1,X2] : addition(multiplication(X0,c(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2349,f98]) ).
fof(f3448,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,c(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2349,f92]) ).
fof(f3449,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,c(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2349,f92]) ).
fof(f3451,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f2349,f47]) ).
fof(f3452,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,c(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2349,f34]) ).
fof(f3467,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)],[f148,f3431]) ).
fof(f3468,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)],[f37,f3467]) ).
fof(f3469,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)],[f148,f3468]) ).
fof(f3470,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)],[f92,f3469]) ).
fof(f3471,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)],[f37,f3432]) ).
fof(f3472,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)],[f37,f3471]) ).
fof(f3473,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)],[f37,f3433]) ).
fof(f3479,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,c(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f3446]) ).
fof(f3481,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,c(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f3449]) ).
fof(f3484,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,c(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3402]) ).
fof(f3488,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f67,f3402]) ).
fof(f3489,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f66,f3402]) ).
fof(f3491,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(c(X1))),X0),
inference(paramodulation,[status(thm)],[f493,f3402]) ).
fof(f3492,plain,
! [X0,X1] : leq(multiplication(X0,domain(c(X1))),X0),
inference(paramodulation,[status(thm)],[f317,f3402]) ).
fof(f3497,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),X0),
inference(resolution,[status(thm)],[f2350,f241]) ).
fof(f3501,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),antidomain(X2)))),
inference(paramodulation,[status(thm)],[f98,f2350]) ).
fof(f3502,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),antidomain(X2)))),
inference(paramodulation,[status(thm)],[f34,f2350]) ).
fof(f3506,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f2350]) ).
fof(f3525,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)],[f2350,f165]) ).
fof(f3526,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),antidomain(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2350,f53]) ).
fof(f3527,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),antidomain(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2350,f51]) ).
fof(f3528,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),antidomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2350,f98]) ).
fof(f3529,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),antidomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2350,f34]) ).
fof(f3536,plain,
! [X0,X1,X2] : leq(multiplication(X0,antidomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2350,f1356]) ).
fof(f3540,plain,
! [X0,X1,X2] : addition(multiplication(X0,antidomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2350,f98]) ).
fof(f3542,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,antidomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2350,f92]) ).
fof(f3543,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,antidomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2350,f92]) ).
fof(f3545,plain,
! [X0,X1] :
( X0 != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f2350,f47]) ).
fof(f3546,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,antidomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2350,f34]) ).
fof(f3563,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)],[f148,f3525]) ).
fof(f3564,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)],[f37,f3563]) ).
fof(f3565,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)],[f148,f3564]) ).
fof(f3566,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)],[f92,f3565]) ).
fof(f3567,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)],[f37,f3526]) ).
fof(f3568,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)],[f37,f3567]) ).
fof(f3569,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)],[f37,f3527]) ).
fof(f3575,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,antidomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f3540]) ).
fof(f3577,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,antidomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f3543]) ).
fof(f3580,plain,
! [X0,X1] : leq(domain_difference(X0,X1),domain(X0)),
inference(paramodulation,[status(thm)],[f63,f3497]) ).
fof(f3581,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,antidomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3497]) ).
fof(f3587,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),X0),
inference(paramodulation,[status(thm)],[f57,f3497]) ).
fof(f3593,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f148,f199]) ).
fof(f3594,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f40,f199]) ).
fof(f3599,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)],[f187,f199]) ).
fof(f3600,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)],[f157,f199]) ).
fof(f3601,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)],[f33,f199]) ).
fof(f3602,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)],[f33,f199]) ).
fof(f3603,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)],[f37,f199]) ).
fof(f3605,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(antidomain(multiplication(X0,X1)),X0),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f54,f199]) ).
fof(f3609,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)],[f139,f199]) ).
fof(f3610,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)],[f192,f199]) ).
fof(f3611,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)],[f190,f199]) ).
fof(f3612,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)],[f63,f199]) ).
fof(f3613,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)],[f37,f199]) ).
fof(f3614,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)],[f181,f199]) ).
fof(f3615,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)],[f172,f199]) ).
fof(f3616,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)],[f131,f199]) ).
fof(f3617,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = addition(multiplication(X0,zero),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f54,f199]) ).
fof(f3620,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),codomain(X1)) = addition(multiplication(X0,X1),multiplication(X2,codomain(X1))),
inference(paramodulation,[status(thm)],[f2178,f199]) ).
fof(f3621,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)],[f157,f199]) ).
fof(f3622,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)],[f176,f199]) ).
fof(f3623,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)],[f187,f199]) ).
fof(f3624,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)],[f185,f199]) ).
fof(f3625,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)],[f146,f199]) ).
fof(f3626,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)],[f139,f199]) ).
fof(f3627,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = addition(multiplication(X0,zero),multiplication(X2,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f58,f199]) ).
fof(f3630,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)],[f192,f199]) ).
fof(f3631,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)],[f190,f199]) ).
fof(f3632,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)],[f63,f199]) ).
fof(f3633,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)],[f37,f199]) ).
fof(f3634,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)],[f181,f199]) ).
fof(f3635,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)],[f172,f199]) ).
fof(f3636,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)],[f131,f199]) ).
fof(f3637,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f54,f199]) ).
fof(f3639,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f39,f199]) ).
fof(f3640,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),codomain(X2)) = addition(multiplication(X0,multiplication(X1,codomain(X2))),X2),
inference(paramodulation,[status(thm)],[f2178,f199]) ).
fof(f3641,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)],[f157,f199]) ).
fof(f3642,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)],[f176,f199]) ).
fof(f3643,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)],[f187,f199]) ).
fof(f3644,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)],[f185,f199]) ).
fof(f3645,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)],[f146,f199]) ).
fof(f3646,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)],[f139,f199]) ).
fof(f3647,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X2)) = addition(multiplication(X0,multiplication(X1,coantidomain(X2))),zero),
inference(paramodulation,[status(thm)],[f58,f199]) ).
fof(f3650,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(multiplication(X0,X2),X0),X1),
inference(paramodulation,[status(thm)],[f199,f148]) ).
fof(f3651,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,X2),X2)) = multiplication(addition(multiplication(X0,X1),X0),X2),
inference(paramodulation,[status(thm)],[f199,f40]) ).
fof(f3652,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)],[f199,f165]) ).
fof(f3653,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)],[f199,f53]) ).
fof(f3654,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)],[f199,f51]) ).
fof(f3659,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)],[f199,f187]) ).
fof(f3660,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)],[f199,f157]) ).
fof(f3661,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)],[f199,f181]) ).
fof(f3662,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)],[f199,f172]) ).
fof(f3663,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)],[f199,f1357]) ).
fof(f3664,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(multiplication(X3,X4),X0),X1))),
inference(paramodulation,[status(thm)],[f199,f1356]) ).
fof(f3665,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(multiplication(X2,X3),X0),X1)),
inference(paramodulation,[status(thm)],[f199,f1359]) ).
fof(f3666,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f199,f1261]) ).
fof(f3668,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)],[f199,f98]) ).
fof(f3670,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)],[f199,f92]) ).
fof(f3671,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)],[f199,f92]) ).
fof(f3672,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)],[f199,f241]) ).
fof(f3673,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)],[f199,f47]) ).
fof(f3674,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)],[f199,f34]) ).
fof(f3675,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)],[f199,f33]) ).
fof(f3676,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)],[f199,f33]) ).
fof(f3677,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f33,f3593]) ).
fof(f3678,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f33,f3594]) ).
fof(f3679,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f33,f3678]) ).
fof(f3692,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)],[f148,f3599]) ).
fof(f3693,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)],[f37,f3692]) ).
fof(f3694,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)],[f33,f3693]) ).
fof(f3695,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)],[f37,f3694]) ).
fof(f3696,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)],[f37,f3695]) ).
fof(f3697,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)],[f148,f3600]) ).
fof(f3698,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)],[f37,f3697]) ).
fof(f3699,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)],[f33,f3698]) ).
fof(f3700,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)],[f37,f3699]) ).
fof(f3701,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)],[f37,f3700]) ).
fof(f3702,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)],[f37,f3603]) ).
fof(f3705,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(antidomain(multiplication(X0,X1)),X0),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f75,f3605]) ).
fof(f3711,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)],[f75,f3609]) ).
fof(f3712,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),domain(X1)) = addition(zero,multiplication(X2,domain(X1))),
inference(forward_demodulation,[status(thm)],[f42,f3610]) ).
fof(f3713,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),domain(X1)) = multiplication(X2,domain(X1)),
inference(forward_demodulation,[status(thm)],[f75,f3712]) ).
fof(f3714,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,coantidomain(X1)),X2),codomain(X1)) = addition(zero,multiplication(X2,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f42,f3611]) ).
fof(f3715,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,coantidomain(X1)),X2),codomain(X1)) = multiplication(X2,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f75,f3714]) ).
fof(f3716,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)],[f42,f3616]) ).
fof(f3717,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)],[f75,f3716]) ).
fof(f3718,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f42,f3617]) ).
fof(f3719,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f75,f3718]) ).
fof(f3724,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)],[f42,f3625]) ).
fof(f3725,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)],[f75,f3724]) ).
fof(f3726,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)],[f42,f3626]) ).
fof(f3727,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)],[f75,f3726]) ).
fof(f3728,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = addition(zero,multiplication(X2,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f42,f3627]) ).
fof(f3729,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f75,f3728]) ).
fof(f3733,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),domain(X2)) = multiplication(X0,multiplication(X1,domain(X2))),
inference(forward_demodulation,[status(thm)],[f35,f3630]) ).
fof(f3734,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),coantidomain(X2)),codomain(X2)) = multiplication(X0,multiplication(X1,codomain(X2))),
inference(forward_demodulation,[status(thm)],[f35,f3631]) ).
fof(f3735,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)],[f33,f3634]) ).
fof(f3736,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)],[f33,f3635]) ).
fof(f3737,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)],[f35,f3636]) ).
fof(f3738,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),X2) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f35,f3637]) ).
fof(f3741,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(forward_demodulation,[status(thm)],[f33,f3639]) ).
fof(f3742,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f33,f3741]) ).
fof(f3743,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)],[f33,f3640]) ).
fof(f3744,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)],[f33,f3642]) ).
fof(f3745,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)],[f33,f3644]) ).
fof(f3746,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)],[f35,f3645]) ).
fof(f3747,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)],[f35,f3646]) ).
fof(f3748,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X2)) = multiplication(X0,multiplication(X1,coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f35,f3647]) ).
fof(f3753,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f33,f3650]) ).
fof(f3754,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(multiplication(X0,X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f33,f3651]) ).
fof(f3755,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f33,f3754]) ).
fof(f3756,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)],[f37,f3653]) ).
fof(f3769,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)],[f37,f3659]) ).
fof(f3770,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)],[f37,f3769]) ).
fof(f3771,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)],[f148,f3770]) ).
fof(f3772,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)],[f37,f3771]) ).
fof(f3773,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)],[f33,f3772]) ).
fof(f3774,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)],[f37,f3660]) ).
fof(f3775,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)],[f37,f3774]) ).
fof(f3776,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)],[f148,f3775]) ).
fof(f3777,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)],[f37,f3776]) ).
fof(f3778,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)],[f33,f3777]) ).
fof(f3786,plain,
! [X0,X1] : addition(domain_difference(X0,X1),domain(X0)) = domain(X0),
inference(resolution,[status(thm)],[f3580,f46]) ).
fof(f3792,plain,
! [X0,X1,X2] : leq(domain_difference(multiplication(X0,domain(X1)),X2),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f64,f3580]) ).
fof(f3794,plain,
! [X0,X1] : leq(domain_difference(domain(X0),X1),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f191,f3580]) ).
fof(f3795,plain,
! [X0,X1] : leq(domain_difference(antidomain(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f316,f3580]) ).
fof(f3797,plain,
! [X0,X1] : addition(domain(X0),domain_difference(X0,X1)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f33,f3786]) ).
fof(f3804,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,domain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3587]) ).
fof(f3808,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f64,f3587]) ).
fof(f3817,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),X0),
inference(resolution,[status(thm)],[f2351,f241]) ).
fof(f3822,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),coantidomain(X2)))),
inference(paramodulation,[status(thm)],[f98,f2351]) ).
fof(f3823,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),coantidomain(X2)))),
inference(paramodulation,[status(thm)],[f34,f2351]) ).
fof(f3846,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)],[f2351,f165]) ).
fof(f3847,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),coantidomain(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2351,f53]) ).
fof(f3848,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),coantidomain(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2351,f51]) ).
fof(f3849,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),coantidomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2351,f98]) ).
fof(f3850,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),coantidomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2351,f34]) ).
fof(f3857,plain,
! [X0,X1,X2] : leq(multiplication(X0,coantidomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2351,f1356]) ).
fof(f3861,plain,
! [X0,X1,X2] : addition(multiplication(X0,coantidomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2351,f98]) ).
fof(f3863,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,coantidomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2351,f92]) ).
fof(f3864,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,coantidomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2351,f92]) ).
fof(f3866,plain,
! [X0,X1] :
( X0 != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f2351,f47]) ).
fof(f3867,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,coantidomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2351,f34]) ).
fof(f3888,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)],[f148,f3846]) ).
fof(f3889,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)],[f37,f3888]) ).
fof(f3890,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)],[f148,f3889]) ).
fof(f3891,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)],[f92,f3890]) ).
fof(f3892,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)],[f37,f3847]) ).
fof(f3893,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)],[f37,f3892]) ).
fof(f3894,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)],[f37,f3848]) ).
fof(f3900,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,coantidomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f3861]) ).
fof(f3902,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,coantidomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f3864]) ).
fof(f3907,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f504,f219]) ).
fof(f3908,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),coantidomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2351,f219]) ).
fof(f3909,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),antidomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2350,f219]) ).
fof(f3910,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),c(X1)),X0),
inference(paramodulation,[status(thm)],[f2349,f219]) ).
fof(f3911,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),codomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2348,f219]) ).
fof(f3912,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),divergence(X1)),X0),
inference(paramodulation,[status(thm)],[f2347,f219]) ).
fof(f3913,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),addition(X1,one)),X0) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f187,f219]) ).
fof(f3914,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),addition(one,X1)),X0) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f157,f219]) ).
fof(f3915,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(addition(X1,addition(antidomain(X0),X1)),X0),
inference(paramodulation,[status(thm)],[f94,f219]) ).
fof(f3917,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f92,f219]) ).
fof(f3918,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f92,f219]) ).
fof(f3920,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f33,f219]) ).
fof(f3921,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f33,f219]) ).
fof(f3924,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(paramodulation,[status(thm)],[f62,f219]) ).
fof(f3925,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(paramodulation,[status(thm)],[f57,f219]) ).
fof(f3927,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(antidomain(antidomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f219,f3497]) ).
fof(f3928,plain,
! [X0,X1] : addition(antidomain(antidomain(X0)),X1) = addition(addition(antidomain(antidomain(X0)),X1),multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f219,f2350]) ).
fof(f3929,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),addition(antidomain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f219,f3402]) ).
fof(f3930,plain,
! [X0,X1] : addition(antidomain(c(X0)),X1) = addition(addition(antidomain(c(X0)),X1),multiplication(X1,c(X0))),
inference(paramodulation,[status(thm)],[f219,f2349]) ).
fof(f3931,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),addition(antidomain(divergence(X1)),X0)),
inference(paramodulation,[status(thm)],[f219,f3096]) ).
fof(f3932,plain,
! [X0,X1] : addition(antidomain(divergence(X0)),X1) = addition(addition(antidomain(divergence(X0)),X1),multiplication(X1,divergence(X0))),
inference(paramodulation,[status(thm)],[f219,f2347]) ).
fof(f3933,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),addition(antidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f219,f3175]) ).
fof(f3934,plain,
! [X0,X1] : addition(antidomain(codomain(X0)),X1) = addition(addition(antidomain(codomain(X0)),X1),multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f219,f2348]) ).
fof(f3935,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)],[f219,f199]) ).
fof(f3936,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(antidomain(domain(X1)),X0)),
inference(paramodulation,[status(thm)],[f219,f3587]) ).
fof(f3937,plain,
! [X0,X1] : forward_diamond(addition(antidomain(domain(X0)),X1),X0) = domain(multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f219,f64]) ).
fof(f3938,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)],[f219,f404]) ).
fof(f3939,plain,
! [X0,X1] : addition(antidomain(coantidomain(X0)),X1) = addition(addition(antidomain(coantidomain(X0)),X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f219,f2351]) ).
fof(f3942,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)],[f219,f199]) ).
fof(f3943,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)],[f219,f199]) ).
fof(f3944,plain,
! [X0,X1,X2] : multiplication(addition(addition(antidomain(X0),X1),X2),X0) = addition(multiplication(X2,X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f219,f196]) ).
fof(f3945,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f219,f196]) ).
fof(f3946,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)],[f219,f165]) ).
fof(f3947,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)],[f219,f165]) ).
fof(f3948,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(X0,one)) = addition(addition(antidomain(X0),X1),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f219,f187]) ).
fof(f3949,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(one,X0)) = addition(addition(antidomain(X0),X1),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f219,f157]) ).
fof(f3950,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)],[f219,f148]) ).
fof(f3951,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)],[f219,f148]) ).
fof(f3952,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),multiplication(X0,coantidomain(multiplication(X1,X0)))) = zero,
inference(paramodulation,[status(thm)],[f219,f139]) ).
fof(f3953,plain,
! [X0,X1] : multiplication(antidomain(addition(antidomain(X0),X1)),multiplication(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f219,f131]) ).
fof(f3954,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)],[f219,f561]) ).
fof(f3955,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)],[f219,f404]) ).
fof(f3956,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)],[f219,f53]) ).
fof(f3957,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(antidomain(X1),X0)),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f219,f51]) ).
fof(f3958,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f219,f41]) ).
fof(f3959,plain,
! [X0,X1,X2] : multiplication(addition(addition(antidomain(X0),X1),X2),X0) = addition(multiplication(X1,X0),multiplication(X2,X0)),
inference(paramodulation,[status(thm)],[f219,f41]) ).
fof(f3960,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)],[f219,f40]) ).
fof(f3961,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)],[f219,f40]) ).
fof(f3962,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(multiplication(X1,X0),X2),
inference(paramodulation,[status(thm)],[f219,f37]) ).
fof(f3965,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f39,f3907]) ).
fof(f3966,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),coantidomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f54,f3908]) ).
fof(f3967,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f37,f3966]) ).
fof(f3968,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),antidomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f54,f3909]) ).
fof(f3969,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f37,f3968]) ).
fof(f3970,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),c(X1)),X0),
inference(forward_demodulation,[status(thm)],[f54,f3910]) ).
fof(f3971,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f37,f3970]) ).
fof(f3972,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),codomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f54,f3911]) ).
fof(f3973,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f37,f3972]) ).
fof(f3974,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),divergence(X1)),X0),
inference(forward_demodulation,[status(thm)],[f54,f3912]) ).
fof(f3975,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f37,f3974]) ).
fof(f3976,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(forward_demodulation,[status(thm)],[f37,f3913]) ).
fof(f3977,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f3976]) ).
fof(f3978,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(forward_demodulation,[status(thm)],[f37,f3914]) ).
fof(f3979,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f3978]) ).
fof(f3980,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,addition(antidomain(X1),X0)),X1),
inference(forward_demodulation,[status(thm)],[f219,f3915]) ).
fof(f3985,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f57,f3927]) ).
fof(f3986,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(addition(antidomain(antidomain(X0)),X1),multiplication(X1,antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f57,f3928]) ).
fof(f3987,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(X1,addition(antidomain(antidomain(X0)),multiplication(X1,antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f3986]) ).
fof(f3988,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(X1,addition(domain(X0),multiplication(X1,antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f57,f3987]) ).
fof(f3989,plain,
! [X0,X1] : addition(antidomain(c(X0)),X1) = addition(X1,addition(antidomain(c(X0)),multiplication(X1,c(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f3930]) ).
fof(f3990,plain,
! [X0,X1] : addition(antidomain(divergence(X0)),X1) = addition(X1,addition(antidomain(divergence(X0)),multiplication(X1,divergence(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f3932]) ).
fof(f3991,plain,
! [X0,X1] : addition(antidomain(codomain(X0)),X1) = addition(X1,addition(antidomain(codomain(X0)),multiplication(X1,codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f3934]) ).
fof(f3992,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)],[f199,f3935]) ).
fof(f3993,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f62,f3936]) ).
fof(f3994,plain,
! [X0,X1] : forward_diamond(addition(c(X0),X1),X0) = domain(multiplication(X1,domain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f3937]) ).
fof(f3995,plain,
! [X0,X1] : forward_diamond(addition(c(X0),X1),X0) = forward_diamond(X1,X0),
inference(forward_demodulation,[status(thm)],[f64,f3994]) ).
fof(f3996,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)],[f33,f3938]) ).
fof(f3997,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)],[f62,f3996]) ).
fof(f3998,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)],[f219,f3997]) ).
fof(f3999,plain,
! [X0,X1] : addition(antidomain(coantidomain(X0)),X1) = addition(X1,addition(antidomain(coantidomain(X0)),multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f3939]) ).
fof(f4002,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)],[f199,f3942]) ).
fof(f4003,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)],[f199,f3943]) ).
fof(f4004,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f98,f3944]) ).
fof(f4005,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f196,f4004]) ).
fof(f4006,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f196,f3945]) ).
fof(f4007,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)],[f92,f3946]) ).
fof(f4008,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(X0,one)) = addition(X1,addition(antidomain(X0),multiplication(X1,X0))),
inference(forward_demodulation,[status(thm)],[f98,f3948]) ).
fof(f4009,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(one,X0)) = addition(X1,addition(antidomain(X0),multiplication(X1,X0))),
inference(forward_demodulation,[status(thm)],[f98,f3949]) ).
fof(f4010,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)],[f33,f3950]) ).
fof(f4011,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f196,f3958]) ).
fof(f4012,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f98,f3959]) ).
fof(f4013,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f196,f4012]) ).
fof(f4014,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)],[f33,f3960]) ).
fof(f4015,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f37,f3962]) ).
fof(f4017,plain,
! [X0] : antidomain(X0) = domain_difference(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f63,f3965]) ).
fof(f4020,plain,
! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(forward_diamond(X0,X1),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f64,f3965]) ).
fof(f4022,plain,
! [X0] : domain(X0) = multiplication(antidomain(c(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f191,f3965]) ).
fof(f4023,plain,
! [X0] : antidomain(X0) = multiplication(c(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f316,f3965]) ).
fof(f4026,plain,
! [X0] : leq(antidomain(X0),domain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f3965,f3497]) ).
fof(f4027,plain,
! [X0] : domain(antidomain(X0)) = addition(domain(antidomain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f3965,f2350]) ).
fof(f4028,plain,
! [X0] : leq(c(X0),domain(c(X0))),
inference(paramodulation,[status(thm)],[f3965,f3402]) ).
fof(f4029,plain,
! [X0] : domain(c(X0)) = addition(domain(c(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f3965,f2349]) ).
fof(f4030,plain,
! [X0] : leq(divergence(X0),domain(divergence(X0))),
inference(paramodulation,[status(thm)],[f3965,f3096]) ).
fof(f4031,plain,
! [X0] : domain(divergence(X0)) = addition(domain(divergence(X0)),divergence(X0)),
inference(paramodulation,[status(thm)],[f3965,f2347]) ).
fof(f4032,plain,
! [X0] : leq(codomain(X0),domain(codomain(X0))),
inference(paramodulation,[status(thm)],[f3965,f3175]) ).
fof(f4033,plain,
! [X0] : domain(codomain(X0)) = addition(domain(codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f3965,f2348]) ).
fof(f4034,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)],[f3965,f199]) ).
fof(f4035,plain,
! [X0] : leq(domain(X0),domain(domain(X0))),
inference(paramodulation,[status(thm)],[f3965,f3587]) ).
fof(f4036,plain,
! [X0] : forward_diamond(domain(domain(X0)),X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f3965,f64]) ).
fof(f4037,plain,
! [X0] : addition(antidomain(multiplication(domain(domain(X0)),X0)),antidomain(domain(X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f3965,f404]) ).
fof(f4038,plain,
! [X0] : domain(coantidomain(X0)) = addition(domain(coantidomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f3965,f2351]) ).
fof(f4041,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f3965,f199]) ).
fof(f4042,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f3965,f199]) ).
fof(f4043,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f3965,f196]) ).
fof(f4044,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f3965,f196]) ).
fof(f4045,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),addition(X0,X2)) = addition(multiplication(domain(X0),addition(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f3965,f165]) ).
fof(f4046,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X0),X1),X2)) = addition(multiplication(domain(X0),addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f3965,f165]) ).
fof(f4047,plain,
! [X0] : multiplication(domain(X0),addition(X0,one)) = addition(domain(X0),X0),
inference(paramodulation,[status(thm)],[f3965,f187]) ).
fof(f4048,plain,
! [X0] : multiplication(domain(X0),addition(one,X0)) = addition(domain(X0),X0),
inference(paramodulation,[status(thm)],[f3965,f157]) ).
fof(f4049,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(multiplication(domain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f3965,f148]) ).
fof(f4050,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(X0,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f3965,f148]) ).
fof(f4052,plain,
! [X0] : multiplication(antidomain(domain(X0)),X0) = zero,
inference(paramodulation,[status(thm)],[f3965,f131]) ).
fof(f4053,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(domain(X0)),X0))) = coantidomain(multiplication(codomain(domain(X0)),X0)),
inference(paramodulation,[status(thm)],[f3965,f561]) ).
fof(f4054,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(domain(X0),domain(X0)))) = antidomain(multiplication(domain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f3965,f404]) ).
fof(f4055,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),domain(X0))
| ~ leq(addition(X0,X1),domain(X0)) ),
inference(paramodulation,[status(thm)],[f3965,f53]) ).
fof(f4056,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X0)),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f3965,f51]) ).
fof(f4057,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f3965,f41]) ).
fof(f4058,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f3965,f41]) ).
fof(f4059,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(multiplication(domain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f3965,f40]) ).
fof(f4060,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f3965,f40]) ).
fof(f4061,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(X0,X1)) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f3965,f37]) ).
fof(f4063,plain,
! [X0] : leq(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f316,f4026]) ).
fof(f4064,plain,
! [X0] : c(X0) = addition(domain(antidomain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f316,f4027]) ).
fof(f4065,plain,
! [X0] : c(X0) = addition(antidomain(X0),domain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4064]) ).
fof(f4066,plain,
! [X0] : c(X0) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f316,f4065]) ).
fof(f4067,plain,
! [X0] : domain(c(X0)) = addition(c(X0),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4029]) ).
fof(f4068,plain,
! [X0] : domain(divergence(X0)) = addition(divergence(X0),domain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4031]) ).
fof(f4069,plain,
! [X0] : domain(codomain(X0)) = addition(codomain(X0),domain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4033]) ).
fof(f4070,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(domain(multiplication(X0,X1)),X0),X2),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f196,f4034]) ).
fof(f4071,plain,
! [X0] : leq(domain(X0),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f191,f4035]) ).
fof(f4072,plain,
! [X0] : forward_diamond(antidomain(c(X0)),X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f191,f4036]) ).
fof(f4073,plain,
! [X0] : forward_diamond(antidomain(c(X0)),X0) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f191,f4072]) ).
fof(f4074,plain,
! [X0] : addition(antidomain(domain(X0)),antidomain(multiplication(domain(domain(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4037]) ).
fof(f4075,plain,
! [X0] : addition(c(X0),antidomain(multiplication(domain(domain(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f4074]) ).
fof(f4076,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f191,f4075]) ).
fof(f4077,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f3965,f4076]) ).
fof(f4078,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = c(X0),
inference(forward_demodulation,[status(thm)],[f62,f4077]) ).
fof(f4079,plain,
! [X0] : domain(coantidomain(X0)) = addition(coantidomain(X0),domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4038]) ).
fof(f4080,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f33,f4041]) ).
fof(f4081,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f196,f4042]) ).
fof(f4082,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f33,f4043]) ).
fof(f4083,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)],[f92,f4045]) ).
fof(f4084,plain,
! [X0] : multiplication(domain(X0),addition(X0,one)) = addition(X0,domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f4047]) ).
fof(f4085,plain,
! [X0] : multiplication(domain(X0),addition(one,X0)) = addition(X0,domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f4048]) ).
fof(f4086,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f4049]) ).
fof(f4088,plain,
! [X0] : multiplication(c(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f62,f4052]) ).
fof(f4089,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f4057]) ).
fof(f4090,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(X0,multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f4059]) ).
fof(f4091,plain,
! [X0] : addition(antidomain(X0),c(X0)) = c(X0),
inference(resolution,[status(thm)],[f4063,f46]) ).
fof(f4096,plain,
! [X0,X1] : leq(antidomain(backward_diamond(X0,c(X1))),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f67,f4063]) ).
fof(f4097,plain,
! [X0,X1] : leq(antidomain(forward_diamond(X0,c(X1))),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f66,f4063]) ).
fof(f4113,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f67,f4088]) ).
fof(f4114,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f66,f4088]) ).
fof(f4116,plain,
! [X0] : multiplication(antidomain(c(X0)),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f493,f4088]) ).
fof(f4117,plain,
! [X0] : multiplication(domain(c(X0)),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f317,f4088]) ).
fof(f4127,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(c(multiplication(X0,X1)),X0),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f4088,f199]) ).
fof(f4129,plain,
! [X0] : forward_diamond(c(domain(X0)),X0) = domain(zero),
inference(paramodulation,[status(thm)],[f4088,f64]) ).
fof(f4134,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f4088,f199]) ).
fof(f4135,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = addition(multiplication(X0,zero),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f4088,f199]) ).
fof(f4136,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = addition(multiplication(X1,X0),zero),
inference(paramodulation,[status(thm)],[f4088,f196]) ).
fof(f4137,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f4088,f196]) ).
fof(f4138,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(zero,X2)) = addition(multiplication(c(X0),addition(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f4088,f165]) ).
fof(f4139,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(c(X0),X1),X2)) = addition(multiplication(c(X0),addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f4088,f165]) ).
fof(f4140,plain,
! [X0] : multiplication(c(X0),addition(X0,one)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f4088,f187]) ).
fof(f4141,plain,
! [X0] : multiplication(c(X0),addition(one,X0)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f4088,f157]) ).
fof(f4142,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f4088,f148]) ).
fof(f4143,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f4088,f148]) ).
fof(f4146,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(c(X0)),X0))) = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(paramodulation,[status(thm)],[f4088,f561]) ).
fof(f4148,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),c(X1))
| ~ leq(addition(zero,X0),c(X1)) ),
inference(paramodulation,[status(thm)],[f4088,f53]) ).
fof(f4149,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f4088,f51]) ).
fof(f4150,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f4088,f41]) ).
fof(f4151,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f4088,f41]) ).
fof(f4152,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f4088,f40]) ).
fof(f4153,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f4088,f40]) ).
fof(f4154,plain,
! [X0,X1] : multiplication(c(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f4088,f37]) ).
fof(f4159,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(c(multiplication(X0,X1)),X0),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f75,f4127]) ).
fof(f4161,plain,
! [X0] : forward_diamond(domain(c(X0)),X0) = domain(zero),
inference(forward_demodulation,[status(thm)],[f317,f4129]) ).
fof(f4162,plain,
! [X0] : forward_diamond(domain(c(X0)),X0) = zero,
inference(forward_demodulation,[status(thm)],[f553,f4161]) ).
fof(f4167,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),X2) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f35,f4134]) ).
fof(f4168,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f42,f4135]) ).
fof(f4169,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f75,f4168]) ).
fof(f4170,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f35,f4136]) ).
fof(f4171,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f4137]) ).
fof(f4172,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)],[f92,f4138]) ).
fof(f4173,plain,
! [X0,X1,X2] : addition(X0,multiplication(c(X1),X2)) = addition(multiplication(c(X1),addition(X2,X1)),X0),
inference(forward_demodulation,[status(thm)],[f75,f4172]) ).
fof(f4174,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),X2) = addition(multiplication(c(X0),addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f4139]) ).
fof(f4175,plain,
! [X0] : multiplication(c(X0),addition(X0,one)) = c(X0),
inference(forward_demodulation,[status(thm)],[f35,f4140]) ).
fof(f4176,plain,
! [X0] : multiplication(c(X0),addition(one,X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f35,f4141]) ).
fof(f4177,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f4142]) ).
fof(f4178,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f4143]) ).
fof(f4181,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(c(X0)),X0))) = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f638,f4146]) ).
fof(f4182,plain,
! [X0] : one = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f1313,f4181]) ).
fof(f4186,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f4148]) ).
fof(f4187,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f4149]) ).
fof(f4188,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f4150]) ).
fof(f4189,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f75,f4151]) ).
fof(f4190,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f4152]) ).
fof(f4191,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f4153]) ).
fof(f4192,plain,
! [X0,X1] : multiplication(c(X0),multiplication(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f4154]) ).
fof(f4194,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(antidomain(coantidomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f219,f3817]) ).
fof(f4196,plain,
! [X0] : leq(coantidomain(X0),domain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f3965,f3817]) ).
fof(f4197,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,coantidomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3817]) ).
fof(f4211,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1439,f202]) ).
fof(f4212,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1432,f202]) ).
fof(f4213,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1427,f202]) ).
fof(f4214,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1420,f202]) ).
fof(f4215,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(divergence(X1),X0)),
inference(paramodulation,[status(thm)],[f1423,f202]) ).
fof(f4216,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1412,f202]) ).
fof(f4217,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(c(X1),X0)),
inference(paramodulation,[status(thm)],[f1406,f202]) ).
fof(f4218,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1315,f202]) ).
fof(f4219,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(coantidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1313,f202]) ).
fof(f4220,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f1311,f202]) ).
fof(f4226,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(X0,addition(one,X0)),X1)),
inference(paramodulation,[status(thm)],[f94,f202]) ).
fof(f4227,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f100,f202]) ).
fof(f4228,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f92,f202]) ).
fof(f4229,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f92,f202]) ).
fof(f4231,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f202]) ).
fof(f4232,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f202]) ).
fof(f4234,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f148,f202]) ).
fof(f4235,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f40,f202]) ).
fof(f4236,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X2,addition(X1,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f98,f202]) ).
fof(f4237,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X1,addition(X2,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f34,f202]) ).
fof(f4244,plain,
! [X0] : multiplication(addition(one,X0),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f187,f202]) ).
fof(f4245,plain,
! [X0] : multiplication(addition(one,X0),X0) = multiplication(X0,addition(one,X0)),
inference(paramodulation,[status(thm)],[f157,f202]) ).
fof(f4247,plain,
! [X0,X1] : multiplication(addition(one,addition(antidomain(X0),X1)),X0) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f219,f202]) ).
fof(f4251,plain,
! [X0,X1] : multiplication(addition(one,domain(X0)),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f202]) ).
fof(f4253,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f37,f202]) ).
fof(f4254,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f202]) ).
fof(f4255,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f172,f202]) ).
fof(f4260,plain,
! [X0] : multiplication(addition(one,X0),codomain(X0)) = addition(codomain(X0),X0),
inference(paramodulation,[status(thm)],[f2178,f202]) ).
fof(f4261,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(addition(one,X1),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f157,f202]) ).
fof(f4262,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(coantidomain(X0),X1)) = addition(addition(coantidomain(X0),X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f176,f202]) ).
fof(f4263,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(addition(X1,one),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f187,f202]) ).
fof(f4264,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,coantidomain(X0))) = addition(addition(X1,coantidomain(X0)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f185,f202]) ).
fof(f4265,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(coantidomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f146,f202]) ).
fof(f4266,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)],[f139,f202]) ).
fof(f4267,plain,
! [X0] : multiplication(addition(one,X0),coantidomain(X0)) = addition(coantidomain(X0),zero),
inference(paramodulation,[status(thm)],[f58,f202]) ).
fof(f4270,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)],[f202,f199]) ).
fof(f4271,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)],[f202,f199]) ).
fof(f4272,plain,
! [X0,X1,X2] : multiplication(addition(addition(one,X0),X1),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f202,f196]) ).
fof(f4273,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(addition(X2,multiplication(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f202,f196]) ).
fof(f4274,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)],[f202,f165]) ).
fof(f4275,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)],[f202,f165]) ).
fof(f4276,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(addition(one,X0),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f202,f187]) ).
fof(f4277,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(addition(one,X0),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f202,f157]) ).
fof(f4278,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)],[f202,f148]) ).
fof(f4279,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)],[f202,f148]) ).
fof(f4280,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(addition(X1,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f202,f139]) ).
fof(f4281,plain,
! [X0,X1] : multiplication(antidomain(addition(one,X0)),addition(X1,multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f202,f131]) ).
fof(f4282,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)],[f202,f561]) ).
fof(f4283,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)],[f202,f404]) ).
fof(f4284,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)],[f202,f53]) ).
fof(f4285,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)],[f202,f51]) ).
fof(f4286,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f202,f41]) ).
fof(f4287,plain,
! [X0,X1,X2] : multiplication(addition(addition(one,X0),X1),X2) = addition(addition(X2,multiplication(X0,X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f202,f41]) ).
fof(f4288,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)],[f202,f40]) ).
fof(f4289,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)],[f202,f40]) ).
fof(f4290,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f202,f37]) ).
fof(f4291,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f202,f176]) ).
fof(f4293,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X0,X1),X1)) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f202,f148]) ).
fof(f4294,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f202,f40]) ).
fof(f4295,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)],[f202,f165]) ).
fof(f4296,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)],[f202,f53]) ).
fof(f4297,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)],[f202,f51]) ).
fof(f4298,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X1,X0)))) = multiplication(addition(one,X2),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f202,f98]) ).
fof(f4299,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X0,X1)))) = multiplication(addition(one,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f202,f34]) ).
fof(f4305,plain,
! [X0] : multiplication(X0,addition(X0,one)) = multiplication(addition(one,X0),X0),
inference(paramodulation,[status(thm)],[f202,f187]) ).
fof(f4306,plain,
! [X0] : multiplication(X0,addition(one,X0)) = multiplication(addition(one,X0),X0),
inference(paramodulation,[status(thm)],[f202,f157]) ).
fof(f4307,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(one,X0),X1)) = multiplication(antidomain(multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f202,f181]) ).
fof(f4308,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f202,f172]) ).
fof(f4309,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(one,X2),X0))),
inference(paramodulation,[status(thm)],[f202,f1357]) ).
fof(f4310,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(one,X0),X1))),
inference(paramodulation,[status(thm)],[f202,f1356]) ).
fof(f4311,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f202,f1359]) ).
fof(f4312,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f202,f1261]) ).
fof(f4313,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f202,f100]) ).
fof(f4314,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(one,X0),X1),X2),
inference(paramodulation,[status(thm)],[f202,f98]) ).
fof(f4315,plain,
! [X0,X1] : addition(X0,addition(multiplication(X1,X0),multiplication(addition(one,X1),X0))) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f202,f94]) ).
fof(f4316,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(X2,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f202,f92]) ).
fof(f4317,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(one,X1),X2)) = addition(multiplication(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f202,f92]) ).
fof(f4318,plain,
! [X0,X1] :
( multiplication(addition(one,X0),X1) != X1
| leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f202,f241]) ).
fof(f4319,plain,
! [X0,X1] :
( multiplication(addition(one,X1),X0) != multiplication(X1,X0)
| leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f202,f47]) ).
fof(f4320,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(one,X1),X0),X2),
inference(paramodulation,[status(thm)],[f202,f34]) ).
fof(f4322,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4211]) ).
fof(f4323,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4212]) ).
fof(f4324,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4213]) ).
fof(f4325,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4214]) ).
fof(f4326,plain,
! [X0,X1] : X0 = addition(X0,multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4215]) ).
fof(f4327,plain,
! [X0,X1] : X0 = addition(X0,multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4216]) ).
fof(f4328,plain,
! [X0,X1] : X0 = addition(X0,multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4217]) ).
fof(f4329,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4218]) ).
fof(f4330,plain,
! [X0,X1] : X0 = addition(X0,multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4219]) ).
fof(f4331,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4220]) ).
fof(f4351,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f4234]) ).
fof(f4365,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1311,f4251]) ).
fof(f4366,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f39,f4365]) ).
fof(f4369,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f1315,f4254]) ).
fof(f4370,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f4369]) ).
fof(f4371,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f98,f4370]) ).
fof(f4372,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1315,f4255]) ).
fof(f4373,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f39,f4372]) ).
fof(f4374,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f4373]) ).
fof(f4383,plain,
! [X0] : multiplication(addition(one,X0),codomain(X0)) = addition(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f4260]) ).
fof(f4384,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(X1,addition(one,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f4261]) ).
fof(f4385,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(coantidomain(X0),X1)) = addition(X1,addition(coantidomain(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f4262]) ).
fof(f4386,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(one,addition(X1,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f4263]) ).
fof(f4387,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,coantidomain(X0))) = addition(coantidomain(X0),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f4264]) ).
fof(f4388,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(coantidomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f4265]) ).
fof(f4389,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f4266]) ).
fof(f4390,plain,
! [X0] : multiplication(addition(one,X0),coantidomain(X0)) = coantidomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f4267]) ).
fof(f4392,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)],[f92,f4270]) ).
fof(f4393,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)],[f92,f4392]) ).
fof(f4394,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)],[f98,f4272]) ).
fof(f4395,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)],[f92,f4394]) ).
fof(f4396,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f4395]) ).
fof(f4397,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)],[f98,f4273]) ).
fof(f4398,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)],[f92,f4397]) ).
fof(f4399,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f4398]) ).
fof(f4400,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)],[f98,f4274]) ).
fof(f4401,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)],[f92,f4400]) ).
fof(f4402,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)],[f98,f4275]) ).
fof(f4403,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)],[f92,f4402]) ).
fof(f4404,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)],[f98,f4403]) ).
fof(f4405,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(X0,addition(one,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f4276]) ).
fof(f4406,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(X0,addition(one,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f4277]) ).
fof(f4407,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)],[f98,f4279]) ).
fof(f4408,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)],[f92,f4407]) ).
fof(f4409,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)],[f98,f4284]) ).
fof(f4410,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)],[f92,f4409]) ).
fof(f4411,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)],[f98,f4285]) ).
fof(f4412,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)],[f92,f4411]) ).
fof(f4413,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)],[f92,f4286]) ).
fof(f4414,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f196,f4413]) ).
fof(f4415,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)],[f98,f4287]) ).
fof(f4416,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)],[f98,f4415]) ).
fof(f4417,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)],[f92,f4416]) ).
fof(f4418,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f196,f4417]) ).
fof(f4419,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)],[f98,f4289]) ).
fof(f4420,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)],[f92,f4419]) ).
fof(f4428,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f4293]) ).
fof(f4429,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)],[f37,f4296]) ).
fof(f4430,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)],[f37,f4429]) ).
fof(f4436,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(one,X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f92,f4314]) ).
fof(f4437,plain,
! [X0,X1] : addition(X0,multiplication(addition(addition(one,X1),X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f196,f4315]) ).
fof(f4438,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,addition(one,X1)),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f4437]) ).
fof(f4439,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(one,X1),X2)) = addition(X2,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f92,f4317]) ).
fof(f4443,plain,
! [X0] : antidomain(domain(X0)) = domain_difference(c(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f62,f4017]) ).
fof(f4444,plain,
! [X0] : antidomain(antidomain(X0)) = domain_difference(domain(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f57,f4017]) ).
fof(f4453,plain,
! [X0] : c(X0) = domain_difference(c(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f4443]) ).
fof(f4454,plain,
! [X0] : domain(X0) = domain_difference(domain(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f57,f4444]) ).
fof(f4469,plain,
! [X0] : multiplication(one,coantidomain(domain(X0))) = multiplication(c(X0),coantidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f515,f221]) ).
fof(f4471,plain,
! [X0] : multiplication(one,coantidomain(coantidomain(X0))) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f625,f221]) ).
fof(f4473,plain,
! [X0] : multiplication(one,coantidomain(antidomain(X0))) = multiplication(domain(X0),coantidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f504,f221]) ).
fof(f4474,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)],[f199,f221]) ).
fof(f4475,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)],[f165,f221]) ).
fof(f4476,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)],[f196,f221]) ).
fof(f4477,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)],[f148,f221]) ).
fof(f4478,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)],[f41,f221]) ).
fof(f4479,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)],[f40,f221]) ).
fof(f4480,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X1,X0))) = multiplication(X2,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f98,f221]) ).
fof(f4481,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X0,X1))) = multiplication(X2,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f34,f221]) ).
fof(f4483,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,coantidomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2351,f221]) ).
fof(f4484,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,antidomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2350,f221]) ).
fof(f4485,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,c(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2349,f221]) ).
fof(f4486,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,codomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2348,f221]) ).
fof(f4487,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,divergence(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2347,f221]) ).
fof(f4489,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(X1,one)),coantidomain(X0)) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f187,f221]) ).
fof(f4490,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(one,X1)),coantidomain(X0)) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f157,f221]) ).
fof(f4491,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(addition(X1,addition(X0,X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f94,f221]) ).
fof(f4493,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f92,f221]) ).
fof(f4494,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(paramodulation,[status(thm)],[f92,f221]) ).
fof(f4496,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(paramodulation,[status(thm)],[f33,f221]) ).
fof(f4497,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(paramodulation,[status(thm)],[f33,f221]) ).
fof(f4500,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,coantidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f61,f221]) ).
fof(f4502,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f221,f3817]) ).
fof(f4503,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f221,f2351]) ).
fof(f4504,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X0)) = addition(coantidomain(X0),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f221,f202]) ).
fof(f4505,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)],[f221,f199]) ).
fof(f4506,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)],[f221,f199]) ).
fof(f4507,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)],[f221,f196]) ).
fof(f4508,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)],[f221,f196]) ).
fof(f4509,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)],[f221,f165]) ).
fof(f4510,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)],[f221,f165]) ).
fof(f4511,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(coantidomain(X0),one)) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f221,f187]) ).
fof(f4512,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,coantidomain(X0))) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f221,f157]) ).
fof(f4513,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)],[f221,f148]) ).
fof(f4514,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)],[f221,f148]) ).
fof(f4515,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),coantidomain(multiplication(X1,coantidomain(X0))))) = zero,
inference(paramodulation,[status(thm)],[f221,f139]) ).
fof(f4516,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),multiplication(X1,coantidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f221,f131]) ).
fof(f4517,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)],[f221,f561]) ).
fof(f4518,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)],[f221,f404]) ).
fof(f4519,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)],[f221,f53]) ).
fof(f4520,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)],[f221,f51]) ).
fof(f4521,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)],[f221,f41]) ).
fof(f4522,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)],[f221,f41]) ).
fof(f4523,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)],[f221,f40]) ).
fof(f4524,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)],[f221,f40]) ).
fof(f4525,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(multiplication(X1,coantidomain(X0)),X2),
inference(paramodulation,[status(thm)],[f221,f37]) ).
fof(f4556,plain,
! [X0] : coantidomain(domain(X0)) = multiplication(c(X0),coantidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4469]) ).
fof(f4557,plain,
! [X0] : coantidomain(coantidomain(X0)) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4471]) ).
fof(f4558,plain,
! [X0] : codomain(X0) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f61,f4557]) ).
fof(f4559,plain,
! [X0] : codomain(X0) = multiplication(codomain(X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f61,f4558]) ).
fof(f4560,plain,
! [X0] : coantidomain(antidomain(X0)) = multiplication(domain(X0),coantidomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f4473]) ).
fof(f4561,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)],[f37,f4474]) ).
fof(f4562,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)],[f37,f4561]) ).
fof(f4563,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)],[f37,f4476]) ).
fof(f4564,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,f4563]) ).
fof(f4565,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)],[f37,f4477]) ).
fof(f4566,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)],[f37,f4565]) ).
fof(f4567,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)],[f37,f4478]) ).
fof(f4568,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,f4567]) ).
fof(f4569,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)],[f37,f4479]) ).
fof(f4570,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)],[f37,f4569]) ).
fof(f4571,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,coantidomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f4483]) ).
fof(f4572,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f4571]) ).
fof(f4573,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,antidomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f4484]) ).
fof(f4574,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f4573]) ).
fof(f4575,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,c(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f4485]) ).
fof(f4576,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f4575]) ).
fof(f4577,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,codomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f4486]) ).
fof(f4578,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f4577]) ).
fof(f4579,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,divergence(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f4487]) ).
fof(f4580,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f4579]) ).
fof(f4588,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f4489]) ).
fof(f4589,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f4588]) ).
fof(f4590,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f4490]) ).
fof(f4591,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f4590]) ).
fof(f4592,plain,
! [X0,X1] : multiplication(X0,coantidomain(X1)) = multiplication(addition(X0,addition(X1,X0)),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f221,f4491]) ).
fof(f4597,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f61,f4500]) ).
fof(f4602,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f4503]) ).
fof(f4603,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X0)) = multiplication(addition(one,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f202,f4504]) ).
fof(f4604,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)],[f199,f4505]) ).
fof(f4605,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)],[f199,f4506]) ).
fof(f4606,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)],[f98,f4507]) ).
fof(f4607,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X0,X2),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f196,f4606]) ).
fof(f4608,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X0,X2),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f196,f4508]) ).
fof(f4609,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)],[f92,f4509]) ).
fof(f4610,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,coantidomain(X0))) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4511]) ).
fof(f4611,plain,
! [X0,X1] : multiplication(addition(X0,X1),one) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f1313,f4610]) ).
fof(f4612,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f38,f4611]) ).
fof(f4613,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f4612]) ).
fof(f4614,plain,
! [X0,X1] : multiplication(addition(X0,X1),one) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f1313,f4512]) ).
fof(f4615,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f38,f4614]) ).
fof(f4616,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f4615]) ).
fof(f4617,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)],[f33,f4513]) ).
fof(f4618,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f196,f4521]) ).
fof(f4619,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)],[f98,f4522]) ).
fof(f4620,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f196,f4619]) ).
fof(f4621,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)],[f33,f4523]) ).
fof(f4622,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f37,f4525]) ).
fof(f4628,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f98,f2352]) ).
fof(f4629,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f34,f2352]) ).
fof(f4634,plain,
! [X0,X1] : addition(antidomain(domain(X0)),X1) = addition(addition(antidomain(domain(X0)),X1),multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f219,f2352]) ).
fof(f4637,plain,
! [X0] : domain(domain(X0)) = addition(domain(domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f3965,f2352]) ).
fof(f4642,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f64,f2352]) ).
fof(f4648,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),domain(X1)),X0),
inference(paramodulation,[status(thm)],[f2352,f219]) ).
fof(f4660,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)],[f2352,f165]) ).
fof(f4661,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),domain(X2)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2352,f53]) ).
fof(f4662,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),domain(X2))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2352,f51]) ).
fof(f4663,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),domain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2352,f98]) ).
fof(f4664,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),domain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2352,f34]) ).
fof(f4669,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,domain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2352,f221]) ).
fof(f4673,plain,
! [X0,X1,X2] : leq(multiplication(X0,domain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2352,f1356]) ).
fof(f4677,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2352,f98]) ).
fof(f4679,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,domain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2352,f92]) ).
fof(f4680,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,domain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2352,f92]) ).
fof(f4682,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f2352,f47]) ).
fof(f4683,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,domain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2352,f34]) ).
fof(f4694,plain,
! [X0,X1] : addition(c(X0),X1) = addition(addition(antidomain(domain(X0)),X1),multiplication(X1,domain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f4634]) ).
fof(f4695,plain,
! [X0,X1] : addition(c(X0),X1) = addition(X1,addition(antidomain(domain(X0)),multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f98,f4694]) ).
fof(f4696,plain,
! [X0,X1] : addition(c(X0),X1) = addition(X1,addition(c(X0),multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f4695]) ).
fof(f4699,plain,
! [X0] : antidomain(c(X0)) = addition(domain(domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f191,f4637]) ).
fof(f4700,plain,
! [X0] : antidomain(c(X0)) = addition(domain(X0),domain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4699]) ).
fof(f4701,plain,
! [X0] : antidomain(c(X0)) = addition(domain(X0),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f191,f4700]) ).
fof(f4709,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),domain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f54,f4648]) ).
fof(f4710,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f37,f4709]) ).
fof(f4720,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)],[f148,f4660]) ).
fof(f4721,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)],[f37,f4720]) ).
fof(f4722,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)],[f148,f4721]) ).
fof(f4723,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)],[f92,f4722]) ).
fof(f4724,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)],[f37,f4661]) ).
fof(f4725,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)],[f37,f4724]) ).
fof(f4726,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)],[f37,f4662]) ).
fof(f4731,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,domain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f4669]) ).
fof(f4732,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f4731]) ).
fof(f4735,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,domain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f4677]) ).
fof(f4737,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,domain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f4680]) ).
fof(f4739,plain,
! [X0,X1,X2] : addition(multiplication(X0,backward_diamond(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3259,f46]) ).
fof(f4740,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(antidomain(backward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f219,f3259]) ).
fof(f4742,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f3965,f3259]) ).
fof(f4743,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,backward_diamond(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3259]) ).
fof(f4752,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,backward_diamond(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f33,f4739]) ).
fof(f4756,plain,
! [X0,X1,X2] : addition(multiplication(X0,backward_box(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3488,f46]) ).
fof(f4757,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),addition(antidomain(backward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f219,f3488]) ).
fof(f4759,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f3965,f3488]) ).
fof(f4760,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,backward_box(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3488]) ).
fof(f4766,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,backward_box(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f33,f4756]) ).
fof(f4769,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f148,f206]) ).
fof(f4770,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f40,f206]) ).
fof(f4771,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(addition(one,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f202,f206]) ).
fof(f4772,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)],[f187,f206]) ).
fof(f4773,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)],[f157,f206]) ).
fof(f4774,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)],[f33,f206]) ).
fof(f4775,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)],[f33,f206]) ).
fof(f4776,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)],[f202,f206]) ).
fof(f4777,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)],[f219,f206]) ).
fof(f4778,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)],[f221,f206]) ).
fof(f4779,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)],[f192,f206]) ).
fof(f4780,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),X0) = addition(zero,multiplication(X1,multiplication(X2,X0))),
inference(paramodulation,[status(thm)],[f4088,f206]) ).
fof(f4781,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)],[f190,f206]) ).
fof(f4782,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)],[f63,f206]) ).
fof(f4783,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),multiplication(X1,X2)),X0) = addition(X0,multiplication(X1,multiplication(X2,X0))),
inference(paramodulation,[status(thm)],[f3965,f206]) ).
fof(f4784,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)],[f37,f206]) ).
fof(f4785,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)],[f181,f206]) ).
fof(f4786,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)],[f172,f206]) ).
fof(f4787,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)],[f131,f206]) ).
fof(f4790,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f39,f206]) ).
fof(f4791,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),codomain(X0)) = addition(X0,multiplication(X1,multiplication(X2,codomain(X0)))),
inference(paramodulation,[status(thm)],[f2178,f206]) ).
fof(f4792,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)],[f157,f206]) ).
fof(f4793,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)],[f176,f206]) ).
fof(f4794,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)],[f187,f206]) ).
fof(f4795,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)],[f185,f206]) ).
fof(f4796,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)],[f146,f206]) ).
fof(f4797,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)],[f139,f206]) ).
fof(f4801,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)],[f219,f206]) ).
fof(f4802,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(c(multiplication(X1,X2)),X1)),X2) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f4088,f206]) ).
fof(f4803,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)],[f3965,f206]) ).
fof(f4804,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)],[f37,f206]) ).
fof(f4806,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(antidomain(multiplication(X1,X2)),X1)),X2) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f54,f206]) ).
fof(f4810,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)],[f139,f206]) ).
fof(f4811,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)],[f202,f206]) ).
fof(f4812,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)],[f219,f206]) ).
fof(f4813,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)],[f221,f206]) ).
fof(f4814,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)],[f192,f206]) ).
fof(f4815,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f4088,f206]) ).
fof(f4816,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)],[f190,f206]) ).
fof(f4817,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)],[f63,f206]) ).
fof(f4818,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f3965,f206]) ).
fof(f4819,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)],[f37,f206]) ).
fof(f4820,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)],[f181,f206]) ).
fof(f4821,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)],[f172,f206]) ).
fof(f4822,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)],[f131,f206]) ).
fof(f4823,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f54,f206]) ).
fof(f4826,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),codomain(X2)) = addition(multiplication(X0,codomain(X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f2178,f206]) ).
fof(f4827,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)],[f157,f206]) ).
fof(f4828,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)],[f176,f206]) ).
fof(f4829,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)],[f187,f206]) ).
fof(f4830,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)],[f185,f206]) ).
fof(f4831,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)],[f146,f206]) ).
fof(f4832,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)],[f139,f206]) ).
fof(f4833,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f58,f206]) ).
fof(f4836,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,X2),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f206,f148]) ).
fof(f4837,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(paramodulation,[status(thm)],[f206,f40]) ).
fof(f4838,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)],[f206,f165]) ).
fof(f4839,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)],[f206,f53]) ).
fof(f4840,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)],[f206,f51]) ).
fof(f4841,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f206,f202]) ).
fof(f4842,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)],[f206,f187]) ).
fof(f4843,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)],[f206,f157]) ).
fof(f4844,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)],[f206,f221]) ).
fof(f4845,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)],[f206,f181]) ).
fof(f4846,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)],[f206,f172]) ).
fof(f4847,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,multiplication(X3,X4)),X1))),
inference(paramodulation,[status(thm)],[f206,f1357]) ).
fof(f4848,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)],[f206,f1356]) ).
fof(f4849,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f206,f1359]) ).
fof(f4850,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(X0,multiplication(X2,X3)),X1)),
inference(paramodulation,[status(thm)],[f206,f1261]) ).
fof(f4851,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)],[f206,f100]) ).
fof(f4852,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)],[f206,f98]) ).
fof(f4853,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)],[f206,f94]) ).
fof(f4854,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)],[f206,f92]) ).
fof(f4855,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)],[f206,f92]) ).
fof(f4856,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)],[f206,f241]) ).
fof(f4857,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)],[f206,f47]) ).
fof(f4858,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)],[f206,f34]) ).
fof(f4859,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)],[f206,f33]) ).
fof(f4860,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)],[f206,f33]) ).
fof(f4861,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f33,f4769]) ).
fof(f4862,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)],[f37,f4772]) ).
fof(f4863,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)],[f37,f4862]) ).
fof(f4864,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)],[f33,f4863]) ).
fof(f4865,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)],[f37,f4773]) ).
fof(f4866,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)],[f37,f4865]) ).
fof(f4867,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)],[f98,f4776]) ).
fof(f4868,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)],[f98,f4867]) ).
fof(f4869,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)],[f92,f4868]) ).
fof(f4870,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)],[f199,f4869]) ).
fof(f4871,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)],[f98,f4777]) ).
fof(f4872,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)],[f206,f4871]) ).
fof(f4873,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)],[f98,f4778]) ).
fof(f4874,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)],[f206,f4873]) ).
fof(f4875,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),domain(X0)) = multiplication(X1,multiplication(X2,domain(X0))),
inference(forward_demodulation,[status(thm)],[f75,f4779]) ).
fof(f4876,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),X0) = multiplication(X1,multiplication(X2,X0)),
inference(forward_demodulation,[status(thm)],[f75,f4780]) ).
fof(f4877,plain,
! [X0,X1,X2] : multiplication(addition(coantidomain(X0),multiplication(X1,X2)),codomain(X0)) = multiplication(X1,multiplication(X2,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f75,f4781]) ).
fof(f4878,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)],[f75,f4787]) ).
fof(f4883,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)],[f98,f4792]) ).
fof(f4884,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)],[f92,f4883]) ).
fof(f4885,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)],[f98,f4794]) ).
fof(f4886,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)],[f92,f4885]) ).
fof(f4887,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)],[f75,f4796]) ).
fof(f4888,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)],[f75,f4797]) ).
fof(f4895,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)],[f206,f4801]) ).
fof(f4896,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(c(multiplication(X1,X2)),X1)),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f35,f4802]) ).
fof(f4897,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(domain(multiplication(X1,X2)),X1)),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f196,f4803]) ).
fof(f4898,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)],[f37,f4804]) ).
fof(f4901,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(antidomain(multiplication(X1,X2)),X1)),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f35,f4806]) ).
fof(f4907,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)],[f35,f4810]) ).
fof(f4908,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)],[f206,f4812]) ).
fof(f4909,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)],[f206,f4813]) ).
fof(f4910,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f42,f4814]) ).
fof(f4911,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),domain(X2)) = multiplication(X0,domain(X2)),
inference(forward_demodulation,[status(thm)],[f35,f4910]) ).
fof(f4912,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = addition(multiplication(X0,X2),zero),
inference(forward_demodulation,[status(thm)],[f42,f4815]) ).
fof(f4913,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f35,f4912]) ).
fof(f4914,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,coantidomain(X2))),codomain(X2)) = addition(multiplication(X0,codomain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f42,f4816]) ).
fof(f4915,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,coantidomain(X2))),codomain(X2)) = multiplication(X0,codomain(X2)),
inference(forward_demodulation,[status(thm)],[f35,f4914]) ).
fof(f4916,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f196,f4818]) ).
fof(f4917,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)],[f42,f4822]) ).
fof(f4918,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)],[f35,f4917]) ).
fof(f4919,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),zero),
inference(forward_demodulation,[status(thm)],[f42,f4823]) ).
fof(f4920,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f35,f4919]) ).
fof(f4925,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)],[f42,f4831]) ).
fof(f4926,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)],[f35,f4925]) ).
fof(f4927,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)],[f42,f4832]) ).
fof(f4928,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)],[f35,f4927]) ).
fof(f4929,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f42,f4833]) ).
fof(f4930,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = multiplication(X0,coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f35,f4929]) ).
fof(f4934,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f33,f4836]) ).
fof(f4935,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)],[f37,f4839]) ).
fof(f4936,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)],[f37,f4935]) ).
fof(f4937,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)],[f37,f4842]) ).
fof(f4938,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)],[f33,f4937]) ).
fof(f4939,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)],[f37,f4938]) ).
fof(f4940,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)],[f37,f4843]) ).
fof(f4941,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)],[f37,f4940]) ).
fof(f4942,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)],[f37,f4844]) ).
fof(f4943,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)],[f37,f4942]) ).
fof(f4944,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)],[f37,f4943]) ).
fof(f4945,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)],[f196,f4851]) ).
fof(f4946,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)],[f98,f4945]) ).
fof(f4947,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)],[f36,f4946]) ).
fof(f4948,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)],[f199,f4853]) ).
fof(f4949,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)],[f196,f4948]) ).
fof(f4950,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)],[f98,f4949]) ).
fof(f4951,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)],[f98,f4950]) ).
fof(f4952,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)],[f94,f4951]) ).
fof(f4953,plain,
! [X0,X1,X2] : addition(multiplication(X0,forward_box(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3489,f46]) ).
fof(f4954,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),addition(antidomain(forward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f219,f3489]) ).
fof(f4956,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f3965,f3489]) ).
fof(f4957,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,forward_box(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3489]) ).
fof(f4964,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,forward_box(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f33,f4953]) ).
fof(f4968,plain,
! [X0,X1,X2] : addition(multiplication(X0,forward_diamond(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3808,f46]) ).
fof(f4969,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(antidomain(forward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f219,f3808]) ).
fof(f4971,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),domain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f3965,f3808]) ).
fof(f4972,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,forward_diamond(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f3808]) ).
fof(f4982,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,forward_diamond(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f33,f4968]) ).
fof(f4992,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)],[f404,f225]) ).
fof(f4993,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f98,f225]) ).
fof(f4994,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f34,f225]) ).
fof(f5000,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f62,f225]) ).
fof(f5001,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = multiplication(X0,antidomain(X1)),
inference(paramodulation,[status(thm)],[f57,f225]) ).
fof(f5006,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(X0,antidomain(forward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f225,f3808]) ).
fof(f5007,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),addition(X0,antidomain(forward_box(X1,X2)))),
inference(paramodulation,[status(thm)],[f225,f3489]) ).
fof(f5008,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),addition(X0,antidomain(backward_box(X1,X2)))),
inference(paramodulation,[status(thm)],[f225,f3488]) ).
fof(f5009,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(X0,antidomain(backward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f225,f3259]) ).
fof(f5010,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(X0,antidomain(antidomain(X1)))),
inference(paramodulation,[status(thm)],[f225,f3497]) ).
fof(f5012,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),addition(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f225,f3402]) ).
fof(f5014,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),addition(X0,antidomain(divergence(X1)))),
inference(paramodulation,[status(thm)],[f225,f3096]) ).
fof(f5016,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),addition(X0,antidomain(codomain(X1)))),
inference(paramodulation,[status(thm)],[f225,f3175]) ).
fof(f5018,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)],[f225,f206]) ).
fof(f5019,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)],[f225,f199]) ).
fof(f5021,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(X0,antidomain(domain(X1)))),
inference(paramodulation,[status(thm)],[f225,f3587]) ).
fof(f5022,plain,
! [X0,X1] : forward_diamond(addition(X0,antidomain(domain(X1))),X1) = domain(multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f225,f64]) ).
fof(f5023,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)],[f225,f404]) ).
fof(f5024,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X0,antidomain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f225,f3817]) ).
fof(f5028,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)],[f225,f206]) ).
fof(f5030,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,antidomain(X1))),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f225,f202]) ).
fof(f5031,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)],[f225,f199]) ).
fof(f5032,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)],[f225,f199]) ).
fof(f5034,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f225,f196]) ).
fof(f5035,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)],[f225,f165]) ).
fof(f5036,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)],[f225,f165]) ).
fof(f5037,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(X1,one)) = addition(addition(X0,antidomain(X1)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f225,f187]) ).
fof(f5038,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(one,X1)) = addition(addition(X0,antidomain(X1)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f225,f157]) ).
fof(f5039,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)],[f225,f148]) ).
fof(f5040,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)],[f225,f148]) ).
fof(f5041,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f225,f139]) ).
fof(f5042,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,antidomain(X1))),multiplication(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f225,f131]) ).
fof(f5043,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)],[f225,f561]) ).
fof(f5044,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)],[f225,f404]) ).
fof(f5045,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)],[f225,f53]) ).
fof(f5046,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,antidomain(X1))),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f225,f51]) ).
fof(f5047,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f225,f41]) ).
fof(f5049,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)],[f225,f40]) ).
fof(f5050,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)],[f225,f40]) ).
fof(f5051,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f225,f37]) ).
fof(f5057,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f54,f4992]) ).
fof(f5065,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f57,f5010]) ).
fof(f5076,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)],[f206,f5018]) ).
fof(f5077,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)],[f199,f5019]) ).
fof(f5082,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f62,f5021]) ).
fof(f5083,plain,
! [X0,X1] : forward_diamond(addition(X0,c(X1)),X1) = domain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f62,f5022]) ).
fof(f5084,plain,
! [X0,X1] : forward_diamond(addition(X0,c(X1)),X1) = forward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f64,f5083]) ).
fof(f5085,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)],[f33,f5023]) ).
fof(f5086,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)],[f62,f5085]) ).
fof(f5087,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)],[f225,f5086]) ).
fof(f5092,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)],[f206,f5028]) ).
fof(f5095,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)],[f199,f5031]) ).
fof(f5096,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)],[f199,f5032]) ).
fof(f5099,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f196,f5034]) ).
fof(f5100,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)],[f92,f5035]) ).
fof(f5101,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(X1,one)) = addition(antidomain(X1),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f5037]) ).
fof(f5102,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(one,X1)) = addition(antidomain(X1),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f5038]) ).
fof(f5103,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)],[f33,f5039]) ).
fof(f5104,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f196,f5047]) ).
fof(f5107,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)],[f33,f5049]) ).
fof(f5108,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f37,f5051]) ).
fof(f5109,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(resolution,[status(thm)],[f4028,f46]) ).
fof(f5110,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(c(backward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f67,f4028]) ).
fof(f5111,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(c(forward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f66,f4028]) ).
fof(f5114,plain,
! [X0] : leq(domain(c(X0)),domain(c(domain(X0)))),
inference(paramodulation,[status(thm)],[f317,f4028]) ).
fof(f5116,plain,
! [X0,X1] : leq(c(backward_diamond(X0,c(X1))),domain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f67,f4028]) ).
fof(f5117,plain,
! [X0,X1] : leq(c(forward_diamond(X0,c(X1))),domain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f66,f4028]) ).
fof(f5120,plain,
! [X0] : leq(c(domain(X0)),domain(domain(c(X0)))),
inference(paramodulation,[status(thm)],[f317,f4028]) ).
fof(f5122,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f67,f5110]) ).
fof(f5123,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f66,f5111]) ).
fof(f5128,plain,
! [X0] : leq(domain(c(X0)),domain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f317,f5114]) ).
fof(f5129,plain,
! [X0] : leq(domain(c(X0)),antidomain(c(c(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f5128]) ).
fof(f5132,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f67,f5116]) ).
fof(f5133,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f66,f5117]) ).
fof(f5138,plain,
! [X0] : leq(domain(c(X0)),domain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f317,f5120]) ).
fof(f5139,plain,
! [X0] : leq(domain(c(X0)),antidomain(c(c(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f5138]) ).
fof(f5142,plain,
! [X0] : addition(divergence(X0),domain(divergence(X0))) = domain(divergence(X0)),
inference(resolution,[status(thm)],[f4030,f46]) ).
fof(f5149,plain,
! [X0] : addition(codomain(X0),domain(codomain(X0))) = domain(codomain(X0)),
inference(resolution,[status(thm)],[f4032,f46]) ).
fof(f5150,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(codomain(multiplication(codomain(X1),X0)))),
inference(paramodulation,[status(thm)],[f65,f4032]) ).
fof(f5152,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(codomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f188,f4032]) ).
fof(f5154,plain,
! [X0,X1] : leq(codomain(multiplication(codomain(X0),X1)),domain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f65,f4032]) ).
fof(f5156,plain,
! [X0] : leq(codomain(coantidomain(X0)),domain(coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f188,f4032]) ).
fof(f5158,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f65,f5150]) ).
fof(f5161,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f188,f5152]) ).
fof(f5164,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f65,f5154]) ).
fof(f5167,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f188,f5156]) ).
fof(f5170,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(resolution,[status(thm)],[f4071,f46]) ).
fof(f5171,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),antidomain(c(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f64,f4071]) ).
fof(f5176,plain,
! [X0,X1] : leq(domain(backward_diamond(X0,c(X1))),antidomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f67,f4071]) ).
fof(f5177,plain,
! [X0,X1] : leq(domain(forward_diamond(X0,c(X1))),antidomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f66,f4071]) ).
fof(f5203,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f98,f227]) ).
fof(f5204,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f34,f227]) ).
fof(f5209,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f206,f227]) ).
fof(f5210,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f148,f227]) ).
fof(f5211,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f40,f227]) ).
fof(f5212,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X2,addition(X1,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f98,f227]) ).
fof(f5213,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X1,addition(X2,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f34,f227]) ).
fof(f5221,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = multiplication(addition(one,X0),X1),
inference(paramodulation,[status(thm)],[f202,f227]) ).
fof(f5222,plain,
! [X0] : multiplication(addition(X0,one),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f187,f227]) ).
fof(f5223,plain,
! [X0] : multiplication(addition(X0,one),X0) = multiplication(X0,addition(one,X0)),
inference(paramodulation,[status(thm)],[f157,f227]) ).
fof(f5226,plain,
! [X0,X1] : multiplication(addition(addition(X0,one),one),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f227,f227]) ).
fof(f5228,plain,
! [X0,X1] : multiplication(addition(addition(X0,X1),one),coantidomain(X0)) = addition(coantidomain(X0),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f221,f227]) ).
fof(f5232,plain,
! [X0,X1] : multiplication(addition(domain(X0),one),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f227]) ).
fof(f5234,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f37,f227]) ).
fof(f5235,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),one),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f181,f227]) ).
fof(f5236,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),one),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f172,f227]) ).
fof(f5241,plain,
! [X0] : multiplication(addition(X0,one),codomain(X0)) = addition(codomain(X0),X0),
inference(paramodulation,[status(thm)],[f2178,f227]) ).
fof(f5242,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(addition(one,X1),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f157,f227]) ).
fof(f5243,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(coantidomain(X0),X1)) = addition(addition(coantidomain(X0),X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f176,f227]) ).
fof(f5244,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(addition(X1,one),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f187,f227]) ).
fof(f5245,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,coantidomain(X0))) = addition(addition(X1,coantidomain(X0)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f185,f227]) ).
fof(f5246,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(coantidomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f146,f227]) ).
fof(f5247,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)],[f139,f227]) ).
fof(f5253,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)],[f227,f206]) ).
fof(f5254,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)],[f227,f206]) ).
fof(f5255,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f227,f202]) ).
fof(f5256,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)],[f227,f199]) ).
fof(f5257,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)],[f227,f199]) ).
fof(f5258,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f227,f196]) ).
fof(f5259,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(addition(X2,multiplication(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f227,f196]) ).
fof(f5260,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)],[f227,f165]) ).
fof(f5261,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)],[f227,f165]) ).
fof(f5262,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(addition(X0,one),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f227,f187]) ).
fof(f5263,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(addition(X0,one),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f227,f157]) ).
fof(f5264,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)],[f227,f148]) ).
fof(f5265,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)],[f227,f148]) ).
fof(f5266,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(addition(X1,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f227,f139]) ).
fof(f5267,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,one)),addition(X1,multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f227,f131]) ).
fof(f5268,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)],[f227,f561]) ).
fof(f5269,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)],[f227,f404]) ).
fof(f5270,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)],[f227,f53]) ).
fof(f5271,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)],[f227,f51]) ).
fof(f5272,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f227,f41]) ).
fof(f5274,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)],[f227,f40]) ).
fof(f5275,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)],[f227,f40]) ).
fof(f5276,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f227,f37]) ).
fof(f5277,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f227,f176]) ).
fof(f5279,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(addition(X1,one),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f227,f206]) ).
fof(f5280,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X0,X1),X1)) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f227,f148]) ).
fof(f5281,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f227,f40]) ).
fof(f5282,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)],[f227,f165]) ).
fof(f5283,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)],[f227,f53]) ).
fof(f5284,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)],[f227,f51]) ).
fof(f5285,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X1,X0)))) = multiplication(addition(X2,one),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f227,f98]) ).
fof(f5286,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X0,X1)))) = multiplication(addition(X2,one),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f227,f34]) ).
fof(f5293,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = multiplication(addition(X0,one),X1),
inference(paramodulation,[status(thm)],[f227,f202]) ).
fof(f5294,plain,
! [X0] : multiplication(X0,addition(X0,one)) = multiplication(addition(X0,one),X0),
inference(paramodulation,[status(thm)],[f227,f187]) ).
fof(f5295,plain,
! [X0] : multiplication(X0,addition(one,X0)) = multiplication(addition(X0,one),X0),
inference(paramodulation,[status(thm)],[f227,f157]) ).
fof(f5297,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(X0,one),X1)) = multiplication(antidomain(multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f227,f181]) ).
fof(f5298,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f227,f172]) ).
fof(f5299,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(X2,one),X0))),
inference(paramodulation,[status(thm)],[f227,f1357]) ).
fof(f5300,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,one),X1))),
inference(paramodulation,[status(thm)],[f227,f1356]) ).
fof(f5301,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f227,f1359]) ).
fof(f5302,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f227,f1261]) ).
fof(f5303,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f227,f100]) ).
fof(f5304,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),X2),
inference(paramodulation,[status(thm)],[f227,f98]) ).
fof(f5305,plain,
! [X0,X1] : addition(X0,addition(multiplication(X1,X0),multiplication(addition(X1,one),X0))) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f227,f94]) ).
fof(f5306,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(X2,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f227,f92]) ).
fof(f5307,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X1,one),X2)) = addition(multiplication(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f227,f92]) ).
fof(f5308,plain,
! [X0,X1] :
( multiplication(addition(X0,one),X1) != X1
| leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f227,f241]) ).
fof(f5309,plain,
! [X0,X1] :
( multiplication(addition(X1,one),X0) != multiplication(X1,X0)
| leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f227,f47]) ).
fof(f5310,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(X1,one),X0),X2),
inference(paramodulation,[status(thm)],[f227,f34]) ).
fof(f5319,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f5210]) ).
fof(f5338,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f5226]) ).
fof(f5339,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f100,f5338]) ).
fof(f5342,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),coantidomain(X1)) = addition(coantidomain(X1),multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f98,f5228]) ).
fof(f5343,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),coantidomain(X1)) = multiplication(addition(X0,one),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f227,f5342]) ).
fof(f5353,plain,
! [X0,X1] : multiplication(addition(one,domain(X0)),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f5232]) ).
fof(f5354,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1311,f5353]) ).
fof(f5355,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f39,f5354]) ).
fof(f5359,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f33,f5234]) ).
fof(f5360,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f5235]) ).
fof(f5361,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f1315,f5360]) ).
fof(f5362,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f39,f5361]) ).
fof(f5363,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f98,f5362]) ).
fof(f5364,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f5236]) ).
fof(f5365,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1315,f5364]) ).
fof(f5366,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f39,f5365]) ).
fof(f5367,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f5366]) ).
fof(f5377,plain,
! [X0] : multiplication(addition(X0,one),codomain(X0)) = addition(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f5241]) ).
fof(f5378,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(X1,addition(one,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f5242]) ).
fof(f5379,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(coantidomain(X0),X1)) = addition(X1,addition(coantidomain(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f5243]) ).
fof(f5380,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(one,addition(X1,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f5244]) ).
fof(f5381,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,coantidomain(X0))) = addition(coantidomain(X0),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f5245]) ).
fof(f5382,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(coantidomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f5246]) ).
fof(f5383,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f35,f5247]) ).
fof(f5390,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)],[f98,f5254]) ).
fof(f5391,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)],[f98,f5390]) ).
fof(f5392,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)],[f92,f5391]) ).
fof(f5393,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)],[f199,f5392]) ).
fof(f5394,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f100,f5255]) ).
fof(f5395,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)],[f92,f5256]) ).
fof(f5396,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)],[f92,f5395]) ).
fof(f5397,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)],[f206,f5396]) ).
fof(f5398,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)],[f98,f5258]) ).
fof(f5399,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)],[f92,f5398]) ).
fof(f5400,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f5399]) ).
fof(f5401,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)],[f98,f5259]) ).
fof(f5402,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)],[f92,f5401]) ).
fof(f5403,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f5402]) ).
fof(f5404,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)],[f98,f5260]) ).
fof(f5405,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)],[f92,f5404]) ).
fof(f5406,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)],[f98,f5261]) ).
fof(f5407,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)],[f92,f5406]) ).
fof(f5408,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)],[f98,f5407]) ).
fof(f5409,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(one,addition(X0,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f5262]) ).
fof(f5410,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(one,addition(X0,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f5263]) ).
fof(f5411,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)],[f98,f5265]) ).
fof(f5412,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)],[f92,f5411]) ).
fof(f5413,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)],[f98,f5270]) ).
fof(f5414,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)],[f92,f5413]) ).
fof(f5415,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)],[f98,f5271]) ).
fof(f5416,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)],[f92,f5415]) ).
fof(f5417,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)],[f92,f5272]) ).
fof(f5418,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f196,f5417]) ).
fof(f5423,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)],[f98,f5275]) ).
fof(f5424,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)],[f92,f5423]) ).
fof(f5432,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f5280]) ).
fof(f5433,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)],[f37,f5283]) ).
fof(f5434,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)],[f37,f5433]) ).
fof(f5454,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,one),X0),X1),
inference(forward_demodulation,[status(thm)],[f92,f5304]) ).
fof(f5455,plain,
! [X0,X1] : addition(X0,multiplication(addition(addition(X1,one),X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f196,f5305]) ).
fof(f5456,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,addition(X1,X1)),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f5455]) ).
fof(f5457,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f36,f5456]) ).
fof(f5458,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X1,one),X2)) = addition(X2,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f92,f5307]) ).
fof(f5471,plain,
! [X0] : multiplication(one,coantidomain(c(X0))) = multiplication(domain(X0),coantidomain(c(X0))),
inference(paramodulation,[status(thm)],[f515,f228]) ).
fof(f5472,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)],[f561,f228]) ).
fof(f5473,plain,
! [X0] : multiplication(one,coantidomain(codomain(X0))) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f625,f228]) ).
fof(f5474,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)],[f404,f228]) ).
fof(f5475,plain,
! [X0] : multiplication(one,coantidomain(domain(X0))) = multiplication(antidomain(X0),coantidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f504,f228]) ).
fof(f5476,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)],[f199,f228]) ).
fof(f5477,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)],[f165,f228]) ).
fof(f5478,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)],[f206,f228]) ).
fof(f5479,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)],[f196,f228]) ).
fof(f5480,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)],[f148,f228]) ).
fof(f5481,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)],[f41,f228]) ).
fof(f5482,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)],[f40,f228]) ).
fof(f5483,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f98,f228]) ).
fof(f5484,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f34,f228]) ).
fof(f5492,plain,
! [X0,X1] : multiplication(multiplication(addition(X0,one),X1),coantidomain(multiplication(X0,X1))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f227,f228]) ).
fof(f5493,plain,
! [X0,X1] : multiplication(multiplication(addition(one,X0),X1),coantidomain(multiplication(X0,X1))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f202,f228]) ).
fof(f5494,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(X1,one)),coantidomain(multiplication(X0,X1))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f187,f228]) ).
fof(f5495,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(one,X1)),coantidomain(multiplication(X0,X1))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f157,f228]) ).
fof(f5496,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)],[f94,f228]) ).
fof(f5497,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X0,X1))) = multiplication(X0,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f100,f228]) ).
fof(f5498,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X0,X1))) = multiplication(X2,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f92,f228]) ).
fof(f5499,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X2,X0))) = multiplication(X1,coantidomain(addition(X2,X0))),
inference(paramodulation,[status(thm)],[f92,f228]) ).
fof(f5505,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,coantidomain(coantidomain(X1))),
inference(paramodulation,[status(thm)],[f61,f228]) ).
fof(f5509,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f228,f3817]) ).
fof(f5512,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)],[f228,f206]) ).
fof(f5514,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X1)) = addition(coantidomain(X1),multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f228,f202]) ).
fof(f5515,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)],[f228,f199]) ).
fof(f5516,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)],[f228,f199]) ).
fof(f5518,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)],[f228,f196]) ).
fof(f5519,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)],[f228,f165]) ).
fof(f5520,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)],[f228,f165]) ).
fof(f5523,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)],[f228,f148]) ).
fof(f5524,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)],[f228,f148]) ).
fof(f5525,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),coantidomain(multiplication(X0,coantidomain(X1))))) = zero,
inference(paramodulation,[status(thm)],[f228,f139]) ).
fof(f5526,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),multiplication(X0,coantidomain(X1))) = zero,
inference(paramodulation,[status(thm)],[f228,f131]) ).
fof(f5527,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)],[f228,f561]) ).
fof(f5528,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)],[f228,f404]) ).
fof(f5529,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)],[f228,f53]) ).
fof(f5530,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)],[f228,f51]) ).
fof(f5531,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)],[f228,f41]) ).
fof(f5532,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)],[f228,f41]) ).
fof(f5533,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)],[f228,f40]) ).
fof(f5534,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)],[f228,f40]) ).
fof(f5535,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(multiplication(X0,coantidomain(X1)),X2),
inference(paramodulation,[status(thm)],[f228,f37]) ).
fof(f5537,plain,
! [X0] : coantidomain(c(X0)) = multiplication(domain(X0),coantidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f39,f5471]) ).
fof(f5538,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),coantidomain(coantidomain(multiplication(codomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f58,f5472]) ).
fof(f5539,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),codomain(multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f61,f5538]) ).
fof(f5540,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),backward_diamond(X1,X0)),
inference(forward_demodulation,[status(thm)],[f65,f5539]) ).
fof(f5541,plain,
! [X0] : coantidomain(codomain(X0)) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f5473]) ).
fof(f5542,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),coantidomain(antidomain(multiplication(X0,domain(X1))))),
inference(forward_demodulation,[status(thm)],[f58,f5474]) ).
fof(f5543,plain,
! [X0] : coantidomain(domain(X0)) = multiplication(antidomain(X0),coantidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f39,f5475]) ).
fof(f5544,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)],[f37,f5476]) ).
fof(f5545,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)],[f37,f5544]) ).
fof(f5546,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,f5545]) ).
fof(f5547,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)],[f37,f5477]) ).
fof(f5548,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)],[f37,f5478]) ).
fof(f5549,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)],[f37,f5548]) ).
fof(f5550,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)],[f37,f5479]) ).
fof(f5551,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,f5550]) ).
fof(f5552,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)],[f37,f5480]) ).
fof(f5553,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)],[f37,f5552]) ).
fof(f5554,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)],[f37,f5481]) ).
fof(f5555,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,f5554]) ).
fof(f5556,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)],[f37,f5482]) ).
fof(f5557,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)],[f37,f5556]) ).
fof(f5559,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,f5492]) ).
fof(f5560,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,f5493]) ).
fof(f5561,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(multiplication(X0,X1)))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f37,f5494]) ).
fof(f5562,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(multiplication(X0,X1)))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f37,f5495]) ).
fof(f5563,plain,
! [X0,X1] : zero = multiplication(X0,coantidomain(addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f58,f5497]) ).
fof(f5567,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f61,f5505]) ).
fof(f5577,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)],[f206,f5512]) ).
fof(f5580,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X1)) = multiplication(addition(X0,one),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f227,f5514]) ).
fof(f5581,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)],[f199,f5515]) ).
fof(f5582,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)],[f199,f5516]) ).
fof(f5585,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f196,f5518]) ).
fof(f5586,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)],[f92,f5519]) ).
fof(f5596,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)],[f33,f5523]) ).
fof(f5597,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f196,f5531]) ).
fof(f5598,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)],[f98,f5532]) ).
fof(f5599,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),multiplication(X1,coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f221,f5598]) ).
fof(f5600,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f196,f5599]) ).
fof(f5601,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)],[f33,f5533]) ).
fof(f5602,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f37,f5535]) ).
fof(f5606,plain,
! [X0,X1] : forward_diamond(domain(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f67,f4162]) ).
fof(f5607,plain,
! [X0,X1] : forward_diamond(domain(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f66,f4162]) ).
fof(f5609,plain,
! [X0] : forward_diamond(domain(antidomain(c(X0))),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f493,f4162]) ).
fof(f5610,plain,
! [X0] : forward_diamond(domain(domain(c(X0))),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f317,f4162]) ).
fof(f5613,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)],[f4162,f70]) ).
fof(f5614,plain,
! [X0] : forward_box(domain(c(c(X0))),X0) = c(zero),
inference(paramodulation,[status(thm)],[f4162,f66]) ).
fof(f5623,plain,
! [X0] : forward_diamond(c(c(X0)),antidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f316,f5609]) ).
fof(f5624,plain,
! [X0] : forward_diamond(antidomain(c(c(X0))),domain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f191,f5610]) ).
fof(f5631,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)],[f92,f5613]) ).
fof(f5632,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)],[f75,f5631]) ).
fof(f5633,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)],[f4162,f5632]) ).
fof(f5634,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)],[f75,f5633]) ).
fof(f5635,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)],[f317,f5634]) ).
fof(f5636,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)],[f191,f5635]) ).
fof(f5637,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)],[f317,f5636]) ).
fof(f5638,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)],[f191,f5637]) ).
fof(f5639,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)],[f317,f5638]) ).
fof(f5640,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)],[f191,f5639]) ).
fof(f5641,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)],[f317,f5640]) ).
fof(f5642,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)],[f191,f5641]) ).
fof(f5643,plain,
! [X0] : forward_box(domain(c(c(X0))),X0) = one,
inference(forward_demodulation,[status(thm)],[f543,f5614]) ).
fof(f5645,plain,
! [X0] : addition(coantidomain(X0),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(resolution,[status(thm)],[f4196,f46]) ).
fof(f5662,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),X1),
inference(resolution,[status(thm)],[f4326,f241]) ).
fof(f5667,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(divergence(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f98,f4326]) ).
fof(f5668,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(divergence(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f34,f4326]) ).
fof(f5675,plain,
! [X0] : codomain(divergence(X0)) = addition(codomain(divergence(X0)),divergence(X0)),
inference(paramodulation,[status(thm)],[f2178,f4326]) ).
fof(f5676,plain,
! [X0,X1] : addition(coantidomain(divergence(X0)),X1) = addition(addition(coantidomain(divergence(X0)),X1),multiplication(divergence(X0),X1)),
inference(paramodulation,[status(thm)],[f176,f4326]) ).
fof(f5684,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4326,f176]) ).
fof(f5697,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)],[f4326,f165]) ).
fof(f5698,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(divergence(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4326,f53]) ).
fof(f5699,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(divergence(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4326,f51]) ).
fof(f5700,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4326,f98]) ).
fof(f5701,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4326,f34]) ).
fof(f5711,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(paramodulation,[status(thm)],[f4326,f172]) ).
fof(f5713,plain,
! [X0,X1,X2] : leq(multiplication(divergence(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4326,f1356]) ).
fof(f5717,plain,
! [X0,X1,X2] : addition(multiplication(divergence(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4326,f98]) ).
fof(f5719,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(divergence(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4326,f92]) ).
fof(f5720,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(divergence(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4326,f92]) ).
fof(f5722,plain,
! [X0,X1] :
( X0 != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4326,f47]) ).
fof(f5723,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(divergence(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4326,f34]) ).
fof(f5733,plain,
! [X0] : codomain(divergence(X0)) = addition(divergence(X0),codomain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f33,f5675]) ).
fof(f5734,plain,
! [X0,X1] : addition(coantidomain(divergence(X0)),X1) = addition(X1,addition(coantidomain(divergence(X0)),multiplication(divergence(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f5676]) ).
fof(f5738,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f58,f5684]) ).
fof(f5748,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)],[f148,f5697]) ).
fof(f5749,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)],[f37,f5698]) ).
fof(f5750,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)],[f37,f5749]) ).
fof(f5760,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f54,f5711]) ).
fof(f5762,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f5717]) ).
fof(f5764,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(divergence(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f5720]) ).
fof(f5767,plain,
! [X0] : leq(divergence(X0),codomain(divergence(X0))),
inference(paramodulation,[status(thm)],[f2178,f5662]) ).
fof(f5768,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),addition(coantidomain(divergence(X0)),X1)),
inference(paramodulation,[status(thm)],[f176,f5662]) ).
fof(f5769,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),addition(X1,coantidomain(divergence(X0)))),
inference(paramodulation,[status(thm)],[f185,f5662]) ).
fof(f5781,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)],[f92,f214]) ).
fof(f5782,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)],[f92,f214]) ).
fof(f5785,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)],[f202,f214]) ).
fof(f5786,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)],[f219,f214]) ).
fof(f5787,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)],[f227,f214]) ).
fof(f5790,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)],[f221,f214]) ).
fof(f5791,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)],[f192,f214]) ).
fof(f5792,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(addition(c(X1),X0),X1),X2),
inference(paramodulation,[status(thm)],[f4088,f214]) ).
fof(f5793,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)],[f190,f214]) ).
fof(f5794,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)],[f63,f214]) ).
fof(f5795,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(domain(X0),X1),X0),X2),
inference(paramodulation,[status(thm)],[f3965,f214]) ).
fof(f5796,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)],[f37,f214]) ).
fof(f5797,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)],[f181,f214]) ).
fof(f5798,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)],[f172,f214]) ).
fof(f5799,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)],[f131,f214]) ).
fof(f5802,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(one,X1),X0),X2),
inference(paramodulation,[status(thm)],[f39,f214]) ).
fof(f5803,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,codomain(X0)),X2)) = addition(multiplication(addition(X0,X1),codomain(X0)),X2),
inference(paramodulation,[status(thm)],[f2178,f214]) ).
fof(f5804,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)],[f157,f214]) ).
fof(f5805,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)],[f176,f214]) ).
fof(f5806,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)],[f187,f214]) ).
fof(f5807,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)],[f185,f214]) ).
fof(f5808,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)],[f146,f214]) ).
fof(f5809,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)],[f139,f214]) ).
fof(f5814,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)],[f214,f214]) ).
fof(f5815,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)],[f165,f214]) ).
fof(f5816,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)],[f206,f214]) ).
fof(f5817,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)],[f196,f214]) ).
fof(f5818,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)],[f148,f214]) ).
fof(f5819,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)],[f41,f214]) ).
fof(f5820,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)],[f40,f214]) ).
fof(f5821,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)],[f4326,f214]) ).
fof(f5822,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)],[f2352,f214]) ).
fof(f5823,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)],[f2351,f214]) ).
fof(f5824,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)],[f2350,f214]) ).
fof(f5825,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)],[f2349,f214]) ).
fof(f5826,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)],[f2348,f214]) ).
fof(f5827,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)],[f2347,f214]) ).
fof(f5828,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)],[f227,f214]) ).
fof(f5829,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)],[f202,f214]) ).
fof(f5830,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)],[f187,f214]) ).
fof(f5831,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)],[f157,f214]) ).
fof(f5832,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)],[f94,f214]) ).
fof(f5833,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)],[f100,f214]) ).
fof(f5834,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)],[f92,f214]) ).
fof(f5835,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)],[f92,f214]) ).
fof(f5836,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),zero),
inference(paramodulation,[status(thm)],[f35,f214]) ).
fof(f5837,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)],[f33,f214]) ).
fof(f5838,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)],[f33,f214]) ).
fof(f5839,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f36,f214]) ).
fof(f5840,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)],[f202,f214]) ).
fof(f5841,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)],[f219,f214]) ).
fof(f5842,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)],[f227,f214]) ).
fof(f5843,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)],[f225,f214]) ).
fof(f5844,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)],[f228,f214]) ).
fof(f5845,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)],[f221,f214]) ).
fof(f5846,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)],[f192,f214]) ).
fof(f5847,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(addition(X0,c(X1)),X1),X2),
inference(paramodulation,[status(thm)],[f4088,f214]) ).
fof(f5848,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)],[f190,f214]) ).
fof(f5849,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)],[f63,f214]) ).
fof(f5850,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,domain(X1)),X1),X2),
inference(paramodulation,[status(thm)],[f3965,f214]) ).
fof(f5851,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)],[f37,f214]) ).
fof(f5852,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)],[f181,f214]) ).
fof(f5853,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)],[f172,f214]) ).
fof(f5854,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)],[f131,f214]) ).
fof(f5857,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),X2),
inference(paramodulation,[status(thm)],[f39,f214]) ).
fof(f5858,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),addition(X1,X2)) = addition(multiplication(addition(X0,X1),codomain(X1)),X2),
inference(paramodulation,[status(thm)],[f2178,f214]) ).
fof(f5859,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)],[f157,f214]) ).
fof(f5860,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)],[f176,f214]) ).
fof(f5861,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)],[f187,f214]) ).
fof(f5862,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)],[f185,f214]) ).
fof(f5863,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)],[f146,f214]) ).
fof(f5864,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)],[f139,f214]) ).
fof(f5869,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)],[f214,f165]) ).
fof(f5870,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)],[f214,f53]) ).
fof(f5871,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)],[f214,f51]) ).
fof(f5873,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(addition(X2,X0),X1),X3)),
inference(paramodulation,[status(thm)],[f214,f1357]) ).
fof(f5877,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)],[f214,f92]) ).
fof(f5878,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)],[f214,f92]) ).
fof(f5879,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)],[f214,f228]) ).
fof(f5880,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)],[f214,f221]) ).
fof(f5881,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)],[f214,f181]) ).
fof(f5882,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)],[f214,f172]) ).
fof(f5883,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(addition(X0,X3),X1),X4))),
inference(paramodulation,[status(thm)],[f214,f1357]) ).
fof(f5884,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)],[f214,f1356]) ).
fof(f5885,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(addition(X3,X0),X1),X2)),
inference(paramodulation,[status(thm)],[f214,f1359]) ).
fof(f5886,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f214,f1261]) ).
fof(f5888,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)],[f214,f98]) ).
fof(f5889,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)],[f214,f94]) ).
fof(f5890,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)],[f214,f92]) ).
fof(f5891,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)],[f214,f92]) ).
fof(f5892,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)],[f214,f241]) ).
fof(f5893,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)],[f214,f47]) ).
fof(f5894,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)],[f214,f34]) ).
fof(f5903,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(addition(X2,X1),X3),X0),
inference(forward_demodulation,[status(thm)],[f196,f5782]) ).
fof(f5908,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)],[f98,f5785]) ).
fof(f5909,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)],[f92,f5908]) ).
fof(f5910,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)],[f98,f5909]) ).
fof(f5911,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)],[f196,f5910]) ).
fof(f5912,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)],[f98,f5911]) ).
fof(f5913,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)],[f214,f5786]) ).
fof(f5914,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)],[f98,f5913]) ).
fof(f5915,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)],[f98,f5787]) ).
fof(f5916,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)],[f92,f5915]) ).
fof(f5917,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)],[f98,f5916]) ).
fof(f5918,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)],[f196,f5917]) ).
fof(f5919,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)],[f98,f5918]) ).
fof(f5924,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)],[f214,f5790]) ).
fof(f5925,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)],[f98,f5924]) ).
fof(f5926,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),X2) = addition(multiplication(addition(c(X1),X0),domain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f5791]) ).
fof(f5927,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),X2) = addition(multiplication(addition(c(X1),X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f75,f5792]) ).
fof(f5928,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),X2) = addition(multiplication(addition(coantidomain(X1),X0),codomain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f5793]) ).
fof(f5929,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)],[f75,f5799]) ).
fof(f5932,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)],[f98,f5804]) ).
fof(f5933,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)],[f92,f5932]) ).
fof(f5934,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)],[f98,f5933]) ).
fof(f5935,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)],[f98,f5806]) ).
fof(f5936,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)],[f92,f5935]) ).
fof(f5937,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)],[f98,f5936]) ).
fof(f5938,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)],[f75,f5808]) ).
fof(f5939,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)],[f75,f5809]) ).
fof(f5949,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)],[f214,f5814]) ).
fof(f5950,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)],[f214,f5949]) ).
fof(f5951,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)],[f98,f5950]) ).
fof(f5952,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)],[f196,f5816]) ).
fof(f5953,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)],[f98,f5952]) ).
fof(f5954,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)],[f206,f5953]) ).
fof(f5955,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)],[f98,f5954]) ).
fof(f5956,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)],[f196,f5817]) ).
fof(f5957,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)],[f98,f5956]) ).
fof(f5958,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f196,f5957]) ).
fof(f5959,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)],[f196,f5819]) ).
fof(f5960,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)],[f98,f5959]) ).
fof(f5961,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f196,f5960]) ).
fof(f5962,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)],[f196,f5821]) ).
fof(f5963,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)],[f206,f5962]) ).
fof(f5964,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)],[f98,f5963]) ).
fof(f5965,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)],[f196,f5822]) ).
fof(f5966,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)],[f37,f5965]) ).
fof(f5967,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)],[f196,f5823]) ).
fof(f5968,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)],[f37,f5967]) ).
fof(f5969,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)],[f196,f5824]) ).
fof(f5970,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)],[f37,f5969]) ).
fof(f5971,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)],[f196,f5825]) ).
fof(f5972,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)],[f37,f5971]) ).
fof(f5973,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)],[f196,f5826]) ).
fof(f5974,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)],[f37,f5973]) ).
fof(f5975,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)],[f196,f5827]) ).
fof(f5976,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)],[f37,f5975]) ).
fof(f5977,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)],[f206,f5828]) ).
fof(f5978,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)],[f206,f5977]) ).
fof(f5979,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)],[f98,f5978]) ).
fof(f5980,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)],[f206,f5829]) ).
fof(f5981,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)],[f206,f5980]) ).
fof(f5982,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)],[f98,f5981]) ).
fof(f5983,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)],[f37,f5830]) ).
fof(f5984,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)],[f37,f5983]) ).
fof(f5985,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)],[f37,f5831]) ).
fof(f5986,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)],[f37,f5985]) ).
fof(f5987,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)],[f214,f5832]) ).
fof(f5988,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)],[f214,f5833]) ).
fof(f5989,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)],[f214,f5988]) ).
fof(f5990,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)],[f98,f5989]) ).
fof(f5991,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),zero),
inference(forward_demodulation,[status(thm)],[f196,f5836]) ).
fof(f5992,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f35,f5991]) ).
fof(f5993,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f196,f5839]) ).
fof(f5994,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f196,f5993]) ).
fof(f5995,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)],[f98,f5840]) ).
fof(f5996,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)],[f214,f5995]) ).
fof(f5997,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)],[f92,f5996]) ).
fof(f5998,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)],[f214,f5841]) ).
fof(f5999,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)],[f98,f5842]) ).
fof(f6000,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)],[f214,f5999]) ).
fof(f6001,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)],[f92,f6000]) ).
fof(f6002,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)],[f214,f5843]) ).
fof(f6003,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)],[f214,f5844]) ).
fof(f6004,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)],[f214,f5845]) ).
fof(f6005,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)],[f92,f5846]) ).
fof(f6006,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,domain(X2))) = addition(multiplication(addition(X1,c(X2)),domain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f75,f6005]) ).
fof(f6007,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,X2))) = addition(multiplication(addition(X1,c(X2)),X2),X0),
inference(forward_demodulation,[status(thm)],[f92,f5847]) ).
fof(f6008,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,X2)) = addition(multiplication(addition(X1,c(X2)),X2),X0),
inference(forward_demodulation,[status(thm)],[f75,f6007]) ).
fof(f6009,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)],[f92,f5848]) ).
fof(f6010,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,codomain(X2))) = addition(multiplication(addition(X1,coantidomain(X2)),codomain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f75,f6009]) ).
fof(f6011,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,domain(X0)),X0),X1),
inference(forward_demodulation,[status(thm)],[f92,f5850]) ).
fof(f6012,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)],[f92,f5852]) ).
fof(f6013,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)],[f92,f5853]) ).
fof(f6014,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)],[f92,f5854]) ).
fof(f6015,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)],[f75,f6014]) ).
fof(f6022,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,one),X0),X1),
inference(forward_demodulation,[status(thm)],[f92,f5857]) ).
fof(f6023,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)],[f92,f5858]) ).
fof(f6024,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)],[f98,f5859]) ).
fof(f6025,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)],[f92,f6024]) ).
fof(f6026,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)],[f92,f5860]) ).
fof(f6027,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)],[f98,f5861]) ).
fof(f6028,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)],[f92,f6027]) ).
fof(f6029,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)],[f92,f5862]) ).
fof(f6030,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)],[f92,f5863]) ).
fof(f6031,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)],[f75,f6030]) ).
fof(f6032,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)],[f92,f5864]) ).
fof(f6033,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)],[f75,f6032]) ).
fof(f6053,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f5878]) ).
fof(f6054,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)],[f37,f5879]) ).
fof(f6057,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)],[f98,f5888]) ).
fof(f6058,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)],[f214,f6057]) ).
fof(f6059,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)],[f98,f6058]) ).
fof(f6060,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)],[f98,f5889]) ).
fof(f6061,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)],[f214,f6060]) ).
fof(f6062,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)],[f214,f6061]) ).
fof(f6063,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)],[f98,f5890]) ).
fof(f6064,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)],[f98,f5891]) ).
fof(f6065,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)],[f98,f5894]) ).
fof(f6066,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)],[f98,f6065]) ).
fof(f6071,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4327,f241]) ).
fof(f6076,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(codomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f98,f4327]) ).
fof(f6077,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(codomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f34,f4327]) ).
fof(f6084,plain,
! [X0] : codomain(codomain(X0)) = addition(codomain(codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f2178,f4327]) ).
fof(f6085,plain,
! [X0,X1] : addition(coantidomain(codomain(X0)),X1) = addition(addition(coantidomain(codomain(X0)),X1),multiplication(codomain(X0),X1)),
inference(paramodulation,[status(thm)],[f176,f4327]) ).
fof(f6092,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f65,f4327]) ).
fof(f6094,plain,
! [X0,X1] : X0 = addition(X0,multiplication(coantidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f188,f4327]) ).
fof(f6096,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4327,f176]) ).
fof(f6109,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)],[f4327,f214]) ).
fof(f6110,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)],[f4327,f165]) ).
fof(f6111,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(codomain(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4327,f53]) ).
fof(f6112,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(codomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4327,f51]) ).
fof(f6113,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4327,f98]) ).
fof(f6114,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4327,f34]) ).
fof(f6124,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4327,f172]) ).
fof(f6126,plain,
! [X0,X1,X2] : leq(multiplication(codomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4327,f1356]) ).
fof(f6130,plain,
! [X0,X1,X2] : addition(multiplication(codomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4327,f98]) ).
fof(f6132,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(codomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4327,f92]) ).
fof(f6133,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(codomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4327,f92]) ).
fof(f6135,plain,
! [X0,X1] :
( X0 != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4327,f47]) ).
fof(f6136,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(codomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4327,f34]) ).
fof(f6146,plain,
! [X0] : codomain(codomain(X0)) = addition(codomain(X0),codomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f6084]) ).
fof(f6147,plain,
! [X0,X1] : addition(coantidomain(codomain(X0)),X1) = addition(X1,addition(coantidomain(codomain(X0)),multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f6085]) ).
fof(f6152,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f58,f6096]) ).
fof(f6162,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)],[f196,f6109]) ).
fof(f6163,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)],[f206,f6162]) ).
fof(f6164,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)],[f98,f6163]) ).
fof(f6165,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)],[f148,f6110]) ).
fof(f6166,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)],[f37,f6111]) ).
fof(f6167,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)],[f37,f6166]) ).
fof(f6177,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f54,f6124]) ).
fof(f6179,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f6130]) ).
fof(f6181,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(codomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f6133]) ).
fof(f6184,plain,
! [X0] : leq(codomain(X0),codomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f2178,f6071]) ).
fof(f6185,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),addition(coantidomain(codomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f176,f6071]) ).
fof(f6186,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),addition(X1,coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f185,f6071]) ).
fof(f6192,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f65,f6071]) ).
fof(f6194,plain,
! [X0,X1] : leq(multiplication(coantidomain(codomain(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f188,f6071]) ).
fof(f6199,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),X1),
inference(resolution,[status(thm)],[f4328,f241]) ).
fof(f6204,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(c(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f98,f4328]) ).
fof(f6205,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(c(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f34,f4328]) ).
fof(f6214,plain,
! [X0] : codomain(c(X0)) = addition(codomain(c(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f2178,f4328]) ).
fof(f6215,plain,
! [X0,X1] : addition(coantidomain(c(X0)),X1) = addition(addition(coantidomain(c(X0)),X1),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f176,f4328]) ).
fof(f6222,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f67,f4328]) ).
fof(f6223,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f66,f4328]) ).
fof(f6225,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f493,f4328]) ).
fof(f6226,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f317,f4328]) ).
fof(f6228,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4328,f176]) ).
fof(f6241,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)],[f4328,f214]) ).
fof(f6242,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)],[f4328,f165]) ).
fof(f6243,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(c(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4328,f53]) ).
fof(f6244,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(c(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4328,f51]) ).
fof(f6245,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4328,f98]) ).
fof(f6246,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4328,f34]) ).
fof(f6256,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(paramodulation,[status(thm)],[f4328,f172]) ).
fof(f6258,plain,
! [X0,X1,X2] : leq(multiplication(c(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4328,f1356]) ).
fof(f6262,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4328,f98]) ).
fof(f6264,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(c(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4328,f92]) ).
fof(f6265,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(c(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4328,f92]) ).
fof(f6267,plain,
! [X0,X1] :
( X0 != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4328,f47]) ).
fof(f6268,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(c(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4328,f34]) ).
fof(f6278,plain,
! [X0] : codomain(c(X0)) = addition(c(X0),codomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f33,f6214]) ).
fof(f6279,plain,
! [X0,X1] : addition(coantidomain(c(X0)),X1) = addition(X1,addition(coantidomain(c(X0)),multiplication(c(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f6215]) ).
fof(f6284,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f58,f6228]) ).
fof(f6294,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)],[f196,f6241]) ).
fof(f6295,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)],[f206,f6294]) ).
fof(f6296,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)],[f98,f6295]) ).
fof(f6297,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)],[f148,f6242]) ).
fof(f6298,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)],[f37,f6243]) ).
fof(f6299,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)],[f37,f6298]) ).
fof(f6309,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f54,f6256]) ).
fof(f6311,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f6262]) ).
fof(f6313,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(c(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f6265]) ).
fof(f6318,plain,
! [X0] : leq(c(X0),codomain(c(X0))),
inference(paramodulation,[status(thm)],[f2178,f6199]) ).
fof(f6319,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),addition(coantidomain(c(X0)),X1)),
inference(paramodulation,[status(thm)],[f176,f6199]) ).
fof(f6320,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),addition(X1,coantidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f185,f6199]) ).
fof(f6326,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f67,f6199]) ).
fof(f6327,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f66,f6199]) ).
fof(f6329,plain,
! [X0,X1] : leq(multiplication(antidomain(c(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f493,f6199]) ).
fof(f6330,plain,
! [X0,X1] : leq(multiplication(domain(c(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f317,f6199]) ).
fof(f6335,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4329,f241]) ).
fof(f6340,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f98,f4329]) ).
fof(f6341,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(antidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f34,f4329]) ).
fof(f6349,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f172,f4329]) ).
fof(f6352,plain,
! [X0] : codomain(antidomain(X0)) = addition(codomain(antidomain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f2178,f4329]) ).
fof(f6353,plain,
! [X0,X1] : addition(coantidomain(antidomain(X0)),X1) = addition(addition(coantidomain(antidomain(X0)),X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f176,f4329]) ).
fof(f6364,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4329,f176]) ).
fof(f6377,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)],[f4329,f214]) ).
fof(f6378,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)],[f4329,f165]) ).
fof(f6379,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(antidomain(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4329,f53]) ).
fof(f6380,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(antidomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4329,f51]) ).
fof(f6381,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4329,f98]) ).
fof(f6382,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4329,f34]) ).
fof(f6392,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4329,f172]) ).
fof(f6394,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4329,f1356]) ).
fof(f6398,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4329,f98]) ).
fof(f6400,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(antidomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4329,f92]) ).
fof(f6401,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(antidomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4329,f92]) ).
fof(f6403,plain,
! [X0,X1] :
( X0 != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4329,f47]) ).
fof(f6404,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(antidomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4329,f34]) ).
fof(f6416,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f6349]) ).
fof(f6417,plain,
! [X0] : codomain(antidomain(X0)) = addition(antidomain(X0),codomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f6352]) ).
fof(f6418,plain,
! [X0,X1] : addition(coantidomain(antidomain(X0)),X1) = addition(X1,addition(coantidomain(antidomain(X0)),multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f6353]) ).
fof(f6423,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f58,f6364]) ).
fof(f6433,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)],[f196,f6377]) ).
fof(f6434,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)],[f206,f6433]) ).
fof(f6435,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)],[f98,f6434]) ).
fof(f6436,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)],[f148,f6378]) ).
fof(f6437,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)],[f37,f6379]) ).
fof(f6438,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)],[f37,f6437]) ).
fof(f6448,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f54,f6392]) ).
fof(f6450,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f6398]) ).
fof(f6452,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(antidomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f6401]) ).
fof(f6455,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f181,f6335]) ).
fof(f6456,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f172,f6335]) ).
fof(f6459,plain,
! [X0] : leq(antidomain(X0),codomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f2178,f6335]) ).
fof(f6460,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(coantidomain(antidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f176,f6335]) ).
fof(f6461,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X1,coantidomain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f185,f6335]) ).
fof(f6469,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),X1),
inference(paramodulation,[status(thm)],[f57,f6335]) ).
fof(f6484,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)],[f2178,f236]) ).
fof(f6485,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)],[f176,f236]) ).
fof(f6486,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)],[f185,f236]) ).
fof(f6487,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)],[f146,f236]) ).
fof(f6488,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)],[f139,f236]) ).
fof(f6489,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)],[f58,f236]) ).
fof(f6492,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)],[f1439,f236]) ).
fof(f6493,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)],[f1432,f236]) ).
fof(f6494,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)],[f1427,f236]) ).
fof(f6495,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)],[f1420,f236]) ).
fof(f6496,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(divergence(X1),X0)
| leq(multiplication(one,X0),multiplication(divergence(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1423,f236]) ).
fof(f6497,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(codomain(X1),X0)
| leq(multiplication(one,X0),multiplication(codomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1412,f236]) ).
fof(f6498,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(c(X1),X0)
| leq(multiplication(one,X0),multiplication(c(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1406,f236]) ).
fof(f6499,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(antidomain(X1),X0)
| leq(multiplication(one,X0),multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1315,f236]) ).
fof(f6500,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(coantidomain(X1),X0)
| leq(multiplication(one,X0),multiplication(coantidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1313,f236]) ).
fof(f6501,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(domain(X1),X0)
| leq(multiplication(one,X0),multiplication(domain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1311,f236]) ).
fof(f6502,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(c(X0),X1)
| leq(multiplication(domain(X0),X1),multiplication(c(X0),X1)) ),
inference(paramodulation,[status(thm)],[f515,f236]) ).
fof(f6503,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)],[f561,f236]) ).
fof(f6504,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(codomain(X0),X1)
| leq(multiplication(coantidomain(X0),X1),multiplication(codomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f625,f236]) ).
fof(f6505,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)],[f404,f236]) ).
fof(f6506,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(domain(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(domain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f504,f236]) ).
fof(f6507,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)],[f199,f236]) ).
fof(f6508,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)],[f214,f236]) ).
fof(f6509,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)],[f165,f236]) ).
fof(f6510,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)],[f206,f236]) ).
fof(f6511,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)],[f196,f236]) ).
fof(f6512,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)],[f148,f236]) ).
fof(f6514,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)],[f40,f236]) ).
fof(f6515,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)],[f98,f236]) ).
fof(f6516,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)],[f34,f236]) ).
fof(f6518,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)],[f4329,f236]) ).
fof(f6519,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)],[f4328,f236]) ).
fof(f6520,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)],[f4327,f236]) ).
fof(f6521,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)],[f4326,f236]) ).
fof(f6522,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)],[f2352,f236]) ).
fof(f6523,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)],[f2351,f236]) ).
fof(f6524,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)],[f2350,f236]) ).
fof(f6525,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)],[f2349,f236]) ).
fof(f6526,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)],[f2348,f236]) ).
fof(f6527,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)],[f2347,f236]) ).
fof(f6528,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)],[f227,f236]) ).
fof(f6529,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)],[f202,f236]) ).
fof(f6530,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)],[f187,f236]) ).
fof(f6531,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)],[f157,f236]) ).
fof(f6532,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)],[f94,f236]) ).
fof(f6533,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)],[f100,f236]) ).
fof(f6534,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)],[f92,f236]) ).
fof(f6535,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)],[f92,f236]) ).
fof(f6537,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f33,f236]) ).
fof(f6538,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f33,f236]) ).
fof(f6564,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)],[f39,f6492]) ).
fof(f6565,plain,
! [X0,X1,X2] :
( X0 != multiplication(backward_diamond(X1,X2),X0)
| leq(X0,multiplication(backward_diamond(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6564]) ).
fof(f6566,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)],[f39,f6493]) ).
fof(f6567,plain,
! [X0,X1,X2] :
( X0 != multiplication(forward_box(X1,X2),X0)
| leq(X0,multiplication(forward_box(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6566]) ).
fof(f6568,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)],[f39,f6494]) ).
fof(f6569,plain,
! [X0,X1,X2] :
( X0 != multiplication(backward_box(X1,X2),X0)
| leq(X0,multiplication(backward_box(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6568]) ).
fof(f6570,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)],[f39,f6495]) ).
fof(f6571,plain,
! [X0,X1,X2] :
( X0 != multiplication(forward_diamond(X1,X2),X0)
| leq(X0,multiplication(forward_diamond(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6570]) ).
fof(f6572,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6496]) ).
fof(f6573,plain,
! [X0,X1] :
( X0 != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6572]) ).
fof(f6574,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6497]) ).
fof(f6575,plain,
! [X0,X1] :
( X0 != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6574]) ).
fof(f6576,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6498]) ).
fof(f6577,plain,
! [X0,X1] :
( X0 != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6576]) ).
fof(f6578,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6499]) ).
fof(f6579,plain,
! [X0,X1] :
( X0 != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6578]) ).
fof(f6580,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6500]) ).
fof(f6581,plain,
! [X0,X1] :
( X0 != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6580]) ).
fof(f6582,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6501]) ).
fof(f6583,plain,
! [X0,X1] :
( X0 != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f6582]) ).
fof(f6584,plain,
! [X0,X1] :
( X1 != multiplication(c(X0),X1)
| leq(multiplication(domain(X0),X1),multiplication(c(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f6502]) ).
fof(f6585,plain,
! [X0,X1,X2] : leq(multiplication(coantidomain(multiplication(X0,X1)),X2),multiplication(coantidomain(multiplication(codomain(X0),X1)),X2)),
inference(trivial_equality_resolution,[status(thm)],[f6503]) ).
fof(f6586,plain,
! [X0,X1] :
( X1 != multiplication(codomain(X0),X1)
| leq(multiplication(coantidomain(X0),X1),multiplication(codomain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f6504]) ).
fof(f6587,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(multiplication(X0,X1)),X2),multiplication(antidomain(multiplication(X0,domain(X1))),X2)),
inference(trivial_equality_resolution,[status(thm)],[f6505]) ).
fof(f6588,plain,
! [X0,X1] :
( X1 != multiplication(domain(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(domain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f6506]) ).
fof(f6589,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)],[f37,f6507]) ).
fof(f6590,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)],[f37,f6589]) ).
fof(f6591,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)],[f37,f6590]) ).
fof(f6592,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)],[f37,f6591]) ).
fof(f6593,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)],[f37,f6592]) ).
fof(f6594,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)],[f37,f6508]) ).
fof(f6595,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)],[f37,f6509]) ).
fof(f6596,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)],[f37,f6510]) ).
fof(f6597,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)],[f37,f6596]) ).
fof(f6598,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)],[f37,f6597]) ).
fof(f6599,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)],[f37,f6598]) ).
fof(f6600,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)],[f37,f6599]) ).
fof(f6601,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)],[f37,f6600]) ).
fof(f6602,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)],[f37,f6511]) ).
fof(f6603,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)],[f37,f6602]) ).
fof(f6604,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)],[f37,f6603]) ).
fof(f6605,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)],[f37,f6604]) ).
fof(f6606,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)],[f37,f6512]) ).
fof(f6607,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)],[f37,f6606]) ).
fof(f6608,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)],[f37,f6607]) ).
fof(f6609,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)],[f37,f6608]) ).
fof(f6614,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)],[f37,f6514]) ).
fof(f6615,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)],[f37,f6614]) ).
fof(f6616,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)],[f37,f6615]) ).
fof(f6617,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)],[f37,f6616]) ).
fof(f6620,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)],[f37,f6518]) ).
fof(f6621,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)],[f37,f6620]) ).
fof(f6622,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)],[f37,f6519]) ).
fof(f6623,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)],[f37,f6622]) ).
fof(f6624,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)],[f37,f6520]) ).
fof(f6625,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)],[f37,f6624]) ).
fof(f6626,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)],[f37,f6521]) ).
fof(f6627,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)],[f37,f6626]) ).
fof(f6628,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)],[f37,f6522]) ).
fof(f6629,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)],[f37,f6628]) ).
fof(f6630,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)],[f37,f6523]) ).
fof(f6631,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)],[f37,f6630]) ).
fof(f6632,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)],[f37,f6524]) ).
fof(f6633,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)],[f37,f6632]) ).
fof(f6634,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)],[f37,f6525]) ).
fof(f6635,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)],[f37,f6634]) ).
fof(f6636,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)],[f37,f6526]) ).
fof(f6637,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)],[f37,f6636]) ).
fof(f6638,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)],[f37,f6527]) ).
fof(f6639,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)],[f37,f6638]) ).
fof(f6640,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)],[f37,f6528]) ).
fof(f6641,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)],[f37,f6640]) ).
fof(f6642,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)],[f37,f6641]) ).
fof(f6643,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)],[f37,f6529]) ).
fof(f6644,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)],[f37,f6643]) ).
fof(f6645,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)],[f37,f6644]) ).
fof(f6646,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)],[f37,f6530]) ).
fof(f6647,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)],[f37,f6646]) ).
fof(f6648,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)],[f37,f6647]) ).
fof(f6649,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)],[f37,f6531]) ).
fof(f6650,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)],[f37,f6649]) ).
fof(f6651,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)],[f37,f6650]) ).
fof(f6652,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(trivial_equality_resolution,[status(thm)],[f6533]) ).
fof(f6657,plain,
! [X0,X1] : leq(domain_difference(X0,X1),antidomain(X1)),
inference(paramodulation,[status(thm)],[f63,f6469]) ).
fof(f6659,plain,
! [X0] : leq(domain(X0),codomain(domain(X0))),
inference(paramodulation,[status(thm)],[f2178,f6469]) ).
fof(f6660,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),addition(coantidomain(domain(X0)),X1)),
inference(paramodulation,[status(thm)],[f176,f6469]) ).
fof(f6661,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),addition(X1,coantidomain(domain(X0)))),
inference(paramodulation,[status(thm)],[f185,f6469]) ).
fof(f6667,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f64,f6469]) ).
fof(f6675,plain,
! [X0,X1] : addition(domain_difference(X0,X1),antidomain(X1)) = antidomain(X1),
inference(resolution,[status(thm)],[f6657,f46]) ).
fof(f6683,plain,
! [X0,X1] : leq(domain_difference(X0,domain(X1)),c(X1)),
inference(paramodulation,[status(thm)],[f62,f6657]) ).
fof(f6684,plain,
! [X0,X1] : leq(domain_difference(X0,antidomain(X1)),domain(X1)),
inference(paramodulation,[status(thm)],[f57,f6657]) ).
fof(f6686,plain,
! [X0,X1] : addition(antidomain(X0),domain_difference(X1,X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f33,f6675]) ).
fof(f6695,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)],[f219,f237]) ).
fof(f6696,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)],[f225,f237]) ).
fof(f6697,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)],[f4088,f237]) ).
fof(f6698,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)],[f3965,f237]) ).
fof(f6699,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)],[f37,f237]) ).
fof(f6702,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)],[f54,f237]) ).
fof(f6709,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)],[f1439,f237]) ).
fof(f6710,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)],[f1432,f237]) ).
fof(f6711,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)],[f1427,f237]) ).
fof(f6712,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)],[f1420,f237]) ).
fof(f6713,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,divergence(X1))
| leq(multiplication(X0,one),multiplication(X0,divergence(X1))) ),
inference(paramodulation,[status(thm)],[f1423,f237]) ).
fof(f6714,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(multiplication(X0,one),multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f1412,f237]) ).
fof(f6715,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(multiplication(X0,one),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f1406,f237]) ).
fof(f6716,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,antidomain(X1))
| leq(multiplication(X0,one),multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f1315,f237]) ).
fof(f6717,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,coantidomain(X1))
| leq(multiplication(X0,one),multiplication(X0,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f1313,f237]) ).
fof(f6718,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(multiplication(X0,one),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f1311,f237]) ).
fof(f6719,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(multiplication(X0,domain(X1)),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f515,f237]) ).
fof(f6720,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)],[f561,f237]) ).
fof(f6721,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(multiplication(X0,coantidomain(X1)),multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f625,f237]) ).
fof(f6722,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)],[f404,f237]) ).
fof(f6723,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f504,f237]) ).
fof(f6724,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)],[f199,f237]) ).
fof(f6725,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)],[f214,f237]) ).
fof(f6726,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)],[f165,f237]) ).
fof(f6727,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)],[f206,f237]) ).
fof(f6728,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)],[f196,f237]) ).
fof(f6729,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)],[f148,f237]) ).
fof(f6730,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)],[f41,f237]) ).
fof(f6731,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)],[f40,f237]) ).
fof(f6732,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)],[f98,f237]) ).
fof(f6733,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)],[f34,f237]) ).
fof(f6735,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)],[f4329,f237]) ).
fof(f6736,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)],[f4328,f237]) ).
fof(f6737,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)],[f4327,f237]) ).
fof(f6738,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)],[f4326,f237]) ).
fof(f6739,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)],[f2352,f237]) ).
fof(f6740,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)],[f2351,f237]) ).
fof(f6741,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)],[f2350,f237]) ).
fof(f6742,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)],[f2349,f237]) ).
fof(f6743,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)],[f2348,f237]) ).
fof(f6744,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)],[f2347,f237]) ).
fof(f6745,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)],[f227,f237]) ).
fof(f6746,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)],[f202,f237]) ).
fof(f6747,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)],[f187,f237]) ).
fof(f6748,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)],[f157,f237]) ).
fof(f6749,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)],[f94,f237]) ).
fof(f6750,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)],[f100,f237]) ).
fof(f6751,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)],[f92,f237]) ).
fof(f6752,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)],[f92,f237]) ).
fof(f6754,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f33,f237]) ).
fof(f6755,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f33,f237]) ).
fof(f6763,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)],[f37,f6699]) ).
fof(f6764,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)],[f37,f6763]) ).
fof(f6765,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)],[f37,f6764]) ).
fof(f6784,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)],[f38,f6709]) ).
fof(f6785,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_diamond(X1,X2))
| leq(X0,multiplication(X0,backward_diamond(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f38,f6784]) ).
fof(f6786,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)],[f38,f6710]) ).
fof(f6787,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_box(X1,X2))
| leq(X0,multiplication(X0,forward_box(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f38,f6786]) ).
fof(f6788,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)],[f38,f6711]) ).
fof(f6789,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_box(X1,X2))
| leq(X0,multiplication(X0,backward_box(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f38,f6788]) ).
fof(f6790,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)],[f38,f6712]) ).
fof(f6791,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_diamond(X1,X2))
| leq(X0,multiplication(X0,forward_diamond(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f38,f6790]) ).
fof(f6792,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6713]) ).
fof(f6793,plain,
! [X0,X1] :
( X0 != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6792]) ).
fof(f6794,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6714]) ).
fof(f6795,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6794]) ).
fof(f6796,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6715]) ).
fof(f6797,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6796]) ).
fof(f6798,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6716]) ).
fof(f6799,plain,
! [X0,X1] :
( X0 != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6798]) ).
fof(f6800,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6717]) ).
fof(f6801,plain,
! [X0,X1] :
( X0 != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6800]) ).
fof(f6802,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6718]) ).
fof(f6803,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6802]) ).
fof(f6804,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(multiplication(X0,domain(X1)),multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6719]) ).
fof(f6805,plain,
! [X0,X1,X2] : leq(multiplication(X0,coantidomain(multiplication(X1,X2))),multiplication(X0,coantidomain(multiplication(codomain(X1),X2)))),
inference(trivial_equality_resolution,[status(thm)],[f6720]) ).
fof(f6806,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(multiplication(X0,coantidomain(X1)),multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6721]) ).
fof(f6807,plain,
! [X0,X1,X2] : leq(multiplication(X0,antidomain(multiplication(X1,X2))),multiplication(X0,antidomain(multiplication(X1,domain(X2))))),
inference(trivial_equality_resolution,[status(thm)],[f6722]) ).
fof(f6808,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f6723]) ).
fof(f6811,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(trivial_equality_resolution,[status(thm)],[f6750]) ).
fof(f6815,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4330,f241]) ).
fof(f6820,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(coantidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f98,f4330]) ).
fof(f6821,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f34,f4330]) ).
fof(f6829,plain,
! [X0] : codomain(coantidomain(X0)) = addition(codomain(coantidomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2178,f4330]) ).
fof(f6830,plain,
! [X0,X1] : addition(coantidomain(coantidomain(X0)),X1) = addition(addition(coantidomain(coantidomain(X0)),X1),multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f176,f4330]) ).
fof(f6840,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4330,f176]) ).
fof(f6853,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)],[f4330,f214]) ).
fof(f6854,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)],[f4330,f165]) ).
fof(f6855,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(coantidomain(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4330,f53]) ).
fof(f6856,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(coantidomain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4330,f51]) ).
fof(f6857,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4330,f98]) ).
fof(f6858,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4330,f34]) ).
fof(f6865,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)],[f4330,f237]) ).
fof(f6866,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)],[f4330,f236]) ).
fof(f6870,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4330,f172]) ).
fof(f6872,plain,
! [X0,X1,X2] : leq(multiplication(coantidomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4330,f1356]) ).
fof(f6876,plain,
! [X0,X1,X2] : addition(multiplication(coantidomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4330,f98]) ).
fof(f6878,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(coantidomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4330,f92]) ).
fof(f6879,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(coantidomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4330,f92]) ).
fof(f6881,plain,
! [X0,X1] :
( X0 != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4330,f47]) ).
fof(f6882,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(coantidomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4330,f34]) ).
fof(f6892,plain,
! [X0] : coantidomain(codomain(X0)) = addition(codomain(coantidomain(X0)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f188,f6829]) ).
fof(f6893,plain,
! [X0] : coantidomain(codomain(X0)) = addition(coantidomain(X0),codomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f6892]) ).
fof(f6894,plain,
! [X0] : coantidomain(codomain(X0)) = addition(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f188,f6893]) ).
fof(f6895,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(addition(coantidomain(coantidomain(X0)),X1),multiplication(coantidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f61,f6830]) ).
fof(f6896,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(X1,addition(coantidomain(coantidomain(X0)),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f6895]) ).
fof(f6897,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(X1,addition(codomain(X0),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f61,f6896]) ).
fof(f6908,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f58,f6840]) ).
fof(f6918,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)],[f196,f6853]) ).
fof(f6919,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)],[f206,f6918]) ).
fof(f6920,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)],[f98,f6919]) ).
fof(f6921,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)],[f148,f6854]) ).
fof(f6922,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)],[f37,f6855]) ).
fof(f6923,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)],[f37,f6922]) ).
fof(f6930,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)],[f37,f6866]) ).
fof(f6931,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)],[f37,f6930]) ).
fof(f6935,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f54,f6870]) ).
fof(f6937,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f6876]) ).
fof(f6939,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(coantidomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f6879]) ).
fof(f6943,plain,
! [X0] : leq(coantidomain(X0),codomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f2178,f6815]) ).
fof(f6944,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(coantidomain(coantidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f176,f6815]) ).
fof(f6945,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(X1,coantidomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f185,f6815]) ).
fof(f6955,plain,
! [X0] : leq(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f188,f6943]) ).
fof(f6956,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(codomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f61,f6944]) ).
fof(f6957,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(X1,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f61,f6945]) ).
fof(f6963,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)],[f214,f238]) ).
fof(f6964,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)],[f165,f238]) ).
fof(f6965,plain,
! [X0,X1,X2,X3] :
( addition(X1,addition(X0,addition(X2,X3))) != X3
| leq(addition(addition(X0,X1),X2),X3) ),
inference(paramodulation,[status(thm)],[f98,f238]) ).
fof(f6966,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(addition(X0,X1),X2),X3) ),
inference(paramodulation,[status(thm)],[f34,f238]) ).
fof(f6970,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f92,f238]) ).
fof(f6972,plain,
! [X0,X1,X2] :
( addition(addition(X1,X2),X0) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f33,f238]) ).
fof(f6973,plain,
! [X0,X1,X2] :
( addition(addition(X1,X2),X0) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f33,f238]) ).
fof(f6974,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(addition(X0,X1),X0),X1) ),
inference(paramodulation,[status(thm)],[f36,f238]) ).
fof(f6975,plain,
! [X0,X1,X2] :
( addition(X0,one) != backward_diamond(X1,X2)
| leq(addition(X0,one),backward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1439,f238]) ).
fof(f6976,plain,
! [X0,X1,X2] :
( addition(X0,one) != forward_box(X1,X2)
| leq(addition(X0,one),forward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1432,f238]) ).
fof(f6977,plain,
! [X0,X1,X2] :
( addition(X0,one) != backward_box(X1,X2)
| leq(addition(X0,one),backward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1427,f238]) ).
fof(f6978,plain,
! [X0,X1,X2] :
( addition(X0,one) != forward_diamond(X1,X2)
| leq(addition(X0,one),forward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1420,f238]) ).
fof(f6979,plain,
! [X0,X1] :
( addition(X0,one) != divergence(X1)
| leq(addition(X0,one),divergence(X1)) ),
inference(paramodulation,[status(thm)],[f1423,f238]) ).
fof(f6980,plain,
! [X0,X1] :
( addition(X0,one) != codomain(X1)
| leq(addition(X0,one),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f1412,f238]) ).
fof(f6981,plain,
! [X0,X1] :
( addition(X0,one) != c(X1)
| leq(addition(X0,one),c(X1)) ),
inference(paramodulation,[status(thm)],[f1406,f238]) ).
fof(f6982,plain,
! [X0,X1] :
( addition(X0,one) != antidomain(X1)
| leq(addition(X0,one),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f1315,f238]) ).
fof(f6983,plain,
! [X0,X1] :
( addition(X0,one) != coantidomain(X1)
| leq(addition(X0,one),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f1313,f238]) ).
fof(f6984,plain,
! [X0,X1] :
( addition(X0,one) != domain(X1)
| leq(addition(X0,one),domain(X1)) ),
inference(paramodulation,[status(thm)],[f1311,f238]) ).
fof(f6985,plain,
! [X0,X1] :
( addition(X0,one) != c(X1)
| leq(addition(X0,domain(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f515,f238]) ).
fof(f6986,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)],[f561,f238]) ).
fof(f6987,plain,
! [X0,X1] :
( addition(X0,one) != codomain(X1)
| leq(addition(X0,coantidomain(X1)),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f625,f238]) ).
fof(f6988,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)],[f404,f238]) ).
fof(f6989,plain,
! [X0,X1] :
( addition(X0,one) != domain(X1)
| leq(addition(X0,antidomain(X1)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f504,f238]) ).
fof(f6990,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)],[f199,f238]) ).
fof(f6991,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)],[f214,f238]) ).
fof(f6992,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)],[f165,f238]) ).
fof(f6993,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)],[f206,f238]) ).
fof(f6994,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)],[f196,f238]) ).
fof(f6995,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)],[f148,f238]) ).
fof(f6996,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)],[f41,f238]) ).
fof(f6997,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)],[f40,f238]) ).
fof(f6998,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X2,addition(X1,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(paramodulation,[status(thm)],[f98,f238]) ).
fof(f6999,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(paramodulation,[status(thm)],[f34,f238]) ).
fof(f7001,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(coantidomain(X2),X1)
| leq(addition(X0,X1),multiplication(coantidomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4330,f238]) ).
fof(f7002,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(antidomain(X2),X1)
| leq(addition(X0,X1),multiplication(antidomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4329,f238]) ).
fof(f7003,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(c(X2),X1)
| leq(addition(X0,X1),multiplication(c(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4328,f238]) ).
fof(f7004,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(codomain(X2),X1)
| leq(addition(X0,X1),multiplication(codomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4327,f238]) ).
fof(f7005,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(divergence(X2),X1)
| leq(addition(X0,X1),multiplication(divergence(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4326,f238]) ).
fof(f7006,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,domain(X2))
| leq(addition(X0,X1),multiplication(X1,domain(X2))) ),
inference(paramodulation,[status(thm)],[f2352,f238]) ).
fof(f7007,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,coantidomain(X2))
| leq(addition(X0,X1),multiplication(X1,coantidomain(X2))) ),
inference(paramodulation,[status(thm)],[f2351,f238]) ).
fof(f7008,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,antidomain(X2))
| leq(addition(X0,X1),multiplication(X1,antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f2350,f238]) ).
fof(f7009,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,c(X2))
| leq(addition(X0,X1),multiplication(X1,c(X2))) ),
inference(paramodulation,[status(thm)],[f2349,f238]) ).
fof(f7010,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,codomain(X2))
| leq(addition(X0,X1),multiplication(X1,codomain(X2))) ),
inference(paramodulation,[status(thm)],[f2348,f238]) ).
fof(f7011,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,divergence(X2))
| leq(addition(X0,X1),multiplication(X1,divergence(X2))) ),
inference(paramodulation,[status(thm)],[f2347,f238]) ).
fof(f7012,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)],[f227,f238]) ).
fof(f7013,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)],[f202,f238]) ).
fof(f7014,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)],[f187,f238]) ).
fof(f7015,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)],[f157,f238]) ).
fof(f7016,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)],[f94,f238]) ).
fof(f7017,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X1,X2)
| leq(addition(X0,X1),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f100,f238]) ).
fof(f7018,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)],[f92,f238]) ).
fof(f7019,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)],[f92,f238]) ).
fof(f7021,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f33,f238]) ).
fof(f7022,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f33,f238]) ).
fof(f7023,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f36,f238]) ).
fof(f7024,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)],[f196,f6963]) ).
fof(f7025,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)],[f148,f6964]) ).
fof(f7026,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)],[f98,f6965]) ).
fof(f7027,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)],[f98,f6966]) ).
fof(f7031,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f98,f6972]) ).
fof(f7032,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f98,f6973]) ).
fof(f7033,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,addition(X1,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f98,f6974]) ).
fof(f7034,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f36,f7033]) ).
fof(f7041,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(domain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f98,f4331]) ).
fof(f7042,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(domain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f34,f4331]) ).
fof(f7049,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(paramodulation,[status(thm)],[f63,f4331]) ).
fof(f7051,plain,
! [X0] : codomain(domain(X0)) = addition(codomain(domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f2178,f4331]) ).
fof(f7052,plain,
! [X0,X1] : addition(coantidomain(domain(X0)),X1) = addition(addition(coantidomain(domain(X0)),X1),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f176,f4331]) ).
fof(f7059,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f64,f4331]) ).
fof(f7064,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4331,f176]) ).
fof(f7077,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)],[f4331,f214]) ).
fof(f7078,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)],[f4331,f165]) ).
fof(f7079,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(domain(X2),multiplication(X0,X1)),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4331,f53]) ).
fof(f7080,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(domain(X2),multiplication(X0,X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4331,f51]) ).
fof(f7081,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4331,f98]) ).
fof(f7082,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4331,f34]) ).
fof(f7089,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(domain(X2),X1)
| leq(addition(X0,X1),multiplication(domain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4331,f238]) ).
fof(f7090,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)],[f4331,f237]) ).
fof(f7091,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)],[f4331,f236]) ).
fof(f7095,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f4331,f172]) ).
fof(f7097,plain,
! [X0,X1,X2] : leq(multiplication(domain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4331,f1356]) ).
fof(f7101,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4331,f98]) ).
fof(f7103,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4331,f92]) ).
fof(f7104,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(domain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4331,f92]) ).
fof(f7106,plain,
! [X0,X1] :
( X0 != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4331,f47]) ).
fof(f7107,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4331,f34]) ).
fof(f7117,plain,
! [X0] : codomain(domain(X0)) = addition(domain(X0),codomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f7051]) ).
fof(f7118,plain,
! [X0,X1] : addition(coantidomain(domain(X0)),X1) = addition(X1,addition(coantidomain(domain(X0)),multiplication(domain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f98,f7052]) ).
fof(f7123,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f58,f7064]) ).
fof(f7133,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)],[f196,f7077]) ).
fof(f7134,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)],[f206,f7133]) ).
fof(f7135,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)],[f98,f7134]) ).
fof(f7136,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)],[f148,f7078]) ).
fof(f7137,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)],[f37,f7079]) ).
fof(f7138,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)],[f37,f7137]) ).
fof(f7145,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)],[f37,f7091]) ).
fof(f7146,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)],[f37,f7145]) ).
fof(f7150,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f54,f7095]) ).
fof(f7152,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f7101]) ).
fof(f7154,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(domain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f7104]) ).
fof(f7156,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f227,f251]) ).
fof(f7157,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,addition(X1,one)),star(addition(X1,X0)))) = star(addition(X1,X0)),
inference(paramodulation,[status(thm)],[f98,f7156]) ).
fof(f7158,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,addition(X1,one)),star(addition(X0,X1)))) = star(addition(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f7156]) ).
fof(f7159,plain,
addition(one,multiplication(one,star(zero))) = star(zero),
inference(paramodulation,[status(thm)],[f75,f7156]) ).
fof(f7160,plain,
! [X0] : addition(one,multiplication(addition(one,X0),star(X0))) = star(X0),
inference(paramodulation,[status(thm)],[f33,f7156]) ).
fof(f7161,plain,
! [X0] : addition(one,multiplication(addition(one,X0),star(X0))) = star(X0),
inference(paramodulation,[status(thm)],[f33,f7156]) ).
fof(f7162,plain,
addition(one,multiplication(one,star(one))) = star(one),
inference(paramodulation,[status(thm)],[f36,f7156]) ).
fof(f7163,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(addition(X0,one),star(X0)),X1)),
inference(paramodulation,[status(thm)],[f7156,f202]) ).
fof(f7164,plain,
! [X0,X1] : leq(domain(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7156,f2264]) ).
fof(f7165,plain,
! [X0,X1] : leq(coantidomain(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7156,f2251]) ).
fof(f7166,plain,
! [X0,X1] : leq(antidomain(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7156,f2240]) ).
fof(f7167,plain,
! [X0,X1] : leq(c(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7156,f2136]) ).
fof(f7168,plain,
! [X0,X1] : leq(codomain(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7156,f2122]) ).
fof(f7169,plain,
! [X0,X1] : leq(divergence(X0),star(X1)),
inference(paramodulation,[status(thm)],[f7156,f2110]) ).
fof(f7170,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,multiplication(addition(X1,one),star(X1)))),
inference(paramodulation,[status(thm)],[f7156,f157]) ).
fof(f7171,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)],[f7156,f238]) ).
fof(f7172,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)],[f7156,f237]) ).
fof(f7173,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)],[f7156,f236]) ).
fof(f7174,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)],[f7156,f228]) ).
fof(f7176,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)],[f7156,f181]) ).
fof(f7178,plain,
! [X0,X1] : leq(one,addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f7156,f1357]) ).
fof(f7179,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),star(X0)),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f7156,f1356]) ).
fof(f7180,plain,
! [X0] : leq(multiplication(addition(X0,one),star(X0)),star(X0)),
inference(paramodulation,[status(thm)],[f7156,f1359]) ).
fof(f7181,plain,
! [X0] : leq(one,star(X0)),
inference(paramodulation,[status(thm)],[f7156,f1261]) ).
fof(f7182,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(paramodulation,[status(thm)],[f7156,f100]) ).
fof(f7183,plain,
! [X0,X1] : addition(multiplication(addition(X0,one),star(X0)),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7156,f98]) ).
fof(f7184,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)],[f7156,f94]) ).
fof(f7185,plain,
! [X0,X1] : addition(one,addition(multiplication(addition(X0,one),star(X0)),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f7156,f92]) ).
fof(f7186,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(multiplication(addition(X1,one),star(X1)),addition(X0,one)),
inference(paramodulation,[status(thm)],[f7156,f92]) ).
fof(f7187,plain,
! [X0] :
( star(X0) != one
| leq(multiplication(addition(X0,one),star(X0)),one) ),
inference(paramodulation,[status(thm)],[f7156,f241]) ).
fof(f7188,plain,
! [X0] :
( star(X0) != multiplication(addition(X0,one),star(X0))
| leq(one,multiplication(addition(X0,one),star(X0))) ),
inference(paramodulation,[status(thm)],[f7156,f47]) ).
fof(f7189,plain,
! [X0,X1] : addition(one,addition(multiplication(addition(X0,one),star(X0)),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7156,f34]) ).
fof(f7190,plain,
addition(one,star(zero)) = star(zero),
inference(forward_demodulation,[status(thm)],[f39,f7159]) ).
fof(f7191,plain,
addition(one,star(one)) = star(one),
inference(forward_demodulation,[status(thm)],[f39,f7162]) ).
fof(f7192,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(addition(X0,one),multiplication(star(X0),X1))),
inference(forward_demodulation,[status(thm)],[f37,f7163]) ).
fof(f7193,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)],[f38,f7172]) ).
fof(f7194,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)],[f39,f7173]) ).
fof(f7195,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)],[f37,f7194]) ).
fof(f7196,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)],[f37,f7195]) ).
fof(f7197,plain,
! [X0] : multiplication(star(X0),coantidomain(multiplication(addition(X0,one),star(X0)))) = coantidomain(multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f39,f7174]) ).
fof(f7205,plain,
! [X0] : multiplication(antidomain(multiplication(addition(X0,one),star(X0))),star(X0)) = antidomain(multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f38,f7176]) ).
fof(f7209,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f7156,f7182]) ).
fof(f7210,plain,
! [X0,X1] : addition(one,addition(X0,multiplication(addition(X1,one),star(X1)))) = addition(star(X1),X0),
inference(forward_demodulation,[status(thm)],[f92,f7183]) ).
fof(f7211,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)],[f33,f7184]) ).
fof(f7212,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)],[f227,f7211]) ).
fof(f7213,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)],[f98,f7212]) ).
fof(f7214,plain,
! [X0] : addition(one,multiplication(addition(one,addition(X0,one)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f7156,f7213]) ).
fof(f7215,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(multiplication(addition(X1,one),star(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f7186]) ).
fof(f7217,plain,
! [X0,X1] : addition(domain(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7164,f46]) ).
fof(f7218,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),star(X2)),
inference(paramodulation,[status(thm)],[f64,f7164]) ).
fof(f7223,plain,
! [X0,X1] : addition(coantidomain(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7165,f46]) ).
fof(f7227,plain,
! [X0,X1] : addition(antidomain(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7166,f46]) ).
fof(f7232,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)],[f247,f46]) ).
fof(f7233,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)],[f37,f247]) ).
fof(f7238,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)],[f37,f247]) ).
fof(f7241,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)],[f202,f247]) ).
fof(f7242,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)],[f219,f247]) ).
fof(f7243,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)],[f227,f247]) ).
fof(f7244,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)],[f225,f247]) ).
fof(f7245,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)],[f228,f247]) ).
fof(f7246,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)],[f221,f247]) ).
fof(f7247,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(domain(X0),star(zero)))),star(multiplication(c(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f192,f247]) ).
fof(f7248,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(X0,star(zero)))),star(multiplication(c(X0),X0))),
inference(paramodulation,[status(thm)],[f4088,f247]) ).
fof(f7249,plain,
! [X0] : leq(addition(one,multiplication(coantidomain(X0),multiplication(codomain(X0),star(zero)))),star(multiplication(coantidomain(X0),codomain(X0)))),
inference(paramodulation,[status(thm)],[f190,f247]) ).
fof(f7250,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)],[f63,f247]) ).
fof(f7251,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(X0,star(X0)))),star(multiplication(domain(X0),X0))),
inference(paramodulation,[status(thm)],[f3965,f247]) ).
fof(f7252,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)],[f37,f247]) ).
fof(f7253,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)],[f181,f247]) ).
fof(f7254,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)],[f172,f247]) ).
fof(f7259,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(codomain(X0),star(X0)))),star(multiplication(X0,codomain(X0)))),
inference(paramodulation,[status(thm)],[f2178,f247]) ).
fof(f7260,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)],[f157,f247]) ).
fof(f7261,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)],[f176,f247]) ).
fof(f7262,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)],[f187,f247]) ).
fof(f7263,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)],[f185,f247]) ).
fof(f7265,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)],[f139,f247]) ).
fof(f7269,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)],[f202,f247]) ).
fof(f7270,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)],[f219,f247]) ).
fof(f7271,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)],[f227,f247]) ).
fof(f7272,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)],[f225,f247]) ).
fof(f7273,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)],[f228,f247]) ).
fof(f7274,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)],[f221,f247]) ).
fof(f7275,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(domain(X0),star(multiplication(c(X0),domain(X0)))))),star(zero)),
inference(paramodulation,[status(thm)],[f192,f247]) ).
fof(f7276,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(X0,star(multiplication(c(X0),X0))))),star(zero)),
inference(paramodulation,[status(thm)],[f4088,f247]) ).
fof(f7277,plain,
! [X0] : leq(addition(one,multiplication(coantidomain(X0),multiplication(codomain(X0),star(multiplication(coantidomain(X0),codomain(X0)))))),star(zero)),
inference(paramodulation,[status(thm)],[f190,f247]) ).
fof(f7278,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)],[f63,f247]) ).
fof(f7279,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(X0,star(multiplication(domain(X0),X0))))),star(X0)),
inference(paramodulation,[status(thm)],[f3965,f247]) ).
fof(f7280,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)],[f37,f247]) ).
fof(f7281,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)],[f181,f247]) ).
fof(f7282,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)],[f172,f247]) ).
fof(f7287,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(codomain(X0),star(multiplication(X0,codomain(X0)))))),star(X0)),
inference(paramodulation,[status(thm)],[f2178,f247]) ).
fof(f7288,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)],[f157,f247]) ).
fof(f7289,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)],[f176,f247]) ).
fof(f7290,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)],[f187,f247]) ).
fof(f7291,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)],[f185,f247]) ).
fof(f7293,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)],[f139,f247]) ).
fof(f7297,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)],[f98,f7232]) ).
fof(f7298,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)],[f92,f7297]) ).
fof(f7299,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)],[f37,f7233]) ).
fof(f7300,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)],[f37,f7299]) ).
fof(f7314,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)],[f219,f7242]) ).
fof(f7315,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)],[f225,f7244]) ).
fof(f7316,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)],[f228,f7245]) ).
fof(f7317,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)],[f221,f7246]) ).
fof(f7318,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(domain(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f192,f7247]) ).
fof(f7319,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(X0,star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f4088,f7248]) ).
fof(f7320,plain,
! [X0] : leq(addition(one,multiplication(coantidomain(X0),multiplication(codomain(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f190,f7249]) ).
fof(f7321,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)],[f63,f7250]) ).
fof(f7322,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(X0,star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f3965,f7251]) ).
fof(f7323,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)],[f37,f7252]) ).
fof(f7324,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)],[f37,f7323]) ).
fof(f7325,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)],[f181,f7253]) ).
fof(f7326,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)],[f172,f7254]) ).
fof(f7339,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(codomain(X0),star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f2178,f7259]) ).
fof(f7340,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)],[f176,f7261]) ).
fof(f7341,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)],[f185,f7263]) ).
fof(f7346,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)],[f37,f7265]) ).
fof(f7347,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),star(zero))))),star(zero)),
inference(forward_demodulation,[status(thm)],[f139,f7346]) ).
fof(f7357,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)],[f219,f7270]) ).
fof(f7358,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)],[f225,f7272]) ).
fof(f7359,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)],[f228,f7273]) ).
fof(f7360,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)],[f221,f7274]) ).
fof(f7361,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(domain(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f192,f7275]) ).
fof(f7362,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(X0,star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f4088,f7276]) ).
fof(f7363,plain,
! [X0] : leq(addition(one,multiplication(coantidomain(X0),multiplication(codomain(X0),star(zero)))),star(zero)),
inference(forward_demodulation,[status(thm)],[f190,f7277]) ).
fof(f7364,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)],[f63,f7278]) ).
fof(f7365,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(X0,star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f3965,f7279]) ).
fof(f7366,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)],[f37,f7280]) ).
fof(f7367,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)],[f37,f7366]) ).
fof(f7368,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)],[f181,f7281]) ).
fof(f7369,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)],[f172,f7282]) ).
fof(f7379,plain,
! [X0] : leq(addition(one,multiplication(X0,multiplication(codomain(X0),star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f2178,f7287]) ).
fof(f7380,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)],[f176,f7289]) ).
fof(f7381,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)],[f185,f7291]) ).
fof(f7385,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)],[f37,f7293]) ).
fof(f7386,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),star(zero))))),star(zero)),
inference(forward_demodulation,[status(thm)],[f139,f7385]) ).
fof(f7394,plain,
! [X0,X1] : addition(c(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7167,f46]) ).
fof(f7395,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),star(X2)),
inference(paramodulation,[status(thm)],[f67,f7167]) ).
fof(f7396,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),star(X2)),
inference(paramodulation,[status(thm)],[f66,f7167]) ).
fof(f7401,plain,
! [X0,X1] : addition(codomain(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7168,f46]) ).
fof(f7402,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),star(X2)),
inference(paramodulation,[status(thm)],[f65,f7168]) ).
fof(f7406,plain,
! [X0,X1] : addition(divergence(X0),star(X1)) = star(X1),
inference(resolution,[status(thm)],[f7169,f46]) ).
fof(f7408,plain,
addition(addition(one,star(one)),star(one)) = star(one),
inference(resolution,[status(thm)],[f249,f46]) ).
fof(f7409,plain,
addition(star(one),addition(one,star(one))) = star(one),
inference(forward_demodulation,[status(thm)],[f98,f7408]) ).
fof(f7410,plain,
addition(one,addition(star(one),star(one))) = star(one),
inference(forward_demodulation,[status(thm)],[f92,f7409]) ).
fof(f7411,plain,
addition(one,star(one)) = star(one),
inference(forward_demodulation,[status(thm)],[f36,f7410]) ).
fof(f7412,plain,
! [X0,X1,X2] : addition(forward_diamond(X0,X1),star(X2)) = star(X2),
inference(resolution,[status(thm)],[f7218,f46]) ).
fof(f7420,plain,
! [X0,X1,X2] : addition(backward_box(X0,X1),star(X2)) = star(X2),
inference(resolution,[status(thm)],[f7395,f46]) ).
fof(f7423,plain,
! [X0] : addition(one,multiplication(star(X0),addition(X0,one))) = star(X0),
inference(forward_demodulation,[status(thm)],[f187,f259]) ).
fof(f7424,plain,
! [X0,X1] : addition(one,multiplication(star(addition(X0,X1)),addition(X1,addition(X0,one)))) = star(addition(X0,X1)),
inference(paramodulation,[status(thm)],[f98,f7423]) ).
fof(f7425,plain,
! [X0,X1] : addition(one,multiplication(star(addition(X0,X1)),addition(X0,addition(X1,one)))) = star(addition(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f7423]) ).
fof(f7426,plain,
addition(one,multiplication(star(zero),one)) = star(zero),
inference(paramodulation,[status(thm)],[f75,f7423]) ).
fof(f7427,plain,
! [X0] : addition(one,multiplication(star(X0),addition(one,X0))) = star(X0),
inference(paramodulation,[status(thm)],[f33,f7423]) ).
fof(f7428,plain,
! [X0] : addition(one,multiplication(star(X0),addition(one,X0))) = star(X0),
inference(paramodulation,[status(thm)],[f33,f7423]) ).
fof(f7429,plain,
addition(one,multiplication(star(one),one)) = star(one),
inference(paramodulation,[status(thm)],[f36,f7423]) ).
fof(f7430,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(star(X0),addition(X0,one)),X1)),
inference(paramodulation,[status(thm)],[f7423,f202]) ).
fof(f7437,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,multiplication(star(X1),addition(X1,one)))),
inference(paramodulation,[status(thm)],[f7423,f157]) ).
fof(f7438,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)],[f7423,f238]) ).
fof(f7439,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)],[f7423,f237]) ).
fof(f7440,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)],[f7423,f236]) ).
fof(f7441,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)],[f7423,f228]) ).
fof(f7443,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)],[f7423,f181]) ).
fof(f7446,plain,
! [X0,X1] : leq(multiplication(star(X0),addition(X0,one)),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f7423,f1356]) ).
fof(f7447,plain,
! [X0] : leq(multiplication(star(X0),addition(X0,one)),star(X0)),
inference(paramodulation,[status(thm)],[f7423,f1359]) ).
fof(f7450,plain,
! [X0,X1] : addition(multiplication(star(X0),addition(X0,one)),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7423,f98]) ).
fof(f7451,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)],[f7423,f94]) ).
fof(f7452,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),addition(X0,one)),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f7423,f92]) ).
fof(f7453,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(multiplication(star(X1),addition(X1,one)),addition(X0,one)),
inference(paramodulation,[status(thm)],[f7423,f92]) ).
fof(f7454,plain,
! [X0] :
( star(X0) != one
| leq(multiplication(star(X0),addition(X0,one)),one) ),
inference(paramodulation,[status(thm)],[f7423,f241]) ).
fof(f7455,plain,
! [X0] :
( star(X0) != multiplication(star(X0),addition(X0,one))
| leq(one,multiplication(star(X0),addition(X0,one))) ),
inference(paramodulation,[status(thm)],[f7423,f47]) ).
fof(f7456,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),addition(X0,one)),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7423,f34]) ).
fof(f7457,plain,
addition(one,star(zero)) = star(zero),
inference(forward_demodulation,[status(thm)],[f38,f7426]) ).
fof(f7458,plain,
addition(one,star(one)) = star(one),
inference(forward_demodulation,[status(thm)],[f38,f7429]) ).
fof(f7459,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),multiplication(addition(X0,one),X1))),
inference(forward_demodulation,[status(thm)],[f37,f7430]) ).
fof(f7460,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)],[f38,f7439]) ).
fof(f7461,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)],[f39,f7440]) ).
fof(f7462,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)],[f37,f7461]) ).
fof(f7463,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)],[f37,f7462]) ).
fof(f7464,plain,
! [X0] : multiplication(star(X0),coantidomain(multiplication(star(X0),addition(X0,one)))) = coantidomain(multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f39,f7441]) ).
fof(f7471,plain,
! [X0] : multiplication(antidomain(multiplication(star(X0),addition(X0,one))),star(X0)) = antidomain(multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f38,f7443]) ).
fof(f7476,plain,
! [X0,X1] : addition(one,addition(X0,multiplication(star(X1),addition(X1,one)))) = addition(star(X1),X0),
inference(forward_demodulation,[status(thm)],[f92,f7450]) ).
fof(f7477,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)],[f33,f7451]) ).
fof(f7478,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)],[f187,f7477]) ).
fof(f7479,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)],[f98,f7478]) ).
fof(f7480,plain,
! [X0] : addition(one,multiplication(star(X0),addition(one,addition(X0,one)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f7423,f7479]) ).
fof(f7481,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(multiplication(star(X1),addition(X1,one)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f7453]) ).
fof(f7482,plain,
! [X0,X1,X2] : addition(forward_box(X0,X1),star(X2)) = star(X2),
inference(resolution,[status(thm)],[f7396,f46]) ).
fof(f7486,plain,
! [X0,X1,X2] : addition(backward_diamond(X0,X1),star(X2)) = star(X2),
inference(resolution,[status(thm)],[f7402,f46]) ).
fof(f7492,plain,
! [X0] : addition(divergence(X0),codomain(divergence(X0))) = codomain(divergence(X0)),
inference(resolution,[status(thm)],[f5767,f46]) ).
fof(f7499,plain,
! [X0] : addition(codomain(X0),codomain(codomain(X0))) = codomain(codomain(X0)),
inference(resolution,[status(thm)],[f6184,f46]) ).
fof(f7500,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(codomain(multiplication(codomain(X1),X0)))),
inference(paramodulation,[status(thm)],[f65,f6184]) ).
fof(f7502,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(codomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f188,f6184]) ).
fof(f7504,plain,
! [X0,X1] : leq(codomain(multiplication(codomain(X0),X1)),codomain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f65,f6184]) ).
fof(f7506,plain,
! [X0] : leq(codomain(coantidomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f188,f6184]) ).
fof(f7508,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f65,f7500]) ).
fof(f7511,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f188,f7502]) ).
fof(f7512,plain,
! [X0] : leq(coantidomain(codomain(X0)),coantidomain(codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f188,f7511]) ).
fof(f7515,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f65,f7504]) ).
fof(f7518,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f188,f7506]) ).
fof(f7519,plain,
! [X0] : leq(coantidomain(codomain(X0)),coantidomain(codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f188,f7518]) ).
fof(f7522,plain,
! [X0,X1,X2] : addition(multiplication(backward_diamond(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6192,f46]) ).
fof(f7523,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f2178,f6192]) ).
fof(f7524,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),addition(coantidomain(backward_diamond(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f176,f6192]) ).
fof(f7525,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),addition(X2,coantidomain(backward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f185,f6192]) ).
fof(f7536,plain,
! [X0,X1,X2] : addition(X0,multiplication(backward_diamond(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f33,f7522]) ).
fof(f7540,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X1,X0)),X0)
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(paramodulation,[status(thm)],[f202,f285]) ).
fof(f7541,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f219,f285]) ).
fof(f7542,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(one,X0)),X0)
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(paramodulation,[status(thm)],[f227,f285]) ).
fof(f7545,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,coantidomain(X1))),coantidomain(X1))
| ~ leq(multiplication(X0,coantidomain(X1)),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f221,f285]) ).
fof(f7546,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)],[f2178,f285]) ).
fof(f7547,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)],[f176,f285]) ).
fof(f7548,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)],[f185,f285]) ).
fof(f7549,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)],[f146,f285]) ).
fof(f7550,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)],[f139,f285]) ).
fof(f7551,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)],[f58,f285]) ).
fof(f7552,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,zero)),zero)
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f42,f285]) ).
fof(f7553,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,one)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f38,f285]) ).
fof(f7554,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)],[f7423,f285]) ).
fof(f7555,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)],[f7156,f285]) ).
fof(f7556,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(backward_diamond(X1,X2),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1439,f285]) ).
fof(f7557,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(forward_box(X1,X2),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1432,f285]) ).
fof(f7558,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(backward_box(X1,X2),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1427,f285]) ).
fof(f7559,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(forward_diamond(X1,X2),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1420,f285]) ).
fof(f7560,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(divergence(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1423,f285]) ).
fof(f7561,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(codomain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1412,f285]) ).
fof(f7562,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(c(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1406,f285]) ).
fof(f7563,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(antidomain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1315,f285]) ).
fof(f7564,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(coantidomain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1313,f285]) ).
fof(f7565,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(domain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f1311,f285]) ).
fof(f7566,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),multiplication(c(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f515,f285]) ).
fof(f7567,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)],[f561,f285]) ).
fof(f7568,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),multiplication(codomain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f625,f285]) ).
fof(f7569,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)],[f404,f285]) ).
fof(f7570,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),multiplication(domain(X1),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f504,f285]) ).
fof(f7571,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)],[f199,f285]) ).
fof(f7572,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)],[f214,f285]) ).
fof(f7573,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)],[f165,f285]) ).
fof(f7574,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)],[f206,f285]) ).
fof(f7575,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)],[f196,f285]) ).
fof(f7576,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)],[f148,f285]) ).
fof(f7577,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)],[f41,f285]) ).
fof(f7578,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)],[f40,f285]) ).
fof(f7579,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)],[f98,f285]) ).
fof(f7580,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)],[f34,f285]) ).
fof(f7581,plain,
! [X0,X1] :
( leq(multiplication(star(zero),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f75,f285]) ).
fof(f7582,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(domain(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4331,f285]) ).
fof(f7583,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(coantidomain(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4330,f285]) ).
fof(f7584,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(antidomain(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4329,f285]) ).
fof(f7585,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(c(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4328,f285]) ).
fof(f7586,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(codomain(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4327,f285]) ).
fof(f7587,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(divergence(X2),X0),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4326,f285]) ).
fof(f7588,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,domain(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2352,f285]) ).
fof(f7589,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,coantidomain(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2351,f285]) ).
fof(f7590,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,antidomain(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2350,f285]) ).
fof(f7591,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,c(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2349,f285]) ).
fof(f7592,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,codomain(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2348,f285]) ).
fof(f7593,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,divergence(X2)),X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2347,f285]) ).
fof(f7594,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)],[f227,f285]) ).
fof(f7595,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)],[f202,f285]) ).
fof(f7596,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)],[f187,f285]) ).
fof(f7597,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)],[f157,f285]) ).
fof(f7598,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)],[f94,f285]) ).
fof(f7599,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)],[f100,f285]) ).
fof(f7600,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)],[f92,f285]) ).
fof(f7601,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)],[f92,f285]) ).
fof(f7603,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f33,f285]) ).
fof(f7604,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f33,f285]) ).
fof(f7605,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f36,f285]) ).
fof(f7606,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),X0)
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7542]) ).
fof(f7611,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)],[f7549,f235]) ).
fof(f7612,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)],[f7550,f235]) ).
fof(f7613,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(X1,coantidomain(addition(X0,X1)))),coantidomain(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f7551,f235]) ).
fof(f7614,definition,
( sQ11_spl
<=> leq(zero,zero) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f7616,plain,
( sQ11_spl
| ~ leq(zero,zero) ),
inference(component_clause,[status(thm)],[f7614]) ).
fof(f7617,definition,
! [X0,X1] :
( sQ12_spl
<=> leq(multiplication(star(X0),multiplication(X1,zero)),zero) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f7620,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7552,f7614,f7617]) ).
fof(f7621,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(forward_demodulation,[status(thm)],[f38,f7553]) ).
fof(f7622,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)],[f37,f7554]) ).
fof(f7623,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)],[f37,f7555]) ).
fof(f7624,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(backward_diamond(X1,X2),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7556]) ).
fof(f7625,plain,
! [X0,X1,X2] : leq(multiplication(star(one),multiplication(backward_diamond(X0,X1),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7624,f234]) ).
fof(f7626,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(forward_box(X1,X2),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7557]) ).
fof(f7627,plain,
! [X0,X1,X2] : leq(multiplication(star(one),multiplication(forward_box(X0,X1),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7626,f234]) ).
fof(f7628,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(backward_box(X1,X2),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7558]) ).
fof(f7629,plain,
! [X0,X1,X2] : leq(multiplication(star(one),multiplication(backward_box(X0,X1),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7628,f234]) ).
fof(f7630,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),multiplication(forward_diamond(X1,X2),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7559]) ).
fof(f7631,plain,
! [X0,X1,X2] : leq(multiplication(star(one),multiplication(forward_diamond(X0,X1),X2)),X2),
inference(forward_subsumption_resolution,[status(thm)],[f7630,f234]) ).
fof(f7632,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(divergence(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7560]) ).
fof(f7633,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(divergence(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7632,f234]) ).
fof(f7634,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(codomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7561]) ).
fof(f7635,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(codomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7634,f234]) ).
fof(f7636,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(c(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7562]) ).
fof(f7637,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(c(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7636,f234]) ).
fof(f7638,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(antidomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7563]) ).
fof(f7639,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(antidomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7638,f234]) ).
fof(f7640,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(coantidomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7564]) ).
fof(f7641,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(coantidomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7640,f234]) ).
fof(f7642,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(domain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7565]) ).
fof(f7643,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(domain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7642,f234]) ).
fof(f7644,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),multiplication(c(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7566]) ).
fof(f7645,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),multiplication(c(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7644,f234]) ).
fof(f7646,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)],[f7567,f6815]) ).
fof(f7647,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),multiplication(codomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7568]) ).
fof(f7648,plain,
! [X0,X1] : leq(multiplication(star(coantidomain(X0)),multiplication(codomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7647,f234]) ).
fof(f7649,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)],[f7569,f6335]) ).
fof(f7650,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),multiplication(domain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7570]) ).
fof(f7651,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(domain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7650,f234]) ).
fof(f7652,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)],[f37,f7571]) ).
fof(f7653,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)],[f37,f7652]) ).
fof(f7654,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)],[f37,f7574]) ).
fof(f7655,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)],[f37,f7654]) ).
fof(f7656,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)],[f37,f7655]) ).
fof(f7657,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)],[f37,f7575]) ).
fof(f7658,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)],[f37,f7657]) ).
fof(f7659,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)],[f37,f7576]) ).
fof(f7660,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)],[f37,f7659]) ).
fof(f7661,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)],[f37,f7577]) ).
fof(f7662,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)],[f37,f7661]) ).
fof(f7663,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)],[f37,f7578]) ).
fof(f7664,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)],[f37,f7663]) ).
fof(f7665,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)],[f37,f7582]) ).
fof(f7666,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)],[f37,f7583]) ).
fof(f7667,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)],[f37,f7584]) ).
fof(f7668,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)],[f37,f7585]) ).
fof(f7669,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)],[f37,f7586]) ).
fof(f7670,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)],[f37,f7587]) ).
fof(f7671,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)],[f37,f7588]) ).
fof(f7672,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)],[f37,f7589]) ).
fof(f7673,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)],[f37,f7590]) ).
fof(f7674,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)],[f37,f7591]) ).
fof(f7675,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)],[f37,f7592]) ).
fof(f7676,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)],[f37,f7593]) ).
fof(f7677,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)],[f37,f7594]) ).
fof(f7678,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)],[f37,f7677]) ).
fof(f7679,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)],[f37,f7595]) ).
fof(f7680,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)],[f37,f7679]) ).
fof(f7681,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)],[f37,f7596]) ).
fof(f7682,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)],[f37,f7681]) ).
fof(f7683,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)],[f37,f7597]) ).
fof(f7684,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)],[f37,f7683]) ).
fof(f7687,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7616,f235]) ).
fof(f7688,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f7687]) ).
fof(f7691,plain,
! [X0] : addition(c(X0),codomain(c(X0))) = codomain(c(X0)),
inference(resolution,[status(thm)],[f6318,f46]) ).
fof(f7692,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(c(backward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f67,f6318]) ).
fof(f7693,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(c(forward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f66,f6318]) ).
fof(f7695,plain,
! [X0] : leq(antidomain(c(X0)),codomain(c(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f493,f6318]) ).
fof(f7696,plain,
! [X0] : leq(domain(c(X0)),codomain(c(domain(X0)))),
inference(paramodulation,[status(thm)],[f317,f6318]) ).
fof(f7698,plain,
! [X0,X1] : leq(c(backward_diamond(X0,c(X1))),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f67,f6318]) ).
fof(f7699,plain,
! [X0,X1] : leq(c(forward_diamond(X0,c(X1))),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f66,f6318]) ).
fof(f7701,plain,
! [X0] : leq(c(antidomain(X0)),codomain(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f493,f6318]) ).
fof(f7702,plain,
! [X0] : leq(c(domain(X0)),codomain(domain(c(X0)))),
inference(paramodulation,[status(thm)],[f317,f6318]) ).
fof(f7704,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f67,f7692]) ).
fof(f7705,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f66,f7693]) ).
fof(f7708,plain,
! [X0] : leq(antidomain(c(X0)),codomain(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f493,f7695]) ).
fof(f7709,plain,
! [X0] : leq(domain(c(X0)),codomain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f317,f7696]) ).
fof(f7712,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f67,f7698]) ).
fof(f7713,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f66,f7699]) ).
fof(f7716,plain,
! [X0] : leq(antidomain(c(X0)),codomain(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f493,f7701]) ).
fof(f7717,plain,
! [X0] : leq(domain(c(X0)),codomain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f317,f7702]) ).
fof(f7720,plain,
! [X0,X1,X2] : addition(multiplication(backward_box(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6326,f46]) ).
fof(f7721,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f2178,f6326]) ).
fof(f7722,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),addition(coantidomain(backward_box(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f176,f6326]) ).
fof(f7723,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),addition(X2,coantidomain(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f185,f6326]) ).
fof(f7731,plain,
! [X0,X1,X2] : addition(X0,multiplication(backward_box(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f33,f7720]) ).
fof(f7734,plain,
! [X0,X1,X2] : addition(multiplication(forward_box(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6327,f46]) ).
fof(f7735,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f2178,f6327]) ).
fof(f7736,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),addition(coantidomain(forward_box(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f176,f6327]) ).
fof(f7737,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),addition(X2,coantidomain(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f185,f6327]) ).
fof(f7746,plain,
! [X0,X1,X2] : addition(X0,multiplication(forward_box(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f33,f7734]) ).
fof(f7750,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)],[f219,f286]) ).
fof(f7751,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)],[f225,f286]) ).
fof(f7752,plain,
! [X0,X1] :
( leq(multiplication(star(c(addition(X0,X1))),multiplication(c(addition(X0,X1)),X1)),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f4088,f286]) ).
fof(f7753,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)],[f3965,f286]) ).
fof(f7754,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)],[f37,f286]) ).
fof(f7756,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X1)),X0)
| ~ leq(multiplication(antidomain(X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f172,f286]) ).
fof(f7757,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(addition(X0,X1))),multiplication(antidomain(addition(X0,X1)),X1)),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f54,f286]) ).
fof(f7759,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(one,X1)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f39,f286]) ).
fof(f7760,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),one)
| ~ leq(addition(X0,multiplication(X0,X1)),one) ),
inference(paramodulation,[status(thm)],[f157,f286]) ).
fof(f7761,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),coantidomain(X0))
| ~ leq(multiplication(X0,X1),coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f176,f286]) ).
fof(f7762,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,one)),X1)
| ~ leq(addition(X0,multiplication(X0,X1)),X1) ),
inference(paramodulation,[status(thm)],[f187,f286]) ).
fof(f7764,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)],[f7423,f286]) ).
fof(f7765,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)],[f7156,f286]) ).
fof(f7766,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1439,f286]) ).
fof(f7767,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_box(X1,X2))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1432,f286]) ).
fof(f7768,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_box(X1,X2))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1427,f286]) ).
fof(f7769,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1420,f286]) ).
fof(f7770,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,divergence(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1423,f286]) ).
fof(f7771,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1412,f286]) ).
fof(f7772,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1406,f286]) ).
fof(f7773,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1315,f286]) ).
fof(f7774,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,coantidomain(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1313,f286]) ).
fof(f7775,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),one)
| ~ leq(multiplication(X0,one),one) ),
inference(paramodulation,[status(thm)],[f1311,f286]) ).
fof(f7776,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),domain(X1))
| ~ leq(multiplication(X0,one),domain(X1)) ),
inference(paramodulation,[status(thm)],[f515,f286]) ).
fof(f7777,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)],[f561,f286]) ).
fof(f7778,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),coantidomain(X1))
| ~ leq(multiplication(X0,one),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f625,f286]) ).
fof(f7779,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)],[f404,f286]) ).
fof(f7780,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),antidomain(X1))
| ~ leq(multiplication(X0,one),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f504,f286]) ).
fof(f7781,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)],[f199,f286]) ).
fof(f7782,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)],[f214,f286]) ).
fof(f7783,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)],[f165,f286]) ).
fof(f7784,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)],[f206,f286]) ).
fof(f7785,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)],[f196,f286]) ).
fof(f7786,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)],[f148,f286]) ).
fof(f7787,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)],[f41,f286]) ).
fof(f7788,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)],[f40,f286]) ).
fof(f7789,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)],[f98,f286]) ).
fof(f7790,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)],[f34,f286]) ).
fof(f7791,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),zero)
| ~ leq(multiplication(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f75,f286]) ).
fof(f7792,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(domain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4331,f286]) ).
fof(f7793,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(coantidomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4330,f286]) ).
fof(f7794,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(antidomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4329,f286]) ).
fof(f7795,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(c(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4328,f286]) ).
fof(f7796,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(codomain(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4327,f286]) ).
fof(f7797,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(divergence(X2),X1))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f4326,f286]) ).
fof(f7798,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,domain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2352,f286]) ).
fof(f7799,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,coantidomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2351,f286]) ).
fof(f7800,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,antidomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2350,f286]) ).
fof(f7801,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,c(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2349,f286]) ).
fof(f7802,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,codomain(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2348,f286]) ).
fof(f7803,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,divergence(X2)))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2347,f286]) ).
fof(f7804,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)],[f227,f286]) ).
fof(f7805,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)],[f202,f286]) ).
fof(f7806,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)],[f187,f286]) ).
fof(f7807,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)],[f157,f286]) ).
fof(f7808,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)],[f94,f286]) ).
fof(f7809,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)],[f100,f286]) ).
fof(f7810,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)],[f92,f286]) ).
fof(f7811,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)],[f92,f286]) ).
fof(f7813,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f33,f286]) ).
fof(f7814,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f33,f286]) ).
fof(f7815,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f36,f286]) ).
fof(f7816,plain,
! [X0,X1] : leq(multiplication(star(c(addition(X0,X1))),multiplication(c(addition(X0,X1)),X1)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f7752,f235]) ).
fof(f7817,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)],[f37,f7754]) ).
fof(f7820,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,X1))),multiplication(antidomain(addition(X0,X1)),X1)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f7757,f235]) ).
fof(f7822,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f7759]) ).
fof(f7823,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),X1)
| ~ leq(addition(X0,multiplication(X0,X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f38,f7762]) ).
fof(f7826,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7766]) ).
fof(f7827,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_box(X1,X2))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7767]) ).
fof(f7828,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_box(X1,X2))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7768]) ).
fof(f7829,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7769]) ).
fof(f7830,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,divergence(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7770]) ).
fof(f7831,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7771]) ).
fof(f7832,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7772]) ).
fof(f7833,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7773]) ).
fof(f7834,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,coantidomain(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7774]) ).
fof(f7835,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f7775]) ).
fof(f7836,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f38,f7776]) ).
fof(f7837,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f38,f7778]) ).
fof(f7838,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f38,f7780]) ).
fof(f7841,plain,
! [X0] : addition(antidomain(X0),codomain(antidomain(X0))) = codomain(antidomain(X0)),
inference(resolution,[status(thm)],[f6459,f46]) ).
fof(f7862,plain,
! [X0] : addition(domain(X0),codomain(domain(X0))) = codomain(domain(X0)),
inference(resolution,[status(thm)],[f6659,f46]) ).
fof(f7863,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(domain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f64,f6659]) ).
fof(f7868,plain,
! [X0,X1] : leq(domain(multiplication(X0,domain(X1))),codomain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f64,f6659]) ).
fof(f7873,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f64,f7863]) ).
fof(f7880,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f64,f7868]) ).
fof(f7887,plain,
! [X0,X1,X2] : addition(multiplication(forward_diamond(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6667,f46]) ).
fof(f7888,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f2178,f6667]) ).
fof(f7889,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),addition(coantidomain(forward_diamond(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f176,f6667]) ).
fof(f7890,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),addition(X2,coantidomain(forward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f185,f6667]) ).
fof(f7903,plain,
! [X0,X1,X2] : addition(X0,multiplication(forward_diamond(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f33,f7887]) ).
fof(f7909,plain,
! [X0] :
( leq(multiplication(star(star(X0)),one),addition(X0,one))
| ~ leq(star(X0),addition(X0,one)) ),
inference(paramodulation,[status(thm)],[f7423,f288]) ).
fof(f7910,plain,
! [X0] :
( leq(multiplication(star(addition(X0,one)),one),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f7156,f288]) ).
fof(f7911,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)],[f199,f288]) ).
fof(f7912,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)],[f206,f288]) ).
fof(f7915,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f41,f288]) ).
fof(f7916,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f40,f288]) ).
fof(f7917,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)],[f98,f288]) ).
fof(f7918,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)],[f34,f288]) ).
fof(f7920,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4331,f288]) ).
fof(f7921,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4330,f288]) ).
fof(f7922,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4329,f288]) ).
fof(f7923,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4328,f288]) ).
fof(f7924,plain,
! [X0,X1] :
( leq(multiplication(star(codomain(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4327,f288]) ).
fof(f7925,plain,
! [X0,X1] :
( leq(multiplication(star(divergence(X1)),X0),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4326,f288]) ).
fof(f7926,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(paramodulation,[status(thm)],[f2352,f288]) ).
fof(f7927,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f2351,f288]) ).
fof(f7928,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f2350,f288]) ).
fof(f7929,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),c(X1))
| ~ leq(X0,c(X1)) ),
inference(paramodulation,[status(thm)],[f2349,f288]) ).
fof(f7930,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(paramodulation,[status(thm)],[f2348,f288]) ).
fof(f7931,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),divergence(X1))
| ~ leq(X0,divergence(X1)) ),
inference(paramodulation,[status(thm)],[f2347,f288]) ).
fof(f7932,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),X1)
| ~ leq(multiplication(addition(X0,one),X1),X1) ),
inference(paramodulation,[status(thm)],[f227,f288]) ).
fof(f7933,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),X1)
| ~ leq(multiplication(addition(one,X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f202,f288]) ).
fof(f7934,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),X1)
| ~ leq(multiplication(X0,addition(X1,one)),X1) ),
inference(paramodulation,[status(thm)],[f187,f288]) ).
fof(f7935,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),X1)
| ~ leq(multiplication(X0,addition(one,X1)),X1) ),
inference(paramodulation,[status(thm)],[f157,f288]) ).
fof(f7938,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f36,f288]) ).
fof(f7939,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)],[f202,f288]) ).
fof(f7940,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(antidomain(X2),X1)),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f219,f288]) ).
fof(f7941,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)],[f227,f288]) ).
fof(f7942,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,antidomain(X2))),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f225,f288]) ).
fof(f7943,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)],[f228,f288]) ).
fof(f7944,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)],[f221,f288]) ).
fof(f7945,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),domain(X1))
| ~ leq(addition(X0,zero),domain(X1)) ),
inference(paramodulation,[status(thm)],[f192,f288]) ).
fof(f7946,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f4088,f288]) ).
fof(f7947,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(addition(X0,zero),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f190,f288]) ).
fof(f7948,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)],[f63,f288]) ).
fof(f7949,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f3965,f288]) ).
fof(f7950,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)],[f37,f288]) ).
fof(f7951,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)],[f181,f288]) ).
fof(f7952,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)],[f172,f288]) ).
fof(f7953,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),multiplication(X1,X2))
| ~ leq(addition(X0,zero),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f131,f288]) ).
fof(f7954,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f54,f288]) ).
fof(f7955,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f43,f288]) ).
fof(f7956,plain,
! [X0,X1] :
( leq(multiplication(star(one),X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f39,f288]) ).
fof(f7957,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),codomain(X1))
| ~ leq(addition(X0,X1),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f2178,f288]) ).
fof(f7958,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)],[f157,f288]) ).
fof(f7959,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)],[f176,f288]) ).
fof(f7960,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)],[f187,f288]) ).
fof(f7961,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)],[f185,f288]) ).
fof(f7962,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)],[f146,f288]) ).
fof(f7963,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)],[f139,f288]) ).
fof(f7964,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),coantidomain(X1))
| ~ leq(addition(X0,zero),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f58,f288]) ).
fof(f7965,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(addition(X0,zero),zero) ),
inference(paramodulation,[status(thm)],[f42,f288]) ).
fof(f7966,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f38,f288]) ).
fof(f7968,plain,
! [X0] :
( leq(star(star(X0)),addition(X0,one))
| ~ leq(star(X0),addition(X0,one)) ),
inference(forward_demodulation,[status(thm)],[f38,f7909]) ).
fof(f7969,plain,
! [X0] :
( leq(star(addition(X0,one)),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f38,f7910]) ).
fof(f7970,plain,
! [X0] : leq(star(addition(X0,one)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f7969,f234]) ).
fof(f7972,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7920,f234]) ).
fof(f7973,plain,
! [X0,X1] : leq(multiplication(star(coantidomain(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7921,f234]) ).
fof(f7974,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7922,f234]) ).
fof(f7975,plain,
! [X0,X1] : leq(multiplication(star(c(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7923,f234]) ).
fof(f7976,plain,
! [X0,X1] : leq(multiplication(star(codomain(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7924,f234]) ).
fof(f7977,plain,
! [X0,X1] : leq(multiplication(star(divergence(X0)),X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f7925,f234]) ).
fof(f7978,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f7945]) ).
fof(f7979,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f35,f7946]) ).
fof(f7980,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f7947]) ).
fof(f7981,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(X1)),X0),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f35,f7953]) ).
fof(f7982,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f35,f7954]) ).
fof(f7983,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f35,f7955]) ).
fof(f7984,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),multiplication(coantidomain(X1),X2))
| ~ leq(X0,multiplication(coantidomain(X1),X2)) ),
inference(forward_demodulation,[status(thm)],[f35,f7962]) ).
fof(f7985,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)],[f35,f7963]) ).
fof(f7986,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f7964]) ).
fof(f7987,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f35,f7965]) ).
fof(f7988,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(resolution,[status(thm)],[f6955,f46]) ).
fof(f7992,plain,
! [X0,X1] : leq(coantidomain(multiplication(codomain(X0),X1)),coantidomain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f65,f6955]) ).
fof(f8008,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(X0,star(X1)),
inference(resolution,[status(thm)],[f7178,f46]) ).
fof(f8009,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f98,f7178]) ).
fof(f8010,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f34,f7178]) ).
fof(f8012,plain,
! [X0,X1] : leq(one,addition(star(X0),X1)),
inference(paramodulation,[status(thm)],[f33,f7178]) ).
fof(f8017,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f7209,f202]) ).
fof(f8024,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f7209,f157]) ).
fof(f8026,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,star(X1))),one)
| ~ leq(multiplication(X0,star(X1)),one) ),
inference(paramodulation,[status(thm)],[f7209,f286]) ).
fof(f8027,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(star(X0),X1)),X1)
| ~ leq(multiplication(star(X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f7209,f285]) ).
fof(f8028,plain,
! [X0,X1] :
( addition(X0,star(X1)) != star(X1)
| leq(addition(X0,one),star(X1)) ),
inference(paramodulation,[status(thm)],[f7209,f238]) ).
fof(f8029,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,star(X1))
| leq(multiplication(X0,one),multiplication(X0,star(X1))) ),
inference(paramodulation,[status(thm)],[f7209,f237]) ).
fof(f8030,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(star(X1),X0)
| leq(multiplication(one,X0),multiplication(star(X1),X0)) ),
inference(paramodulation,[status(thm)],[f7209,f236]) ).
fof(f8031,plain,
! [X0] : multiplication(star(X0),coantidomain(star(X0))) = multiplication(one,coantidomain(star(X0))),
inference(paramodulation,[status(thm)],[f7209,f228]) ).
fof(f8033,plain,
! [X0] : multiplication(antidomain(star(X0)),star(X0)) = multiplication(antidomain(star(X0)),one),
inference(paramodulation,[status(thm)],[f7209,f181]) ).
fof(f8040,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7209,f98]) ).
fof(f8042,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f7209,f92]) ).
fof(f8043,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(star(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f7209,f92]) ).
fof(f8044,plain,
! [X0] :
( star(X0) != one
| leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7209,f241]) ).
fof(f8046,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f7209,f34]) ).
fof(f8047,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,star(X1))
| leq(X0,multiplication(X0,star(X1))) ),
inference(forward_demodulation,[status(thm)],[f38,f8029]) ).
fof(f8048,plain,
! [X0,X1] : leq(X0,multiplication(X0,star(X1))),
inference(trivial_equality_resolution,[status(thm)],[f8047]) ).
fof(f8049,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(star(X1),X0)
| leq(X0,multiplication(star(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f8030]) ).
fof(f8050,plain,
! [X0,X1] : leq(X0,multiplication(star(X1),X0)),
inference(trivial_equality_resolution,[status(thm)],[f8049]) ).
fof(f8051,plain,
! [X0] : zero = multiplication(one,coantidomain(star(X0))),
inference(forward_demodulation,[status(thm)],[f58,f8031]) ).
fof(f8052,plain,
! [X0] : zero = coantidomain(star(X0)),
inference(forward_demodulation,[status(thm)],[f39,f8051]) ).
fof(f8053,plain,
! [X0] : zero = multiplication(antidomain(star(X0)),one),
inference(forward_demodulation,[status(thm)],[f54,f8033]) ).
fof(f8054,plain,
! [X0] : zero = antidomain(star(X0)),
inference(forward_demodulation,[status(thm)],[f38,f8053]) ).
fof(f8055,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(star(X1),X0),
inference(forward_demodulation,[status(thm)],[f92,f8040]) ).
fof(f8056,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(star(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f8043]) ).
fof(f8076,plain,
! [X0] : addition(zero,codomain(star(X0))) = one,
inference(paramodulation,[status(thm)],[f8052,f625]) ).
fof(f8095,plain,
! [X0] : codomain(star(X0)) = one,
inference(forward_demodulation,[status(thm)],[f75,f8076]) ).
fof(f8118,plain,
! [X0,X1] : domain_difference(X0,star(X1)) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f8054,f63]) ).
fof(f8119,plain,
! [X0] : addition(zero,domain(star(X0))) = one,
inference(paramodulation,[status(thm)],[f8054,f504]) ).
fof(f8121,plain,
! [X0] : domain(zero) = c(star(X0)),
inference(paramodulation,[status(thm)],[f8054,f316]) ).
fof(f8138,plain,
! [X0,X1] : domain_difference(X0,star(X1)) = zero,
inference(forward_demodulation,[status(thm)],[f42,f8118]) ).
fof(f8139,plain,
! [X0] : domain(star(X0)) = one,
inference(forward_demodulation,[status(thm)],[f75,f8119]) ).
fof(f8141,plain,
! [X0] : zero = c(star(X0)),
inference(forward_demodulation,[status(thm)],[f553,f8121]) ).
fof(f8159,plain,
! [X0,X1] : backward_diamond(X0,star(X1)) = codomain(multiplication(one,X0)),
inference(paramodulation,[status(thm)],[f8095,f65]) ).
fof(f8161,plain,
! [X0,X1] : addition(coantidomain(multiplication(star(X0),X1)),coantidomain(multiplication(one,X1))) = coantidomain(multiplication(codomain(star(X0)),X1)),
inference(paramodulation,[status(thm)],[f8095,f561]) ).
fof(f8178,plain,
! [X0,X1] : backward_diamond(X0,star(X1)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f39,f8159]) ).
fof(f8180,plain,
! [X0,X1] : addition(coantidomain(multiplication(one,X0)),coantidomain(multiplication(star(X1),X0))) = coantidomain(multiplication(codomain(star(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f33,f8161]) ).
fof(f8181,plain,
! [X0,X1] : addition(coantidomain(X0),coantidomain(multiplication(star(X1),X0))) = coantidomain(multiplication(codomain(star(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f39,f8180]) ).
fof(f8182,plain,
! [X0,X1] : addition(coantidomain(X0),coantidomain(multiplication(star(X1),X0))) = coantidomain(multiplication(one,X0)),
inference(forward_demodulation,[status(thm)],[f8095,f8181]) ).
fof(f8183,plain,
! [X0,X1] : addition(coantidomain(X0),coantidomain(multiplication(star(X1),X0))) = coantidomain(X0),
inference(forward_demodulation,[status(thm)],[f39,f8182]) ).
fof(f8190,plain,
! [X0] : leq(one,antidomain(c(star(X0)))),
inference(paramodulation,[status(thm)],[f8139,f4071]) ).
fof(f8200,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)],[f8139,f70]) ).
fof(f8201,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)],[f8139,f70]) ).
fof(f8202,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)],[f8139,f70]) ).
fof(f8203,plain,
! [X0,X1] : forward_diamond(X0,star(X1)) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f8139,f64]) ).
fof(f8204,plain,
! [X0,X1] : domain_difference(star(X0),X1) = multiplication(one,antidomain(X1)),
inference(paramodulation,[status(thm)],[f8139,f63]) ).
fof(f8208,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,star(X1))),antidomain(multiplication(X0,one))) = antidomain(multiplication(X0,domain(star(X1)))),
inference(paramodulation,[status(thm)],[f8139,f404]) ).
fof(f8219,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)],[f92,f8200]) ).
fof(f8220,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)],[f8139,f8219]) ).
fof(f8221,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)],[f33,f8220]) ).
fof(f8222,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)],[f1420,f8221]) ).
fof(f8223,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)],[f8139,f8222]) ).
fof(f8224,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)],[f718,f8223]) ).
fof(f8225,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)],[f8139,f8224]) ).
fof(f8226,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)],[f92,f8225]) ).
fof(f8227,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)],[f8139,f8226]) ).
fof(f8228,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)],[f718,f8227]) ).
fof(f8229,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)],[f8139,f8228]) ).
fof(f8230,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)],[f33,f8229]) ).
fof(f8231,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)],[f1423,f8230]) ).
fof(f8232,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)],[f8139,f8201]) ).
fof(f8233,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)],[f718,f8232]) ).
fof(f8234,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)],[f8139,f8233]) ).
fof(f8235,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)],[f718,f8234]) ).
fof(f8236,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)],[f8139,f8235]) ).
fof(f8237,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)],[f8139,f8202]) ).
fof(f8238,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)],[f718,f8237]) ).
fof(f8239,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)],[f8139,f8238]) ).
fof(f8240,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)],[f718,f8239]) ).
fof(f8241,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)],[f8139,f8240]) ).
fof(f8242,plain,
! [X0,X1] : forward_diamond(X0,star(X1)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f38,f8203]) ).
fof(f8243,plain,
! [X0,X1] : domain_difference(star(X0),X1) = antidomain(X1),
inference(forward_demodulation,[status(thm)],[f39,f8204]) ).
fof(f8247,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,one)),antidomain(multiplication(X0,star(X1)))) = antidomain(multiplication(X0,domain(star(X1)))),
inference(forward_demodulation,[status(thm)],[f33,f8208]) ).
fof(f8248,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,star(X1)))) = antidomain(multiplication(X0,domain(star(X1)))),
inference(forward_demodulation,[status(thm)],[f38,f8247]) ).
fof(f8249,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,star(X1)))) = antidomain(multiplication(X0,one)),
inference(forward_demodulation,[status(thm)],[f8139,f8248]) ).
fof(f8250,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,star(X1)))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f38,f8249]) ).
fof(f8253,plain,
! [X0,X1,X2] : leq(multiplication(star(forward_diamond(X0,X1)),multiplication(forward_diamond(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f290,f6667]) ).
fof(f8254,plain,
! [X0,X1,X2] : leq(multiplication(star(forward_box(X0,X1)),multiplication(forward_box(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f290,f6327]) ).
fof(f8255,plain,
! [X0,X1,X2] : leq(multiplication(star(backward_box(X0,X1)),multiplication(backward_box(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f290,f6326]) ).
fof(f8256,plain,
! [X0,X1,X2] : leq(multiplication(star(backward_diamond(X0,X1)),multiplication(backward_diamond(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f290,f6192]) ).
fof(f8257,plain,
! [X0,X1] : leq(multiplication(star(coantidomain(X0)),multiplication(coantidomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f290,f6815]) ).
fof(f8258,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),multiplication(domain(X0),X1)),X1),
inference(resolution,[status(thm)],[f290,f6469]) ).
fof(f8259,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f290,f6335]) ).
fof(f8260,plain,
! [X0,X1] : leq(multiplication(star(c(X0)),multiplication(c(X0),X1)),X1),
inference(resolution,[status(thm)],[f290,f6199]) ).
fof(f8261,plain,
! [X0,X1] : leq(multiplication(star(codomain(X0)),multiplication(codomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f290,f6071]) ).
fof(f8262,plain,
! [X0,X1] : leq(multiplication(star(divergence(X0)),multiplication(divergence(X0),X1)),X1),
inference(resolution,[status(thm)],[f290,f5662]) ).
fof(f8263,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)],[f290,f3808]) ).
fof(f8264,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)],[f290,f3489]) ).
fof(f8265,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)],[f290,f3488]) ).
fof(f8266,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)],[f290,f3259]) ).
fof(f8267,plain,
! [X0] : leq(multiplication(star(coantidomain(X0)),multiplication(coantidomain(X0),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f290,f3817]) ).
fof(f8268,plain,
! [X0] : leq(multiplication(star(domain(X0)),multiplication(domain(X0),domain(X0))),domain(X0)),
inference(resolution,[status(thm)],[f290,f3587]) ).
fof(f8269,plain,
! [X0] : leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X0),antidomain(X0))),antidomain(X0)),
inference(resolution,[status(thm)],[f290,f3497]) ).
fof(f8270,plain,
! [X0] : leq(multiplication(star(c(X0)),multiplication(c(X0),c(X0))),c(X0)),
inference(resolution,[status(thm)],[f290,f3402]) ).
fof(f8271,plain,
! [X0] : leq(multiplication(star(codomain(X0)),multiplication(codomain(X0),codomain(X0))),codomain(X0)),
inference(resolution,[status(thm)],[f290,f3175]) ).
fof(f8272,plain,
! [X0] : leq(multiplication(star(divergence(X0)),multiplication(divergence(X0),divergence(X0))),divergence(X0)),
inference(resolution,[status(thm)],[f290,f3096]) ).
fof(f8273,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)],[f202,f290]) ).
fof(f8274,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)],[f219,f290]) ).
fof(f8275,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)],[f227,f290]) ).
fof(f8276,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)],[f225,f290]) ).
fof(f8277,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)],[f228,f290]) ).
fof(f8278,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)],[f221,f290]) ).
fof(f8282,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)],[f63,f290]) ).
fof(f8283,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),multiplication(domain(X0),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f3965,f290]) ).
fof(f8284,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)],[f37,f290]) ).
fof(f8285,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)],[f181,f290]) ).
fof(f8286,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)],[f172,f290]) ).
fof(f8290,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(one,X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f39,f290]) ).
fof(f8291,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X0))),codomain(X0))
| ~ leq(X0,codomain(X0)) ),
inference(paramodulation,[status(thm)],[f2178,f290]) ).
fof(f8292,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)],[f157,f290]) ).
fof(f8293,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)],[f176,f290]) ).
fof(f8294,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)],[f187,f290]) ).
fof(f8295,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)],[f185,f290]) ).
fof(f8299,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(X0,zero)),zero)
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f42,f290]) ).
fof(f8300,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(X0,one)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f38,f290]) ).
fof(f8301,plain,
! [X0,X1] :
( leq(multiplication(star(addition(antidomain(X1),X0)),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f219,f8274]) ).
fof(f8302,plain,
! [X0,X1] :
( leq(multiplication(star(addition(X0,antidomain(X1))),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f225,f8276]) ).
fof(f8303,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)],[f228,f8277]) ).
fof(f8304,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)],[f221,f8278]) ).
fof(f8308,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)],[f63,f8282]) ).
fof(f8309,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),domain_difference(X0,X1)),antidomain(X1)),
inference(forward_subsumption_resolution,[status(thm)],[f8308,f6657]) ).
fof(f8310,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),X0),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f3965,f8283]) ).
fof(f8311,plain,
! [X0] : leq(multiplication(star(domain(X0)),X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8310,f234]) ).
fof(f8312,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)],[f37,f8284]) ).
fof(f8313,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)],[f181,f8285]) ).
fof(f8314,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)],[f172,f8286]) ).
fof(f8318,plain,
! [X0] :
( leq(multiplication(star(one),X0),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f8290]) ).
fof(f8319,plain,
! [X0] : leq(multiplication(star(one),X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8318,f234]) ).
fof(f8320,plain,
! [X0] :
( leq(multiplication(star(X0),X0),codomain(X0))
| ~ leq(X0,codomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2178,f8291]) ).
fof(f8321,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)],[f176,f8293]) ).
fof(f8322,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)],[f185,f8295]) ).
fof(f8326,definition,
! [X0] :
( sQ13_spl
<=> leq(multiplication(star(X0),multiplication(X0,zero)),zero) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f8329,plain,
( sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8299,f7614,f8326]) ).
fof(f8330,plain,
! [X0] :
( leq(multiplication(star(X0),X0),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f38,f8300]) ).
fof(f8354,plain,
! [X0,X1] : backward_box(X0,star(X1)) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f8141,f67]) ).
fof(f8355,plain,
! [X0,X1] : forward_box(X0,star(X1)) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f8141,f66]) ).
fof(f8376,plain,
! [X0,X1] : backward_box(X0,star(X1)) = c(zero),
inference(forward_demodulation,[status(thm)],[f749,f8354]) ).
fof(f8377,plain,
! [X0,X1] : backward_box(X0,star(X1)) = one,
inference(forward_demodulation,[status(thm)],[f543,f8376]) ).
fof(f8378,plain,
! [X0,X1] : forward_box(X0,star(X1)) = c(zero),
inference(forward_demodulation,[status(thm)],[f717,f8355]) ).
fof(f8379,plain,
! [X0,X1] : forward_box(X0,star(X1)) = one,
inference(forward_demodulation,[status(thm)],[f543,f8378]) ).
fof(f8381,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)],[f214,f291]) ).
fof(f8382,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)],[f165,f291]) ).
fof(f8383,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)],[f206,f291]) ).
fof(f8384,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)],[f196,f291]) ).
fof(f8385,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)],[f148,f291]) ).
fof(f8386,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)],[f41,f291]) ).
fof(f8387,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)],[f40,f291]) ).
fof(f8388,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)],[f4331,f291]) ).
fof(f8389,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)],[f4330,f291]) ).
fof(f8390,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)],[f4329,f291]) ).
fof(f8391,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)],[f4328,f291]) ).
fof(f8392,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)],[f4327,f291]) ).
fof(f8393,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)],[f4326,f291]) ).
fof(f8394,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)],[f2352,f291]) ).
fof(f8395,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)],[f2351,f291]) ).
fof(f8396,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)],[f2350,f291]) ).
fof(f8397,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)],[f2349,f291]) ).
fof(f8398,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)],[f2348,f291]) ).
fof(f8399,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)],[f2347,f291]) ).
fof(f8400,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)],[f227,f291]) ).
fof(f8401,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)],[f202,f291]) ).
fof(f8402,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)],[f187,f291]) ).
fof(f8403,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)],[f157,f291]) ).
fof(f8404,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)],[f94,f291]) ).
fof(f8405,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)],[f100,f291]) ).
fof(f8406,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)],[f92,f291]) ).
fof(f8407,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)],[f92,f291]) ).
fof(f8409,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)],[f33,f291]) ).
fof(f8410,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)],[f33,f291]) ).
fof(f8411,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)],[f36,f291]) ).
fof(f8412,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)],[f219,f291]) ).
fof(f8413,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)],[f225,f291]) ).
fof(f8414,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(c(multiplication(X2,X1)),X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f4088,f291]) ).
fof(f8415,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)],[f3965,f291]) ).
fof(f8416,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)],[f37,f291]) ).
fof(f8417,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(antidomain(X2),X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f131,f291]) ).
fof(f8418,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(antidomain(multiplication(X2,X1)),X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f54,f291]) ).
fof(f8419,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(zero,X2)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f43,f291]) ).
fof(f8421,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,coantidomain(X2))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f146,f291]) ).
fof(f8422,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)],[f139,f291]) ).
fof(f8423,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)],[f202,f291]) ).
fof(f8424,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)],[f219,f291]) ).
fof(f8425,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)],[f227,f291]) ).
fof(f8426,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)],[f225,f291]) ).
fof(f8427,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)],[f228,f291]) ).
fof(f8428,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)],[f221,f291]) ).
fof(f8429,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)],[f192,f291]) ).
fof(f8430,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,c(X2))),X1),X2)
| ~ leq(addition(multiplication(X0,zero),X1),X2) ),
inference(paramodulation,[status(thm)],[f4088,f291]) ).
fof(f8431,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)],[f190,f291]) ).
fof(f8432,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)],[f63,f291]) ).
fof(f8433,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,domain(X1))),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f3965,f291]) ).
fof(f8434,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)],[f37,f291]) ).
fof(f8435,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)],[f181,f291]) ).
fof(f8436,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)],[f172,f291]) ).
fof(f8437,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)],[f131,f291]) ).
fof(f8438,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,antidomain(X2))),X1),X2)
| ~ leq(addition(multiplication(X0,zero),X1),X2) ),
inference(paramodulation,[status(thm)],[f54,f291]) ).
fof(f8439,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,zero)),X1),X2)
| ~ leq(addition(multiplication(X0,zero),X1),X2) ),
inference(paramodulation,[status(thm)],[f43,f291]) ).
fof(f8441,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)],[f2178,f291]) ).
fof(f8442,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)],[f157,f291]) ).
fof(f8443,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)],[f176,f291]) ).
fof(f8444,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)],[f187,f291]) ).
fof(f8445,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)],[f185,f291]) ).
fof(f8446,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)],[f146,f291]) ).
fof(f8447,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)],[f139,f291]) ).
fof(f8448,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)],[f58,f291]) ).
fof(f8449,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X2)),X1),zero)
| ~ leq(addition(multiplication(X0,zero),X1),zero) ),
inference(paramodulation,[status(thm)],[f42,f291]) ).
fof(f8450,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X0,X1)),X2),one)
| ~ leq(addition(multiplication(X0,X1),X2),one) ),
inference(paramodulation,[status(thm)],[f38,f291]) ).
fof(f8451,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)],[f37,f8394]) ).
fof(f8452,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)],[f37,f8451]) ).
fof(f8453,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)],[f37,f8395]) ).
fof(f8454,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)],[f37,f8453]) ).
fof(f8455,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)],[f37,f8396]) ).
fof(f8456,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)],[f37,f8455]) ).
fof(f8457,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)],[f37,f8397]) ).
fof(f8458,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)],[f37,f8457]) ).
fof(f8459,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)],[f37,f8398]) ).
fof(f8460,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)],[f37,f8459]) ).
fof(f8461,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)],[f37,f8399]) ).
fof(f8462,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)],[f37,f8461]) ).
fof(f8463,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)],[f37,f8402]) ).
fof(f8464,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)],[f37,f8463]) ).
fof(f8465,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)],[f37,f8464]) ).
fof(f8466,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)],[f37,f8465]) ).
fof(f8467,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)],[f37,f8403]) ).
fof(f8468,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)],[f37,f8467]) ).
fof(f8469,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)],[f37,f8468]) ).
fof(f8470,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)],[f37,f8469]) ).
fof(f8472,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(c(multiplication(X2,X1)),X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f8414]) ).
fof(f8473,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)],[f37,f8416]) ).
fof(f8474,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(antidomain(X2),X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f8417]) ).
fof(f8475,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f54,f8474]) ).
fof(f8476,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(antidomain(multiplication(X2,X1)),X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f8418]) ).
fof(f8477,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(zero,X2)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f8419]) ).
fof(f8478,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f43,f8477]) ).
fof(f8480,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,coantidomain(X2))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f8421]) ).
fof(f8481,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f58,f8480]) ).
fof(f8482,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)],[f75,f8422]) ).
fof(f8483,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)],[f42,f8429]) ).
fof(f8484,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,c(X1))),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f8483]) ).
fof(f8485,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,c(X1))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f42,f8430]) ).
fof(f8486,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,c(X1))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f8485]) ).
fof(f8487,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)],[f42,f8431]) ).
fof(f8488,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,coantidomain(X1))),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f8487]) ).
fof(f8489,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)],[f42,f8437]) ).
fof(f8490,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)],[f75,f8489]) ).
fof(f8491,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f42,f8438]) ).
fof(f8492,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f8491]) ).
fof(f8493,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,zero)),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f42,f8439]) ).
fof(f8494,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,zero)),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f8493]) ).
fof(f8495,plain,
! [X0,X1] :
( leq(multiplication(star(zero),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f42,f8494]) ).
fof(f8497,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)],[f42,f8446]) ).
fof(f8498,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)],[f75,f8497]) ).
fof(f8499,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)],[f42,f8447]) ).
fof(f8500,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)],[f75,f8499]) ).
fof(f8501,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),coantidomain(X1))
| ~ leq(addition(zero,X0),coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f42,f8448]) ).
fof(f8502,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f8501]) ).
fof(f8503,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X1,X2)),X0),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f42,f8449]) ).
fof(f8504,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X1,X2)),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f8503]) ).
fof(f8538,plain,
! [X0,X1] : addition(X0,multiplication(X0,star(X1))) = multiplication(X0,star(X1)),
inference(resolution,[status(thm)],[f8048,f46]) ).
fof(f8543,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f37,f8048]) ).
fof(f8554,plain,
! [X0,X1] : leq(multiplication(star(antidomain(antidomain(X0))),domain_difference(X1,X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f299,f6657]) ).
fof(f8555,plain,
! [X0,X1] : leq(multiplication(star(antidomain(domain(X0))),domain_difference(X0,X1)),domain(X0)),
inference(resolution,[status(thm)],[f299,f3580]) ).
fof(f8556,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(forward_diamond(X1,X2),X0)),X0),
inference(resolution,[status(thm)],[f299,f6667]) ).
fof(f8557,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(forward_box(X1,X2),X0)),X0),
inference(resolution,[status(thm)],[f299,f6327]) ).
fof(f8558,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(backward_box(X1,X2),X0)),X0),
inference(resolution,[status(thm)],[f299,f6326]) ).
fof(f8559,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(backward_diamond(X1,X2),X0)),X0),
inference(resolution,[status(thm)],[f299,f6192]) ).
fof(f8560,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(coantidomain(X1),X0)),X0),
inference(resolution,[status(thm)],[f299,f6815]) ).
fof(f8561,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(domain(X1),X0)),X0),
inference(resolution,[status(thm)],[f299,f6469]) ).
fof(f8562,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(antidomain(X1),X0)),X0),
inference(resolution,[status(thm)],[f299,f6335]) ).
fof(f8563,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(c(X1),X0)),X0),
inference(resolution,[status(thm)],[f299,f6199]) ).
fof(f8564,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(codomain(X1),X0)),X0),
inference(resolution,[status(thm)],[f299,f6071]) ).
fof(f8565,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(divergence(X1),X0)),X0),
inference(resolution,[status(thm)],[f299,f5662]) ).
fof(f8566,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(X0,forward_diamond(X1,X2))),X0),
inference(resolution,[status(thm)],[f299,f3808]) ).
fof(f8567,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(X0,forward_box(X1,X2))),X0),
inference(resolution,[status(thm)],[f299,f3489]) ).
fof(f8568,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(X0,backward_box(X1,X2))),X0),
inference(resolution,[status(thm)],[f299,f3488]) ).
fof(f8569,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(X0)),multiplication(X0,backward_diamond(X1,X2))),X0),
inference(resolution,[status(thm)],[f299,f3259]) ).
fof(f8570,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,coantidomain(X1))),X0),
inference(resolution,[status(thm)],[f299,f3817]) ).
fof(f8571,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,domain(X1))),X0),
inference(resolution,[status(thm)],[f299,f3587]) ).
fof(f8572,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,antidomain(X1))),X0),
inference(resolution,[status(thm)],[f299,f3497]) ).
fof(f8573,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,c(X1))),X0),
inference(resolution,[status(thm)],[f299,f3402]) ).
fof(f8574,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,codomain(X1))),X0),
inference(resolution,[status(thm)],[f299,f3175]) ).
fof(f8575,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(X0,divergence(X1))),X0),
inference(resolution,[status(thm)],[f299,f3096]) ).
fof(f8576,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(star(X0))),backward_diamond(X1,X2)),star(X0)),
inference(resolution,[status(thm)],[f299,f7402]) ).
fof(f8577,plain,
! [X0,X1] : leq(multiplication(star(antidomain(one)),backward_diamond(X0,X1)),one),
inference(resolution,[status(thm)],[f299,f1408]) ).
fof(f8578,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(star(X0))),forward_box(X1,X2)),star(X0)),
inference(resolution,[status(thm)],[f299,f7396]) ).
fof(f8579,plain,
! [X0,X1] : leq(multiplication(star(antidomain(one)),forward_box(X0,X1)),one),
inference(resolution,[status(thm)],[f299,f1401]) ).
fof(f8580,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(star(X0))),backward_box(X1,X2)),star(X0)),
inference(resolution,[status(thm)],[f299,f7395]) ).
fof(f8581,plain,
! [X0,X1] : leq(multiplication(star(antidomain(one)),backward_box(X0,X1)),one),
inference(resolution,[status(thm)],[f299,f1400]) ).
fof(f8582,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(divergence(X0)))),divergence(X0)),codomain(divergence(X0))),
inference(resolution,[status(thm)],[f299,f5767]) ).
fof(f8583,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),divergence(X1)),star(X0)),
inference(resolution,[status(thm)],[f299,f7169]) ).
fof(f8584,plain,
! [X0] : leq(multiplication(star(antidomain(domain(divergence(X0)))),divergence(X0)),domain(divergence(X0))),
inference(resolution,[status(thm)],[f299,f4030]) ).
fof(f8585,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),divergence(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f299,f2110]) ).
fof(f8586,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),divergence(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f299,f1758]) ).
fof(f8587,plain,
! [X0] : leq(multiplication(star(antidomain(one)),divergence(X0)),one),
inference(resolution,[status(thm)],[f299,f1419]) ).
fof(f8588,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(star(X0))),forward_diamond(X1,X2)),star(X0)),
inference(resolution,[status(thm)],[f299,f7218]) ).
fof(f8589,plain,
! [X0,X1] : leq(multiplication(star(antidomain(one)),forward_diamond(X0,X1)),one),
inference(resolution,[status(thm)],[f299,f1363]) ).
fof(f8590,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(codomain(X0)))),codomain(X0)),codomain(codomain(X0))),
inference(resolution,[status(thm)],[f299,f6184]) ).
fof(f8591,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),codomain(X1)),star(X0)),
inference(resolution,[status(thm)],[f299,f7168]) ).
fof(f8592,plain,
! [X0] : leq(multiplication(star(antidomain(domain(codomain(X0)))),codomain(X0)),domain(codomain(X0))),
inference(resolution,[status(thm)],[f299,f4032]) ).
fof(f8593,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),codomain(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f299,f2122]) ).
fof(f8594,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),codomain(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f299,f1759]) ).
fof(f8595,plain,
! [X0] : leq(multiplication(star(antidomain(one)),codomain(X0)),one),
inference(resolution,[status(thm)],[f299,f1371]) ).
fof(f8596,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(c(X0)))),c(X0)),codomain(c(X0))),
inference(resolution,[status(thm)],[f299,f6318]) ).
fof(f8597,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),c(X1)),star(X0)),
inference(resolution,[status(thm)],[f299,f7167]) ).
fof(f8598,plain,
! [X0] : leq(multiplication(star(antidomain(domain(c(X0)))),c(X0)),domain(c(X0))),
inference(resolution,[status(thm)],[f299,f4028]) ).
fof(f8599,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),c(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f299,f2136]) ).
fof(f8600,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),c(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f299,f1760]) ).
fof(f8601,plain,
! [X0] : leq(multiplication(star(antidomain(one)),c(X0)),one),
inference(resolution,[status(thm)],[f299,f1366]) ).
fof(f8602,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(antidomain(X0)))),antidomain(X0)),codomain(antidomain(X0))),
inference(resolution,[status(thm)],[f299,f6459]) ).
fof(f8603,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),antidomain(X1)),star(X0)),
inference(resolution,[status(thm)],[f299,f7166]) ).
fof(f8604,plain,
! [X0] : leq(multiplication(star(antidomain(c(X0))),antidomain(X0)),c(X0)),
inference(resolution,[status(thm)],[f299,f4063]) ).
fof(f8605,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),antidomain(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f299,f2240]) ).
fof(f8606,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),antidomain(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f299,f1761]) ).
fof(f8607,plain,
! [X0] : leq(multiplication(star(antidomain(one)),antidomain(X0)),one),
inference(resolution,[status(thm)],[f299,f1348]) ).
fof(f8608,plain,
! [X0] : leq(multiplication(star(antidomain(coantidomain(codomain(X0)))),coantidomain(X0)),coantidomain(codomain(X0))),
inference(resolution,[status(thm)],[f299,f6955]) ).
fof(f8609,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),coantidomain(X1)),star(X0)),
inference(resolution,[status(thm)],[f299,f7165]) ).
fof(f8610,plain,
! [X0] : leq(multiplication(star(antidomain(domain(coantidomain(X0)))),coantidomain(X0)),domain(coantidomain(X0))),
inference(resolution,[status(thm)],[f299,f4196]) ).
fof(f8611,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),coantidomain(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f299,f2251]) ).
fof(f8612,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),coantidomain(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f299,f1762]) ).
fof(f8613,plain,
! [X0] : leq(multiplication(star(antidomain(one)),coantidomain(X0)),one),
inference(resolution,[status(thm)],[f299,f1346]) ).
fof(f8614,plain,
! [X0] : leq(multiplication(star(antidomain(codomain(domain(X0)))),domain(X0)),codomain(domain(X0))),
inference(resolution,[status(thm)],[f299,f6659]) ).
fof(f8615,plain,
! [X0,X1] : leq(multiplication(star(antidomain(star(X0))),domain(X1)),star(X0)),
inference(resolution,[status(thm)],[f299,f7164]) ).
fof(f8616,plain,
! [X0] : leq(multiplication(star(antidomain(antidomain(c(X0)))),domain(X0)),antidomain(c(X0))),
inference(resolution,[status(thm)],[f299,f4071]) ).
fof(f8617,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(one,X0))),domain(X1)),addition(one,X0)),
inference(resolution,[status(thm)],[f299,f2264]) ).
fof(f8618,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,one))),domain(X1)),addition(X0,one)),
inference(resolution,[status(thm)],[f299,f1763]) ).
fof(f8619,plain,
! [X0] : leq(multiplication(star(antidomain(one)),domain(X0)),one),
inference(resolution,[status(thm)],[f299,f1344]) ).
fof(f8620,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,star(X1)))),one),addition(X0,star(X1))),
inference(resolution,[status(thm)],[f299,f7178]) ).
fof(f8621,plain,
! [X0] : leq(multiplication(star(antidomain(star(X0))),one),star(X0)),
inference(resolution,[status(thm)],[f299,f7181]) ).
fof(f8623,plain,
! [X0] : leq(multiplication(star(antidomain(star(X0))),addition(one,multiplication(star(X0),X0))),star(X0)),
inference(resolution,[status(thm)],[f299,f49]) ).
fof(f8624,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)],[f299,f247]) ).
fof(f8625,plain,
! [X0] : leq(multiplication(star(antidomain(star(X0))),addition(one,multiplication(X0,star(X0)))),star(X0)),
inference(resolution,[status(thm)],[f299,f48]) ).
fof(f8626,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(X0,star(X1)))),X0),multiplication(X0,star(X1))),
inference(resolution,[status(thm)],[f299,f8048]) ).
fof(f8627,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,addition(X1,X2)))),X1),addition(X0,addition(X1,X2))),
inference(resolution,[status(thm)],[f299,f1357]) ).
fof(f8628,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,addition(X1,X2)))),X2),addition(X0,addition(X1,X2))),
inference(resolution,[status(thm)],[f299,f1356]) ).
fof(f8629,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,X1))),X1),addition(X0,X1)),
inference(resolution,[status(thm)],[f299,f1359]) ).
fof(f8630,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,X1))),X0),addition(X0,X1)),
inference(resolution,[status(thm)],[f299,f1261]) ).
fof(f8631,plain,
! [X0] : leq(multiplication(star(antidomain(X0)),X0),X0),
inference(resolution,[status(thm)],[f299,f234]) ).
fof(f8632,plain,
! [X0,X1] : leq(multiplication(star(domain(X0)),domain_difference(X1,X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f57,f8554]) ).
fof(f8633,plain,
! [X0,X1] : leq(multiplication(star(c(X0)),domain_difference(X0,X1)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f8555]) ).
fof(f8634,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),backward_diamond(X0,X1)),star(X2)),
inference(forward_demodulation,[status(thm)],[f8054,f8576]) ).
fof(f8635,plain,
! [X0,X1] : leq(multiplication(star(zero),backward_diamond(X0,X1)),one),
inference(forward_demodulation,[status(thm)],[f114,f8577]) ).
fof(f8636,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),forward_box(X0,X1)),star(X2)),
inference(forward_demodulation,[status(thm)],[f8054,f8578]) ).
fof(f8637,plain,
! [X0,X1] : leq(multiplication(star(zero),forward_box(X0,X1)),one),
inference(forward_demodulation,[status(thm)],[f114,f8579]) ).
fof(f8638,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),backward_box(X0,X1)),star(X2)),
inference(forward_demodulation,[status(thm)],[f8054,f8580]) ).
fof(f8639,plain,
! [X0,X1] : leq(multiplication(star(zero),backward_box(X0,X1)),one),
inference(forward_demodulation,[status(thm)],[f114,f8581]) ).
fof(f8640,plain,
! [X0,X1] : leq(multiplication(star(zero),divergence(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8054,f8583]) ).
fof(f8641,plain,
! [X0] : leq(multiplication(star(c(divergence(X0))),divergence(X0)),domain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f62,f8584]) ).
fof(f8642,plain,
! [X0] : leq(multiplication(star(zero),divergence(X0)),one),
inference(forward_demodulation,[status(thm)],[f114,f8587]) ).
fof(f8643,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),forward_diamond(X0,X1)),star(X2)),
inference(forward_demodulation,[status(thm)],[f8054,f8588]) ).
fof(f8644,plain,
! [X0,X1] : leq(multiplication(star(zero),forward_diamond(X0,X1)),one),
inference(forward_demodulation,[status(thm)],[f114,f8589]) ).
fof(f8645,plain,
! [X0,X1] : leq(multiplication(star(zero),codomain(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8054,f8591]) ).
fof(f8646,plain,
! [X0] : leq(multiplication(star(c(codomain(X0))),codomain(X0)),domain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f8592]) ).
fof(f8647,plain,
! [X0] : leq(multiplication(star(zero),codomain(X0)),one),
inference(forward_demodulation,[status(thm)],[f114,f8595]) ).
fof(f8648,plain,
! [X0,X1] : leq(multiplication(star(zero),c(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8054,f8597]) ).
fof(f8649,plain,
! [X0] : leq(multiplication(star(c(c(X0))),c(X0)),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f62,f8598]) ).
fof(f8650,plain,
! [X0] : leq(multiplication(star(zero),c(X0)),one),
inference(forward_demodulation,[status(thm)],[f114,f8601]) ).
fof(f8651,plain,
! [X0,X1] : leq(multiplication(star(zero),antidomain(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8054,f8603]) ).
fof(f8652,plain,
! [X0] : leq(multiplication(star(zero),antidomain(X0)),one),
inference(forward_demodulation,[status(thm)],[f114,f8607]) ).
fof(f8653,plain,
! [X0,X1] : leq(multiplication(star(zero),coantidomain(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8054,f8609]) ).
fof(f8654,plain,
! [X0] : leq(multiplication(star(c(coantidomain(X0))),coantidomain(X0)),domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f8610]) ).
fof(f8655,plain,
! [X0] : leq(multiplication(star(zero),coantidomain(X0)),one),
inference(forward_demodulation,[status(thm)],[f114,f8613]) ).
fof(f8656,plain,
! [X0,X1] : leq(multiplication(star(zero),domain(X0)),star(X1)),
inference(forward_demodulation,[status(thm)],[f8054,f8615]) ).
fof(f8657,plain,
! [X0] : leq(multiplication(star(domain(c(X0))),domain(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f57,f8616]) ).
fof(f8658,plain,
! [X0] : leq(multiplication(star(zero),domain(X0)),one),
inference(forward_demodulation,[status(thm)],[f114,f8619]) ).
fof(f8659,plain,
! [X0,X1] : leq(star(antidomain(addition(X0,star(X1)))),addition(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f38,f8620]) ).
fof(f8660,plain,
! [X0] : leq(star(antidomain(star(X0))),star(X0)),
inference(forward_demodulation,[status(thm)],[f38,f8621]) ).
fof(f8661,plain,
! [X0] : leq(star(zero),star(X0)),
inference(forward_demodulation,[status(thm)],[f8054,f8660]) ).
fof(f8663,plain,
! [X0] : leq(multiplication(star(zero),addition(one,multiplication(star(X0),X0))),star(X0)),
inference(forward_demodulation,[status(thm)],[f8054,f8623]) ).
fof(f8664,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)],[f8054,f8624]) ).
fof(f8665,plain,
! [X0] : leq(multiplication(star(zero),addition(one,multiplication(X0,star(X0)))),star(X0)),
inference(forward_demodulation,[status(thm)],[f8054,f8625]) ).
fof(f8666,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(star(X0),X1))),X1),multiplication(star(X0),X1)),
inference(resolution,[status(thm)],[f8050,f299]) ).
fof(f8667,plain,
! [X0,X1] : addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(resolution,[status(thm)],[f8050,f46]) ).
fof(f8672,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(multiplication(star(X1),X0))),zero),
inference(paramodulation,[status(thm)],[f139,f8050]) ).
fof(f8705,plain,
! [X0,X1] : leq(multiplication(star(zero),domain_difference(X0,X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f300,f6657]) ).
fof(f8706,plain,
! [X0,X1] : leq(multiplication(star(zero),domain_difference(X0,X1)),domain(X0)),
inference(resolution,[status(thm)],[f300,f3580]) ).
fof(f8707,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(forward_diamond(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f300,f6667]) ).
fof(f8708,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(forward_box(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f300,f6327]) ).
fof(f8709,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(backward_box(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f300,f6326]) ).
fof(f8710,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(backward_diamond(X0,X1),X2)),X2),
inference(resolution,[status(thm)],[f300,f6192]) ).
fof(f8711,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(coantidomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f300,f6815]) ).
fof(f8712,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(domain(X0),X1)),X1),
inference(resolution,[status(thm)],[f300,f6469]) ).
fof(f8713,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(antidomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f300,f6335]) ).
fof(f8714,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(c(X0),X1)),X1),
inference(resolution,[status(thm)],[f300,f6199]) ).
fof(f8715,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(codomain(X0),X1)),X1),
inference(resolution,[status(thm)],[f300,f6071]) ).
fof(f8716,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(divergence(X0),X1)),X1),
inference(resolution,[status(thm)],[f300,f5662]) ).
fof(f8717,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(X0,forward_diamond(X1,X2))),X0),
inference(resolution,[status(thm)],[f300,f3808]) ).
fof(f8718,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(X0,forward_box(X1,X2))),X0),
inference(resolution,[status(thm)],[f300,f3489]) ).
fof(f8719,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(X0,backward_box(X1,X2))),X0),
inference(resolution,[status(thm)],[f300,f3488]) ).
fof(f8720,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),multiplication(X0,backward_diamond(X1,X2))),X0),
inference(resolution,[status(thm)],[f300,f3259]) ).
fof(f8721,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,coantidomain(X1))),X0),
inference(resolution,[status(thm)],[f300,f3817]) ).
fof(f8722,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,domain(X1))),X0),
inference(resolution,[status(thm)],[f300,f3587]) ).
fof(f8723,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,antidomain(X1))),X0),
inference(resolution,[status(thm)],[f300,f3497]) ).
fof(f8724,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,c(X1))),X0),
inference(resolution,[status(thm)],[f300,f3402]) ).
fof(f8725,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,codomain(X1))),X0),
inference(resolution,[status(thm)],[f300,f3175]) ).
fof(f8726,plain,
! [X0,X1] : leq(multiplication(star(zero),multiplication(X0,divergence(X1))),X0),
inference(resolution,[status(thm)],[f300,f3096]) ).
fof(f8727,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),backward_diamond(X0,X1)),star(X2)),
inference(resolution,[status(thm)],[f300,f7402]) ).
fof(f8728,plain,
! [X0,X1] : leq(multiplication(star(zero),backward_diamond(X0,X1)),one),
inference(resolution,[status(thm)],[f300,f1408]) ).
fof(f8729,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),forward_box(X0,X1)),star(X2)),
inference(resolution,[status(thm)],[f300,f7396]) ).
fof(f8730,plain,
! [X0,X1] : leq(multiplication(star(zero),forward_box(X0,X1)),one),
inference(resolution,[status(thm)],[f300,f1401]) ).
fof(f8731,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),backward_box(X0,X1)),star(X2)),
inference(resolution,[status(thm)],[f300,f7395]) ).
fof(f8732,plain,
! [X0,X1] : leq(multiplication(star(zero),backward_box(X0,X1)),one),
inference(resolution,[status(thm)],[f300,f1400]) ).
fof(f8733,plain,
! [X0] : leq(multiplication(star(zero),divergence(X0)),codomain(divergence(X0))),
inference(resolution,[status(thm)],[f300,f5767]) ).
fof(f8734,plain,
! [X0,X1] : leq(multiplication(star(zero),divergence(X0)),star(X1)),
inference(resolution,[status(thm)],[f300,f7169]) ).
fof(f8735,plain,
! [X0] : leq(multiplication(star(zero),divergence(X0)),domain(divergence(X0))),
inference(resolution,[status(thm)],[f300,f4030]) ).
fof(f8736,plain,
! [X0,X1] : leq(multiplication(star(zero),divergence(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f300,f2110]) ).
fof(f8737,plain,
! [X0,X1] : leq(multiplication(star(zero),divergence(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f300,f1758]) ).
fof(f8738,plain,
! [X0] : leq(multiplication(star(zero),divergence(X0)),one),
inference(resolution,[status(thm)],[f300,f1419]) ).
fof(f8739,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),forward_diamond(X0,X1)),star(X2)),
inference(resolution,[status(thm)],[f300,f7218]) ).
fof(f8740,plain,
! [X0,X1] : leq(multiplication(star(zero),forward_diamond(X0,X1)),one),
inference(resolution,[status(thm)],[f300,f1363]) ).
fof(f8741,plain,
! [X0] : leq(multiplication(star(zero),codomain(X0)),codomain(codomain(X0))),
inference(resolution,[status(thm)],[f300,f6184]) ).
fof(f8742,plain,
! [X0,X1] : leq(multiplication(star(zero),codomain(X0)),star(X1)),
inference(resolution,[status(thm)],[f300,f7168]) ).
fof(f8743,plain,
! [X0] : leq(multiplication(star(zero),codomain(X0)),domain(codomain(X0))),
inference(resolution,[status(thm)],[f300,f4032]) ).
fof(f8744,plain,
! [X0,X1] : leq(multiplication(star(zero),codomain(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f300,f2122]) ).
fof(f8745,plain,
! [X0,X1] : leq(multiplication(star(zero),codomain(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f300,f1759]) ).
fof(f8746,plain,
! [X0] : leq(multiplication(star(zero),codomain(X0)),one),
inference(resolution,[status(thm)],[f300,f1371]) ).
fof(f8747,plain,
! [X0] : leq(multiplication(star(zero),c(X0)),codomain(c(X0))),
inference(resolution,[status(thm)],[f300,f6318]) ).
fof(f8748,plain,
! [X0,X1] : leq(multiplication(star(zero),c(X0)),star(X1)),
inference(resolution,[status(thm)],[f300,f7167]) ).
fof(f8749,plain,
! [X0] : leq(multiplication(star(zero),c(X0)),domain(c(X0))),
inference(resolution,[status(thm)],[f300,f4028]) ).
fof(f8750,plain,
! [X0,X1] : leq(multiplication(star(zero),c(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f300,f2136]) ).
fof(f8751,plain,
! [X0,X1] : leq(multiplication(star(zero),c(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f300,f1760]) ).
fof(f8752,plain,
! [X0] : leq(multiplication(star(zero),c(X0)),one),
inference(resolution,[status(thm)],[f300,f1366]) ).
fof(f8753,plain,
! [X0] : leq(multiplication(star(zero),antidomain(X0)),codomain(antidomain(X0))),
inference(resolution,[status(thm)],[f300,f6459]) ).
fof(f8754,plain,
! [X0,X1] : leq(multiplication(star(zero),antidomain(X0)),star(X1)),
inference(resolution,[status(thm)],[f300,f7166]) ).
fof(f8755,plain,
! [X0] : leq(multiplication(star(zero),antidomain(X0)),c(X0)),
inference(resolution,[status(thm)],[f300,f4063]) ).
fof(f8756,plain,
! [X0,X1] : leq(multiplication(star(zero),antidomain(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f300,f2240]) ).
fof(f8757,plain,
! [X0,X1] : leq(multiplication(star(zero),antidomain(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f300,f1761]) ).
fof(f8758,plain,
! [X0] : leq(multiplication(star(zero),antidomain(X0)),one),
inference(resolution,[status(thm)],[f300,f1348]) ).
fof(f8759,plain,
! [X0] : leq(multiplication(star(zero),coantidomain(X0)),coantidomain(codomain(X0))),
inference(resolution,[status(thm)],[f300,f6955]) ).
fof(f8760,plain,
! [X0,X1] : leq(multiplication(star(zero),coantidomain(X0)),star(X1)),
inference(resolution,[status(thm)],[f300,f7165]) ).
fof(f8761,plain,
! [X0] : leq(multiplication(star(zero),coantidomain(X0)),domain(coantidomain(X0))),
inference(resolution,[status(thm)],[f300,f4196]) ).
fof(f8762,plain,
! [X0,X1] : leq(multiplication(star(zero),coantidomain(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f300,f2251]) ).
fof(f8763,plain,
! [X0,X1] : leq(multiplication(star(zero),coantidomain(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f300,f1762]) ).
fof(f8764,plain,
! [X0] : leq(multiplication(star(zero),coantidomain(X0)),one),
inference(resolution,[status(thm)],[f300,f1346]) ).
fof(f8765,plain,
! [X0] : leq(multiplication(star(zero),domain(X0)),codomain(domain(X0))),
inference(resolution,[status(thm)],[f300,f6659]) ).
fof(f8766,plain,
! [X0,X1] : leq(multiplication(star(zero),domain(X0)),star(X1)),
inference(resolution,[status(thm)],[f300,f7164]) ).
fof(f8767,plain,
! [X0] : leq(multiplication(star(zero),domain(X0)),antidomain(c(X0))),
inference(resolution,[status(thm)],[f300,f4071]) ).
fof(f8768,plain,
! [X0,X1] : leq(multiplication(star(zero),domain(X0)),addition(one,X1)),
inference(resolution,[status(thm)],[f300,f2264]) ).
fof(f8769,plain,
! [X0,X1] : leq(multiplication(star(zero),domain(X0)),addition(X1,one)),
inference(resolution,[status(thm)],[f300,f1763]) ).
fof(f8770,plain,
! [X0] : leq(multiplication(star(zero),domain(X0)),one),
inference(resolution,[status(thm)],[f300,f1344]) ).
fof(f8771,plain,
! [X0,X1] : leq(multiplication(star(zero),one),addition(X0,star(X1))),
inference(resolution,[status(thm)],[f300,f7178]) ).
fof(f8774,plain,
! [X0] : leq(multiplication(star(zero),addition(one,multiplication(star(X0),X0))),star(X0)),
inference(resolution,[status(thm)],[f300,f49]) ).
fof(f8775,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)],[f300,f247]) ).
fof(f8776,plain,
! [X0] : leq(multiplication(star(zero),addition(one,multiplication(X0,star(X0)))),star(X0)),
inference(resolution,[status(thm)],[f300,f48]) ).
fof(f8777,plain,
! [X0,X1] : leq(multiplication(star(zero),X0),multiplication(star(X1),X0)),
inference(resolution,[status(thm)],[f300,f8050]) ).
fof(f8778,plain,
! [X0,X1] : leq(multiplication(star(zero),X0),multiplication(X0,star(X1))),
inference(resolution,[status(thm)],[f300,f8048]) ).
fof(f8779,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),X0),addition(X1,addition(X0,X2))),
inference(resolution,[status(thm)],[f300,f1357]) ).
fof(f8780,plain,
! [X0,X1,X2] : leq(multiplication(star(zero),X0),addition(X1,addition(X2,X0))),
inference(resolution,[status(thm)],[f300,f1356]) ).
fof(f8781,plain,
! [X0,X1] : leq(multiplication(star(zero),X0),addition(X1,X0)),
inference(resolution,[status(thm)],[f300,f1359]) ).
fof(f8782,plain,
! [X0,X1] : leq(multiplication(star(zero),X0),addition(X0,X1)),
inference(resolution,[status(thm)],[f300,f1261]) ).
fof(f8784,plain,
! [X0,X1] : leq(star(zero),addition(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f38,f8771]) ).
fof(f8827,plain,
! [X0] :
( leq(multiplication(star(one),star(X0)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7209,f294]) ).
fof(f8828,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(star(X0),addition(X0,one))),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7423,f294]) ).
fof(f8829,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(addition(X0,one),star(X0))),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7156,f294]) ).
fof(f8830,plain,
! [X0,X1] :
( leq(multiplication(star(one),backward_diamond(X0,X1)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1439,f294]) ).
fof(f8831,plain,
! [X0,X1] :
( leq(multiplication(star(one),forward_box(X0,X1)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1432,f294]) ).
fof(f8832,plain,
! [X0,X1] :
( leq(multiplication(star(one),backward_box(X0,X1)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1427,f294]) ).
fof(f8833,plain,
! [X0,X1] :
( leq(multiplication(star(one),forward_diamond(X0,X1)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1420,f294]) ).
fof(f8834,plain,
! [X0] :
( leq(multiplication(star(one),divergence(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1423,f294]) ).
fof(f8835,plain,
! [X0] :
( leq(multiplication(star(one),codomain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1412,f294]) ).
fof(f8836,plain,
! [X0] :
( leq(multiplication(star(one),c(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1406,f294]) ).
fof(f8837,plain,
! [X0] :
( leq(multiplication(star(one),antidomain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1315,f294]) ).
fof(f8838,plain,
! [X0] :
( leq(multiplication(star(one),coantidomain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1313,f294]) ).
fof(f8839,plain,
! [X0] :
( leq(multiplication(star(one),domain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1311,f294]) ).
fof(f8840,plain,
! [X0] :
( leq(multiplication(star(one),c(X0)),domain(X0))
| ~ leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f515,f294]) ).
fof(f8841,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)],[f561,f294]) ).
fof(f8842,plain,
! [X0] :
( leq(multiplication(star(one),codomain(X0)),coantidomain(X0))
| ~ leq(one,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f625,f294]) ).
fof(f8843,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)],[f404,f294]) ).
fof(f8844,plain,
! [X0] :
( leq(multiplication(star(one),domain(X0)),antidomain(X0))
| ~ leq(one,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f504,f294]) ).
fof(f8845,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)],[f199,f294]) ).
fof(f8846,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)],[f214,f294]) ).
fof(f8847,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)],[f165,f294]) ).
fof(f8848,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)],[f206,f294]) ).
fof(f8849,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)],[f196,f294]) ).
fof(f8850,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)],[f148,f294]) ).
fof(f8851,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)],[f41,f294]) ).
fof(f8852,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)],[f40,f294]) ).
fof(f8853,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)],[f98,f294]) ).
fof(f8854,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)],[f34,f294]) ).
fof(f8855,plain,
! [X0] :
( leq(multiplication(star(one),X0),zero)
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f75,f294]) ).
fof(f8856,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(domain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4331,f294]) ).
fof(f8857,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(coantidomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4330,f294]) ).
fof(f8858,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(antidomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4329,f294]) ).
fof(f8859,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(c(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4328,f294]) ).
fof(f8860,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(codomain(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4327,f294]) ).
fof(f8861,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(divergence(X1),X0)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f4326,f294]) ).
fof(f8862,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,domain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2352,f294]) ).
fof(f8863,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,coantidomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2351,f294]) ).
fof(f8864,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,antidomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2350,f294]) ).
fof(f8865,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,c(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2349,f294]) ).
fof(f8866,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,codomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2348,f294]) ).
fof(f8867,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,divergence(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2347,f294]) ).
fof(f8868,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,X1)),X1)
| ~ leq(multiplication(addition(X0,one),X1),X1) ),
inference(paramodulation,[status(thm)],[f227,f294]) ).
fof(f8870,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,X1)),X0)
| ~ leq(multiplication(X0,addition(X1,one)),X0) ),
inference(paramodulation,[status(thm)],[f187,f294]) ).
fof(f8871,plain,
! [X0,X1] :
( leq(multiplication(star(one),multiplication(X0,X1)),X0)
| ~ leq(multiplication(X0,addition(one,X1)),X0) ),
inference(paramodulation,[status(thm)],[f157,f294]) ).
fof(f8872,plain,
! [X0,X1] :
( leq(multiplication(star(one),addition(X1,addition(X0,X1))),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f94,f294]) ).
fof(f8873,plain,
! [X0,X1] :
( leq(multiplication(star(one),addition(X0,X1)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f100,f294]) ).
fof(f8874,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),addition(X0,X1)),X2)
| ~ leq(addition(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f92,f294]) ).
fof(f8875,plain,
! [X0,X1,X2] :
( leq(multiplication(star(one),addition(X2,X0)),X1)
| ~ leq(addition(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f92,f294]) ).
fof(f8877,plain,
! [X0,X1] :
( leq(multiplication(star(one),X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f33,f294]) ).
fof(f8878,plain,
! [X0,X1] :
( leq(multiplication(star(one),X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f33,f294]) ).
fof(f8880,definition,
( sQ14_spl
<=> leq(one,one) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f8882,plain,
( sQ14_spl
| ~ leq(one,one) ),
inference(component_clause,[status(thm)],[f8880]) ).
fof(f8883,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(f8884,plain,
! [X0,X1] :
( ~ sQ15_spl
| leq(multiplication(star(one),backward_diamond(X0,X1)),one) ),
inference(component_clause,[status(thm)],[f8883]) ).
fof(f8886,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8830,f8880,f8883]) ).
fof(f8887,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(f8888,plain,
! [X0,X1] :
( ~ sQ16_spl
| leq(multiplication(star(one),forward_box(X0,X1)),one) ),
inference(component_clause,[status(thm)],[f8887]) ).
fof(f8890,plain,
( sQ16_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8831,f8880,f8887]) ).
fof(f8891,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(f8892,plain,
! [X0,X1] :
( ~ sQ17_spl
| leq(multiplication(star(one),backward_box(X0,X1)),one) ),
inference(component_clause,[status(thm)],[f8891]) ).
fof(f8894,plain,
( sQ17_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8832,f8880,f8891]) ).
fof(f8895,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(f8896,plain,
! [X0,X1] :
( ~ sQ18_spl
| leq(multiplication(star(one),forward_diamond(X0,X1)),one) ),
inference(component_clause,[status(thm)],[f8895]) ).
fof(f8898,plain,
( sQ18_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8833,f8880,f8895]) ).
fof(f8899,definition,
! [X0] :
( sQ19_spl
<=> leq(multiplication(star(one),divergence(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f8900,plain,
! [X0] :
( ~ sQ19_spl
| leq(multiplication(star(one),divergence(X0)),one) ),
inference(component_clause,[status(thm)],[f8899]) ).
fof(f8902,plain,
( sQ19_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8834,f8880,f8899]) ).
fof(f8903,definition,
! [X0] :
( sQ20_spl
<=> leq(multiplication(star(one),codomain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f8904,plain,
! [X0] :
( ~ sQ20_spl
| leq(multiplication(star(one),codomain(X0)),one) ),
inference(component_clause,[status(thm)],[f8903]) ).
fof(f8906,plain,
( sQ20_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8835,f8880,f8903]) ).
fof(f8907,definition,
! [X0] :
( sQ21_spl
<=> leq(multiplication(star(one),c(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f8908,plain,
! [X0] :
( ~ sQ21_spl
| leq(multiplication(star(one),c(X0)),one) ),
inference(component_clause,[status(thm)],[f8907]) ).
fof(f8910,plain,
( sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8836,f8880,f8907]) ).
fof(f8911,definition,
! [X0] :
( sQ22_spl
<=> leq(multiplication(star(one),antidomain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f8912,plain,
! [X0] :
( ~ sQ22_spl
| leq(multiplication(star(one),antidomain(X0)),one) ),
inference(component_clause,[status(thm)],[f8911]) ).
fof(f8914,plain,
( sQ22_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8837,f8880,f8911]) ).
fof(f8915,definition,
! [X0] :
( sQ23_spl
<=> leq(multiplication(star(one),coantidomain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f8916,plain,
! [X0] :
( ~ sQ23_spl
| leq(multiplication(star(one),coantidomain(X0)),one) ),
inference(component_clause,[status(thm)],[f8915]) ).
fof(f8918,plain,
( sQ23_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8838,f8880,f8915]) ).
fof(f8919,definition,
! [X0] :
( sQ24_spl
<=> leq(multiplication(star(one),domain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f8920,plain,
! [X0] :
( ~ sQ24_spl
| leq(multiplication(star(one),domain(X0)),one) ),
inference(component_clause,[status(thm)],[f8919]) ).
fof(f8922,plain,
( sQ24_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f8839,f8880,f8919]) ).
fof(f8923,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(domain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8856,f234]) ).
fof(f8924,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(coantidomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8857,f234]) ).
fof(f8925,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(antidomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8858,f234]) ).
fof(f8926,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(c(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8859,f234]) ).
fof(f8927,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(codomain(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8860,f234]) ).
fof(f8928,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(divergence(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f8861,f234]) ).
fof(f8929,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,domain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8862,f234]) ).
fof(f8930,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,coantidomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8863,f234]) ).
fof(f8931,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,antidomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8864,f234]) ).
fof(f8932,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,c(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8865,f234]) ).
fof(f8933,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,codomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8866,f234]) ).
fof(f8934,plain,
! [X0,X1] : leq(multiplication(star(one),multiplication(X0,divergence(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f8867,f234]) ).
fof(f8937,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8882,f234]) ).
fof(f8938,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f8937]) ).
fof(f8939,plain,
! [X0] : leq(multiplication(star(zero),star(zero)),star(X0)),
inference(resolution,[status(thm)],[f8661,f300]) ).
fof(f8940,plain,
! [X0] : leq(multiplication(star(antidomain(star(X0))),star(zero)),star(X0)),
inference(resolution,[status(thm)],[f8661,f299]) ).
fof(f8941,plain,
! [X0] : addition(star(zero),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f8661,f46]) ).
fof(f8942,plain,
! [X0] : leq(multiplication(star(zero),star(zero)),star(X0)),
inference(forward_demodulation,[status(thm)],[f8054,f8940]) ).
fof(f8943,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(forward_diamond(X1,X2),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6667]) ).
fof(f8944,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(forward_box(X1,X2),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6327]) ).
fof(f8945,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(backward_box(X1,X2),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6326]) ).
fof(f8946,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(backward_diamond(X1,X2),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6192]) ).
fof(f8947,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6815]) ).
fof(f8948,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(domain(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6469]) ).
fof(f8949,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(antidomain(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6335]) ).
fof(f8950,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(c(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6199]) ).
fof(f8951,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(codomain(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f6071]) ).
fof(f8952,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(divergence(X1),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f5662]) ).
fof(f8953,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(coantidomain(X0),forward_diamond(X1,X2))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3808]) ).
fof(f8954,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(coantidomain(X0),forward_box(X1,X2))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3489]) ).
fof(f8955,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(coantidomain(X0),backward_box(X1,X2))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3488]) ).
fof(f8956,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),multiplication(coantidomain(X0),backward_diamond(X1,X2))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3259]) ).
fof(f8957,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),coantidomain(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3817]) ).
fof(f8958,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),domain(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3587]) ).
fof(f8959,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),antidomain(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3497]) ).
fof(f8960,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),c(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3402]) ).
fof(f8961,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),codomain(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3175]) ).
fof(f8962,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(coantidomain(X0),divergence(X1))),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f3096]) ).
fof(f8963,plain,
! [X0] : leq(multiplication(star(codomain(X0)),coantidomain(X0)),coantidomain(codomain(X0))),
inference(resolution,[status(thm)],[f301,f6955]) ).
fof(f8965,plain,
! [X0] : leq(multiplication(star(X0),coantidomain(X0)),coantidomain(X0)),
inference(resolution,[status(thm)],[f301,f234]) ).
fof(f8966,plain,
! [X0,X1] :
( leq(multiplication(star(star(X1)),X0),coantidomain(star(X1)))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f8052,f301]) ).
fof(f8968,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),coantidomain(coantidomain(X1)))
| ~ leq(X0,codomain(X1)) ),
inference(paramodulation,[status(thm)],[f61,f301]) ).
fof(f8969,plain,
! [X0] :
( leq(multiplication(star(one),X0),coantidomain(one))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f141,f301]) ).
fof(f8971,plain,
! [X0,X1] :
( leq(multiplication(star(star(X1)),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f8052,f8966]) ).
fof(f8973,plain,
! [X0,X1] :
( leq(multiplication(star(coantidomain(X1)),X0),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f61,f8968]) ).
fof(f8974,plain,
! [X0] :
( leq(multiplication(star(one),X0),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f141,f8969]) ).
fof(f9039,plain,
! [X0,X1] : leq(multiplication(star(zero),one),addition(star(X0),X1)),
inference(resolution,[status(thm)],[f8012,f300]) ).
fof(f9040,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(star(X0),X1))),one),addition(star(X0),X1)),
inference(resolution,[status(thm)],[f8012,f299]) ).
fof(f9041,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(resolution,[status(thm)],[f8012,f46]) ).
fof(f9054,plain,
! [X0,X1] : leq(one,multiplication(addition(X0,one),star(X1))),
inference(paramodulation,[status(thm)],[f227,f8012]) ).
fof(f9055,plain,
! [X0,X1] : leq(one,multiplication(addition(one,X0),star(X1))),
inference(paramodulation,[status(thm)],[f202,f8012]) ).
fof(f9056,plain,
! [X0,X1] : leq(one,multiplication(star(X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f187,f8012]) ).
fof(f9057,plain,
! [X0,X1] : leq(one,multiplication(star(X0),addition(one,X1))),
inference(paramodulation,[status(thm)],[f157,f8012]) ).
fof(f9060,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f92,f8012]) ).
fof(f9061,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(star(X1),X2))),
inference(paramodulation,[status(thm)],[f92,f8012]) ).
fof(f9066,plain,
! [X0,X1] : leq(star(zero),addition(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f38,f9039]) ).
fof(f9067,plain,
! [X0,X1] : leq(star(antidomain(addition(star(X0),X1))),addition(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f38,f9040]) ).
fof(f9069,plain,
! [X0] :
( leq(multiplication(star(one),star(X0)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7209,f297]) ).
fof(f9070,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(star(X0),addition(X0,one))),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7423,f297]) ).
fof(f9071,plain,
! [X0] :
( leq(multiplication(star(one),multiplication(addition(X0,one),star(X0))),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7156,f297]) ).
fof(f9082,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),c(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f515,f297]) ).
fof(f9083,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)],[f561,f297]) ).
fof(f9084,plain,
! [X0] :
( leq(multiplication(star(coantidomain(X0)),codomain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f625,f297]) ).
fof(f9085,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)],[f404,f297]) ).
fof(f9086,plain,
! [X0] :
( leq(multiplication(star(antidomain(X0)),domain(X0)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f504,f297]) ).
fof(f9087,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)],[f199,f297]) ).
fof(f9088,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)],[f214,f297]) ).
fof(f9089,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)],[f165,f297]) ).
fof(f9090,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)],[f206,f297]) ).
fof(f9091,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)],[f196,f297]) ).
fof(f9092,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)],[f148,f297]) ).
fof(f9093,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)],[f41,f297]) ).
fof(f9094,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)],[f40,f297]) ).
fof(f9095,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,X0)),X2),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f98,f297]) ).
fof(f9096,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,X1)),X2),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f34,f297]) ).
fof(f9098,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(domain(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4331,f297]) ).
fof(f9099,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(coantidomain(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4330,f297]) ).
fof(f9100,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(antidomain(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4329,f297]) ).
fof(f9101,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(c(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4328,f297]) ).
fof(f9102,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(codomain(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4327,f297]) ).
fof(f9103,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(divergence(X1),X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4326,f297]) ).
fof(f9104,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,domain(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2352,f297]) ).
fof(f9105,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,coantidomain(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2351,f297]) ).
fof(f9106,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2350,f297]) ).
fof(f9107,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2349,f297]) ).
fof(f9108,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,codomain(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2348,f297]) ).
fof(f9109,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,divergence(X1))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2347,f297]) ).
fof(f9110,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,X1)),one)
| ~ leq(multiplication(addition(X0,one),X1),one) ),
inference(paramodulation,[status(thm)],[f227,f297]) ).
fof(f9111,plain,
! [X0,X1] :
( leq(multiplication(star(X1),multiplication(X0,X1)),one)
| ~ leq(multiplication(addition(one,X0),X1),one) ),
inference(paramodulation,[status(thm)],[f202,f297]) ).
fof(f9112,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),one)
| ~ leq(multiplication(X0,addition(X1,one)),one) ),
inference(paramodulation,[status(thm)],[f187,f297]) ).
fof(f9114,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(X1,addition(X0,X1))),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f94,f297]) ).
fof(f9115,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(X0,X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f100,f297]) ).
fof(f9116,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X2),addition(X0,X1)),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f92,f297]) ).
fof(f9117,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(X2,X0)),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f92,f297]) ).
fof(f9119,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f33,f297]) ).
fof(f9120,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f33,f297]) ).
fof(f9121,plain,
! [X0] :
( leq(multiplication(star(X0),X0),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f36,f297]) ).
fof(f9132,definition,
! [X0] :
( sQ25_spl
<=> leq(multiplication(star(domain(X0)),c(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f9133,plain,
! [X0] :
( ~ sQ25_spl
| leq(multiplication(star(domain(X0)),c(X0)),one) ),
inference(component_clause,[status(thm)],[f9132]) ).
fof(f9135,plain,
( sQ25_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9082,f8880,f9132]) ).
fof(f9136,plain,
! [X0,X1] : leq(multiplication(star(coantidomain(multiplication(X0,X1))),coantidomain(multiplication(codomain(X0),X1))),one),
inference(forward_subsumption_resolution,[status(thm)],[f9083,f1346]) ).
fof(f9137,definition,
! [X0] :
( sQ26_spl
<=> leq(multiplication(star(coantidomain(X0)),codomain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f9138,plain,
! [X0] :
( ~ sQ26_spl
| leq(multiplication(star(coantidomain(X0)),codomain(X0)),one) ),
inference(component_clause,[status(thm)],[f9137]) ).
fof(f9140,plain,
( sQ26_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9084,f8880,f9137]) ).
fof(f9141,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))),one),
inference(forward_subsumption_resolution,[status(thm)],[f9085,f1348]) ).
fof(f9142,definition,
! [X0] :
( sQ27_spl
<=> leq(multiplication(star(antidomain(X0)),domain(X0)),one) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f9143,plain,
! [X0] :
( ~ sQ27_spl
| leq(multiplication(star(antidomain(X0)),domain(X0)),one) ),
inference(component_clause,[status(thm)],[f9142]) ).
fof(f9145,plain,
( sQ27_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f9086,f8880,f9142]) ).
fof(f9148,plain,
! [X0] : leq(multiplication(star(star(one)),multiplication(star(one),X0)),X0),
inference(resolution,[status(thm)],[f8319,f290]) ).
fof(f9150,plain,
! [X0] : leq(multiplication(star(X0),multiplication(star(one),coantidomain(X0))),coantidomain(X0)),
inference(resolution,[status(thm)],[f8319,f301]) ).
fof(f9151,plain,
! [X0] : leq(multiplication(star(zero),multiplication(star(one),X0)),X0),
inference(resolution,[status(thm)],[f8319,f300]) ).
fof(f9152,plain,
! [X0] : leq(multiplication(star(antidomain(X0)),multiplication(star(one),X0)),X0),
inference(resolution,[status(thm)],[f8319,f299]) ).
fof(f9153,plain,
! [X0] : addition(multiplication(star(one),X0),X0) = X0,
inference(resolution,[status(thm)],[f8319,f46]) ).
fof(f9154,plain,
leq(star(one),codomain(star(one))),
inference(paramodulation,[status(thm)],[f2178,f8319]) ).
fof(f9164,plain,
! [X0] : addition(X0,multiplication(star(one),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f33,f9153]) ).
fof(f9165,plain,
leq(star(one),one),
inference(forward_demodulation,[status(thm)],[f8095,f9154]) ).
fof(f9173,plain,
leq(multiplication(star(zero),star(one)),one),
inference(resolution,[status(thm)],[f9165,f300]) ).
fof(f9174,plain,
leq(multiplication(star(antidomain(one)),star(one)),one),
inference(resolution,[status(thm)],[f9165,f299]) ).
fof(f9175,plain,
addition(star(one),one) = one,
inference(resolution,[status(thm)],[f9165,f46]) ).
fof(f9176,plain,
leq(multiplication(star(zero),star(one)),one),
inference(forward_demodulation,[status(thm)],[f114,f9174]) ).
fof(f9177,plain,
addition(one,star(one)) = one,
inference(forward_demodulation,[status(thm)],[f33,f9175]) ).
fof(f9178,plain,
star(one) = one,
inference(forward_demodulation,[status(thm)],[f7209,f9177]) ).
fof(f9181,plain,
! [X0,X1] :
( leq(multiplication(one,X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(backward_demodulation,[status(thm)],[f9178,f294]) ).
fof(f9183,plain,
leq(star(zero),one),
inference(paramodulation,[status(thm)],[f9178,f8661]) ).
fof(f9217,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f9181]) ).
fof(f9240,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(X0,star(X0))),one)
| ~ leq(addition(X0,multiplication(X1,X0)),one) ),
inference(paramodulation,[status(thm)],[f202,f334]) ).
fof(f9241,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),antidomain(X1))
| ~ leq(multiplication(X0,X1),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f219,f334]) ).
fof(f9242,plain,
! [X0,X1] :
( leq(multiplication(one,multiplication(X0,star(X0))),X1)
| ~ leq(addition(X0,multiplication(X1,X0)),X1) ),
inference(paramodulation,[status(thm)],[f227,f334]) ).
fof(f9245,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(coantidomain(X1),star(coantidomain(X1)))),X1)
| ~ leq(multiplication(X0,coantidomain(X1)),X1) ),
inference(paramodulation,[status(thm)],[f221,f334]) ).
fof(f9246,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)],[f2178,f334]) ).
fof(f9247,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)],[f176,f334]) ).
fof(f9248,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)],[f185,f334]) ).
fof(f9249,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)],[f146,f334]) ).
fof(f9250,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)],[f139,f334]) ).
fof(f9251,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(coantidomain(addition(X0,X1)),star(coantidomain(addition(X0,X1))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f58,f334]) ).
fof(f9253,plain,
! [X0,X1] :
( leq(multiplication(X1,multiplication(one,star(one))),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f38,f334]) ).
fof(f9254,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X1,star(X1))),one)
| ~ leq(multiplication(star(X0),X1),one) ),
inference(paramodulation,[status(thm)],[f7209,f334]) ).
fof(f9255,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)],[f7423,f334]) ).
fof(f9256,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)],[f7156,f334]) ).
fof(f9257,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1439,f334]) ).
fof(f9258,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1432,f334]) ).
fof(f9259,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1427,f334]) ).
fof(f9260,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1420,f334]) ).
fof(f9261,plain,
! [X0,X1] :
( leq(multiplication(divergence(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1423,f334]) ).
fof(f9262,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1412,f334]) ).
fof(f9263,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1406,f334]) ).
fof(f9264,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1315,f334]) ).
fof(f9265,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1313,f334]) ).
fof(f9266,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),one)
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f1311,f334]) ).
fof(f9267,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),domain(X1))
| ~ leq(multiplication(one,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f515,f334]) ).
fof(f9268,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)],[f561,f334]) ).
fof(f9269,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),coantidomain(X1))
| ~ leq(multiplication(one,X0),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f625,f334]) ).
fof(f9270,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)],[f404,f334]) ).
fof(f9271,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),antidomain(X1))
| ~ leq(multiplication(one,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f504,f334]) ).
fof(f9272,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)],[f199,f334]) ).
fof(f9273,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)],[f214,f334]) ).
fof(f9274,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)],[f165,f334]) ).
fof(f9275,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)],[f206,f334]) ).
fof(f9276,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)],[f196,f334]) ).
fof(f9277,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)],[f148,f334]) ).
fof(f9278,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)],[f41,f334]) ).
fof(f9279,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)],[f40,f334]) ).
fof(f9280,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)],[f98,f334]) ).
fof(f9281,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)],[f34,f334]) ).
fof(f9282,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),zero)
| ~ leq(multiplication(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f75,f334]) ).
fof(f9283,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(domain(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4331,f334]) ).
fof(f9284,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(coantidomain(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4330,f334]) ).
fof(f9285,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(antidomain(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4329,f334]) ).
fof(f9286,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(c(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4328,f334]) ).
fof(f9287,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(codomain(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4327,f334]) ).
fof(f9288,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(divergence(X2),X0),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4326,f334]) ).
fof(f9289,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,domain(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2352,f334]) ).
fof(f9290,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,coantidomain(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2351,f334]) ).
fof(f9291,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,antidomain(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2350,f334]) ).
fof(f9292,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,c(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2349,f334]) ).
fof(f9293,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,codomain(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2348,f334]) ).
fof(f9294,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,divergence(X2)),multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2347,f334]) ).
fof(f9295,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)],[f227,f334]) ).
fof(f9296,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)],[f202,f334]) ).
fof(f9297,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)],[f187,f334]) ).
fof(f9298,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)],[f157,f334]) ).
fof(f9299,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X1,addition(X0,X1)),multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f94,f334]) ).
fof(f9300,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)],[f100,f334]) ).
fof(f9301,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)],[f92,f334]) ).
fof(f9302,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)],[f92,f334]) ).
fof(f9304,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f33,f334]) ).
fof(f9305,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f33,f334]) ).
fof(f9306,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f36,f334]) ).
fof(f9307,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),X1)
| ~ leq(addition(X0,multiplication(X1,X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f39,f9242]) ).
fof(f9310,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)],[f37,f9249]) ).
fof(f9311,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)],[f9310,f235]) ).
fof(f9312,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)],[f37,f9250]) ).
fof(f9313,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)],[f9312,f235]) ).
fof(f9314,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(coantidomain(addition(X1,X0)),star(coantidomain(addition(X1,X0))))),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9251,f235]) ).
fof(f9316,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f9253]) ).
fof(f9317,plain,
! [X0,X1] :
( leq(multiplication(X1,one),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f9178,f9316]) ).
fof(f9318,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f38,f9317]) ).
fof(f9319,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)],[f37,f9255]) ).
fof(f9320,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)],[f37,f9256]) ).
fof(f9321,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9257]) ).
fof(f9322,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9258]) ).
fof(f9323,plain,
! [X0,X1,X2] :
( leq(multiplication(backward_box(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9259]) ).
fof(f9324,plain,
! [X0,X1,X2] :
( leq(multiplication(forward_diamond(X1,X2),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9260]) ).
fof(f9325,plain,
! [X0,X1] :
( leq(multiplication(divergence(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9261]) ).
fof(f9326,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9262]) ).
fof(f9327,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9263]) ).
fof(f9328,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9264]) ).
fof(f9329,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9265]) ).
fof(f9330,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f9266]) ).
fof(f9331,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f9267]) ).
fof(f9332,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f9269]) ).
fof(f9333,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f9271]) ).
fof(f9334,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)],[f37,f9272]) ).
fof(f9335,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)],[f37,f9334]) ).
fof(f9336,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)],[f37,f9275]) ).
fof(f9337,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)],[f37,f9336]) ).
fof(f9338,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)],[f37,f9337]) ).
fof(f9339,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)],[f37,f9276]) ).
fof(f9340,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)],[f37,f9339]) ).
fof(f9341,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)],[f37,f9277]) ).
fof(f9342,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)],[f37,f9341]) ).
fof(f9343,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)],[f37,f9278]) ).
fof(f9344,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)],[f37,f9343]) ).
fof(f9345,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)],[f37,f9279]) ).
fof(f9346,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)],[f37,f9345]) ).
fof(f9347,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)],[f37,f9283]) ).
fof(f9348,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)],[f37,f9284]) ).
fof(f9349,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)],[f37,f9285]) ).
fof(f9350,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)],[f37,f9286]) ).
fof(f9351,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)],[f37,f9287]) ).
fof(f9352,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)],[f37,f9288]) ).
fof(f9353,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)],[f37,f9289]) ).
fof(f9354,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)],[f37,f9290]) ).
fof(f9355,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)],[f37,f9291]) ).
fof(f9356,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)],[f37,f9292]) ).
fof(f9357,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)],[f37,f9293]) ).
fof(f9358,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)],[f37,f9294]) ).
fof(f9359,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)],[f37,f9295]) ).
fof(f9360,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)],[f37,f9359]) ).
fof(f9361,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)],[f37,f9296]) ).
fof(f9362,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)],[f37,f9361]) ).
fof(f9363,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)],[f37,f9297]) ).
fof(f9364,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)],[f37,f9363]) ).
fof(f9365,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)],[f37,f9298]) ).
fof(f9366,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)],[f37,f9365]) ).
fof(f9369,plain,
leq(multiplication(star(zero),star(zero)),one),
inference(resolution,[status(thm)],[f9183,f300]) ).
fof(f9370,plain,
leq(multiplication(star(antidomain(one)),star(zero)),one),
inference(resolution,[status(thm)],[f9183,f299]) ).
fof(f9371,plain,
addition(star(zero),one) = one,
inference(resolution,[status(thm)],[f9183,f46]) ).
fof(f9372,plain,
leq(multiplication(star(zero),star(zero)),one),
inference(forward_demodulation,[status(thm)],[f114,f9370]) ).
fof(f9373,plain,
addition(one,star(zero)) = one,
inference(forward_demodulation,[status(thm)],[f33,f9371]) ).
fof(f9374,plain,
star(zero) = one,
inference(forward_demodulation,[status(thm)],[f7209,f9373]) ).
fof(f9434,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)],[f219,f335]) ).
fof(f9435,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)],[f225,f335]) ).
fof(f9436,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)],[f4088,f335]) ).
fof(f9437,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)],[f3965,f335]) ).
fof(f9438,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)],[f37,f335]) ).
fof(f9440,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X0),multiplication(X1,star(X0))),antidomain(X0))
| ~ leq(multiplication(antidomain(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f172,f335]) ).
fof(f9441,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)],[f54,f335]) ).
fof(f9442,plain,
! [X0,X1] :
( leq(multiplication(zero,multiplication(X0,star(X1))),zero)
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f43,f335]) ).
fof(f9443,plain,
! [X0,X1] :
( leq(multiplication(one,multiplication(X1,star(X0))),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f39,f335]) ).
fof(f9444,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(one))),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f157,f335]) ).
fof(f9445,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(coantidomain(X0)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f176,f335]) ).
fof(f9446,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(one,star(X1))),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f187,f335]) ).
fof(f9449,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)],[f7423,f335]) ).
fof(f9450,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)],[f7156,f335]) ).
fof(f9461,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(c(X1),star(domain(X1)))),X0)
| ~ leq(multiplication(X0,one),X0) ),
inference(paramodulation,[status(thm)],[f515,f335]) ).
fof(f9462,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)],[f561,f335]) ).
fof(f9463,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(codomain(X1),star(coantidomain(X1)))),X0)
| ~ leq(multiplication(X0,one),X0) ),
inference(paramodulation,[status(thm)],[f625,f335]) ).
fof(f9464,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)],[f404,f335]) ).
fof(f9465,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(domain(X1),star(antidomain(X1)))),X0)
| ~ leq(multiplication(X0,one),X0) ),
inference(paramodulation,[status(thm)],[f504,f335]) ).
fof(f9466,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)],[f199,f335]) ).
fof(f9467,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)],[f214,f335]) ).
fof(f9468,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)],[f165,f335]) ).
fof(f9469,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)],[f206,f335]) ).
fof(f9470,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)],[f196,f335]) ).
fof(f9471,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)],[f148,f335]) ).
fof(f9472,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)],[f41,f335]) ).
fof(f9473,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)],[f40,f335]) ).
fof(f9474,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)],[f98,f335]) ).
fof(f9475,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)],[f34,f335]) ).
fof(f9477,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(domain(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4331,f335]) ).
fof(f9478,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(coantidomain(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4330,f335]) ).
fof(f9479,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(antidomain(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4329,f335]) ).
fof(f9480,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(c(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4328,f335]) ).
fof(f9481,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(codomain(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4327,f335]) ).
fof(f9482,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(divergence(X2),X1),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f4326,f335]) ).
fof(f9483,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,domain(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2352,f335]) ).
fof(f9484,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,coantidomain(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2351,f335]) ).
fof(f9485,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,antidomain(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2350,f335]) ).
fof(f9486,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,c(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2349,f335]) ).
fof(f9487,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,codomain(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2348,f335]) ).
fof(f9488,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,divergence(X2)),star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2347,f335]) ).
fof(f9489,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)],[f227,f335]) ).
fof(f9490,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)],[f202,f335]) ).
fof(f9491,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)],[f187,f335]) ).
fof(f9492,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)],[f157,f335]) ).
fof(f9493,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(addition(X2,addition(X1,X2)),star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f94,f335]) ).
fof(f9494,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)],[f100,f335]) ).
fof(f9495,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)],[f92,f335]) ).
fof(f9496,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)],[f92,f335]) ).
fof(f9498,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f33,f335]) ).
fof(f9499,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f33,f335]) ).
fof(f9500,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f36,f335]) ).
fof(f9501,plain,
! [X0,X1] : leq(multiplication(c(addition(X0,X1)),multiplication(X1,star(X0))),c(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f9436,f235]) ).
fof(f9502,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)],[f37,f9438]) ).
fof(f9504,plain,
! [X0,X1] : leq(multiplication(antidomain(addition(X0,X1)),multiplication(X1,star(X0))),antidomain(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f9441,f235]) ).
fof(f9505,definition,
! [X0,X1] :
( sQ28_spl
<=> leq(multiplication(zero,multiplication(X0,star(X1))),zero) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f9508,plain,
( sQ28_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9442,f7614,f9505]) ).
fof(f9509,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(forward_demodulation,[status(thm)],[f39,f9443]) ).
fof(f9510,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,one)),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f9178,f9444]) ).
fof(f9511,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f38,f9510]) ).
fof(f9512,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),X0)
| ~ leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f39,f9446]) ).
fof(f9515,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)],[f37,f9449]) ).
fof(f9516,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)],[f9178,f9515]) ).
fof(f9517,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)],[f227,f9516]) ).
fof(f9518,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(star(X1),addition(one,X1))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f38,f9517]) ).
fof(f9519,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)],[f37,f9450]) ).
fof(f9520,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)],[f9178,f9519]) ).
fof(f9521,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(addition(X1,one),star(X1))),X0)
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f38,f9520]) ).
fof(f9552,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(c(X1),star(domain(X1)))),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f38,f9461]) ).
fof(f9553,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(c(X1),star(domain(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9552,f234]) ).
fof(f9554,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)],[f9462,f3817]) ).
fof(f9555,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(codomain(X1),star(coantidomain(X1)))),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f38,f9463]) ).
fof(f9556,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(codomain(X1),star(coantidomain(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9555,f234]) ).
fof(f9557,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)],[f9464,f3497]) ).
fof(f9558,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(domain(X1),star(antidomain(X1)))),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f38,f9465]) ).
fof(f9559,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(domain(X1),star(antidomain(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9558,f234]) ).
fof(f9560,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)],[f37,f9466]) ).
fof(f9561,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)],[f37,f9469]) ).
fof(f9562,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)],[f37,f9561]) ).
fof(f9563,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)],[f37,f9470]) ).
fof(f9564,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)],[f37,f9471]) ).
fof(f9565,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)],[f37,f9472]) ).
fof(f9566,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)],[f37,f9473]) ).
fof(f9568,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)],[f37,f9477]) ).
fof(f9569,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)],[f37,f9478]) ).
fof(f9570,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)],[f37,f9479]) ).
fof(f9571,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)],[f37,f9480]) ).
fof(f9572,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)],[f37,f9481]) ).
fof(f9573,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)],[f37,f9482]) ).
fof(f9574,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)],[f37,f9483]) ).
fof(f9575,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)],[f37,f9484]) ).
fof(f9576,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)],[f37,f9485]) ).
fof(f9577,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)],[f37,f9486]) ).
fof(f9578,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)],[f37,f9487]) ).
fof(f9579,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)],[f37,f9488]) ).
fof(f9580,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)],[f37,f9489]) ).
fof(f9581,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)],[f37,f9490]) ).
fof(f9582,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)],[f37,f9491]) ).
fof(f9583,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)],[f37,f9492]) ).
fof(f9592,plain,
! [X0] : addition(c(X0),c(domain(X0))) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f62,f434]) ).
fof(f9593,plain,
! [X0] : addition(domain(X0),c(antidomain(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f57,f434]) ).
fof(f9596,plain,
! [X0,X1] : addition(antidomain(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f67,f434]) ).
fof(f9597,plain,
! [X0,X1] : addition(antidomain(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f66,f434]) ).
fof(f9599,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(c(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f493,f434]) ).
fof(f9600,plain,
! [X0] : addition(antidomain(domain(X0)),domain(c(X0))) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f317,f434]) ).
fof(f9603,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(c(X1),star(antidomain(X1)))),X0)
| ~ leq(multiplication(X0,c(X1)),X0) ),
inference(paramodulation,[status(thm)],[f434,f335]) ).
fof(f9604,plain,
! [X0,X1] :
( leq(multiplication(c(X0),multiplication(X1,star(X1))),antidomain(X0))
| ~ leq(multiplication(c(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f434,f334]) ).
fof(f9605,plain,
! [X0] :
( leq(multiplication(star(antidomain(X0)),c(X0)),one)
| ~ leq(c(X0),one) ),
inference(paramodulation,[status(thm)],[f434,f297]) ).
fof(f9606,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,c(X1))),antidomain(X1))
| ~ leq(multiplication(X0,c(X1)),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f434,f286]) ).
fof(f9607,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X0)),multiplication(c(X0),X1)),X1)
| ~ leq(multiplication(c(X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f434,f285]) ).
fof(f9608,plain,
! [X0,X1] :
( addition(X0,c(X1)) != c(X1)
| leq(addition(X0,antidomain(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f434,f238]) ).
fof(f9609,plain,
! [X0,X1] :
( multiplication(X0,c(X1)) != multiplication(X0,c(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f434,f237]) ).
fof(f9610,plain,
! [X0,X1] :
( multiplication(c(X0),X1) != multiplication(c(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(c(X0),X1)) ),
inference(paramodulation,[status(thm)],[f434,f236]) ).
fof(f9611,plain,
! [X0] : multiplication(c(X0),coantidomain(c(X0))) = multiplication(antidomain(X0),coantidomain(c(X0))),
inference(paramodulation,[status(thm)],[f434,f228]) ).
fof(f9613,plain,
! [X0] : multiplication(antidomain(c(X0)),c(X0)) = multiplication(antidomain(c(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f434,f181]) ).
fof(f9615,plain,
! [X0,X1] : leq(antidomain(X0),addition(X1,c(X0))),
inference(paramodulation,[status(thm)],[f434,f1357]) ).
fof(f9620,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(X0),X1)) = addition(c(X0),X1),
inference(paramodulation,[status(thm)],[f434,f98]) ).
fof(f9622,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(X1,c(X0)),
inference(paramodulation,[status(thm)],[f434,f92]) ).
fof(f9623,plain,
! [X0,X1] : addition(X0,c(X1)) = addition(c(X1),addition(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f434,f92]) ).
fof(f9624,plain,
! [X0] :
( c(X0) != antidomain(X0)
| leq(c(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f434,f241]) ).
fof(f9626,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(paramodulation,[status(thm)],[f434,f34]) ).
fof(f9628,plain,
! [X0] : addition(c(X0),domain(c(X0))) = c(domain(X0)),
inference(forward_demodulation,[status(thm)],[f317,f9592]) ).
fof(f9629,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(forward_demodulation,[status(thm)],[f317,f9628]) ).
fof(f9630,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f493,f9593]) ).
fof(f9631,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f493,f9630]) ).
fof(f9634,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)],[f33,f9596]) ).
fof(f9635,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f67,f9634]) ).
fof(f9636,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)],[f33,f9597]) ).
fof(f9637,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f66,f9636]) ).
fof(f9640,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f57,f9599]) ).
fof(f9641,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f493,f9640]) ).
fof(f9642,plain,
! [X0] : addition(c(X0),domain(c(X0))) = c(domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f9600]) ).
fof(f9643,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(forward_demodulation,[status(thm)],[f317,f9642]) ).
fof(f9646,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(c(X1),star(antidomain(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9603,f3402]) ).
fof(f9647,plain,
! [X0] : leq(multiplication(star(antidomain(X0)),c(X0)),one),
inference(forward_subsumption_resolution,[status(thm)],[f9605,f1366]) ).
fof(f9648,plain,
! [X0,X1] : leq(multiplication(star(antidomain(X0)),multiplication(c(X0),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f9607,f6199]) ).
fof(f9649,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),multiplication(X0,c(X1))),
inference(trivial_equality_resolution,[status(thm)],[f9609]) ).
fof(f9650,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),multiplication(c(X0),X1)),
inference(trivial_equality_resolution,[status(thm)],[f9610]) ).
fof(f9651,plain,
! [X0] : zero = multiplication(antidomain(X0),coantidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f58,f9611]) ).
fof(f9652,plain,
! [X0] : zero = multiplication(antidomain(c(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f54,f9613]) ).
fof(f9653,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,c(X0))) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f92,f9620]) ).
fof(f9654,plain,
! [X0,X1] : addition(X0,c(X1)) = addition(antidomain(X1),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f92,f9623]) ).
fof(f9657,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)],[f945,f70]) ).
fof(f9661,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f98,f945]) ).
fof(f9662,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f34,f945]) ).
fof(f9666,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f92,f945]) ).
fof(f9668,plain,
! [X0] : addition(one,multiplication(star(X0),addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),star(X0)),
inference(paramodulation,[status(thm)],[f7423,f945]) ).
fof(f9669,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = addition(multiplication(addition(X0,one),star(X0)),star(X0)),
inference(paramodulation,[status(thm)],[f7156,f945]) ).
fof(f9690,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(X2,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f196,f945]) ).
fof(f9691,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,X2),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f148,f945]) ).
fof(f9692,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(X2,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f41,f945]) ).
fof(f9693,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,X2),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f40,f945]) ).
fof(f9694,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X2,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f98,f945]) ).
fof(f9695,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X2,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f34,f945]) ).
fof(f9715,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f92,f945]) ).
fof(f9716,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f92,f945]) ).
fof(f9718,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f33,f945]) ).
fof(f9719,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f33,f945]) ).
fof(f9722,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)],[f945,f70]) ).
fof(f9725,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f945,f202]) ).
fof(f9732,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f945,f157]) ).
fof(f9733,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)],[f945,f291]) ).
fof(f9736,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)],[f945,f214]) ).
fof(f9737,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)],[f945,f165]) ).
fof(f9738,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)],[f945,f53]) ).
fof(f9739,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)],[f945,f51]) ).
fof(f9740,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f945,f98]) ).
fof(f9741,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f945,f34]) ).
fof(f9743,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f945,f238]) ).
fof(f9748,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f945,f92]) ).
fof(f9749,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)],[f945,f335]) ).
fof(f9750,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)],[f945,f334]) ).
fof(f9751,plain,
! [X0,X1] :
( leq(multiplication(star(X1),addition(X0,X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f945,f297]) ).
fof(f9752,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)],[f945,f286]) ).
fof(f9753,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)],[f945,f285]) ).
fof(f9754,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != addition(X2,X1)
| leq(addition(X0,X1),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f945,f238]) ).
fof(f9755,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)],[f945,f237]) ).
fof(f9756,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)],[f945,f236]) ).
fof(f9757,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X0,X1))) = multiplication(X1,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f945,f228]) ).
fof(f9759,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,X1)) = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f945,f181]) ).
fof(f9766,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f945,f98]) ).
fof(f9767,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f945,f92]) ).
fof(f9768,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f945,f92]) ).
fof(f9769,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f945,f241]) ).
fof(f9777,plain,
! [X0] : star(X0) = addition(multiplication(star(X0),addition(X0,one)),star(X0)),
inference(forward_demodulation,[status(thm)],[f7423,f9668]) ).
fof(f9778,plain,
! [X0] : star(X0) = addition(star(X0),multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f33,f9777]) ).
fof(f9779,plain,
! [X0] : star(X0) = multiplication(star(X0),addition(addition(X0,one),one)),
inference(forward_demodulation,[status(thm)],[f187,f9778]) ).
fof(f9780,plain,
! [X0] : star(X0) = multiplication(star(X0),addition(one,addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f98,f9779]) ).
fof(f9781,plain,
! [X0] : star(X0) = multiplication(star(X0),addition(X0,one)),
inference(forward_demodulation,[status(thm)],[f945,f9780]) ).
fof(f9782,plain,
! [X0] : star(X0) = addition(multiplication(addition(X0,one),star(X0)),star(X0)),
inference(forward_demodulation,[status(thm)],[f7156,f9669]) ).
fof(f9783,plain,
! [X0] : star(X0) = addition(star(X0),multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f33,f9782]) ).
fof(f9784,plain,
! [X0] : star(X0) = multiplication(addition(addition(X0,one),one),star(X0)),
inference(forward_demodulation,[status(thm)],[f227,f9783]) ).
fof(f9785,plain,
! [X0] : star(X0) = multiplication(addition(one,addition(X0,one)),star(X0)),
inference(forward_demodulation,[status(thm)],[f98,f9784]) ).
fof(f9786,plain,
! [X0] : star(X0) = multiplication(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f945,f9785]) ).
fof(f9829,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f196,f9690]) ).
fof(f9830,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X0,X1),X0),X2),
inference(forward_demodulation,[status(thm)],[f196,f9829]) ).
fof(f9831,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,addition(X0,X0)),X2),
inference(forward_demodulation,[status(thm)],[f98,f9830]) ).
fof(f9832,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f36,f9831]) ).
fof(f9833,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f148,f9691]) ).
fof(f9834,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(addition(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f148,f9833]) ).
fof(f9835,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,addition(X1,X1))),
inference(forward_demodulation,[status(thm)],[f98,f9834]) ).
fof(f9836,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f36,f9835]) ).
fof(f9837,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f9692]) ).
fof(f9838,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),X0),X2),
inference(forward_demodulation,[status(thm)],[f196,f9837]) ).
fof(f9839,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f98,f9838]) ).
fof(f9840,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f945,f9839]) ).
fof(f9841,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f9693]) ).
fof(f9842,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(addition(X2,X1),X1)),
inference(forward_demodulation,[status(thm)],[f148,f9841]) ).
fof(f9843,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f98,f9842]) ).
fof(f9844,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f945,f9843]) ).
fof(f9845,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f98,f9694]) ).
fof(f9846,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f98,f9695]) ).
fof(f9890,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X1,addition(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f98,f9715]) ).
fof(f9891,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f100,f9890]) ).
fof(f9892,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,addition(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f98,f9716]) ).
fof(f9894,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)],[f33,f9722]) ).
fof(f9895,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)],[f33,f9894]) ).
fof(f9896,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)],[f9895]) ).
fof(f9901,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)],[f92,f9736]) ).
fof(f9902,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)],[f214,f9901]) ).
fof(f9903,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)],[f945,f9902]) ).
fof(f9904,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)],[f92,f9737]) ).
fof(f9905,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)],[f165,f9904]) ).
fof(f9906,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)],[f945,f9905]) ).
fof(f9907,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(trivial_equality_resolution,[status(thm)],[f9755]) ).
fof(f9908,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(trivial_equality_resolution,[status(thm)],[f9756]) ).
fof(f9909,plain,
! [X0,X1] : zero = multiplication(X0,coantidomain(addition(X1,X0))),
inference(forward_demodulation,[status(thm)],[f58,f9757]) ).
fof(f9910,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f54,f9759]) ).
fof(f9911,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f9766]) ).
fof(f9912,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f9911]) ).
fof(f9913,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f9767]) ).
fof(f9914,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f100,f9913]) ).
fof(f9915,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f98,f9768]) ).
fof(f9920,plain,
! [X0] :
( leq(multiplication(one,star(addition(X0,one))),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f7423,f324]) ).
fof(f9921,plain,
! [X0] :
( leq(multiplication(one,star(star(X0))),addition(X0,one))
| ~ leq(star(X0),addition(X0,one)) ),
inference(paramodulation,[status(thm)],[f7156,f324]) ).
fof(f9922,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)],[f199,f324]) ).
fof(f9923,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)],[f206,f324]) ).
fof(f9926,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X2)),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f41,f324]) ).
fof(f9927,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),star(X2)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f40,f324]) ).
fof(f9928,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)],[f98,f324]) ).
fof(f9929,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)],[f34,f324]) ).
fof(f9931,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(paramodulation,[status(thm)],[f4331,f324]) ).
fof(f9932,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f4330,f324]) ).
fof(f9933,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f4329,f324]) ).
fof(f9934,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),c(X1))
| ~ leq(X0,c(X1)) ),
inference(paramodulation,[status(thm)],[f4328,f324]) ).
fof(f9935,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),codomain(X1))
| ~ leq(X0,codomain(X1)) ),
inference(paramodulation,[status(thm)],[f4327,f324]) ).
fof(f9936,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X0)),divergence(X1))
| ~ leq(X0,divergence(X1)) ),
inference(paramodulation,[status(thm)],[f4326,f324]) ).
fof(f9937,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2352,f324]) ).
fof(f9938,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2351,f324]) ).
fof(f9939,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2350,f324]) ).
fof(f9940,plain,
! [X0,X1] :
( leq(multiplication(X0,star(c(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2349,f324]) ).
fof(f9941,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2348,f324]) ).
fof(f9942,plain,
! [X0,X1] :
( leq(multiplication(X0,star(divergence(X1))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2347,f324]) ).
fof(f9943,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X1)),X0)
| ~ leq(multiplication(addition(X0,one),X1),X0) ),
inference(paramodulation,[status(thm)],[f227,f324]) ).
fof(f9944,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X1)),X0)
| ~ leq(multiplication(addition(one,X0),X1),X0) ),
inference(paramodulation,[status(thm)],[f202,f324]) ).
fof(f9945,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,one)),X0) ),
inference(paramodulation,[status(thm)],[f187,f324]) ).
fof(f9946,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),X0)
| ~ leq(multiplication(X0,addition(one,X1)),X0) ),
inference(paramodulation,[status(thm)],[f157,f324]) ).
fof(f9949,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f36,f324]) ).
fof(f9950,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)],[f202,f324]) ).
fof(f9951,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)],[f219,f324]) ).
fof(f9952,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)],[f227,f324]) ).
fof(f9953,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)],[f225,f324]) ).
fof(f9954,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)],[f228,f324]) ).
fof(f9955,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)],[f221,f324]) ).
fof(f9956,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(addition(X0,zero),c(X1)) ),
inference(paramodulation,[status(thm)],[f192,f324]) ).
fof(f9957,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),c(X1))
| ~ leq(addition(X0,zero),c(X1)) ),
inference(paramodulation,[status(thm)],[f4088,f324]) ).
fof(f9958,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),coantidomain(X1))
| ~ leq(addition(X0,zero),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f190,f324]) ).
fof(f9959,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)],[f63,f324]) ).
fof(f9960,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),domain(X1))
| ~ leq(addition(X0,X1),domain(X1)) ),
inference(paramodulation,[status(thm)],[f3965,f324]) ).
fof(f9961,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)],[f37,f324]) ).
fof(f9962,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)],[f181,f324]) ).
fof(f9963,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)],[f172,f324]) ).
fof(f9964,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X1,X2))),antidomain(X1))
| ~ leq(addition(X0,zero),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f131,f324]) ).
fof(f9965,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),antidomain(X1))
| ~ leq(addition(X0,zero),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f54,f324]) ).
fof(f9966,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(addition(X0,zero),zero) ),
inference(paramodulation,[status(thm)],[f43,f324]) ).
fof(f9967,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f39,f324]) ).
fof(f9968,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2178,f324]) ).
fof(f9969,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)],[f157,f324]) ).
fof(f9970,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(coantidomain(X1),X2))),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f176,f324]) ).
fof(f9971,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)],[f187,f324]) ).
fof(f9972,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(addition(X2,coantidomain(X1)))),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f185,f324]) ).
fof(f9973,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(coantidomain(X1),X2))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f146,f324]) ).
fof(f9974,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,coantidomain(multiplication(X1,X2))))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f139,f324]) ).
fof(f9975,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f58,f324]) ).
fof(f9977,plain,
! [X0,X1] :
( leq(multiplication(X0,star(one)),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f38,f324]) ).
fof(f9979,plain,
! [X0] :
( leq(star(addition(X0,one)),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f39,f9920]) ).
fof(f9980,plain,
! [X0] : leq(star(addition(X0,one)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f9979,f234]) ).
fof(f9981,plain,
! [X0] :
( leq(star(star(X0)),addition(X0,one))
| ~ leq(star(X0),addition(X0,one)) ),
inference(forward_demodulation,[status(thm)],[f39,f9921]) ).
fof(f9982,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)],[f37,f9922]) ).
fof(f9983,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)],[f37,f9982]) ).
fof(f9984,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)],[f37,f9923]) ).
fof(f9987,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(forward_demodulation,[status(thm)],[f37,f9926]) ).
fof(f9988,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f37,f9927]) ).
fof(f9990,plain,
! [X0,X1] : leq(multiplication(X0,star(domain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9937,f234]) ).
fof(f9991,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9938,f234]) ).
fof(f9992,plain,
! [X0,X1] : leq(multiplication(X0,star(antidomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9939,f234]) ).
fof(f9993,plain,
! [X0,X1] : leq(multiplication(X0,star(c(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9940,f234]) ).
fof(f9994,plain,
! [X0,X1] : leq(multiplication(X0,star(codomain(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9941,f234]) ).
fof(f9995,plain,
! [X0,X1] : leq(multiplication(X0,star(divergence(X1))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9942,f234]) ).
fof(f9996,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f37,f9949]) ).
fof(f9997,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f9956]) ).
fof(f9998,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f9957]) ).
fof(f9999,plain,
! [X0,X1] :
( leq(multiplication(X0,star(codomain(X1))),coantidomain(X1))
| ~ leq(X0,coantidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f9958]) ).
fof(f10000,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X1,X2))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f9964]) ).
fof(f10001,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f9965]) ).
fof(f10002,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f35,f9966]) ).
fof(f10003,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(coantidomain(X1),X2))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f35,f9973]) ).
fof(f10004,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(multiplication(X2,coantidomain(multiplication(X1,X2))))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f35,f9974]) ).
fof(f10005,plain,
! [X0,X1] :
( leq(multiplication(X0,star(coantidomain(X1))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f35,f9975]) ).
fof(f10008,plain,
! [X0,X1] :
( leq(multiplication(X0,one),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f9178,f9977]) ).
fof(f10009,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(addition(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f38,f10008]) ).
fof(f10013,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f98,f966]) ).
fof(f10014,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f966]) ).
fof(f10039,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)],[f199,f966]) ).
fof(f10040,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)],[f214,f966]) ).
fof(f10041,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)],[f165,f966]) ).
fof(f10047,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f98,f966]) ).
fof(f10048,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f966]) ).
fof(f10062,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f227,f966]) ).
fof(f10063,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f202,f966]) ).
fof(f10064,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f187,f966]) ).
fof(f10065,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f157,f966]) ).
fof(f10069,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f92,f966]) ).
fof(f10070,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X2,X1),X0),
inference(paramodulation,[status(thm)],[f92,f966]) ).
fof(f10078,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f966,f202]) ).
fof(f10085,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f966,f157]) ).
fof(f10086,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)],[f966,f291]) ).
fof(f10089,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)],[f966,f214]) ).
fof(f10090,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)],[f966,f165]) ).
fof(f10091,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)],[f966,f53]) ).
fof(f10092,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)],[f966,f51]) ).
fof(f10093,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f966,f98]) ).
fof(f10094,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f966,f34]) ).
fof(f10104,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)],[f966,f335]) ).
fof(f10105,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)],[f966,f334]) ).
fof(f10106,plain,
! [X0,X1] :
( leq(multiplication(star(X1),addition(X1,X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f966,f297]) ).
fof(f10107,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)],[f966,f286]) ).
fof(f10108,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)],[f966,f285]) ).
fof(f10109,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != addition(X1,X2)
| leq(addition(X0,X1),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f966,f238]) ).
fof(f10110,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)],[f966,f237]) ).
fof(f10111,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)],[f966,f236]) ).
fof(f10112,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X1,X0))) = multiplication(X1,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f966,f228]) ).
fof(f10114,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X1,X0)) = multiplication(antidomain(addition(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f966,f181]) ).
fof(f10117,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f966,f1356]) ).
fof(f10118,plain,
! [X0,X1] : leq(addition(X0,X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f966,f1359]) ).
fof(f10121,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f966,f98]) ).
fof(f10122,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f966,f92]) ).
fof(f10123,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f966,f92]) ).
fof(f10124,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f966,f241]) ).
fof(f10126,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f966,f34]) ).
fof(f10130,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f10013]) ).
fof(f10131,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f98,f10014]) ).
fof(f10132,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f966,f10131]) ).
fof(f10133,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10132]) ).
fof(f10176,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)],[f199,f10039]) ).
fof(f10177,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)],[f214,f10176]) ).
fof(f10178,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)],[f36,f10177]) ).
fof(f10179,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)],[f214,f10040]) ).
fof(f10180,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)],[f966,f10179]) ).
fof(f10181,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)],[f98,f10180]) ).
fof(f10182,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f10181]) ).
fof(f10183,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)],[f165,f10041]) ).
fof(f10184,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)],[f966,f10183]) ).
fof(f10185,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)],[f98,f10184]) ).
fof(f10186,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f10185]) ).
fof(f10202,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f10047]) ).
fof(f10203,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f10048]) ).
fof(f10204,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f966,f10203]) ).
fof(f10205,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f98,f10204]) ).
fof(f10231,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f33,f10062]) ).
fof(f10232,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f33,f10063]) ).
fof(f10233,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f10064]) ).
fof(f10234,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f10065]) ).
fof(f10241,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f10069]) ).
fof(f10242,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f98,f10070]) ).
fof(f10248,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)],[f214,f10089]) ).
fof(f10249,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)],[f98,f10248]) ).
fof(f10250,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)],[f945,f10249]) ).
fof(f10251,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)],[f165,f10090]) ).
fof(f10252,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)],[f98,f10251]) ).
fof(f10253,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)],[f945,f10252]) ).
fof(f10254,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f10093]) ).
fof(f10255,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f98,f10094]) ).
fof(f10256,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f966,f10255]) ).
fof(f10257,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10256]) ).
fof(f10266,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f98,f10121]) ).
fof(f10267,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f966,f10266]) ).
fof(f10268,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f98,f10122]) ).
fof(f10269,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f98,f10123]) ).
fof(f10270,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f945,f10269]) ).
fof(f10271,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f10126]) ).
fof(f10272,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10271]) ).
fof(f10273,plain,
! [X0,X1] : leq(multiplication(star(antidomain(addition(X0,X1))),addition(X1,X0)),addition(X0,X1)),
inference(resolution,[status(thm)],[f10118,f299]) ).
fof(f10294,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)],[f199,f10118]) ).
fof(f10297,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)],[f206,f10118]) ).
fof(f10298,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f196,f10118]) ).
fof(f10299,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f148,f10118]) ).
fof(f10302,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f98,f10118]) ).
fof(f10303,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f34,f10118]) ).
fof(f10317,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),X1),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f227,f10118]) ).
fof(f10318,plain,
! [X0,X1] : leq(multiplication(addition(one,X0),X1),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f202,f10118]) ).
fof(f10319,plain,
! [X0,X1] : leq(multiplication(X0,addition(X1,one)),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f187,f10118]) ).
fof(f10320,plain,
! [X0,X1] : leq(multiplication(X0,addition(one,X1)),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f157,f10118]) ).
fof(f10324,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f92,f10118]) ).
fof(f10325,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f92,f10118]) ).
fof(f10349,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)],[f199,f10118]) ).
fof(f10352,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)],[f206,f10118]) ).
fof(f10353,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f196,f10118]) ).
fof(f10354,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f148,f10118]) ).
fof(f10357,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f98,f10118]) ).
fof(f10358,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f34,f10118]) ).
fof(f10372,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f227,f10118]) ).
fof(f10373,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f202,f10118]) ).
fof(f10374,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f187,f10118]) ).
fof(f10375,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f157,f10118]) ).
fof(f10379,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f92,f10118]) ).
fof(f10380,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f92,f10118]) ).
fof(f10425,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)],[f206,f10294]) ).
fof(f10430,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)],[f199,f10297]) ).
fof(f10431,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f10298]) ).
fof(f10432,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f10299]) ).
fof(f10460,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),X1),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f10317]) ).
fof(f10461,plain,
! [X0,X1] : leq(multiplication(addition(one,X0),X1),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f10318]) ).
fof(f10462,plain,
! [X0,X1] : leq(multiplication(X0,addition(X1,one)),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f10319]) ).
fof(f10463,plain,
! [X0,X1] : leq(multiplication(X0,addition(one,X1)),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f10320]) ).
fof(f10470,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f98,f10324]) ).
fof(f10471,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f98,f10325]) ).
fof(f10512,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)],[f206,f10349]) ).
fof(f10517,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)],[f199,f10352]) ).
fof(f10518,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f196,f10353]) ).
fof(f10519,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f148,f10354]) ).
fof(f10547,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(X1,one),X0)),
inference(forward_demodulation,[status(thm)],[f33,f10372]) ).
fof(f10548,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(one,X1),X0)),
inference(forward_demodulation,[status(thm)],[f33,f10373]) ).
fof(f10549,plain,
! [X0,X1] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f33,f10374]) ).
fof(f10550,plain,
! [X0,X1] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f33,f10375]) ).
fof(f10557,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f98,f10379]) ).
fof(f10558,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f98,f10380]) ).
fof(f10564,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f98,f1266]) ).
fof(f10565,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f34,f1266]) ).
fof(f10573,plain,
! [X0] : addition(multiplication(star(X0),addition(X0,one)),star(X0)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(paramodulation,[status(thm)],[f7423,f1266]) ).
fof(f10574,plain,
! [X0] : addition(multiplication(addition(X0,one),star(X0)),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(paramodulation,[status(thm)],[f7156,f1266]) ).
fof(f10592,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)],[f214,f1266]) ).
fof(f10593,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)],[f165,f1266]) ).
fof(f10599,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f98,f1266]) ).
fof(f10600,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f34,f1266]) ).
fof(f10622,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f92,f1266]) ).
fof(f10623,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X2,X0))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f92,f1266]) ).
fof(f10629,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)],[f1266,f70]) ).
fof(f10632,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f1266,f202]) ).
fof(f10639,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f1266,f157]) ).
fof(f10640,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)],[f1266,f291]) ).
fof(f10643,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)],[f1266,f214]) ).
fof(f10644,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)],[f1266,f165]) ).
fof(f10645,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)],[f1266,f53]) ).
fof(f10646,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)],[f1266,f51]) ).
fof(f10647,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1266,f98]) ).
fof(f10648,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f1266,f34]) ).
fof(f10652,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f1266,f238]) ).
fof(f10662,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)],[f1266,f335]) ).
fof(f10663,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)],[f1266,f334]) ).
fof(f10664,plain,
! [X0,X1] :
( leq(multiplication(star(X0),addition(X1,X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1266,f297]) ).
fof(f10665,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)],[f1266,f286]) ).
fof(f10666,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)],[f1266,f285]) ).
fof(f10667,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X2,X1)
| leq(addition(X0,X1),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f1266,f238]) ).
fof(f10668,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)],[f1266,f237]) ).
fof(f10669,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)],[f1266,f236]) ).
fof(f10670,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X1,X0))) = multiplication(X0,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1266,f228]) ).
fof(f10672,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X1,X0)) = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f1266,f181]) ).
fof(f10675,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1266,f1356]) ).
fof(f10679,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1266,f98]) ).
fof(f10680,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1266,f92]) ).
fof(f10681,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1266,f92]) ).
fof(f10682,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f1266,f241]) ).
fof(f10684,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f1266,f34]) ).
fof(f10690,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10564]) ).
fof(f10691,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10565]) ).
fof(f10696,plain,
! [X0] : addition(star(X0),multiplication(star(X0),addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f33,f10573]) ).
fof(f10697,plain,
! [X0] : multiplication(star(X0),addition(addition(X0,one),one)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f187,f10696]) ).
fof(f10698,plain,
! [X0] : multiplication(star(X0),addition(one,addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f98,f10697]) ).
fof(f10699,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f1266,f10698]) ).
fof(f10700,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f33,f10699]) ).
fof(f10701,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f7423,f10700]) ).
fof(f10702,plain,
! [X0] : addition(star(X0),multiplication(addition(X0,one),star(X0))) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f33,f10574]) ).
fof(f10703,plain,
! [X0] : multiplication(addition(addition(X0,one),one),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f227,f10702]) ).
fof(f10704,plain,
! [X0] : multiplication(addition(one,addition(X0,one)),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f98,f10703]) ).
fof(f10705,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f1266,f10704]) ).
fof(f10706,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f33,f10705]) ).
fof(f10707,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f7156,f10706]) ).
fof(f10726,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)],[f98,f10592]) ).
fof(f10727,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)],[f214,f10726]) ).
fof(f10728,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)],[f1266,f10727]) ).
fof(f10729,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)],[f1266,f10728]) ).
fof(f10730,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)],[f98,f10729]) ).
fof(f10731,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(X0,multiplication(addition(X2,X1),X3)),
inference(forward_demodulation,[status(thm)],[f196,f10730]) ).
fof(f10732,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)],[f98,f10593]) ).
fof(f10733,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)],[f165,f10732]) ).
fof(f10734,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)],[f1266,f10733]) ).
fof(f10735,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)],[f1266,f10734]) ).
fof(f10736,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)],[f98,f10735]) ).
fof(f10737,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f148,f10736]) ).
fof(f10786,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f10622]) ).
fof(f10787,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f966,f10786]) ).
fof(f10788,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f98,f10787]) ).
fof(f10789,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f98,f10788]) ).
fof(f10790,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X2,X1)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f98,f10623]) ).
fof(f10791,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X2,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10790]) ).
fof(f10792,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)],[f33,f10629]) ).
fof(f10793,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)],[f10792]) ).
fof(f10800,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)],[f214,f10643]) ).
fof(f10801,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)],[f92,f10800]) ).
fof(f10802,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)],[f214,f10801]) ).
fof(f10803,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X1,X0),X2),X3),
inference(forward_demodulation,[status(thm)],[f1266,f10802]) ).
fof(f10804,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)],[f165,f10644]) ).
fof(f10805,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)],[f92,f10804]) ).
fof(f10806,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)],[f165,f10805]) ).
fof(f10807,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f1266,f10806]) ).
fof(f10808,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10647]) ).
fof(f10809,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10648]) ).
fof(f10824,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f98,f10679]) ).
fof(f10825,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f98,f10824]) ).
fof(f10826,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f98,f10680]) ).
fof(f10827,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f966,f10826]) ).
fof(f10828,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f98,f10681]) ).
fof(f10829,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f98,f10684]) ).
fof(f10830,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f966,f10829]) ).
fof(f10831,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f34,f10830]) ).
fof(f10832,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)],[f337,f6667]) ).
fof(f10833,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)],[f337,f6327]) ).
fof(f10834,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)],[f337,f6326]) ).
fof(f10835,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)],[f337,f6192]) ).
fof(f10836,plain,
! [X0] : leq(multiplication(coantidomain(X0),multiplication(coantidomain(X0),star(coantidomain(X0)))),coantidomain(X0)),
inference(resolution,[status(thm)],[f337,f6815]) ).
fof(f10837,plain,
! [X0] : leq(multiplication(domain(X0),multiplication(domain(X0),star(domain(X0)))),domain(X0)),
inference(resolution,[status(thm)],[f337,f6469]) ).
fof(f10838,plain,
! [X0] : leq(multiplication(antidomain(X0),multiplication(antidomain(X0),star(antidomain(X0)))),antidomain(X0)),
inference(resolution,[status(thm)],[f337,f6335]) ).
fof(f10839,plain,
! [X0] : leq(multiplication(c(X0),multiplication(c(X0),star(c(X0)))),c(X0)),
inference(resolution,[status(thm)],[f337,f6199]) ).
fof(f10840,plain,
! [X0] : leq(multiplication(codomain(X0),multiplication(codomain(X0),star(codomain(X0)))),codomain(X0)),
inference(resolution,[status(thm)],[f337,f6071]) ).
fof(f10841,plain,
! [X0] : leq(multiplication(divergence(X0),multiplication(divergence(X0),star(divergence(X0)))),divergence(X0)),
inference(resolution,[status(thm)],[f337,f5662]) ).
fof(f10842,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(forward_diamond(X1,X2),star(forward_diamond(X1,X2)))),X0),
inference(resolution,[status(thm)],[f337,f3808]) ).
fof(f10843,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(forward_box(X1,X2),star(forward_box(X1,X2)))),X0),
inference(resolution,[status(thm)],[f337,f3489]) ).
fof(f10844,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(backward_box(X1,X2),star(backward_box(X1,X2)))),X0),
inference(resolution,[status(thm)],[f337,f3488]) ).
fof(f10845,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(backward_diamond(X1,X2),star(backward_diamond(X1,X2)))),X0),
inference(resolution,[status(thm)],[f337,f3259]) ).
fof(f10846,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(coantidomain(X1),star(coantidomain(X1)))),X0),
inference(resolution,[status(thm)],[f337,f3817]) ).
fof(f10847,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(domain(X1),star(domain(X1)))),X0),
inference(resolution,[status(thm)],[f337,f3587]) ).
fof(f10848,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(antidomain(X1),star(antidomain(X1)))),X0),
inference(resolution,[status(thm)],[f337,f3497]) ).
fof(f10849,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(c(X1),star(c(X1)))),X0),
inference(resolution,[status(thm)],[f337,f3402]) ).
fof(f10850,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(codomain(X1),star(codomain(X1)))),X0),
inference(resolution,[status(thm)],[f337,f3175]) ).
fof(f10851,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(divergence(X1),star(divergence(X1)))),X0),
inference(resolution,[status(thm)],[f337,f3096]) ).
fof(f10852,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)],[f202,f337]) ).
fof(f10853,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)],[f219,f337]) ).
fof(f10854,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)],[f227,f337]) ).
fof(f10855,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)],[f225,f337]) ).
fof(f10856,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)],[f228,f337]) ).
fof(f10857,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)],[f221,f337]) ).
fof(f10858,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(domain(X0),star(domain(X0)))),c(X0))
| ~ leq(zero,c(X0)) ),
inference(paramodulation,[status(thm)],[f192,f337]) ).
fof(f10859,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(X0,star(X0))),c(X0))
| ~ leq(zero,c(X0)) ),
inference(paramodulation,[status(thm)],[f4088,f337]) ).
fof(f10860,plain,
! [X0] :
( leq(multiplication(coantidomain(X0),multiplication(codomain(X0),star(codomain(X0)))),coantidomain(X0))
| ~ leq(zero,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f190,f337]) ).
fof(f10861,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)],[f63,f337]) ).
fof(f10862,plain,
! [X0] :
( leq(multiplication(domain(X0),multiplication(X0,star(X0))),domain(X0))
| ~ leq(X0,domain(X0)) ),
inference(paramodulation,[status(thm)],[f3965,f337]) ).
fof(f10863,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)],[f37,f337]) ).
fof(f10864,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)],[f181,f337]) ).
fof(f10865,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)],[f172,f337]) ).
fof(f10868,plain,
! [X0] :
( leq(multiplication(zero,multiplication(X0,star(X0))),zero)
| ~ leq(zero,zero) ),
inference(paramodulation,[status(thm)],[f43,f337]) ).
fof(f10869,plain,
! [X0] :
( leq(multiplication(one,multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f39,f337]) ).
fof(f10870,plain,
! [X0] :
( leq(multiplication(X0,multiplication(codomain(X0),star(codomain(X0)))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2178,f337]) ).
fof(f10871,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)],[f157,f337]) ).
fof(f10872,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)],[f176,f337]) ).
fof(f10873,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)],[f187,f337]) ).
fof(f10874,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)],[f185,f337]) ).
fof(f10876,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)],[f139,f337]) ).
fof(f10880,plain,
! [X0] : leq(multiplication(c(X0),multiplication(domain(X0),star(domain(X0)))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10858,f235]) ).
fof(f10881,plain,
! [X0] : leq(multiplication(c(X0),multiplication(X0,star(X0))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10859,f235]) ).
fof(f10882,plain,
! [X0] : leq(multiplication(coantidomain(X0),multiplication(codomain(X0),star(codomain(X0)))),coantidomain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10860,f235]) ).
fof(f10883,plain,
! [X0,X1] : leq(multiplication(domain(X0),multiplication(antidomain(X1),star(antidomain(X1)))),domain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f10861,f3580]) ).
fof(f10884,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)],[f37,f10863]) ).
fof(f10886,definition,
! [X0] :
( sQ29_spl
<=> leq(multiplication(zero,multiplication(X0,star(X0))),zero) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f10889,plain,
( sQ29_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10868,f7614,f10886]) ).
fof(f10890,plain,
! [X0] :
( leq(multiplication(X0,star(X0)),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f39,f10869]) ).
fof(f10891,plain,
! [X0] : leq(multiplication(X0,multiplication(codomain(X0),star(codomain(X0)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f10870,f234]) ).
fof(f10893,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)],[f37,f10876]) ).
fof(f10894,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)],[f10893,f235]) ).
fof(f10901,plain,
! [X0,X1,X2] : multiplication(backward_box(X0,X1),domain_difference(backward_diamond(X0,c(X1)),X2)) = zero,
inference(paramodulation,[status(thm)],[f67,f1494]) ).
fof(f10902,plain,
! [X0,X1,X2] : multiplication(forward_box(X0,X1),domain_difference(forward_diamond(X0,c(X1)),X2)) = zero,
inference(paramodulation,[status(thm)],[f66,f1494]) ).
fof(f10904,plain,
! [X0,X1] : multiplication(antidomain(c(X0)),domain_difference(antidomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f493,f1494]) ).
fof(f10905,plain,
! [X0,X1] : multiplication(domain(c(X0)),domain_difference(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f317,f1494]) ).
fof(f10917,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)],[f1494,f337]) ).
fof(f10918,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain_difference(X1,X2))),c(X1))
| ~ leq(addition(X0,zero),c(X1)) ),
inference(paramodulation,[status(thm)],[f1494,f324]) ).
fof(f10919,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)],[f1494,f291]) ).
fof(f10921,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)],[f1494,f288]) ).
fof(f10924,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)],[f1494,f214]) ).
fof(f10925,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)],[f1494,f214]) ).
fof(f10927,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)],[f1494,f206]) ).
fof(f10928,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)],[f1494,f206]) ).
fof(f10930,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)],[f1494,f199]) ).
fof(f10931,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)],[f1494,f199]) ).
fof(f10932,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)],[f1494,f196]) ).
fof(f10933,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)],[f1494,f196]) ).
fof(f10934,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)],[f1494,f165]) ).
fof(f10935,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)],[f1494,f165]) ).
fof(f10936,plain,
! [X0,X1] : multiplication(c(X0),addition(domain_difference(X0,X1),one)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f1494,f187]) ).
fof(f10937,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f1494,f157]) ).
fof(f10938,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = addition(multiplication(c(X0),X2),zero),
inference(paramodulation,[status(thm)],[f1494,f148]) ).
fof(f10939,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f1494,f148]) ).
fof(f10942,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)],[f1494,f561]) ).
fof(f10943,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)],[f1494,f404]) ).
fof(f10944,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain_difference(X1,X2))),c(X1))
| ~ leq(addition(zero,X0),c(X1)) ),
inference(paramodulation,[status(thm)],[f1494,f53]) ).
fof(f10945,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)],[f1494,f51]) ).
fof(f10946,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)],[f1494,f41]) ).
fof(f10947,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)],[f1494,f41]) ).
fof(f10948,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f1494,f40]) ).
fof(f10949,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = addition(zero,multiplication(c(X0),X2)),
inference(paramodulation,[status(thm)],[f1494,f40]) ).
fof(f10950,plain,
! [X0,X1,X2] : multiplication(c(X0),multiplication(domain_difference(X0,X1),X2)) = multiplication(zero,X2),
inference(paramodulation,[status(thm)],[f1494,f37]) ).
fof(f10955,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)],[f10917,f235]) ).
fof(f10956,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain_difference(X1,X2))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f10918]) ).
fof(f10957,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)],[f42,f10919]) ).
fof(f10958,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)],[f75,f10957]) ).
fof(f10960,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)],[f35,f10921]) ).
fof(f10973,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)],[f92,f10924]) ).
fof(f10974,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)],[f75,f10973]) ).
fof(f10975,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)],[f75,f10925]) ).
fof(f10979,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)],[f42,f10927]) ).
fof(f10980,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)],[f35,f10979]) ).
fof(f10981,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)],[f75,f10928]) ).
fof(f10984,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)],[f35,f10930]) ).
fof(f10985,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)],[f42,f10931]) ).
fof(f10986,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)],[f75,f10985]) ).
fof(f10987,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),X1),domain_difference(X0,X2)) = multiplication(X1,domain_difference(X0,X2)),
inference(forward_demodulation,[status(thm)],[f35,f10932]) ).
fof(f10988,plain,
! [X0,X1,X2] : multiplication(addition(X0,c(X1)),domain_difference(X1,X2)) = multiplication(X0,domain_difference(X1,X2)),
inference(forward_demodulation,[status(thm)],[f75,f10933]) ).
fof(f10989,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)],[f92,f10934]) ).
fof(f10990,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)],[f75,f10989]) ).
fof(f10991,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)],[f75,f10935]) ).
fof(f10992,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = addition(c(X0),zero),
inference(forward_demodulation,[status(thm)],[f33,f10936]) ).
fof(f10993,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = c(X0),
inference(forward_demodulation,[status(thm)],[f35,f10992]) ).
fof(f10994,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = c(X0),
inference(forward_demodulation,[status(thm)],[f35,f10937]) ).
fof(f10995,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = multiplication(c(X0),X2),
inference(forward_demodulation,[status(thm)],[f35,f10938]) ).
fof(f10996,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f10939]) ).
fof(f10999,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)],[f638,f10942]) ).
fof(f11000,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(c(X0)),domain_difference(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1313,f10999]) ).
fof(f11001,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)],[f523,f10943]) ).
fof(f11002,plain,
! [X0,X1] : one = antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1315,f11001]) ).
fof(f11003,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain_difference(X1,X2))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f10944]) ).
fof(f11004,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)],[f75,f10945]) ).
fof(f11005,plain,
! [X0,X1,X2] : multiplication(addition(X0,c(X1)),domain_difference(X1,X2)) = multiplication(X0,domain_difference(X1,X2)),
inference(forward_demodulation,[status(thm)],[f35,f10946]) ).
fof(f11006,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),X1),domain_difference(X0,X2)) = multiplication(X1,domain_difference(X0,X2)),
inference(forward_demodulation,[status(thm)],[f75,f10947]) ).
fof(f11007,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f10948]) ).
fof(f11008,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = multiplication(c(X0),X2),
inference(forward_demodulation,[status(thm)],[f75,f10949]) ).
fof(f11009,plain,
! [X0,X1,X2] : multiplication(c(X0),multiplication(domain_difference(X0,X1),X2)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f10950]) ).
fof(f11010,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,one))),forward_diamond(X1,X2)),addition(X0,one)),
inference(resolution,[status(thm)],[f1923,f299]) ).
fof(f11011,plain,
! [X0,X1,X2] : addition(forward_diamond(X0,X1),addition(X2,one)) = addition(X2,one),
inference(resolution,[status(thm)],[f1923,f46]) ).
fof(f11020,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f98,f1923]) ).
fof(f11021,plain,
! [X0,X1,X2,X3] : leq(forward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f34,f1923]) ).
fof(f11023,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f33,f1923]) ).
fof(f11024,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f33,f1923]) ).
fof(f11026,plain,
! [X0,X1,X2] : addition(one,addition(forward_diamond(X0,X1),X2)) = addition(X2,one),
inference(forward_demodulation,[status(thm)],[f92,f11011]) ).
fof(f11028,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)],[f214,f327]) ).
fof(f11029,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)],[f165,f327]) ).
fof(f11030,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)],[f206,f327]) ).
fof(f11031,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)],[f196,f327]) ).
fof(f11032,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)],[f148,f327]) ).
fof(f11033,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)],[f41,f327]) ).
fof(f11034,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)],[f40,f327]) ).
fof(f11035,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)],[f4331,f327]) ).
fof(f11036,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)],[f4330,f327]) ).
fof(f11037,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)],[f4329,f327]) ).
fof(f11038,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)],[f4328,f327]) ).
fof(f11039,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)],[f4327,f327]) ).
fof(f11040,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)],[f4326,f327]) ).
fof(f11041,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)],[f2352,f327]) ).
fof(f11042,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)],[f2351,f327]) ).
fof(f11043,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)],[f2350,f327]) ).
fof(f11044,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)],[f2349,f327]) ).
fof(f11045,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)],[f2348,f327]) ).
fof(f11046,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)],[f2347,f327]) ).
fof(f11047,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)],[f227,f327]) ).
fof(f11048,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)],[f202,f327]) ).
fof(f11049,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)],[f187,f327]) ).
fof(f11050,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)],[f157,f327]) ).
fof(f11051,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)],[f1266,f327]) ).
fof(f11052,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)],[f966,f327]) ).
fof(f11053,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)],[f945,f327]) ).
fof(f11054,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)],[f100,f327]) ).
fof(f11055,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)],[f92,f327]) ).
fof(f11056,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)],[f92,f327]) ).
fof(f11058,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)],[f33,f327]) ).
fof(f11059,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)],[f33,f327]) ).
fof(f11060,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)],[f36,f327]) ).
fof(f11061,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)],[f219,f327]) ).
fof(f11062,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)],[f225,f327]) ).
fof(f11063,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)],[f4088,f327]) ).
fof(f11064,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)],[f3965,f327]) ).
fof(f11065,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)],[f37,f327]) ).
fof(f11066,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)],[f131,f327]) ).
fof(f11067,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)],[f54,f327]) ).
fof(f11068,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(zero,X1))
| ~ leq(addition(zero,X0),multiplication(zero,X1)) ),
inference(paramodulation,[status(thm)],[f43,f327]) ).
fof(f11070,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)],[f146,f327]) ).
fof(f11071,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)],[f139,f327]) ).
fof(f11072,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)],[f202,f327]) ).
fof(f11073,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)],[f219,f327]) ).
fof(f11074,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)],[f227,f327]) ).
fof(f11075,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)],[f225,f327]) ).
fof(f11076,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)],[f228,f327]) ).
fof(f11077,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)],[f221,f327]) ).
fof(f11078,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)],[f1494,f327]) ).
fof(f11079,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)],[f192,f327]) ).
fof(f11080,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)],[f4088,f327]) ).
fof(f11081,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)],[f190,f327]) ).
fof(f11082,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)],[f63,f327]) ).
fof(f11083,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)],[f3965,f327]) ).
fof(f11084,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)],[f37,f327]) ).
fof(f11085,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)],[f181,f327]) ).
fof(f11086,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)],[f172,f327]) ).
fof(f11087,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)],[f131,f327]) ).
fof(f11088,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)],[f54,f327]) ).
fof(f11089,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)],[f43,f327]) ).
fof(f11091,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)],[f2178,f327]) ).
fof(f11092,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)],[f157,f327]) ).
fof(f11093,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)],[f176,f327]) ).
fof(f11094,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)],[f187,f327]) ).
fof(f11095,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)],[f185,f327]) ).
fof(f11096,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)],[f146,f327]) ).
fof(f11097,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)],[f139,f327]) ).
fof(f11098,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)],[f58,f327]) ).
fof(f11100,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)],[f38,f327]) ).
fof(f11101,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)],[f202,f327]) ).
fof(f11102,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)],[f219,f327]) ).
fof(f11103,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)],[f227,f327]) ).
fof(f11104,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)],[f225,f327]) ).
fof(f11105,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)],[f228,f327]) ).
fof(f11106,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)],[f221,f327]) ).
fof(f11107,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)],[f1494,f327]) ).
fof(f11108,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)],[f192,f327]) ).
fof(f11109,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)],[f4088,f327]) ).
fof(f11110,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)],[f190,f327]) ).
fof(f11111,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)],[f63,f327]) ).
fof(f11112,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)],[f3965,f327]) ).
fof(f11113,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)],[f37,f327]) ).
fof(f11114,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)],[f181,f327]) ).
fof(f11115,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)],[f172,f327]) ).
fof(f11116,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)],[f131,f327]) ).
fof(f11117,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)],[f54,f327]) ).
fof(f11118,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)],[f43,f327]) ).
fof(f11120,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)],[f2178,f327]) ).
fof(f11121,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)],[f157,f327]) ).
fof(f11122,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)],[f176,f327]) ).
fof(f11123,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)],[f187,f327]) ).
fof(f11124,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)],[f185,f327]) ).
fof(f11125,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)],[f146,f327]) ).
fof(f11126,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)],[f139,f327]) ).
fof(f11127,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)],[f58,f327]) ).
fof(f11128,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)],[f42,f327]) ).
fof(f11131,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)],[f37,f11030]) ).
fof(f11132,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)],[f37,f11131]) ).
fof(f11133,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)],[f37,f11132]) ).
fof(f11134,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)],[f37,f11031]) ).
fof(f11135,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)],[f37,f11134]) ).
fof(f11136,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)],[f37,f11032]) ).
fof(f11137,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)],[f37,f11033]) ).
fof(f11138,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)],[f37,f11137]) ).
fof(f11139,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)],[f37,f11034]) ).
fof(f11140,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)],[f37,f11035]) ).
fof(f11141,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)],[f37,f11140]) ).
fof(f11142,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)],[f37,f11141]) ).
fof(f11143,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)],[f37,f11036]) ).
fof(f11144,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)],[f37,f11143]) ).
fof(f11145,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)],[f37,f11144]) ).
fof(f11146,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)],[f37,f11037]) ).
fof(f11147,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)],[f37,f11146]) ).
fof(f11148,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)],[f37,f11147]) ).
fof(f11149,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)],[f37,f11038]) ).
fof(f11150,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)],[f37,f11149]) ).
fof(f11151,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)],[f37,f11150]) ).
fof(f11152,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)],[f37,f11039]) ).
fof(f11153,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)],[f37,f11152]) ).
fof(f11154,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)],[f37,f11153]) ).
fof(f11155,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)],[f37,f11040]) ).
fof(f11156,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)],[f37,f11155]) ).
fof(f11157,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)],[f37,f11156]) ).
fof(f11158,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)],[f37,f11041]) ).
fof(f11159,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)],[f37,f11158]) ).
fof(f11160,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)],[f37,f11159]) ).
fof(f11161,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)],[f37,f11042]) ).
fof(f11162,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)],[f37,f11161]) ).
fof(f11163,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)],[f37,f11162]) ).
fof(f11164,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)],[f37,f11043]) ).
fof(f11165,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)],[f37,f11164]) ).
fof(f11166,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)],[f37,f11165]) ).
fof(f11167,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)],[f37,f11044]) ).
fof(f11168,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)],[f37,f11167]) ).
fof(f11169,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)],[f37,f11168]) ).
fof(f11170,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)],[f37,f11045]) ).
fof(f11171,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)],[f37,f11170]) ).
fof(f11172,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)],[f37,f11171]) ).
fof(f11173,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)],[f37,f11046]) ).
fof(f11174,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)],[f37,f11173]) ).
fof(f11175,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)],[f37,f11174]) ).
fof(f11176,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)],[f37,f11047]) ).
fof(f11177,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)],[f37,f11176]) ).
fof(f11178,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)],[f37,f11177]) ).
fof(f11179,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)],[f37,f11048]) ).
fof(f11180,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)],[f37,f11179]) ).
fof(f11181,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)],[f37,f11180]) ).
fof(f11182,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)],[f37,f11049]) ).
fof(f11183,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)],[f37,f11182]) ).
fof(f11184,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)],[f37,f11183]) ).
fof(f11185,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)],[f37,f11184]) ).
fof(f11186,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)],[f37,f11185]) ).
fof(f11187,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)],[f37,f11050]) ).
fof(f11188,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)],[f37,f11187]) ).
fof(f11189,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)],[f37,f11188]) ).
fof(f11190,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)],[f37,f11189]) ).
fof(f11191,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)],[f37,f11190]) ).
fof(f11193,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)],[f37,f11060]) ).
fof(f11194,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)],[f37,f11193]) ).
fof(f11195,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)],[f75,f11063]) ).
fof(f11196,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)],[f37,f11065]) ).
fof(f11197,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)],[f37,f11196]) ).
fof(f11198,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(antidomain(X1),X1))
| ~ leq(X0,multiplication(antidomain(X1),X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f11066]) ).
fof(f11199,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),X2))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f54,f11198]) ).
fof(f11200,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f54,f11199]) ).
fof(f11201,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)],[f75,f11067]) ).
fof(f11202,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(zero,X1))
| ~ leq(X0,multiplication(zero,X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f11068]) ).
fof(f11203,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(zero,X2))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f43,f11202]) ).
fof(f11204,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f43,f11203]) ).
fof(f11207,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,coantidomain(X1)))
| ~ leq(X0,multiplication(X1,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f75,f11070]) ).
fof(f11208,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,coantidomain(X2)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f58,f11207]) ).
fof(f11209,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f58,f11208]) ).
fof(f11210,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)],[f75,f11071]) ).
fof(f11211,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)],[f42,f11078]) ).
fof(f11212,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)],[f75,f11211]) ).
fof(f11213,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)],[f42,f11079]) ).
fof(f11214,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)],[f75,f11213]) ).
fof(f11215,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)],[f42,f11080]) ).
fof(f11216,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,c(X2)))
| ~ leq(X0,multiplication(X1,c(X2))) ),
inference(forward_demodulation,[status(thm)],[f75,f11215]) ).
fof(f11217,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)],[f42,f11081]) ).
fof(f11218,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)],[f75,f11217]) ).
fof(f11219,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)],[f42,f11087]) ).
fof(f11220,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)],[f75,f11219]) ).
fof(f11221,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)],[f42,f11088]) ).
fof(f11222,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,antidomain(X2)))
| ~ leq(X0,multiplication(X1,antidomain(X2))) ),
inference(forward_demodulation,[status(thm)],[f75,f11221]) ).
fof(f11223,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,zero))
| ~ leq(addition(zero,X0),multiplication(X1,zero)) ),
inference(forward_demodulation,[status(thm)],[f42,f11089]) ).
fof(f11224,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),multiplication(X1,zero))
| ~ leq(X0,multiplication(X1,zero)) ),
inference(forward_demodulation,[status(thm)],[f75,f11223]) ).
fof(f11225,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,zero))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f42,f11224]) ).
fof(f11226,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f42,f11225]) ).
fof(f11229,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)],[f42,f11096]) ).
fof(f11230,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)],[f75,f11229]) ).
fof(f11231,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)],[f42,f11097]) ).
fof(f11232,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)],[f75,f11231]) ).
fof(f11233,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)],[f42,f11098]) ).
fof(f11234,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(coantidomain(X2))),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f75,f11233]) ).
fof(f11238,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)],[f9178,f11100]) ).
fof(f11239,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,X1),X2),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f38,f11238]) ).
fof(f11240,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)],[f219,f11102]) ).
fof(f11241,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)],[f225,f11104]) ).
fof(f11242,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)],[f228,f11105]) ).
fof(f11243,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)],[f221,f11106]) ).
fof(f11244,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)],[f1494,f11107]) ).
fof(f11245,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)],[f192,f11108]) ).
fof(f11246,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)],[f4088,f11109]) ).
fof(f11247,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)],[f190,f11110]) ).
fof(f11248,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)],[f63,f11111]) ).
fof(f11249,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)],[f3965,f11112]) ).
fof(f11250,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)],[f37,f11113]) ).
fof(f11251,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)],[f37,f11250]) ).
fof(f11252,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)],[f181,f11114]) ).
fof(f11253,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)],[f172,f11115]) ).
fof(f11254,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)],[f37,f11116]) ).
fof(f11255,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)],[f131,f11254]) ).
fof(f11256,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),multiplication(X2,X3)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f11255]) ).
fof(f11257,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f131,f11256]) ).
fof(f11258,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),X2))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f131,f11117]) ).
fof(f11259,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(antidomain(X2),X2))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f11258]) ).
fof(f11260,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f54,f11259]) ).
fof(f11261,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(zero,X2))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f43,f11118]) ).
fof(f11262,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(zero,X2))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f11261]) ).
fof(f11263,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f43,f11262]) ).
fof(f11266,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)],[f2178,f11120]) ).
fof(f11267,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)],[f176,f11122]) ).
fof(f11268,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)],[f185,f11124]) ).
fof(f11269,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)],[f37,f11125]) ).
fof(f11270,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)],[f146,f11269]) ).
fof(f11271,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,star(X1)),multiplication(X2,multiplication(coantidomain(X2),X3)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f11270]) ).
fof(f11272,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f146,f11271]) ).
fof(f11273,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)],[f37,f11126]) ).
fof(f11274,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)],[f139,f11273]) ).
fof(f11275,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,coantidomain(X2)))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f146,f11127]) ).
fof(f11276,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,coantidomain(X2)))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f11275]) ).
fof(f11277,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f58,f11276]) ).
fof(f11278,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X2)),multiplication(X0,zero))
| ~ leq(addition(multiplication(X0,zero),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f43,f11128]) ).
fof(f11279,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,zero))
| ~ leq(addition(zero,X0),zero) ),
inference(forward_demodulation,[status(thm)],[f42,f11278]) ).
fof(f11280,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),multiplication(X2,zero))
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f75,f11279]) ).
fof(f11281,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f42,f11280]) ).
fof(f11284,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,one))),backward_box(X1,X2)),addition(X0,one)),
inference(resolution,[status(thm)],[f1946,f299]) ).
fof(f11285,plain,
! [X0,X1,X2] : addition(backward_box(X0,X1),addition(X2,one)) = addition(X2,one),
inference(resolution,[status(thm)],[f1946,f46]) ).
fof(f11289,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f98,f1946]) ).
fof(f11290,plain,
! [X0,X1,X2,X3] : leq(backward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f34,f1946]) ).
fof(f11292,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f33,f1946]) ).
fof(f11293,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f33,f1946]) ).
fof(f11295,plain,
! [X0,X1,X2] : addition(one,addition(backward_box(X0,X1),X2)) = addition(X2,one),
inference(forward_demodulation,[status(thm)],[f92,f11285]) ).
fof(f11296,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,one))),forward_box(X1,X2)),addition(X0,one)),
inference(resolution,[status(thm)],[f1970,f299]) ).
fof(f11297,plain,
! [X0,X1,X2] : addition(forward_box(X0,X1),addition(X2,one)) = addition(X2,one),
inference(resolution,[status(thm)],[f1970,f46]) ).
fof(f11302,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f98,f1970]) ).
fof(f11303,plain,
! [X0,X1,X2,X3] : leq(forward_box(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f34,f1970]) ).
fof(f11305,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f33,f1970]) ).
fof(f11306,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f33,f1970]) ).
fof(f11308,plain,
! [X0,X1,X2] : addition(one,addition(forward_box(X0,X1),X2)) = addition(X2,one),
inference(forward_demodulation,[status(thm)],[f92,f11297]) ).
fof(f11309,plain,
! [X0,X1,X2] : leq(multiplication(star(antidomain(addition(X0,one))),backward_diamond(X1,X2)),addition(X0,one)),
inference(resolution,[status(thm)],[f1996,f299]) ).
fof(f11310,plain,
! [X0,X1,X2] : addition(backward_diamond(X0,X1),addition(X2,one)) = addition(X2,one),
inference(resolution,[status(thm)],[f1996,f46]) ).
fof(f11317,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f98,f1996]) ).
fof(f11318,plain,
! [X0,X1,X2,X3] : leq(backward_diamond(X0,X1),addition(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f34,f1996]) ).
fof(f11320,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f33,f1996]) ).
fof(f11321,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f33,f1996]) ).
fof(f11323,plain,
! [X0,X1,X2] : addition(one,addition(backward_diamond(X0,X1),X2)) = addition(X2,one),
inference(forward_demodulation,[status(thm)],[f92,f11310]) ).
fof(f11325,plain,
! [X0,X1] : c(backward_diamond(X0,c(X1))) = multiplication(backward_box(X0,X1),c(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f67,f2090]) ).
fof(f11326,plain,
! [X0,X1] : c(forward_diamond(X0,c(X1))) = multiplication(forward_box(X0,X1),c(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f66,f2090]) ).
fof(f11328,plain,
! [X0] : c(antidomain(X0)) = multiplication(antidomain(c(X0)),c(antidomain(X0))),
inference(paramodulation,[status(thm)],[f493,f2090]) ).
fof(f11329,plain,
! [X0] : c(domain(X0)) = multiplication(domain(c(X0)),c(domain(X0))),
inference(paramodulation,[status(thm)],[f317,f2090]) ).
fof(f11332,plain,
! [X0,X1] : c(backward_diamond(X0,c(X1))) = multiplication(c(backward_diamond(X0,c(X1))),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f67,f2090]) ).
fof(f11333,plain,
! [X0,X1] : c(forward_diamond(X0,c(X1))) = multiplication(c(forward_diamond(X0,c(X1))),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f66,f2090]) ).
fof(f11335,plain,
! [X0] : c(antidomain(X0)) = multiplication(c(antidomain(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f493,f2090]) ).
fof(f11336,plain,
! [X0] : c(domain(X0)) = multiplication(c(domain(X0)),domain(c(X0))),
inference(paramodulation,[status(thm)],[f317,f2090]) ).
fof(f11342,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)],[f2090,f327]) ).
fof(f11343,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)],[f2090,f327]) ).
fof(f11344,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(c(X0),star(c(X0)))),c(X0))
| ~ leq(c(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2090,f337]) ).
fof(f11345,plain,
! [X0,X1] :
( leq(multiplication(X0,star(c(X1))),c(X1))
| ~ leq(addition(X0,c(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f2090,f324]) ).
fof(f11346,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)],[f2090,f291]) ).
fof(f11347,plain,
! [X0] :
( leq(multiplication(star(c(X0)),multiplication(c(X0),c(X0))),c(X0))
| ~ leq(c(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2090,f290]) ).
fof(f11348,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),c(X1))
| ~ leq(addition(X0,c(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f2090,f288]) ).
fof(f11349,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(c(X0),star(multiplication(c(X0),c(X0)))))),star(c(X0))),
inference(paramodulation,[status(thm)],[f2090,f247]) ).
fof(f11350,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(c(X0),star(c(X0))))),star(multiplication(c(X0),c(X0)))),
inference(paramodulation,[status(thm)],[f2090,f247]) ).
fof(f11351,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)],[f2090,f214]) ).
fof(f11352,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)],[f2090,f214]) ).
fof(f11354,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)],[f2090,f206]) ).
fof(f11355,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)],[f2090,f206]) ).
fof(f11357,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)],[f2090,f199]) ).
fof(f11358,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)],[f2090,f199]) ).
fof(f11359,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = addition(multiplication(X1,c(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f2090,f196]) ).
fof(f11360,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = addition(c(X1),multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f2090,f196]) ).
fof(f11361,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)],[f2090,f165]) ).
fof(f11362,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)],[f2090,f165]) ).
fof(f11365,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = addition(multiplication(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f2090,f148]) ).
fof(f11366,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = addition(c(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f2090,f148]) ).
fof(f11369,plain,
! [X0] : addition(coantidomain(c(X0)),coantidomain(multiplication(codomain(c(X0)),c(X0)))) = coantidomain(multiplication(codomain(c(X0)),c(X0))),
inference(paramodulation,[status(thm)],[f2090,f561]) ).
fof(f11370,plain,
! [X0] : addition(antidomain(c(X0)),antidomain(multiplication(c(X0),domain(c(X0))))) = antidomain(multiplication(c(X0),domain(c(X0)))),
inference(paramodulation,[status(thm)],[f2090,f404]) ).
fof(f11371,plain,
! [X0,X1] :
( leq(multiplication(X1,star(c(X0))),c(X0))
| ~ leq(addition(c(X0),X1),c(X0)) ),
inference(paramodulation,[status(thm)],[f2090,f53]) ).
fof(f11372,plain,
! [X0,X1] :
( leq(multiplication(star(c(X0)),X1),c(X0))
| ~ leq(addition(c(X0),X1),c(X0)) ),
inference(paramodulation,[status(thm)],[f2090,f51]) ).
fof(f11373,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = addition(multiplication(X0,c(X1)),c(X1)),
inference(paramodulation,[status(thm)],[f2090,f41]) ).
fof(f11374,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = addition(c(X0),multiplication(X1,c(X0))),
inference(paramodulation,[status(thm)],[f2090,f41]) ).
fof(f11375,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = addition(multiplication(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f2090,f40]) ).
fof(f11376,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = addition(c(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f2090,f40]) ).
fof(f11377,plain,
! [X0,X1] : multiplication(c(X0),multiplication(c(X0),X1)) = multiplication(c(X0),X1),
inference(paramodulation,[status(thm)],[f2090,f37]) ).
fof(f11379,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),c(backward_diamond(X0,c(X1)))),
inference(forward_demodulation,[status(thm)],[f67,f11325]) ).
fof(f11380,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f67,f11379]) ).
fof(f11381,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),c(forward_diamond(X0,c(X1)))),
inference(forward_demodulation,[status(thm)],[f66,f11326]) ).
fof(f11382,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f66,f11381]) ).
fof(f11385,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),c(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f493,f11328]) ).
fof(f11386,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f493,f11385]) ).
fof(f11387,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),c(domain(X0))),
inference(forward_demodulation,[status(thm)],[f317,f11329]) ).
fof(f11388,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f317,f11387]) ).
fof(f11391,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(c(backward_diamond(X0,c(X1))),backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f67,f11332]) ).
fof(f11392,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f67,f11391]) ).
fof(f11393,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(c(forward_diamond(X0,c(X1))),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f66,f11333]) ).
fof(f11394,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f66,f11393]) ).
fof(f11397,plain,
! [X0] : antidomain(c(X0)) = multiplication(c(antidomain(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f493,f11335]) ).
fof(f11398,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f493,f11397]) ).
fof(f11399,plain,
! [X0] : domain(c(X0)) = multiplication(c(domain(X0)),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f317,f11336]) ).
fof(f11400,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f317,f11399]) ).
fof(f11402,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)],[f2090,f11342]) ).
fof(f11403,plain,
! [X0] : leq(multiplication(c(X0),multiplication(c(X0),star(c(X0)))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f11344,f234]) ).
fof(f11404,plain,
! [X0] :
( leq(multiplication(star(c(X0)),c(X0)),c(X0))
| ~ leq(c(X0),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f2090,f11347]) ).
fof(f11405,plain,
! [X0] : leq(multiplication(star(c(X0)),c(X0)),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f11404,f234]) ).
fof(f11406,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(c(X0),star(c(X0))))),star(c(X0))),
inference(forward_demodulation,[status(thm)],[f2090,f11349]) ).
fof(f11407,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(c(X0),star(c(X0))))),star(c(X0))),
inference(forward_demodulation,[status(thm)],[f2090,f11350]) ).
fof(f11408,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)],[f92,f11351]) ).
fof(f11412,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),c(X2)) = multiplication(addition(X1,X0),c(X2)),
inference(forward_demodulation,[status(thm)],[f196,f11354]) ).
fof(f11415,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)],[f33,f11357]) ).
fof(f11416,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),c(X1)) = multiplication(addition(X2,X0),c(X1)),
inference(forward_demodulation,[status(thm)],[f196,f11358]) ).
fof(f11417,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = addition(c(X0),multiplication(X1,c(X0))),
inference(forward_demodulation,[status(thm)],[f33,f11359]) ).
fof(f11418,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = multiplication(addition(X1,one),c(X0)),
inference(forward_demodulation,[status(thm)],[f227,f11417]) ).
fof(f11419,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = multiplication(addition(X0,one),c(X1)),
inference(forward_demodulation,[status(thm)],[f227,f11360]) ).
fof(f11420,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)],[f92,f11361]) ).
fof(f11426,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = addition(c(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f11365]) ).
fof(f11427,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f11426]) ).
fof(f11428,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f11366]) ).
fof(f11430,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = addition(c(X1),multiplication(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f33,f11373]) ).
fof(f11431,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),c(X1)) = multiplication(addition(X0,one),c(X1)),
inference(forward_demodulation,[status(thm)],[f227,f11430]) ).
fof(f11432,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),c(X0)) = multiplication(addition(X1,one),c(X0)),
inference(forward_demodulation,[status(thm)],[f227,f11374]) ).
fof(f11433,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = addition(c(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f11375]) ).
fof(f11434,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,c(X0))) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f11433]) ).
fof(f11435,plain,
! [X0,X1] : multiplication(c(X0),addition(c(X0),X1)) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f11376]) ).
fof(f11436,plain,
! [X0,X1] : leq(multiplication(domain_difference(X0,X1),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f338,f6657]) ).
fof(f11437,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(forward_diamond(X0,X1),antidomain(X2)),star(X2)),antidomain(X2)),
inference(resolution,[status(thm)],[f338,f6667]) ).
fof(f11438,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(forward_box(X0,X1),antidomain(X2)),star(X2)),antidomain(X2)),
inference(resolution,[status(thm)],[f338,f6327]) ).
fof(f11439,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(backward_box(X0,X1),antidomain(X2)),star(X2)),antidomain(X2)),
inference(resolution,[status(thm)],[f338,f6326]) ).
fof(f11440,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(backward_diamond(X0,X1),antidomain(X2)),star(X2)),antidomain(X2)),
inference(resolution,[status(thm)],[f338,f6192]) ).
fof(f11441,plain,
! [X0,X1] : leq(multiplication(multiplication(coantidomain(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f338,f6815]) ).
fof(f11442,plain,
! [X0,X1] : leq(multiplication(multiplication(domain(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f338,f6469]) ).
fof(f11443,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f338,f6335]) ).
fof(f11444,plain,
! [X0,X1] : leq(multiplication(multiplication(c(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f338,f6199]) ).
fof(f11445,plain,
! [X0,X1] : leq(multiplication(multiplication(codomain(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f338,f6071]) ).
fof(f11446,plain,
! [X0,X1] : leq(multiplication(multiplication(divergence(X0),antidomain(X1)),star(X1)),antidomain(X1)),
inference(resolution,[status(thm)],[f338,f5662]) ).
fof(f11447,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(antidomain(X0),forward_diamond(X1,X2)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3808]) ).
fof(f11448,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(antidomain(X0),forward_box(X1,X2)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3489]) ).
fof(f11449,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(antidomain(X0),backward_box(X1,X2)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3488]) ).
fof(f11450,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(antidomain(X0),backward_diamond(X1,X2)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3259]) ).
fof(f11451,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),coantidomain(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3817]) ).
fof(f11452,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),domain(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3587]) ).
fof(f11453,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),antidomain(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3497]) ).
fof(f11454,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),c(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3402]) ).
fof(f11455,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),codomain(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3175]) ).
fof(f11456,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),divergence(X1)),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f3096]) ).
fof(f11457,plain,
! [X0] : leq(multiplication(domain(X0),star(c(X0))),antidomain(c(X0))),
inference(resolution,[status(thm)],[f338,f4071]) ).
fof(f11459,plain,
! [X0] : leq(multiplication(antidomain(X0),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f338,f234]) ).
fof(f11460,plain,
! [X0,X1] :
( leq(multiplication(X0,star(star(X1))),antidomain(star(X1)))
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f8054,f338]) ).
fof(f11462,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(domain(X1)))
| ~ leq(X0,c(X1)) ),
inference(paramodulation,[status(thm)],[f62,f338]) ).
fof(f11463,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),antidomain(antidomain(X1)))
| ~ leq(X0,domain(X1)) ),
inference(paramodulation,[status(thm)],[f57,f338]) ).
fof(f11465,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),multiplication(antidomain(X2),star(X2))),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f37,f11437]) ).
fof(f11466,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),multiplication(antidomain(X2),star(X2))),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f37,f11438]) ).
fof(f11467,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),multiplication(antidomain(X2),star(X2))),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f37,f11439]) ).
fof(f11468,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),multiplication(antidomain(X2),star(X2))),antidomain(X2)),
inference(forward_demodulation,[status(thm)],[f37,f11440]) ).
fof(f11469,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f11441]) ).
fof(f11470,plain,
! [X0,X1] : leq(multiplication(domain(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f11442]) ).
fof(f11471,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f11443]) ).
fof(f11472,plain,
! [X0,X1] : leq(multiplication(c(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f11444]) ).
fof(f11473,plain,
! [X0,X1] : leq(multiplication(codomain(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f11445]) ).
fof(f11474,plain,
! [X0,X1] : leq(multiplication(divergence(X0),multiplication(antidomain(X1),star(X1))),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f11446]) ).
fof(f11475,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),multiplication(forward_diamond(X1,X2),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11447]) ).
fof(f11476,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),multiplication(forward_box(X1,X2),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11448]) ).
fof(f11477,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),multiplication(backward_box(X1,X2),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11449]) ).
fof(f11478,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),multiplication(backward_diamond(X1,X2),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11450]) ).
fof(f11479,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(coantidomain(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11451]) ).
fof(f11480,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(domain(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11452]) ).
fof(f11481,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(antidomain(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11453]) ).
fof(f11482,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(c(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11454]) ).
fof(f11483,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(codomain(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11455]) ).
fof(f11484,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(divergence(X1),star(X0))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f37,f11456]) ).
fof(f11486,plain,
! [X0,X1] :
( leq(multiplication(X0,star(star(X1))),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f8054,f11460]) ).
fof(f11489,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f62,f11462]) ).
fof(f11490,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f57,f11463]) ).
fof(f11494,plain,
! [X0,X1] : domain(multiplication(X0,domain(X1))) = multiplication(forward_diamond(X0,X1),domain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f64,f2094]) ).
fof(f11496,plain,
! [X0] : domain(domain(X0)) = multiplication(antidomain(c(X0)),domain(domain(X0))),
inference(paramodulation,[status(thm)],[f191,f2094]) ).
fof(f11500,plain,
! [X0,X1] : domain(multiplication(X0,domain(X1))) = multiplication(domain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f64,f2094]) ).
fof(f11502,plain,
! [X0] : domain(domain(X0)) = multiplication(domain(domain(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f191,f2094]) ).
fof(f11509,plain,
! [X0] : forward_diamond(domain(X0),X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f2094,f64]) ).
fof(f11511,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)],[f2094,f327]) ).
fof(f11512,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)],[f2094,f327]) ).
fof(f11513,plain,
! [X0] :
( leq(multiplication(domain(X0),multiplication(domain(X0),star(domain(X0)))),domain(X0))
| ~ leq(domain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2094,f337]) ).
fof(f11514,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),domain(X1))
| ~ leq(addition(X0,domain(X1)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f2094,f324]) ).
fof(f11515,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)],[f2094,f291]) ).
fof(f11516,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),multiplication(domain(X0),domain(X0))),domain(X0))
| ~ leq(domain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2094,f290]) ).
fof(f11517,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X1)),X0),domain(X1))
| ~ leq(addition(X0,domain(X1)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f2094,f288]) ).
fof(f11518,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(domain(X0),star(multiplication(domain(X0),domain(X0)))))),star(domain(X0))),
inference(paramodulation,[status(thm)],[f2094,f247]) ).
fof(f11519,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(domain(X0),star(domain(X0))))),star(multiplication(domain(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f2094,f247]) ).
fof(f11520,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)],[f2094,f214]) ).
fof(f11521,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)],[f2094,f214]) ).
fof(f11523,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)],[f2094,f206]) ).
fof(f11524,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)],[f2094,f206]) ).
fof(f11526,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)],[f2094,f199]) ).
fof(f11527,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)],[f2094,f199]) ).
fof(f11528,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = addition(multiplication(X1,domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f2094,f196]) ).
fof(f11529,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = addition(domain(X1),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f2094,f196]) ).
fof(f11530,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)],[f2094,f165]) ).
fof(f11531,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)],[f2094,f165]) ).
fof(f11534,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = addition(multiplication(domain(X0),X1),domain(X0)),
inference(paramodulation,[status(thm)],[f2094,f148]) ).
fof(f11535,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = addition(domain(X0),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f2094,f148]) ).
fof(f11538,plain,
! [X0] : addition(coantidomain(domain(X0)),coantidomain(multiplication(codomain(domain(X0)),domain(X0)))) = coantidomain(multiplication(codomain(domain(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f2094,f561]) ).
fof(f11539,plain,
! [X0] : addition(antidomain(domain(X0)),antidomain(multiplication(domain(X0),domain(domain(X0))))) = antidomain(multiplication(domain(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f2094,f404]) ).
fof(f11540,plain,
! [X0,X1] :
( leq(multiplication(X1,star(domain(X0))),domain(X0))
| ~ leq(addition(domain(X0),X1),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2094,f53]) ).
fof(f11541,plain,
! [X0,X1] :
( leq(multiplication(star(domain(X0)),X1),domain(X0))
| ~ leq(addition(domain(X0),X1),domain(X0)) ),
inference(paramodulation,[status(thm)],[f2094,f51]) ).
fof(f11542,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = addition(multiplication(X0,domain(X1)),domain(X1)),
inference(paramodulation,[status(thm)],[f2094,f41]) ).
fof(f11543,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = addition(domain(X0),multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f2094,f41]) ).
fof(f11544,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = addition(multiplication(domain(X0),X1),domain(X0)),
inference(paramodulation,[status(thm)],[f2094,f40]) ).
fof(f11545,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = addition(domain(X0),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f2094,f40]) ).
fof(f11546,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(domain(X0),X1)) = multiplication(domain(X0),X1),
inference(paramodulation,[status(thm)],[f2094,f37]) ).
fof(f11549,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),domain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f64,f11494]) ).
fof(f11550,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),forward_diamond(X0,X1)),
inference(forward_demodulation,[status(thm)],[f64,f11549]) ).
fof(f11552,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f191,f11496]) ).
fof(f11553,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f191,f11552]) ).
fof(f11560,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(domain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)),
inference(forward_demodulation,[status(thm)],[f64,f11500]) ).
fof(f11561,plain,
! [X0,X1] : forward_diamond(X0,X1) = multiplication(forward_diamond(X0,X1),forward_diamond(X0,X1)),
inference(forward_demodulation,[status(thm)],[f64,f11560]) ).
fof(f11563,plain,
! [X0] : antidomain(c(X0)) = multiplication(domain(domain(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f191,f11502]) ).
fof(f11564,plain,
! [X0] : antidomain(c(X0)) = domain_difference(domain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f63,f11563]) ).
fof(f11568,plain,
! [X0] : forward_diamond(domain(X0),X0) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f191,f11509]) ).
fof(f11575,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)],[f2094,f11511]) ).
fof(f11576,plain,
! [X0] : leq(multiplication(domain(X0),multiplication(domain(X0),star(domain(X0)))),domain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f11513,f234]) ).
fof(f11577,plain,
! [X0] :
( leq(multiplication(star(domain(X0)),domain(X0)),domain(X0))
| ~ leq(domain(X0),domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2094,f11516]) ).
fof(f11578,plain,
! [X0] : leq(multiplication(star(domain(X0)),domain(X0)),domain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f11577,f234]) ).
fof(f11579,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(domain(X0),star(domain(X0))))),star(domain(X0))),
inference(forward_demodulation,[status(thm)],[f2094,f11518]) ).
fof(f11580,plain,
! [X0] : leq(addition(one,multiplication(domain(X0),multiplication(domain(X0),star(domain(X0))))),star(domain(X0))),
inference(forward_demodulation,[status(thm)],[f2094,f11519]) ).
fof(f11581,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)],[f92,f11520]) ).
fof(f11585,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),domain(X2)) = multiplication(addition(X1,X0),domain(X2)),
inference(forward_demodulation,[status(thm)],[f196,f11523]) ).
fof(f11588,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)],[f33,f11526]) ).
fof(f11589,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),domain(X1)) = multiplication(addition(X2,X0),domain(X1)),
inference(forward_demodulation,[status(thm)],[f196,f11527]) ).
fof(f11590,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = addition(domain(X0),multiplication(X1,domain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f11528]) ).
fof(f11591,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = multiplication(addition(X1,one),domain(X0)),
inference(forward_demodulation,[status(thm)],[f227,f11590]) ).
fof(f11592,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = multiplication(addition(X0,one),domain(X1)),
inference(forward_demodulation,[status(thm)],[f227,f11529]) ).
fof(f11593,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)],[f92,f11530]) ).
fof(f11599,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = addition(domain(X0),multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f11534]) ).
fof(f11600,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = multiplication(domain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f11599]) ).
fof(f11601,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = multiplication(domain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f11535]) ).
fof(f11603,plain,
! [X0] : addition(c(X0),antidomain(multiplication(domain(X0),domain(domain(X0))))) = antidomain(multiplication(domain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f11539]) ).
fof(f11604,plain,
! [X0] : addition(c(X0),antidomain(multiplication(domain(X0),antidomain(c(X0))))) = antidomain(multiplication(domain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f11603]) ).
fof(f11605,plain,
! [X0] : addition(c(X0),antidomain(domain_difference(X0,c(X0)))) = antidomain(multiplication(domain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f63,f11604]) ).
fof(f11606,plain,
! [X0] : addition(c(X0),antidomain(domain_difference(X0,c(X0)))) = antidomain(multiplication(domain(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f11605]) ).
fof(f11607,plain,
! [X0] : addition(c(X0),antidomain(domain_difference(X0,c(X0)))) = antidomain(domain_difference(X0,c(X0))),
inference(forward_demodulation,[status(thm)],[f63,f11606]) ).
fof(f11608,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = addition(domain(X1),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f33,f11542]) ).
fof(f11609,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),domain(X1)) = multiplication(addition(X0,one),domain(X1)),
inference(forward_demodulation,[status(thm)],[f227,f11608]) ).
fof(f11610,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),domain(X0)) = multiplication(addition(X1,one),domain(X0)),
inference(forward_demodulation,[status(thm)],[f227,f11543]) ).
fof(f11611,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = addition(domain(X0),multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f11544]) ).
fof(f11612,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,domain(X0))) = multiplication(domain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f11611]) ).
fof(f11613,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),X1)) = multiplication(domain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f11545]) ).
fof(f11693,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),backward_diamond(X2,X3)))),
inference(paramodulation,[status(thm)],[f98,f2343]) ).
fof(f11694,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),backward_diamond(X2,X3)))),
inference(paramodulation,[status(thm)],[f34,f2343]) ).
fof(f11700,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)],[f219,f2343]) ).
fof(f11703,plain,
! [X0,X1] : domain(backward_diamond(X0,X1)) = addition(domain(backward_diamond(X0,X1)),backward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f3965,f2343]) ).
fof(f11716,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),backward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f2343,f219]) ).
fof(f11717,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(multiplication(one,backward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f2343,f202]) ).
fof(f11726,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)],[f2343,f327]) ).
fof(f11727,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)],[f2343,f291]) ).
fof(f11730,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)],[f2343,f214]) ).
fof(f11731,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)],[f2343,f165]) ).
fof(f11732,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)],[f2343,f53]) ).
fof(f11733,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)],[f2343,f51]) ).
fof(f11734,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X1,X0),backward_diamond(X2,X3)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2343,f98]) ).
fof(f11735,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X0,X1),backward_diamond(X2,X3)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2343,f34]) ).
fof(f11737,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(backward_diamond(X1,X2))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2343,f324]) ).
fof(f11738,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X0),backward_diamond(X1,X2))
| ~ leq(X0,backward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f2343,f288]) ).
fof(f11748,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)],[f2343,f335]) ).
fof(f11749,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)],[f2343,f334]) ).
fof(f11750,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_diamond(X1,X2))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2343,f297]) ).
fof(f11751,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)],[f2343,f286]) ).
fof(f11752,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)],[f2343,f285]) ).
fof(f11753,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)],[f2343,f238]) ).
fof(f11754,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)],[f2343,f237]) ).
fof(f11755,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)],[f2343,f236]) ).
fof(f11757,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,backward_diamond(X1,X2)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2343,f221]) ).
fof(f11761,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(X3,X0)),
inference(paramodulation,[status(thm)],[f2343,f1356]) ).
fof(f11765,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,backward_diamond(X1,X2)),addition(X0,X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2343,f98]) ).
fof(f11766,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,backward_diamond(X1,X2)),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f2343,f92]) ).
fof(f11767,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(X1,backward_diamond(X2,X3)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2343,f92]) ).
fof(f11769,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_diamond(X1,X2))
| leq(X0,multiplication(X0,backward_diamond(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2343,f47]) ).
fof(f11770,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,backward_diamond(X1,X2)),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2343,f34]) ).
fof(f11783,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)],[f98,f11700]) ).
fof(f11786,plain,
! [X0,X1] : domain(backward_diamond(X0,X1)) = addition(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f11703]) ).
fof(f11793,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(antidomain(X0),backward_diamond(X1,X2)),X0),
inference(forward_demodulation,[status(thm)],[f54,f11716]) ).
fof(f11794,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f37,f11793]) ).
fof(f11795,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(multiplication(one,backward_diamond(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f39,f11717]) ).
fof(f11796,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(one,multiplication(backward_diamond(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f37,f11795]) ).
fof(f11797,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f11796]) ).
fof(f11803,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)],[f37,f11726]) ).
fof(f11804,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)],[f37,f11803]) ).
fof(f11805,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)],[f37,f11804]) ).
fof(f11806,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)],[f37,f11727]) ).
fof(f11807,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)],[f37,f11806]) ).
fof(f11809,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)],[f196,f11730]) ).
fof(f11810,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)],[f37,f11809]) ).
fof(f11811,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)],[f148,f11731]) ).
fof(f11812,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)],[f37,f11811]) ).
fof(f11813,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)],[f148,f11812]) ).
fof(f11814,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)],[f92,f11813]) ).
fof(f11815,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)],[f37,f11732]) ).
fof(f11816,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)],[f37,f11815]) ).
fof(f11817,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)],[f37,f11733]) ).
fof(f11818,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(backward_diamond(X1,X2))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f11737,f234]) ).
fof(f11833,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)],[f37,f11748]) ).
fof(f11834,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)],[f37,f11749]) ).
fof(f11835,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)],[f37,f11752]) ).
fof(f11836,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)],[f37,f11755]) ).
fof(f11837,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)],[f37,f11836]) ).
fof(f11838,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(X0,backward_diamond(X1,X2)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f11757]) ).
fof(f11839,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(backward_diamond(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f11838]) ).
fof(f11842,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,backward_diamond(X2,X3)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f11765]) ).
fof(f11843,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(X1,backward_diamond(X2,X3)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f11767]) ).
fof(f11850,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),forward_box(X2,X3)))),
inference(paramodulation,[status(thm)],[f98,f2344]) ).
fof(f11851,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),forward_box(X2,X3)))),
inference(paramodulation,[status(thm)],[f34,f2344]) ).
fof(f11857,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)],[f219,f2344]) ).
fof(f11860,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = addition(domain(forward_box(X0,X1)),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f3965,f2344]) ).
fof(f11871,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),forward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f2344,f219]) ).
fof(f11872,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(multiplication(one,forward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f2344,f202]) ).
fof(f11881,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)],[f2344,f327]) ).
fof(f11882,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)],[f2344,f291]) ).
fof(f11885,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)],[f2344,f214]) ).
fof(f11886,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)],[f2344,f165]) ).
fof(f11887,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)],[f2344,f53]) ).
fof(f11888,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)],[f2344,f51]) ).
fof(f11889,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X1,X0),forward_box(X2,X3)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2344,f98]) ).
fof(f11890,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X0,X1),forward_box(X2,X3)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2344,f34]) ).
fof(f11892,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(forward_box(X1,X2))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2344,f324]) ).
fof(f11893,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X0),forward_box(X1,X2))
| ~ leq(X0,forward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f2344,f288]) ).
fof(f11903,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)],[f2344,f335]) ).
fof(f11904,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)],[f2344,f334]) ).
fof(f11905,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_box(X1,X2))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2344,f297]) ).
fof(f11906,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)],[f2344,f286]) ).
fof(f11907,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)],[f2344,f285]) ).
fof(f11908,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)],[f2344,f238]) ).
fof(f11909,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)],[f2344,f237]) ).
fof(f11910,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)],[f2344,f236]) ).
fof(f11912,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,forward_box(X1,X2)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2344,f221]) ).
fof(f11916,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,forward_box(X1,X2)),addition(X3,X0)),
inference(paramodulation,[status(thm)],[f2344,f1356]) ).
fof(f11920,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,forward_box(X1,X2)),addition(X0,X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2344,f98]) ).
fof(f11921,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,forward_box(X1,X2)),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f2344,f92]) ).
fof(f11922,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(X1,forward_box(X2,X3)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2344,f92]) ).
fof(f11924,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_box(X1,X2))
| leq(X0,multiplication(X0,forward_box(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2344,f47]) ).
fof(f11925,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,forward_box(X1,X2)),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2344,f34]) ).
fof(f11938,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)],[f98,f11857]) ).
fof(f11941,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = addition(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f11860]) ).
fof(f11949,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(antidomain(X0),forward_box(X1,X2)),X0),
inference(forward_demodulation,[status(thm)],[f54,f11871]) ).
fof(f11950,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f37,f11949]) ).
fof(f11951,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(multiplication(one,forward_box(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f39,f11872]) ).
fof(f11952,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(one,multiplication(forward_box(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f37,f11951]) ).
fof(f11953,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f11952]) ).
fof(f11959,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)],[f37,f11881]) ).
fof(f11960,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)],[f37,f11959]) ).
fof(f11961,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)],[f37,f11960]) ).
fof(f11962,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)],[f37,f11882]) ).
fof(f11963,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)],[f37,f11962]) ).
fof(f11965,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)],[f196,f11885]) ).
fof(f11966,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)],[f37,f11965]) ).
fof(f11967,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)],[f148,f11886]) ).
fof(f11968,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)],[f37,f11967]) ).
fof(f11969,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)],[f148,f11968]) ).
fof(f11970,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)],[f92,f11969]) ).
fof(f11971,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)],[f37,f11887]) ).
fof(f11972,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)],[f37,f11971]) ).
fof(f11973,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)],[f37,f11888]) ).
fof(f11974,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(forward_box(X1,X2))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f11892,f234]) ).
fof(f11989,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)],[f37,f11903]) ).
fof(f11990,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)],[f37,f11904]) ).
fof(f11991,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)],[f37,f11907]) ).
fof(f11992,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)],[f37,f11910]) ).
fof(f11993,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)],[f37,f11992]) ).
fof(f11994,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(X0,forward_box(X1,X2)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f11912]) ).
fof(f11995,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(forward_box(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f11994]) ).
fof(f11998,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,forward_box(X2,X3)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f11920]) ).
fof(f11999,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(X1,forward_box(X2,X3)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f11922]) ).
fof(f12006,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),backward_box(X2,X3)))),
inference(paramodulation,[status(thm)],[f98,f2345]) ).
fof(f12007,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),backward_box(X2,X3)))),
inference(paramodulation,[status(thm)],[f34,f2345]) ).
fof(f12013,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)],[f219,f2345]) ).
fof(f12016,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = addition(domain(backward_box(X0,X1)),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f3965,f2345]) ).
fof(f12026,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),backward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f2345,f219]) ).
fof(f12027,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(multiplication(one,backward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f2345,f202]) ).
fof(f12036,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)],[f2345,f327]) ).
fof(f12037,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)],[f2345,f291]) ).
fof(f12040,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)],[f2345,f214]) ).
fof(f12041,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)],[f2345,f165]) ).
fof(f12042,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)],[f2345,f53]) ).
fof(f12043,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)],[f2345,f51]) ).
fof(f12044,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X1,X0),backward_box(X2,X3)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2345,f98]) ).
fof(f12045,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X0,X1),backward_box(X2,X3)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2345,f34]) ).
fof(f12047,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(backward_box(X1,X2))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2345,f324]) ).
fof(f12048,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X0),backward_box(X1,X2))
| ~ leq(X0,backward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f2345,f288]) ).
fof(f12058,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)],[f2345,f335]) ).
fof(f12059,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)],[f2345,f334]) ).
fof(f12060,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,backward_box(X1,X2))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2345,f297]) ).
fof(f12061,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)],[f2345,f286]) ).
fof(f12062,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)],[f2345,f285]) ).
fof(f12063,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)],[f2345,f238]) ).
fof(f12064,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)],[f2345,f237]) ).
fof(f12065,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)],[f2345,f236]) ).
fof(f12067,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,backward_box(X1,X2)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2345,f221]) ).
fof(f12071,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,backward_box(X1,X2)),addition(X3,X0)),
inference(paramodulation,[status(thm)],[f2345,f1356]) ).
fof(f12075,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,backward_box(X1,X2)),addition(X0,X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2345,f98]) ).
fof(f12076,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,backward_box(X1,X2)),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f2345,f92]) ).
fof(f12077,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(X1,backward_box(X2,X3)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2345,f92]) ).
fof(f12079,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_box(X1,X2))
| leq(X0,multiplication(X0,backward_box(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2345,f47]) ).
fof(f12080,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,backward_box(X1,X2)),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2345,f34]) ).
fof(f12093,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)],[f98,f12013]) ).
fof(f12096,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = addition(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f12016]) ).
fof(f12103,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(antidomain(X0),backward_box(X1,X2)),X0),
inference(forward_demodulation,[status(thm)],[f54,f12026]) ).
fof(f12104,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f37,f12103]) ).
fof(f12105,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(multiplication(one,backward_box(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f39,f12027]) ).
fof(f12106,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(one,multiplication(backward_box(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f37,f12105]) ).
fof(f12107,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f12106]) ).
fof(f12113,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)],[f37,f12036]) ).
fof(f12114,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)],[f37,f12113]) ).
fof(f12115,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)],[f37,f12114]) ).
fof(f12116,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)],[f37,f12037]) ).
fof(f12117,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)],[f37,f12116]) ).
fof(f12119,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)],[f196,f12040]) ).
fof(f12120,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)],[f37,f12119]) ).
fof(f12121,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)],[f148,f12041]) ).
fof(f12122,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)],[f37,f12121]) ).
fof(f12123,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)],[f148,f12122]) ).
fof(f12124,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)],[f92,f12123]) ).
fof(f12125,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)],[f37,f12042]) ).
fof(f12126,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)],[f37,f12125]) ).
fof(f12127,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)],[f37,f12043]) ).
fof(f12128,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(backward_box(X1,X2))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f12047,f234]) ).
fof(f12143,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)],[f37,f12058]) ).
fof(f12144,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)],[f37,f12059]) ).
fof(f12145,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)],[f37,f12062]) ).
fof(f12146,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)],[f37,f12065]) ).
fof(f12147,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)],[f37,f12146]) ).
fof(f12148,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(X0,backward_box(X1,X2)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f12067]) ).
fof(f12149,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(backward_box(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f12148]) ).
fof(f12152,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,backward_box(X2,X3)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f12075]) ).
fof(f12153,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(X1,backward_box(X2,X3)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f12077]) ).
fof(f12156,plain,
! [X0] :
( leq(multiplication(multiplication(star(X0),addition(X0,one)),star(one)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7423,f330]) ).
fof(f12157,plain,
! [X0] :
( leq(multiplication(multiplication(addition(X0,one),star(X0)),star(one)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7156,f330]) ).
fof(f12158,plain,
! [X0,X1] :
( leq(multiplication(backward_diamond(X0,X1),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1439,f330]) ).
fof(f12159,plain,
! [X0,X1] :
( leq(multiplication(forward_box(X0,X1),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1432,f330]) ).
fof(f12160,plain,
! [X0,X1] :
( leq(multiplication(backward_box(X0,X1),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1427,f330]) ).
fof(f12161,plain,
! [X0,X1] :
( leq(multiplication(forward_diamond(X0,X1),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1420,f330]) ).
fof(f12162,plain,
! [X0] :
( leq(multiplication(divergence(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1423,f330]) ).
fof(f12163,plain,
! [X0] :
( leq(multiplication(codomain(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1412,f330]) ).
fof(f12164,plain,
! [X0] :
( leq(multiplication(c(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1406,f330]) ).
fof(f12165,plain,
! [X0] :
( leq(multiplication(antidomain(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1315,f330]) ).
fof(f12166,plain,
! [X0] :
( leq(multiplication(coantidomain(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1313,f330]) ).
fof(f12167,plain,
! [X0] :
( leq(multiplication(domain(X0),star(one)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1311,f330]) ).
fof(f12168,plain,
! [X0] :
( leq(multiplication(c(X0),star(domain(X0))),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f515,f330]) ).
fof(f12169,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)],[f561,f330]) ).
fof(f12170,plain,
! [X0] :
( leq(multiplication(codomain(X0),star(coantidomain(X0))),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f625,f330]) ).
fof(f12171,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)],[f404,f330]) ).
fof(f12172,plain,
! [X0] :
( leq(multiplication(c(X0),star(antidomain(X0))),one)
| ~ leq(c(X0),one) ),
inference(paramodulation,[status(thm)],[f434,f330]) ).
fof(f12173,plain,
! [X0] :
( leq(multiplication(domain(X0),star(antidomain(X0))),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f504,f330]) ).
fof(f12174,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)],[f199,f330]) ).
fof(f12175,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)],[f214,f330]) ).
fof(f12176,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)],[f165,f330]) ).
fof(f12177,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)],[f206,f330]) ).
fof(f12178,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)],[f196,f330]) ).
fof(f12179,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)],[f148,f330]) ).
fof(f12180,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)],[f41,f330]) ).
fof(f12181,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)],[f40,f330]) ).
fof(f12182,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,X0))),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f98,f330]) ).
fof(f12183,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X0,X1))),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f34,f330]) ).
fof(f12185,plain,
! [X0,X1] :
( leq(multiplication(multiplication(domain(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4331,f330]) ).
fof(f12186,plain,
! [X0,X1] :
( leq(multiplication(multiplication(coantidomain(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4330,f330]) ).
fof(f12187,plain,
! [X0,X1] :
( leq(multiplication(multiplication(antidomain(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4329,f330]) ).
fof(f12188,plain,
! [X0,X1] :
( leq(multiplication(multiplication(c(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4328,f330]) ).
fof(f12189,plain,
! [X0,X1] :
( leq(multiplication(multiplication(codomain(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4327,f330]) ).
fof(f12190,plain,
! [X0,X1] :
( leq(multiplication(multiplication(divergence(X1),X0),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f4326,f330]) ).
fof(f12191,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,backward_box(X1,X2)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2345,f330]) ).
fof(f12192,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,forward_box(X1,X2)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2344,f330]) ).
fof(f12193,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,backward_diamond(X1,X2)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2343,f330]) ).
fof(f12194,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,domain(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2352,f330]) ).
fof(f12195,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,coantidomain(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2351,f330]) ).
fof(f12196,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,antidomain(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2350,f330]) ).
fof(f12197,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,c(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2349,f330]) ).
fof(f12198,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,codomain(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2348,f330]) ).
fof(f12199,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,divergence(X1)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2347,f330]) ).
fof(f12200,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),one)
| ~ leq(multiplication(addition(X0,one),X1),one) ),
inference(paramodulation,[status(thm)],[f227,f330]) ).
fof(f12202,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X0)),one)
| ~ leq(multiplication(X0,addition(X1,one)),one) ),
inference(paramodulation,[status(thm)],[f187,f330]) ).
fof(f12203,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X0)),one)
| ~ leq(multiplication(X0,addition(one,X1)),one) ),
inference(paramodulation,[status(thm)],[f157,f330]) ).
fof(f12204,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,X0),star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1266,f330]) ).
fof(f12205,plain,
! [X0,X1] :
( leq(multiplication(addition(X1,X0),star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f966,f330]) ).
fof(f12206,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,X1),star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f945,f330]) ).
fof(f12207,plain,
! [X0,X1] :
( leq(multiplication(addition(X0,X1),star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f100,f330]) ).
fof(f12208,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,X1),star(X2)),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f92,f330]) ).
fof(f12209,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X2,X0),star(X1)),one)
| ~ leq(addition(X0,addition(X1,X2)),one) ),
inference(paramodulation,[status(thm)],[f92,f330]) ).
fof(f12211,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f33,f330]) ).
fof(f12212,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f33,f330]) ).
fof(f12213,plain,
! [X0] :
( leq(multiplication(X0,star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f36,f330]) ).
fof(f12215,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(addition(X0,one),star(one))),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f37,f12156]) ).
fof(f12216,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(addition(X0,one),one)),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f9178,f12215]) ).
fof(f12217,plain,
! [X0] :
( leq(multiplication(star(X0),addition(one,multiplication(X0,one))),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f227,f12216]) ).
fof(f12218,plain,
! [X0] :
( leq(multiplication(star(X0),addition(one,X0)),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f38,f12217]) ).
fof(f12219,plain,
! [X0] :
( leq(multiplication(addition(X0,one),multiplication(star(X0),star(one))),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f37,f12157]) ).
fof(f12220,plain,
! [X0] :
( leq(multiplication(addition(X0,one),multiplication(star(X0),one)),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f9178,f12219]) ).
fof(f12221,plain,
! [X0] :
( leq(multiplication(addition(X0,one),star(X0)),one)
| ~ leq(star(X0),one) ),
inference(forward_demodulation,[status(thm)],[f38,f12220]) ).
fof(f12222,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(f12225,plain,
( sQ30_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12158,f8880,f12222]) ).
fof(f12226,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(f12229,plain,
( sQ31_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12159,f8880,f12226]) ).
fof(f12230,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(f12233,plain,
( sQ32_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12160,f8880,f12230]) ).
fof(f12234,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(f12237,plain,
( sQ33_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12161,f8880,f12234]) ).
fof(f12238,definition,
! [X0] :
( sQ34_spl
<=> leq(multiplication(divergence(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f12241,plain,
( sQ34_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12162,f8880,f12238]) ).
fof(f12242,definition,
! [X0] :
( sQ35_spl
<=> leq(multiplication(codomain(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f12245,plain,
( sQ35_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12163,f8880,f12242]) ).
fof(f12246,definition,
! [X0] :
( sQ36_spl
<=> leq(multiplication(c(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f12249,plain,
( sQ36_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12164,f8880,f12246]) ).
fof(f12250,definition,
! [X0] :
( sQ37_spl
<=> leq(multiplication(antidomain(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f12253,plain,
( sQ37_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12165,f8880,f12250]) ).
fof(f12254,definition,
! [X0] :
( sQ38_spl
<=> leq(multiplication(coantidomain(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f12257,plain,
( sQ38_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12166,f8880,f12254]) ).
fof(f12258,definition,
! [X0] :
( sQ39_spl
<=> leq(multiplication(domain(X0),star(one)),one) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f12261,plain,
( sQ39_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12167,f8880,f12258]) ).
fof(f12262,definition,
! [X0] :
( sQ40_spl
<=> leq(multiplication(c(X0),star(domain(X0))),one) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f12263,plain,
! [X0] :
( ~ sQ40_spl
| leq(multiplication(c(X0),star(domain(X0))),one) ),
inference(component_clause,[status(thm)],[f12262]) ).
fof(f12265,plain,
( sQ40_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12168,f8880,f12262]) ).
fof(f12266,plain,
! [X0,X1] : leq(multiplication(coantidomain(multiplication(codomain(X0),X1)),star(coantidomain(multiplication(X0,X1)))),one),
inference(forward_subsumption_resolution,[status(thm)],[f12169,f1346]) ).
fof(f12267,definition,
! [X0] :
( sQ41_spl
<=> leq(multiplication(codomain(X0),star(coantidomain(X0))),one) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f12268,plain,
! [X0] :
( ~ sQ41_spl
| leq(multiplication(codomain(X0),star(coantidomain(X0))),one) ),
inference(component_clause,[status(thm)],[f12267]) ).
fof(f12270,plain,
( sQ41_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12170,f8880,f12267]) ).
fof(f12271,plain,
! [X0,X1] : leq(multiplication(antidomain(multiplication(X0,domain(X1))),star(antidomain(multiplication(X0,X1)))),one),
inference(forward_subsumption_resolution,[status(thm)],[f12171,f1348]) ).
fof(f12272,plain,
! [X0] : leq(multiplication(c(X0),star(antidomain(X0))),one),
inference(forward_subsumption_resolution,[status(thm)],[f12172,f1366]) ).
fof(f12273,definition,
! [X0] :
( sQ42_spl
<=> leq(multiplication(domain(X0),star(antidomain(X0))),one) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f12274,plain,
! [X0] :
( ~ sQ42_spl
| leq(multiplication(domain(X0),star(antidomain(X0))),one) ),
inference(component_clause,[status(thm)],[f12273]) ).
fof(f12276,plain,
( sQ42_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f12173,f8880,f12273]) ).
fof(f12277,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)],[f37,f12174]) ).
fof(f12278,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)],[f37,f12177]) ).
fof(f12279,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)],[f37,f12278]) ).
fof(f12280,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)],[f37,f12178]) ).
fof(f12281,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)],[f37,f12179]) ).
fof(f12282,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)],[f37,f12180]) ).
fof(f12283,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)],[f37,f12181]) ).
fof(f12285,plain,
! [X0,X1] :
( leq(multiplication(domain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12185]) ).
fof(f12286,plain,
! [X0,X1] :
( leq(multiplication(coantidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12186]) ).
fof(f12287,plain,
! [X0,X1] :
( leq(multiplication(antidomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12187]) ).
fof(f12288,plain,
! [X0,X1] :
( leq(multiplication(c(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12188]) ).
fof(f12289,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12189]) ).
fof(f12290,plain,
! [X0,X1] :
( leq(multiplication(divergence(X1),multiplication(X0,star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12190]) ).
fof(f12291,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(backward_box(X1,X2),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12191]) ).
fof(f12292,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(forward_box(X1,X2),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12192]) ).
fof(f12293,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(backward_diamond(X1,X2),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12193]) ).
fof(f12294,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(domain(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12194]) ).
fof(f12295,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(coantidomain(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12195]) ).
fof(f12296,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(antidomain(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12196]) ).
fof(f12297,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(c(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12197]) ).
fof(f12298,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(codomain(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12198]) ).
fof(f12299,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(divergence(X1),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12199]) ).
fof(f12300,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),one)
| ~ leq(multiplication(addition(X0,one),X1),one) ),
inference(forward_demodulation,[status(thm)],[f37,f12200]) ).
fof(f12302,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X0))),one)
| ~ leq(multiplication(X0,addition(X1,one)),one) ),
inference(forward_demodulation,[status(thm)],[f37,f12202]) ).
fof(f12303,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X0))),one)
| ~ leq(multiplication(X0,addition(one,X1)),one) ),
inference(forward_demodulation,[status(thm)],[f37,f12203]) ).
fof(f12330,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),forward_diamond(X2,X3)))),
inference(paramodulation,[status(thm)],[f98,f2346]) ).
fof(f12331,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),forward_diamond(X2,X3)))),
inference(paramodulation,[status(thm)],[f34,f2346]) ).
fof(f12337,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)],[f219,f2346]) ).
fof(f12340,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = addition(domain(forward_diamond(X0,X1)),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f3965,f2346]) ).
fof(f12355,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),forward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f2346,f219]) ).
fof(f12356,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(multiplication(one,forward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f2346,f202]) ).
fof(f12365,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)],[f2346,f327]) ).
fof(f12366,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)],[f2346,f291]) ).
fof(f12369,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)],[f2346,f214]) ).
fof(f12370,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)],[f2346,f165]) ).
fof(f12371,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)],[f2346,f53]) ).
fof(f12372,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)],[f2346,f51]) ).
fof(f12373,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X1,X0),forward_diamond(X2,X3)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2346,f98]) ).
fof(f12374,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(addition(X0,X1),forward_diamond(X2,X3)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2346,f34]) ).
fof(f12376,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(forward_diamond(X1,X2))),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f2346,f324]) ).
fof(f12377,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X0),forward_diamond(X1,X2))
| ~ leq(X0,forward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f2346,f288]) ).
fof(f12382,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,forward_diamond(X1,X2)),star(X0)),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2346,f330]) ).
fof(f12388,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)],[f2346,f335]) ).
fof(f12389,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)],[f2346,f334]) ).
fof(f12390,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,forward_diamond(X1,X2))),one)
| ~ leq(X0,one) ),
inference(paramodulation,[status(thm)],[f2346,f297]) ).
fof(f12391,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)],[f2346,f286]) ).
fof(f12392,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)],[f2346,f285]) ).
fof(f12393,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)],[f2346,f238]) ).
fof(f12394,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)],[f2346,f237]) ).
fof(f12395,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)],[f2346,f236]) ).
fof(f12397,plain,
! [X0,X1,X2] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,forward_diamond(X1,X2)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2346,f221]) ).
fof(f12401,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(X3,X0)),
inference(paramodulation,[status(thm)],[f2346,f1356]) ).
fof(f12405,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,forward_diamond(X1,X2)),addition(X0,X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2346,f98]) ).
fof(f12406,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,forward_diamond(X1,X2)),X3)) = addition(X3,X0),
inference(paramodulation,[status(thm)],[f2346,f92]) ).
fof(f12407,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(multiplication(X1,forward_diamond(X2,X3)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2346,f92]) ).
fof(f12409,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_diamond(X1,X2))
| leq(X0,multiplication(X0,forward_diamond(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2346,f47]) ).
fof(f12410,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,forward_diamond(X1,X2)),X3)) = addition(X0,X3),
inference(paramodulation,[status(thm)],[f2346,f34]) ).
fof(f12423,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)],[f98,f12337]) ).
fof(f12426,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = addition(forward_diamond(X0,X1),domain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f12340]) ).
fof(f12434,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(antidomain(X0),forward_diamond(X1,X2)),X0),
inference(forward_demodulation,[status(thm)],[f54,f12355]) ).
fof(f12435,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(X0),multiplication(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f37,f12434]) ).
fof(f12436,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(multiplication(one,forward_diamond(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f39,f12356]) ).
fof(f12437,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(one,multiplication(forward_diamond(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f37,f12436]) ).
fof(f12438,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f39,f12437]) ).
fof(f12444,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)],[f37,f12365]) ).
fof(f12445,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)],[f37,f12444]) ).
fof(f12446,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)],[f37,f12445]) ).
fof(f12447,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)],[f37,f12366]) ).
fof(f12448,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)],[f37,f12447]) ).
fof(f12450,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)],[f196,f12369]) ).
fof(f12451,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)],[f37,f12450]) ).
fof(f12452,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)],[f148,f12370]) ).
fof(f12453,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)],[f37,f12452]) ).
fof(f12454,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)],[f148,f12453]) ).
fof(f12455,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)],[f92,f12454]) ).
fof(f12456,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)],[f37,f12371]) ).
fof(f12457,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)],[f37,f12456]) ).
fof(f12458,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)],[f37,f12372]) ).
fof(f12459,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(forward_diamond(X1,X2))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f12376,f234]) ).
fof(f12466,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(forward_diamond(X1,X2),star(X0))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f37,f12382]) ).
fof(f12475,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)],[f37,f12388]) ).
fof(f12476,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)],[f37,f12389]) ).
fof(f12477,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)],[f37,f12392]) ).
fof(f12478,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)],[f37,f12395]) ).
fof(f12479,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)],[f37,f12478]) ).
fof(f12480,plain,
! [X0,X1,X2] : zero = multiplication(multiplication(X0,forward_diamond(X1,X2)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f58,f12397]) ).
fof(f12481,plain,
! [X0,X1,X2] : zero = multiplication(X0,multiplication(forward_diamond(X1,X2),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f12480]) ).
fof(f12484,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,multiplication(X0,forward_diamond(X2,X3)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f92,f12405]) ).
fof(f12485,plain,
! [X0,X1,X2,X3] : addition(X0,X1) = addition(X1,addition(multiplication(X1,forward_diamond(X2,X3)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f12407]) ).
fof(f12487,plain,
! [X0,X1] : leq(multiplication(star(antidomain(multiplication(X0,addition(one,X1)))),X0),multiplication(X0,addition(one,X1))),
inference(resolution,[status(thm)],[f2333,f299]) ).
fof(f12488,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = multiplication(X0,addition(one,X1)),
inference(resolution,[status(thm)],[f2333,f46]) ).
fof(f12489,plain,
! [X0,X1] : leq(addition(antidomain(addition(one,X0)),X1),multiplication(X1,addition(one,X0))),
inference(paramodulation,[status(thm)],[f219,f2333]) ).
fof(f12490,plain,
! [X0,X1] : leq(addition(X0,antidomain(addition(one,X1))),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f225,f2333]) ).
fof(f12491,plain,
! [X0] : leq(c(addition(one,X0)),zero),
inference(paramodulation,[status(thm)],[f4088,f2333]) ).
fof(f12493,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f37,f2333]) ).
fof(f12496,plain,
! [X0] : leq(antidomain(addition(one,X0)),zero),
inference(paramodulation,[status(thm)],[f54,f2333]) ).
fof(f12532,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f966,f2333]) ).
fof(f12533,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f945,f2333]) ).
fof(f12535,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f92,f2333]) ).
fof(f12536,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f92,f2333]) ).
fof(f12538,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f33,f2333]) ).
fof(f12539,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f33,f2333]) ).
fof(f12577,plain,
! [X0,X1] : c(backward_diamond(X0,c(X1))) = multiplication(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f67,f2482]) ).
fof(f12578,plain,
! [X0,X1] : c(forward_diamond(X0,c(X1))) = multiplication(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f66,f2482]) ).
fof(f12580,plain,
! [X0] : c(antidomain(X0)) = multiplication(antidomain(c(X0)),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f493,f2482]) ).
fof(f12581,plain,
! [X0] : c(domain(X0)) = multiplication(domain(c(X0)),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f317,f2482]) ).
fof(f12585,plain,
! [X0] : c(domain(X0)) = multiplication(c(domain(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f62,f2482]) ).
fof(f12586,plain,
! [X0] : c(antidomain(X0)) = multiplication(c(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f57,f2482]) ).
fof(f12588,plain,
! [X0] : leq(c(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f2482,f6199]) ).
fof(f12589,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f2482,f4328]) ).
fof(f12592,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)],[f2482,f327]) ).
fof(f12593,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)],[f2482,f327]) ).
fof(f12594,plain,
! [X0] :
( leq(multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0)))),c(X0))
| ~ leq(c(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f2482,f337]) ).
fof(f12595,plain,
! [X0,X1] :
( leq(multiplication(X0,star(antidomain(X1))),c(X1))
| ~ leq(addition(X0,c(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f2482,f324]) ).
fof(f12596,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)],[f2482,f291]) ).
fof(f12597,plain,
! [X0] :
( leq(multiplication(star(c(X0)),multiplication(c(X0),antidomain(X0))),antidomain(X0))
| ~ leq(c(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f2482,f290]) ).
fof(f12598,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),X0),antidomain(X1))
| ~ leq(addition(X0,c(X1)),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f2482,f288]) ).
fof(f12599,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(multiplication(c(X0),antidomain(X0)))))),star(c(X0))),
inference(paramodulation,[status(thm)],[f2482,f247]) ).
fof(f12600,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(c(X0))))),star(multiplication(c(X0),antidomain(X0)))),
inference(paramodulation,[status(thm)],[f2482,f247]) ).
fof(f12601,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)],[f2482,f214]) ).
fof(f12602,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)],[f2482,f214]) ).
fof(f12603,plain,
! [X0] : multiplication(addition(c(X0),one),antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f2482,f227]) ).
fof(f12604,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)],[f2482,f206]) ).
fof(f12605,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)],[f2482,f206]) ).
fof(f12606,plain,
! [X0] : multiplication(addition(one,c(X0)),antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f2482,f202]) ).
fof(f12607,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)],[f2482,f199]) ).
fof(f12608,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)],[f2482,f199]) ).
fof(f12609,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(multiplication(X1,antidomain(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f2482,f196]) ).
fof(f12610,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(c(X1),multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f2482,f196]) ).
fof(f12611,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)],[f2482,f165]) ).
fof(f12612,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)],[f2482,f165]) ).
fof(f12615,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(multiplication(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f2482,f148]) ).
fof(f12616,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(c(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f2482,f148]) ).
fof(f12617,plain,
! [X0] : multiplication(c(X0),multiplication(antidomain(X0),coantidomain(c(X0)))) = zero,
inference(paramodulation,[status(thm)],[f2482,f139]) ).
fof(f12619,plain,
! [X0] : addition(coantidomain(c(X0)),coantidomain(multiplication(codomain(c(X0)),antidomain(X0)))) = coantidomain(multiplication(codomain(c(X0)),antidomain(X0))),
inference(paramodulation,[status(thm)],[f2482,f561]) ).
fof(f12621,plain,
! [X0,X1] :
( leq(multiplication(X1,star(antidomain(X0))),c(X0))
| ~ leq(addition(c(X0),X1),c(X0)) ),
inference(paramodulation,[status(thm)],[f2482,f53]) ).
fof(f12622,plain,
! [X0,X1] :
( leq(multiplication(star(c(X0)),X1),antidomain(X0))
| ~ leq(addition(c(X0),X1),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f2482,f51]) ).
fof(f12623,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(multiplication(X0,antidomain(X1)),c(X1)),
inference(paramodulation,[status(thm)],[f2482,f41]) ).
fof(f12624,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(c(X0),multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f2482,f41]) ).
fof(f12625,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(multiplication(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f2482,f40]) ).
fof(f12626,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(c(X0),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f2482,f40]) ).
fof(f12627,plain,
! [X0,X1] : multiplication(c(X0),multiplication(antidomain(X0),X1)) = multiplication(c(X0),X1),
inference(paramodulation,[status(thm)],[f2482,f37]) ).
fof(f12629,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))),
inference(forward_demodulation,[status(thm)],[f67,f12577]) ).
fof(f12630,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))),
inference(forward_demodulation,[status(thm)],[f66,f12578]) ).
fof(f12633,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f493,f12580]) ).
fof(f12634,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f57,f12633]) ).
fof(f12635,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),antidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f317,f12581]) ).
fof(f12636,plain,
! [X0] : domain(c(X0)) = domain_difference(c(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f63,f12635]) ).
fof(f12641,plain,
! [X0] : domain(c(X0)) = multiplication(c(domain(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f317,f12585]) ).
fof(f12642,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f317,f12641]) ).
fof(f12643,plain,
! [X0] : domain(c(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f3965,f12642]) ).
fof(f12644,plain,
! [X0] : antidomain(c(X0)) = multiplication(c(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f493,f12586]) ).
fof(f12645,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f493,f12644]) ).
fof(f12647,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)],[f2482,f12592]) ).
fof(f12648,plain,
! [X0] : leq(multiplication(c(X0),multiplication(antidomain(X0),star(antidomain(X0)))),c(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f12594,f234]) ).
fof(f12649,plain,
! [X0] :
( leq(multiplication(star(c(X0)),c(X0)),antidomain(X0))
| ~ leq(c(X0),antidomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2482,f12597]) ).
fof(f12650,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(c(X0))))),star(c(X0))),
inference(forward_demodulation,[status(thm)],[f2482,f12599]) ).
fof(f12651,plain,
! [X0] : leq(addition(one,multiplication(c(X0),multiplication(antidomain(X0),star(c(X0))))),star(c(X0))),
inference(forward_demodulation,[status(thm)],[f2482,f12600]) ).
fof(f12652,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)],[f92,f12601]) ).
fof(f12653,plain,
! [X0] : multiplication(addition(one,c(X0)),antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f33,f12603]) ).
fof(f12654,plain,
! [X0] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f1406,f12653]) ).
fof(f12655,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f39,f12654]) ).
fof(f12656,plain,
! [X0] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f1406,f12606]) ).
fof(f12657,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f39,f12656]) ).
fof(f12658,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)],[f33,f12607]) ).
fof(f12659,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),antidomain(X0)) = addition(c(X0),multiplication(X1,antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f12609]) ).
fof(f12660,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)],[f92,f12611]) ).
fof(f12666,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = addition(c(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f12615]) ).
fof(f12667,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f12666]) ).
fof(f12668,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f12616]) ).
fof(f12673,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),antidomain(X1)) = addition(c(X1),multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f33,f12623]) ).
fof(f12674,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = addition(c(X0),multiplication(c(X0),X1)),
inference(forward_demodulation,[status(thm)],[f33,f12625]) ).
fof(f12675,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,antidomain(X0))) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f12674]) ).
fof(f12676,plain,
! [X0,X1] : multiplication(c(X0),addition(antidomain(X0),X1)) = multiplication(c(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f187,f12626]) ).
fof(f12679,plain,
! [X0] : c(X0) = c(domain(X0)),
inference(backward_demodulation,[status(thm)],[f12643,f317]) ).
fof(f12681,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f67,f12643]) ).
fof(f12682,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f66,f12643]) ).
fof(f12684,plain,
! [X0] : domain(antidomain(c(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f493,f12643]) ).
fof(f12693,plain,
! [X0] : leq(c(X0),antidomain(c(c(X0)))),
inference(paramodulation,[status(thm)],[f12643,f4071]) ).
fof(f12697,plain,
! [X0,X1] : leq(domain_difference(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f12643,f3580]) ).
fof(f12702,plain,
! [X0] : addition(c(X0),c(c(X0))) = one,
inference(paramodulation,[status(thm)],[f12643,f515]) ).
fof(f12703,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)],[f12643,f70]) ).
fof(f12704,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)],[f12643,f70]) ).
fof(f12705,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)],[f12643,f70]) ).
fof(f12706,plain,
! [X0,X1] : forward_diamond(X0,c(X1)) = domain(multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f12643,f64]) ).
fof(f12707,plain,
! [X0,X1] : domain_difference(c(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f12643,f63]) ).
fof(f12708,plain,
! [X0] : addition(antidomain(c(X0)),c(X0)) = one,
inference(paramodulation,[status(thm)],[f12643,f504]) ).
fof(f12714,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f67,f12681]) ).
fof(f12715,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f66,f12682]) ).
fof(f12717,plain,
! [X0] : c(c(X0)) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f316,f12684]) ).
fof(f12718,plain,
! [X0] : c(c(X0)) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f493,f12717]) ).
fof(f12725,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)],[f12643,f12703]) ).
fof(f12726,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)],[f12643,f12725]) ).
fof(f12727,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)],[f12643,f12726]) ).
fof(f12728,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)],[f12643,f12704]) ).
fof(f12729,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)],[f12643,f12728]) ).
fof(f12730,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)],[f12643,f12729]) ).
fof(f12731,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)],[f12643,f12705]) ).
fof(f12732,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)],[f12643,f12731]) ).
fof(f12733,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)],[f12643,f12732]) ).
fof(f12734,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f33,f12708]) ).
fof(f12737,plain,
! [X0,X1] : leq(multiplication(domain_difference(X0,X1),star(coantidomain(antidomain(X1)))),antidomain(X1)),
inference(resolution,[status(thm)],[f340,f6657]) ).
fof(f12738,plain,
! [X0,X1] : leq(multiplication(domain_difference(X0,X1),star(coantidomain(domain(X0)))),domain(X0)),
inference(resolution,[status(thm)],[f340,f3580]) ).
fof(f12739,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(forward_diamond(X0,X1),X2),star(coantidomain(X2))),X2),
inference(resolution,[status(thm)],[f340,f6667]) ).
fof(f12740,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(forward_box(X0,X1),X2),star(coantidomain(X2))),X2),
inference(resolution,[status(thm)],[f340,f6327]) ).
fof(f12741,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(backward_box(X0,X1),X2),star(coantidomain(X2))),X2),
inference(resolution,[status(thm)],[f340,f6326]) ).
fof(f12742,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(backward_diamond(X0,X1),X2),star(coantidomain(X2))),X2),
inference(resolution,[status(thm)],[f340,f6192]) ).
fof(f12743,plain,
! [X0,X1] : leq(multiplication(multiplication(coantidomain(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f340,f6815]) ).
fof(f12744,plain,
! [X0,X1] : leq(multiplication(multiplication(domain(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f340,f6469]) ).
fof(f12745,plain,
! [X0,X1] : leq(multiplication(multiplication(antidomain(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f340,f6335]) ).
fof(f12746,plain,
! [X0,X1] : leq(multiplication(multiplication(c(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f340,f6199]) ).
fof(f12747,plain,
! [X0,X1] : leq(multiplication(multiplication(codomain(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f340,f6071]) ).
fof(f12748,plain,
! [X0,X1] : leq(multiplication(multiplication(divergence(X0),X1),star(coantidomain(X1))),X1),
inference(resolution,[status(thm)],[f340,f5662]) ).
fof(f12749,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,forward_diamond(X1,X2)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3808]) ).
fof(f12750,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,forward_box(X1,X2)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3489]) ).
fof(f12751,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,backward_box(X1,X2)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3488]) ).
fof(f12752,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,backward_diamond(X1,X2)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3259]) ).
fof(f12753,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,coantidomain(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3817]) ).
fof(f12754,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,domain(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3587]) ).
fof(f12755,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,antidomain(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3497]) ).
fof(f12756,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,c(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3402]) ).
fof(f12757,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,codomain(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3175]) ).
fof(f12758,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,divergence(X1)),star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f3096]) ).
fof(f12759,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),star(coantidomain(addition(X2,one)))),addition(X2,one)),
inference(resolution,[status(thm)],[f340,f1996]) ).
fof(f12762,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),star(coantidomain(addition(X2,one)))),addition(X2,one)),
inference(resolution,[status(thm)],[f340,f1970]) ).
fof(f12765,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),star(coantidomain(addition(X2,one)))),addition(X2,one)),
inference(resolution,[status(thm)],[f340,f1946]) ).
fof(f12768,plain,
! [X0] : leq(multiplication(divergence(X0),star(coantidomain(codomain(divergence(X0))))),codomain(divergence(X0))),
inference(resolution,[status(thm)],[f340,f5767]) ).
fof(f12770,plain,
! [X0] : leq(multiplication(divergence(X0),star(coantidomain(domain(divergence(X0))))),domain(divergence(X0))),
inference(resolution,[status(thm)],[f340,f4030]) ).
fof(f12771,plain,
! [X0,X1] : leq(multiplication(divergence(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f340,f2110]) ).
fof(f12772,plain,
! [X0,X1] : leq(multiplication(divergence(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f340,f1758]) ).
fof(f12774,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),star(coantidomain(addition(X2,one)))),addition(X2,one)),
inference(resolution,[status(thm)],[f340,f1923]) ).
fof(f12777,plain,
! [X0] : leq(multiplication(codomain(X0),star(coantidomain(codomain(codomain(X0))))),codomain(codomain(X0))),
inference(resolution,[status(thm)],[f340,f6184]) ).
fof(f12779,plain,
! [X0] : leq(multiplication(codomain(X0),star(coantidomain(domain(codomain(X0))))),domain(codomain(X0))),
inference(resolution,[status(thm)],[f340,f4032]) ).
fof(f12780,plain,
! [X0,X1] : leq(multiplication(codomain(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f340,f2122]) ).
fof(f12781,plain,
! [X0,X1] : leq(multiplication(codomain(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f340,f1759]) ).
fof(f12783,plain,
! [X0] : leq(multiplication(c(X0),star(coantidomain(codomain(c(X0))))),codomain(c(X0))),
inference(resolution,[status(thm)],[f340,f6318]) ).
fof(f12785,plain,
! [X0,X1] : leq(multiplication(c(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f340,f2136]) ).
fof(f12786,plain,
! [X0,X1] : leq(multiplication(c(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f340,f1760]) ).
fof(f12788,plain,
! [X0] : leq(multiplication(antidomain(X0),star(coantidomain(codomain(antidomain(X0))))),codomain(antidomain(X0))),
inference(resolution,[status(thm)],[f340,f6459]) ).
fof(f12790,plain,
! [X0] : leq(multiplication(antidomain(X0),star(coantidomain(c(X0)))),c(X0)),
inference(resolution,[status(thm)],[f340,f4063]) ).
fof(f12791,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f340,f2240]) ).
fof(f12792,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f340,f1761]) ).
fof(f12794,plain,
! [X0] : leq(multiplication(coantidomain(X0),star(coantidomain(coantidomain(codomain(X0))))),coantidomain(codomain(X0))),
inference(resolution,[status(thm)],[f340,f6955]) ).
fof(f12796,plain,
! [X0] : leq(multiplication(coantidomain(X0),star(coantidomain(domain(coantidomain(X0))))),domain(coantidomain(X0))),
inference(resolution,[status(thm)],[f340,f4196]) ).
fof(f12797,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f340,f2251]) ).
fof(f12798,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f340,f1762]) ).
fof(f12800,plain,
! [X0] : leq(multiplication(domain(X0),star(coantidomain(codomain(domain(X0))))),codomain(domain(X0))),
inference(resolution,[status(thm)],[f340,f6659]) ).
fof(f12802,plain,
! [X0] : leq(multiplication(domain(X0),star(coantidomain(antidomain(c(X0))))),antidomain(c(X0))),
inference(resolution,[status(thm)],[f340,f4071]) ).
fof(f12803,plain,
! [X0,X1] : leq(multiplication(domain(X0),star(coantidomain(addition(one,X1)))),addition(one,X1)),
inference(resolution,[status(thm)],[f340,f2264]) ).
fof(f12804,plain,
! [X0,X1] : leq(multiplication(domain(X0),star(coantidomain(addition(X1,one)))),addition(X1,one)),
inference(resolution,[status(thm)],[f340,f1763]) ).
fof(f12806,plain,
! [X0,X1] : leq(multiplication(one,star(coantidomain(addition(star(X0),X1)))),addition(star(X0),X1)),
inference(resolution,[status(thm)],[f340,f8012]) ).
fof(f12807,plain,
! [X0,X1] : leq(multiplication(one,star(coantidomain(addition(X0,star(X1))))),addition(X0,star(X1))),
inference(resolution,[status(thm)],[f340,f7178]) ).
fof(f12813,plain,
! [X0,X1] : leq(multiplication(addition(X0,X1),star(coantidomain(addition(X1,X0)))),addition(X1,X0)),
inference(resolution,[status(thm)],[f340,f10118]) ).
fof(f12814,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(multiplication(star(X1),X0)))),multiplication(star(X1),X0)),
inference(resolution,[status(thm)],[f340,f8050]) ).
fof(f12815,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(multiplication(X0,addition(one,X1))))),multiplication(X0,addition(one,X1))),
inference(resolution,[status(thm)],[f340,f2333]) ).
fof(f12816,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(multiplication(X0,star(X1))))),multiplication(X0,star(X1))),
inference(resolution,[status(thm)],[f340,f8048]) ).
fof(f12817,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(coantidomain(addition(X1,addition(X0,X2))))),addition(X1,addition(X0,X2))),
inference(resolution,[status(thm)],[f340,f1357]) ).
fof(f12818,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(coantidomain(addition(X1,addition(X2,X0))))),addition(X1,addition(X2,X0))),
inference(resolution,[status(thm)],[f340,f1356]) ).
fof(f12819,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(addition(X1,X0)))),addition(X1,X0)),
inference(resolution,[status(thm)],[f340,f1359]) ).
fof(f12820,plain,
! [X0,X1] : leq(multiplication(X0,star(coantidomain(addition(X0,X1)))),addition(X0,X1)),
inference(resolution,[status(thm)],[f340,f1261]) ).
fof(f12821,plain,
! [X0] : leq(multiplication(X0,star(coantidomain(X0))),X0),
inference(resolution,[status(thm)],[f340,f234]) ).
fof(f12822,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),multiplication(X2,star(coantidomain(X2)))),X2),
inference(forward_demodulation,[status(thm)],[f37,f12739]) ).
fof(f12823,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),multiplication(X2,star(coantidomain(X2)))),X2),
inference(forward_demodulation,[status(thm)],[f37,f12740]) ).
fof(f12824,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),multiplication(X2,star(coantidomain(X2)))),X2),
inference(forward_demodulation,[status(thm)],[f37,f12741]) ).
fof(f12825,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),multiplication(X2,star(coantidomain(X2)))),X2),
inference(forward_demodulation,[status(thm)],[f37,f12742]) ).
fof(f12826,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f37,f12743]) ).
fof(f12827,plain,
! [X0,X1] : leq(multiplication(domain(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f37,f12744]) ).
fof(f12828,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f37,f12745]) ).
fof(f12829,plain,
! [X0,X1] : leq(multiplication(c(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f37,f12746]) ).
fof(f12830,plain,
! [X0,X1] : leq(multiplication(codomain(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f37,f12747]) ).
fof(f12831,plain,
! [X0,X1] : leq(multiplication(divergence(X0),multiplication(X1,star(coantidomain(X1)))),X1),
inference(forward_demodulation,[status(thm)],[f37,f12748]) ).
fof(f12832,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(forward_diamond(X1,X2),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12749]) ).
fof(f12833,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(forward_box(X1,X2),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12750]) ).
fof(f12834,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(backward_box(X1,X2),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12751]) ).
fof(f12835,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(backward_diamond(X1,X2),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12752]) ).
fof(f12836,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(coantidomain(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12753]) ).
fof(f12837,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(domain(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12754]) ).
fof(f12838,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(antidomain(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12755]) ).
fof(f12839,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(c(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12756]) ).
fof(f12840,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(codomain(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12757]) ).
fof(f12841,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(divergence(X1),star(coantidomain(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f37,f12758]) ).
fof(f12890,plain,
! [X0] : leq(multiplication(coantidomain(X0),star(codomain(codomain(X0)))),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f61,f12794]) ).
fof(f12903,plain,
! [X0,X1] : leq(star(coantidomain(addition(star(X0),X1))),addition(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f39,f12806]) ).
fof(f12904,plain,
! [X0,X1] : leq(star(coantidomain(addition(X0,star(X1)))),addition(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f39,f12807]) ).
fof(f12925,plain,
! [X0] : leq(multiplication(c(X0),star(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f12588,f338]) ).
fof(f12926,plain,
! [X0] : leq(multiplication(c(X0),star(coantidomain(antidomain(X0)))),antidomain(X0)),
inference(resolution,[status(thm)],[f12588,f340]) ).
fof(f12927,plain,
! [X0] : leq(multiplication(star(antidomain(antidomain(X0))),c(X0)),antidomain(X0)),
inference(resolution,[status(thm)],[f12588,f299]) ).
fof(f12928,plain,
! [X0] : addition(c(X0),antidomain(X0)) = antidomain(X0),
inference(resolution,[status(thm)],[f12588,f46]) ).
fof(f12930,plain,
! [X0,X1] : leq(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f67,f12588]) ).
fof(f12931,plain,
! [X0,X1] : leq(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f66,f12588]) ).
fof(f12933,plain,
! [X0] : leq(antidomain(c(X0)),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f493,f12588]) ).
fof(f12940,plain,
! [X0] : leq(multiplication(star(domain(X0)),c(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f57,f12927]) ).
fof(f12941,plain,
! [X0] : addition(antidomain(X0),c(X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f33,f12928]) ).
fof(f12944,plain,
! [X0] : leq(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f57,f12933]) ).
fof(f12952,plain,
! [X0,X1] : c(multiplication(X0,domain(X1))) = c(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f64,f12679]) ).
fof(f12962,plain,
! [X0,X1] : multiplication(c(X0),domain_difference(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f12679,f1494]) ).
fof(f12978,plain,
! [X0] : forward_box(c(c(X0)),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f12679,f916]) ).
fof(f12979,plain,
! [X0] : addition(domain(domain(X0)),c(X0)) = one,
inference(paramodulation,[status(thm)],[f12679,f515]) ).
fof(f12980,plain,
! [X0] : forward_diamond(c(X0),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f12679,f711]) ).
fof(f12981,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f12679,f67]) ).
fof(f12982,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f12679,f66]) ).
fof(f12983,plain,
! [X0] : multiplication(c(X0),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f12679,f192]) ).
fof(f13003,plain,
! [X0] : addition(c(X0),domain(domain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f33,f12979]) ).
fof(f13004,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f191,f13003]) ).
fof(f13005,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f67,f12981]) ).
fof(f13006,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f66,f12982]) ).
fof(f13007,plain,
! [X0] : multiplication(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f191,f12983]) ).
fof(f13013,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = multiplication(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f12714,f2094]) ).
fof(f13014,plain,
! [X0,X1] : leq(domain(backward_box(X0,X1)),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f12714,f6659]) ).
fof(f13015,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(domain(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f12714,f6659]) ).
fof(f13017,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f12714,f4331]) ).
fof(f13019,plain,
! [X0,X1] : leq(backward_box(X0,X1),antidomain(c(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f12714,f4071]) ).
fof(f13021,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f12714,f3965]) ).
fof(f13023,plain,
! [X0,X1,X2] : leq(domain_difference(backward_box(X0,X1),X2),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f12714,f3580]) ).
fof(f13024,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f12714,f2264]) ).
fof(f13028,plain,
! [X0,X1] : addition(backward_box(X0,X1),c(backward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f12714,f515]) ).
fof(f13029,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)],[f12714,f70]) ).
fof(f13030,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)],[f12714,f70]) ).
fof(f13031,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)],[f12714,f70]) ).
fof(f13032,plain,
! [X0,X1,X2] : forward_diamond(X0,backward_box(X1,X2)) = domain(multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f12714,f64]) ).
fof(f13033,plain,
! [X0,X1,X2] : domain_difference(backward_box(X0,X1),X2) = multiplication(backward_box(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f12714,f63]) ).
fof(f13034,plain,
! [X0,X1] : addition(antidomain(backward_box(X0,X1)),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f12714,f504]) ).
fof(f13037,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = antidomain(c(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f12714,f191]) ).
fof(f13038,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f12714,f62]) ).
fof(f13043,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12714,f13013]) ).
fof(f13044,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f12714,f13043]) ).
fof(f13045,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12714,f13014]) ).
fof(f13046,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12714,f13015]) ).
fof(f13047,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)],[f12714,f13029]) ).
fof(f13048,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)],[f12714,f13047]) ).
fof(f13049,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)],[f12714,f13048]) ).
fof(f13050,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)],[f12714,f13030]) ).
fof(f13051,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)],[f12714,f13050]) ).
fof(f13052,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)],[f12714,f13051]) ).
fof(f13053,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)],[f12714,f13031]) ).
fof(f13054,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)],[f12714,f13053]) ).
fof(f13055,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)],[f12714,f13054]) ).
fof(f13056,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f33,f13034]) ).
fof(f13058,plain,
! [X0,X1] : backward_box(X0,X1) = antidomain(c(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12714,f13037]) ).
fof(f13065,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = multiplication(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f12715,f2094]) ).
fof(f13066,plain,
! [X0,X1] : leq(domain(forward_box(X0,X1)),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f12715,f6659]) ).
fof(f13067,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(domain(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f12715,f6659]) ).
fof(f13069,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f12715,f4331]) ).
fof(f13071,plain,
! [X0,X1] : leq(forward_box(X0,X1),antidomain(c(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f12715,f4071]) ).
fof(f13073,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f12715,f3965]) ).
fof(f13075,plain,
! [X0,X1,X2] : leq(domain_difference(forward_box(X0,X1),X2),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f12715,f3580]) ).
fof(f13076,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f12715,f2264]) ).
fof(f13080,plain,
! [X0,X1] : addition(forward_box(X0,X1),c(forward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f12715,f515]) ).
fof(f13081,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)],[f12715,f70]) ).
fof(f13082,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)],[f12715,f70]) ).
fof(f13083,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)],[f12715,f70]) ).
fof(f13084,plain,
! [X0,X1,X2] : forward_diamond(X0,forward_box(X1,X2)) = domain(multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f12715,f64]) ).
fof(f13085,plain,
! [X0,X1,X2] : domain_difference(forward_box(X0,X1),X2) = multiplication(forward_box(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f12715,f63]) ).
fof(f13086,plain,
! [X0,X1] : addition(antidomain(forward_box(X0,X1)),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f12715,f504]) ).
fof(f13089,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = antidomain(c(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f12715,f191]) ).
fof(f13090,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f12715,f62]) ).
fof(f13096,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12715,f13065]) ).
fof(f13097,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f12715,f13096]) ).
fof(f13098,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12715,f13066]) ).
fof(f13099,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12715,f13067]) ).
fof(f13100,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)],[f12715,f13081]) ).
fof(f13101,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)],[f12715,f13100]) ).
fof(f13102,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)],[f12715,f13101]) ).
fof(f13103,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)],[f12715,f13082]) ).
fof(f13104,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)],[f12715,f13103]) ).
fof(f13105,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)],[f12715,f13104]) ).
fof(f13106,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)],[f12715,f13083]) ).
fof(f13107,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)],[f12715,f13106]) ).
fof(f13108,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)],[f12715,f13107]) ).
fof(f13109,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f33,f13086]) ).
fof(f13111,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(c(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12715,f13089]) ).
fof(f13113,plain,
! [X0] : forward_box(antidomain(c(X0)),X0) = one,
inference(backward_demodulation,[status(thm)],[f12718,f916]) ).
fof(f13117,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(c(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f67,f12718]) ).
fof(f13118,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(c(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f66,f12718]) ).
fof(f13124,plain,
! [X0] : c(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f12718,f2482]) ).
fof(f13126,plain,
! [X0] : c(c(X0)) = multiplication(antidomain(c(X0)),c(c(X0))),
inference(paramodulation,[status(thm)],[f12718,f2090]) ).
fof(f13127,plain,
! [X0,X1] : multiplication(antidomain(c(X0)),domain_difference(c(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f12718,f1494]) ).
fof(f13144,plain,
! [X0] : forward_diamond(antidomain(c(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f12718,f711]) ).
fof(f13145,plain,
! [X0,X1] : backward_box(X0,c(X1)) = c(backward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f12718,f67]) ).
fof(f13146,plain,
! [X0,X1] : forward_box(X0,c(X1)) = c(forward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f12718,f66]) ).
fof(f13151,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f67,f13117]) ).
fof(f13152,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f66,f13118]) ).
fof(f13163,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f12718,f13124]) ).
fof(f13166,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),c(c(X0))),
inference(forward_demodulation,[status(thm)],[f12718,f13126]) ).
fof(f13167,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f12718,f13166]) ).
fof(f13178,plain,
! [X0] : leq(multiplication(antidomain(c(X0)),star(coantidomain(domain(X0)))),domain(X0)),
inference(resolution,[status(thm)],[f12944,f340]) ).
fof(f13179,plain,
! [X0] : leq(multiplication(star(antidomain(domain(X0))),antidomain(c(X0))),domain(X0)),
inference(resolution,[status(thm)],[f12944,f299]) ).
fof(f13180,plain,
! [X0] : addition(antidomain(c(X0)),domain(X0)) = domain(X0),
inference(resolution,[status(thm)],[f12944,f46]) ).
fof(f13184,plain,
! [X0,X1] : leq(antidomain(backward_box(X0,X1)),domain(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f67,f12944]) ).
fof(f13185,plain,
! [X0,X1] : leq(antidomain(forward_box(X0,X1)),domain(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f66,f12944]) ).
fof(f13189,plain,
! [X0,X1] : leq(antidomain(c(forward_box(X0,X1))),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f12715,f12944]) ).
fof(f13190,plain,
! [X0,X1] : leq(antidomain(c(backward_box(X0,X1))),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f12714,f12944]) ).
fof(f13193,plain,
! [X0,X1] : leq(antidomain(c(multiplication(X0,domain(X1)))),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f64,f12944]) ).
fof(f13198,plain,
! [X0] : leq(multiplication(star(c(X0)),antidomain(c(X0))),domain(X0)),
inference(forward_demodulation,[status(thm)],[f62,f13179]) ).
fof(f13199,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f33,f13180]) ).
fof(f13226,plain,
! [X0,X1] :
( leq(multiplication(X1,one),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f9178,f333]) ).
fof(f13227,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f38,f13226]) ).
fof(f13229,plain,
! [X0] :
( leq(multiplication(star(X0),addition(X0,one)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7423,f13227]) ).
fof(f13230,plain,
! [X0] :
( leq(multiplication(addition(X0,one),star(X0)),one)
| ~ leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f7156,f13227]) ).
fof(f13231,plain,
! [X0,X1] :
( leq(backward_diamond(X0,X1),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1439,f13227]) ).
fof(f13232,plain,
! [X0,X1] :
( leq(forward_box(X0,X1),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1432,f13227]) ).
fof(f13233,plain,
! [X0,X1] :
( leq(backward_box(X0,X1),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1427,f13227]) ).
fof(f13234,plain,
! [X0,X1] :
( leq(forward_diamond(X0,X1),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1420,f13227]) ).
fof(f13235,plain,
! [X0] :
( leq(divergence(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1423,f13227]) ).
fof(f13236,plain,
! [X0] :
( leq(codomain(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1412,f13227]) ).
fof(f13237,plain,
! [X0] :
( leq(c(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1406,f13227]) ).
fof(f13238,plain,
! [X0] :
( leq(antidomain(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1315,f13227]) ).
fof(f13239,plain,
! [X0] :
( leq(coantidomain(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1313,f13227]) ).
fof(f13240,plain,
! [X0] :
( leq(domain(X0),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f1311,f13227]) ).
fof(f13241,plain,
! [X0] :
( leq(c(X0),domain(X0))
| ~ leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f515,f13227]) ).
fof(f13243,plain,
! [X0] :
( leq(codomain(X0),coantidomain(X0))
| ~ leq(one,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f625,f13227]) ).
fof(f13246,plain,
! [X0] :
( leq(domain(X0),antidomain(X0))
| ~ leq(one,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f504,f13227]) ).
fof(f13247,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)],[f199,f13227]) ).
fof(f13248,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)],[f214,f13227]) ).
fof(f13249,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)],[f165,f13227]) ).
fof(f13250,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)],[f206,f13227]) ).
fof(f13251,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X1,X2))
| ~ leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f196,f13227]) ).
fof(f13252,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X0,X2))
| ~ leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f148,f13227]) ).
fof(f13253,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,X2),multiplication(X0,X2))
| ~ leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f41,f13227]) ).
fof(f13254,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X0,X1))
| ~ leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f40,f13227]) ).
fof(f13255,plain,
! [X0,X1,X2] :
( leq(X2,addition(X1,X0))
| ~ leq(addition(X0,addition(X1,X2)),addition(X1,X0)) ),
inference(paramodulation,[status(thm)],[f98,f13227]) ).
fof(f13256,plain,
! [X0,X1,X2] :
( leq(X2,addition(X0,X1))
| ~ leq(addition(X0,addition(X1,X2)),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f34,f13227]) ).
fof(f13274,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X1)
| ~ leq(multiplication(addition(X0,one),X1),X1) ),
inference(paramodulation,[status(thm)],[f227,f13227]) ).
fof(f13275,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X1)
| ~ leq(multiplication(addition(one,X0),X1),X1) ),
inference(paramodulation,[status(thm)],[f202,f13227]) ).
fof(f13276,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X0)
| ~ leq(multiplication(X0,addition(X1,one)),X0) ),
inference(paramodulation,[status(thm)],[f187,f13227]) ).
fof(f13277,plain,
! [X0,X1] :
( leq(multiplication(X0,X1),X0)
| ~ leq(multiplication(X0,addition(one,X1)),X0) ),
inference(paramodulation,[status(thm)],[f157,f13227]) ).
fof(f13278,plain,
! [X0,X1] :
( leq(addition(X1,X0),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f1266,f13227]) ).
fof(f13279,plain,
! [X0,X1] :
( leq(addition(X1,X0),X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f966,f13227]) ).
fof(f13282,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),X2)
| ~ leq(addition(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f92,f13227]) ).
fof(f13283,plain,
! [X0,X1,X2] :
( leq(addition(X2,X0),X1)
| ~ leq(addition(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f92,f13227]) ).
fof(f13285,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f33,f13227]) ).
fof(f13286,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f33,f13227]) ).
fof(f13288,plain,
( sQ10_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13231,f8880,f2011]) ).
fof(f13289,plain,
( sQ9_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13232,f8880,f1985]) ).
fof(f13290,plain,
( sQ8_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13233,f8880,f1961]) ).
fof(f13291,plain,
( sQ7_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13234,f8880,f1938]) ).
fof(f13292,plain,
( sQ6_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13235,f8880,f1690]) ).
fof(f13293,plain,
( sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13236,f8880,f1670]) ).
fof(f13294,plain,
( sQ4_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13237,f8880,f1647]) ).
fof(f13295,plain,
( sQ3_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13238,f8880,f1549]) ).
fof(f13296,plain,
( sQ2_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13239,f8880,f1524]) ).
fof(f13297,plain,
( sQ0_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f13240,f8880,f1460]) ).
fof(f13301,plain,
! [X0,X1] : leq(multiplication(antidomain(multiplication(X0,X1)),star(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,domain(X1)))),
inference(resolution,[status(thm)],[f405,f338]) ).
fof(f13302,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)],[f405,f340]) ).
fof(f13303,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)],[f405,f299]) ).
fof(f13305,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X1,X0))),antidomain(multiplication(addition(one,X1),domain(X0)))),
inference(paramodulation,[status(thm)],[f202,f405]) ).
fof(f13306,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(addition(antidomain(X1),X0),domain(X1)))),
inference(paramodulation,[status(thm)],[f219,f405]) ).
fof(f13307,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X1,X0))),antidomain(multiplication(addition(X1,one),domain(X0)))),
inference(paramodulation,[status(thm)],[f227,f405]) ).
fof(f13308,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(addition(X0,antidomain(X1)),domain(X1)))),
inference(paramodulation,[status(thm)],[f225,f405]) ).
fof(f13309,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,coantidomain(X1))),antidomain(multiplication(addition(X0,X1),domain(coantidomain(X1))))),
inference(paramodulation,[status(thm)],[f228,f405]) ).
fof(f13310,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,coantidomain(X1))),antidomain(multiplication(addition(X1,X0),domain(coantidomain(X1))))),
inference(paramodulation,[status(thm)],[f221,f405]) ).
fof(f13313,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(c(X0),domain(domain_difference(X0,X1))))),
inference(paramodulation,[status(thm)],[f1494,f405]) ).
fof(f13314,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(c(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f192,f405]) ).
fof(f13316,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))),
inference(paramodulation,[status(thm)],[f190,f405]) ).
fof(f13317,plain,
! [X0] : leq(antidomain(domain(X0)),antidomain(multiplication(domain(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f2094,f405]) ).
fof(f13318,plain,
! [X0,X1] : leq(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),domain(antidomain(X1))))),
inference(paramodulation,[status(thm)],[f63,f405]) ).
fof(f13320,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(multiplication(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f37,f405]) ).
fof(f13321,plain,
! [X0,X1] : leq(antidomain(multiplication(antidomain(X0),X1)),antidomain(multiplication(antidomain(X0),domain(addition(X1,X0))))),
inference(paramodulation,[status(thm)],[f181,f405]) ).
fof(f13322,plain,
! [X0,X1] : leq(antidomain(multiplication(antidomain(X0),X1)),antidomain(multiplication(antidomain(X0),domain(addition(X0,X1))))),
inference(paramodulation,[status(thm)],[f172,f405]) ).
fof(f13323,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f131,f405]) ).
fof(f13324,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f54,f405]) ).
fof(f13327,plain,
! [X0] : leq(antidomain(X0),antidomain(multiplication(X0,domain(codomain(X0))))),
inference(paramodulation,[status(thm)],[f2178,f405]) ).
fof(f13328,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(one,X1))))),
inference(paramodulation,[status(thm)],[f157,f405]) ).
fof(f13329,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(addition(coantidomain(X0),X1))))),
inference(paramodulation,[status(thm)],[f176,f405]) ).
fof(f13330,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(X1,one))))),
inference(paramodulation,[status(thm)],[f187,f405]) ).
fof(f13331,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(addition(X1,coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f185,f405]) ).
fof(f13332,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1))))),
inference(paramodulation,[status(thm)],[f146,f405]) ).
fof(f13333,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1))))))),
inference(paramodulation,[status(thm)],[f139,f405]) ).
fof(f13334,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(X0,domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f58,f405]) ).
fof(f13337,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(antidomain(domain(X0)),X1),X0)),antidomain(multiplication(X1,domain(X0)))),
inference(paramodulation,[status(thm)],[f219,f405]) ).
fof(f13338,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,antidomain(domain(X1))),X1)),antidomain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f225,f405]) ).
fof(f13342,plain,
! [X0] : leq(antidomain(multiplication(domain(domain(X0)),X0)),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f3965,f405]) ).
fof(f13343,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(multiplication(X0,X1),X2)),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(paramodulation,[status(thm)],[f37,f405]) ).
fof(f13350,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,star(X1))),antidomain(multiplication(X0,one))),
inference(paramodulation,[status(thm)],[f8139,f405]) ).
fof(f13351,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,forward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f64,f405]) ).
fof(f13353,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,antidomain(c(X1))))),
inference(paramodulation,[status(thm)],[f191,f405]) ).
fof(f13354,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f316,f405]) ).
fof(f13356,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)],[f57,f13303]) ).
fof(f13357,plain,
! [X0,X1] : leq(multiplication(star(forward_diamond(X0,X1)),antidomain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f64,f13356]) ).
fof(f13362,plain,
! [X0,X1] : leq(one,antidomain(multiplication(c(X0),domain(domain_difference(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f523,f13313]) ).
fof(f13363,plain,
! [X0] : leq(one,antidomain(multiplication(c(X0),domain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f523,f13314]) ).
fof(f13364,plain,
! [X0] : leq(one,antidomain(multiplication(c(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f191,f13363]) ).
fof(f13368,plain,
! [X0] : leq(one,antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))),
inference(forward_demodulation,[status(thm)],[f523,f13316]) ).
fof(f13369,plain,
! [X0] : leq(c(X0),antidomain(multiplication(domain(X0),domain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f62,f13317]) ).
fof(f13370,plain,
! [X0] : leq(c(X0),antidomain(multiplication(domain(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f191,f13369]) ).
fof(f13371,plain,
! [X0] : leq(c(X0),antidomain(domain_difference(X0,c(X0)))),
inference(forward_demodulation,[status(thm)],[f63,f13370]) ).
fof(f13372,plain,
! [X0,X1] : leq(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),c(X1)))),
inference(forward_demodulation,[status(thm)],[f316,f13318]) ).
fof(f13375,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(forward_demodulation,[status(thm)],[f37,f13320]) ).
fof(f13376,plain,
! [X0,X1] : leq(one,antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f523,f13323]) ).
fof(f13377,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f523,f13324]) ).
fof(f13383,plain,
! [X0,X1] : leq(one,antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1))))),
inference(forward_demodulation,[status(thm)],[f523,f13332]) ).
fof(f13384,plain,
! [X0,X1] : leq(one,antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1))))))),
inference(forward_demodulation,[status(thm)],[f523,f13333]) ).
fof(f13385,plain,
! [X0] : leq(one,antidomain(multiplication(X0,domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f523,f13334]) ).
fof(f13392,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(c(X0),X1),X0)),antidomain(multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f13337]) ).
fof(f13393,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,c(X1)),X1)),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f62,f13338]) ).
fof(f13403,plain,
! [X0] : leq(antidomain(multiplication(antidomain(c(X0)),X0)),antidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f191,f13342]) ).
fof(f13404,plain,
! [X0] : leq(antidomain(multiplication(antidomain(c(X0)),X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f62,f13403]) ).
fof(f13405,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(forward_demodulation,[status(thm)],[f37,f13343]) ).
fof(f13415,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,star(X1))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f13350]) ).
fof(f13423,plain,
! [X0] : forward_diamond(antidomain(c(X0)),domain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f12718,f12980]) ).
fof(f13424,plain,
! [X0] : forward_diamond(c(X0),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f12679,f12980]) ).
fof(f13426,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f67,f12980]) ).
fof(f13427,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f66,f12980]) ).
fof(f13429,plain,
! [X0] : forward_diamond(antidomain(c(X0)),domain(antidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f493,f12980]) ).
fof(f13435,plain,
! [X0,X1] : forward_diamond(c(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f64,f12980]) ).
fof(f13437,plain,
! [X0] : forward_diamond(c(domain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f191,f12980]) ).
fof(f13438,plain,
! [X0] : forward_diamond(c(antidomain(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f316,f12980]) ).
fof(f13440,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)],[f12980,f70]) ).
fof(f13449,plain,
! [X0] : forward_diamond(antidomain(c(X0)),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f12643,f13423]) ).
fof(f13450,plain,
! [X0] : forward_diamond(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f191,f13424]) ).
fof(f13454,plain,
! [X0] : forward_diamond(antidomain(c(X0)),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f316,f13429]) ).
fof(f13457,plain,
! [X0] : forward_diamond(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f12679,f13437]) ).
fof(f13458,plain,
! [X0] : forward_diamond(antidomain(c(X0)),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f493,f13438]) ).
fof(f13459,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)],[f92,f13440]) ).
fof(f13460,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)],[f75,f13459]) ).
fof(f13461,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)],[f12980,f13460]) ).
fof(f13462,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)],[f75,f13461]) ).
fof(f13471,plain,
! [X0,X1,X2] : backward_box(X0,forward_diamond(X1,X2)) = backward_box(X0,multiplication(X1,domain(X2))),
inference(paramodulation,[status(thm)],[f64,f13005]) ).
fof(f13473,plain,
! [X0,X1] : backward_box(X0,antidomain(c(X1))) = backward_box(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f191,f13005]) ).
fof(f13474,plain,
! [X0,X1] : backward_box(X0,c(X1)) = backward_box(X0,antidomain(X1)),
inference(paramodulation,[status(thm)],[f316,f13005]) ).
fof(f13486,plain,
! [X0,X1] : backward_box(X0,antidomain(c(X1))) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f13005,f13473]) ).
fof(f13493,plain,
! [X0,X1,X2] : forward_box(X0,forward_diamond(X1,X2)) = forward_box(X0,multiplication(X1,domain(X2))),
inference(paramodulation,[status(thm)],[f64,f13006]) ).
fof(f13495,plain,
! [X0,X1] : forward_box(X0,antidomain(c(X1))) = forward_box(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f191,f13006]) ).
fof(f13496,plain,
! [X0,X1] : forward_box(X0,c(X1)) = forward_box(X0,antidomain(X1)),
inference(paramodulation,[status(thm)],[f316,f13006]) ).
fof(f13508,plain,
! [X0,X1] : forward_box(X0,antidomain(c(X1))) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f13006,f13495]) ).
fof(f13513,plain,
! [X0] : forward_box(antidomain(antidomain(c(X0))),c(X0)) = one,
inference(paramodulation,[status(thm)],[f12718,f13113]) ).
fof(f13516,plain,
! [X0,X1] : forward_box(antidomain(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f67,f13113]) ).
fof(f13517,plain,
! [X0,X1] : forward_box(antidomain(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f66,f13113]) ).
fof(f13519,plain,
! [X0] : forward_box(antidomain(antidomain(c(X0))),antidomain(X0)) = one,
inference(paramodulation,[status(thm)],[f493,f13113]) ).
fof(f13533,plain,
! [X0] : forward_box(domain(c(X0)),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f57,f13513]) ).
fof(f13534,plain,
! [X0] : forward_box(c(X0),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f12643,f13533]) ).
fof(f13537,plain,
! [X0] : forward_box(domain(c(X0)),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f57,f13519]) ).
fof(f13538,plain,
! [X0] : forward_box(c(X0),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f12643,f13537]) ).
fof(f13544,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(resolution,[status(thm)],[f428,f47]) ).
fof(f13545,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)],[f219,f428]) ).
fof(f13546,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)],[f225,f428]) ).
fof(f13547,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(c(multiplication(X0,X1)),multiplication(X0,domain(X1))))) = antidomain(multiplication(c(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f4088,f428]) ).
fof(f13548,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)],[f3965,f428]) ).
fof(f13549,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)],[f37,f428]) ).
fof(f13551,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)],[f54,f428]) ).
fof(f13555,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)],[f139,f428]) ).
fof(f13556,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)],[f202,f428]) ).
fof(f13557,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)],[f219,f428]) ).
fof(f13558,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)],[f227,f428]) ).
fof(f13559,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)],[f225,f428]) ).
fof(f13560,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)],[f228,f428]) ).
fof(f13561,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)],[f221,f428]) ).
fof(f13564,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(c(X1),domain(domain_difference(X1,X2)))))) = antidomain(multiplication(X0,multiplication(c(X1),domain(domain_difference(X1,X2))))),
inference(paramodulation,[status(thm)],[f1494,f428]) ).
fof(f13565,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(c(X1),domain(domain(X1)))))) = antidomain(multiplication(X0,multiplication(c(X1),domain(domain(X1))))),
inference(paramodulation,[status(thm)],[f192,f428]) ).
fof(f13567,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)],[f190,f428]) ).
fof(f13568,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,multiplication(domain(X1),domain(domain(X1)))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(domain(X1))))),
inference(paramodulation,[status(thm)],[f2094,f428]) ).
fof(f13569,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain_difference(X1,X2))),antidomain(multiplication(X0,multiplication(domain(X1),domain(antidomain(X2)))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(antidomain(X2))))),
inference(paramodulation,[status(thm)],[f63,f428]) ).
fof(f13571,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)],[f37,f428]) ).
fof(f13572,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)],[f181,f428]) ).
fof(f13573,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)],[f172,f428]) ).
fof(f13574,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)],[f131,f428]) ).
fof(f13575,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)],[f54,f428]) ).
fof(f13578,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)],[f2178,f428]) ).
fof(f13579,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)],[f157,f428]) ).
fof(f13580,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)],[f176,f428]) ).
fof(f13581,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)],[f187,f428]) ).
fof(f13582,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)],[f185,f428]) ).
fof(f13583,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)],[f146,f428]) ).
fof(f13584,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)],[f139,f428]) ).
fof(f13585,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)],[f58,f428]) ).
fof(f13588,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)],[f219,f428]) ).
fof(f13589,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)],[f225,f428]) ).
fof(f13591,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)],[f3965,f428]) ).
fof(f13592,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)],[f37,f428]) ).
fof(f13598,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(addition(antidomain(domain(X1)),X2),X1))),antidomain(multiplication(X0,multiplication(X2,domain(X1))))) = antidomain(multiplication(X0,multiplication(addition(antidomain(domain(X1)),X2),domain(X1)))),
inference(paramodulation,[status(thm)],[f219,f428]) ).
fof(f13599,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(addition(X1,antidomain(domain(X2))),X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))) = antidomain(multiplication(X0,multiplication(addition(X1,antidomain(domain(X2))),domain(X2)))),
inference(paramodulation,[status(thm)],[f225,f428]) ).
fof(f13603,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,multiplication(domain(domain(X1)),X1))),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,multiplication(domain(domain(X1)),domain(X1)))),
inference(paramodulation,[status(thm)],[f3965,f428]) ).
fof(f13604,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)],[f37,f428]) ).
fof(f13611,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)],[f8139,f428]) ).
fof(f13612,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)],[f64,f428]) ).
fof(f13614,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(X1,antidomain(c(X2)))))) = antidomain(multiplication(X0,multiplication(X1,domain(domain(X2))))),
inference(paramodulation,[status(thm)],[f191,f428]) ).
fof(f13615,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,antidomain(X2)))),antidomain(multiplication(X0,multiplication(X1,c(X2))))) = antidomain(multiplication(X0,multiplication(X1,domain(antidomain(X2))))),
inference(paramodulation,[status(thm)],[f316,f428]) ).
fof(f13618,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)],[f428,f225]) ).
fof(f13620,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)],[f428,f330]) ).
fof(f13626,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)],[f428,f335]) ).
fof(f13627,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)],[f428,f334]) ).
fof(f13628,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)],[f428,f297]) ).
fof(f13629,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)],[f428,f286]) ).
fof(f13630,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)],[f428,f285]) ).
fof(f13631,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)],[f428,f238]) ).
fof(f13632,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)],[f428,f237]) ).
fof(f13633,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)],[f428,f236]) ).
fof(f13634,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)],[f428,f228]) ).
fof(f13636,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)],[f428,f181]) ).
fof(f13638,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)],[f428,f1357]) ).
fof(f13641,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(paramodulation,[status(thm)],[f428,f1261]) ).
fof(f13643,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)],[f428,f98]) ).
fof(f13644,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)],[f428,f92]) ).
fof(f13645,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)],[f428,f92]) ).
fof(f13646,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)],[f428,f241]) ).
fof(f13647,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)],[f428,f47]) ).
fof(f13648,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)],[f428,f34]) ).
fof(f13649,plain,
! [X0,X1] : addition(one,antidomain(multiplication(c(multiplication(X0,X1)),multiplication(X0,domain(X1))))) = antidomain(multiplication(c(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f523,f13547]) ).
fof(f13650,plain,
! [X0,X1] : one = antidomain(multiplication(c(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1315,f13649]) ).
fof(f13651,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)],[f37,f13549]) ).
fof(f13652,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)],[f37,f13651]) ).
fof(f13656,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)],[f523,f13551]) ).
fof(f13657,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1315,f13656]) ).
fof(f13666,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)],[f523,f13555]) ).
fof(f13667,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f1315,f13666]) ).
fof(f13676,plain,
! [X0,X1,X2] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(c(X1),domain(domain_difference(X1,X2)))))) = antidomain(multiplication(X0,multiplication(c(X1),domain(domain_difference(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f42,f13564]) ).
fof(f13677,plain,
! [X0,X1,X2] : addition(one,antidomain(multiplication(X0,multiplication(c(X1),domain(domain_difference(X1,X2)))))) = antidomain(multiplication(X0,multiplication(c(X1),domain(domain_difference(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f523,f13676]) ).
fof(f13678,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(c(X1),domain(domain_difference(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f1315,f13677]) ).
fof(f13679,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(c(X1),domain(domain(X1)))))) = antidomain(multiplication(X0,multiplication(c(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f42,f13565]) ).
fof(f13680,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(c(X1),domain(domain(X1)))))) = antidomain(multiplication(X0,multiplication(c(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f523,f13679]) ).
fof(f13681,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(c(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f1315,f13680]) ).
fof(f13682,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(c(X1),antidomain(c(X1))))),
inference(forward_demodulation,[status(thm)],[f191,f13681]) ).
fof(f13688,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)],[f42,f13567]) ).
fof(f13689,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)],[f523,f13688]) ).
fof(f13690,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1))))),
inference(forward_demodulation,[status(thm)],[f1315,f13689]) ).
fof(f13691,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,multiplication(domain(X1),antidomain(c(X1)))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f191,f13568]) ).
fof(f13692,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,domain_difference(X1,c(X1))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f63,f13691]) ).
fof(f13693,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,domain_difference(X1,c(X1))))) = antidomain(multiplication(X0,multiplication(domain(X1),antidomain(c(X1))))),
inference(forward_demodulation,[status(thm)],[f191,f13692]) ).
fof(f13694,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,domain_difference(X1,c(X1))))) = antidomain(multiplication(X0,domain_difference(X1,c(X1)))),
inference(forward_demodulation,[status(thm)],[f63,f13693]) ).
fof(f13695,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain_difference(X1,X2))),antidomain(multiplication(X0,multiplication(domain(X1),c(X2))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(antidomain(X2))))),
inference(forward_demodulation,[status(thm)],[f316,f13569]) ).
fof(f13696,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain_difference(X1,X2))),antidomain(multiplication(X0,multiplication(domain(X1),c(X2))))) = antidomain(multiplication(X0,multiplication(domain(X1),c(X2)))),
inference(forward_demodulation,[status(thm)],[f316,f13695]) ).
fof(f13699,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)],[f37,f13571]) ).
fof(f13700,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)],[f37,f13699]) ).
fof(f13701,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)],[f42,f13574]) ).
fof(f13702,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)],[f523,f13701]) ).
fof(f13703,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f1315,f13702]) ).
fof(f13704,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)],[f42,f13575]) ).
fof(f13705,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)],[f523,f13704]) ).
fof(f13706,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1315,f13705]) ).
fof(f13714,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)],[f42,f13583]) ).
fof(f13715,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)],[f523,f13714]) ).
fof(f13716,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2))))),
inference(forward_demodulation,[status(thm)],[f1315,f13715]) ).
fof(f13717,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)],[f42,f13584]) ).
fof(f13718,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)],[f523,f13717]) ).
fof(f13719,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2))))))),
inference(forward_demodulation,[status(thm)],[f1315,f13718]) ).
fof(f13720,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)],[f42,f13585]) ).
fof(f13721,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)],[f523,f13720]) ).
fof(f13722,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1))))),
inference(forward_demodulation,[status(thm)],[f1315,f13721]) ).
fof(f13733,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)],[f33,f13588]) ).
fof(f13734,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)],[f219,f13733]) ).
fof(f13735,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)],[f33,f13589]) ).
fof(f13736,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)],[f225,f13735]) ).
fof(f13741,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)],[f33,f13591]) ).
fof(f13742,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)],[f64,f13741]) ).
fof(f13743,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)],[f3965,f13742]) ).
fof(f13744,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)],[f37,f13592]) ).
fof(f13745,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)],[f37,f13744]) ).
fof(f13766,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(addition(antidomain(domain(X2)),X1),X2)))) = antidomain(multiplication(X0,multiplication(addition(antidomain(domain(X2)),X1),domain(X2)))),
inference(forward_demodulation,[status(thm)],[f33,f13598]) ).
fof(f13767,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(addition(c(X2),X1),X2)))) = antidomain(multiplication(X0,multiplication(addition(antidomain(domain(X2)),X1),domain(X2)))),
inference(forward_demodulation,[status(thm)],[f62,f13766]) ).
fof(f13768,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(addition(c(X2),X1),X2)))) = antidomain(multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f219,f13767]) ).
fof(f13769,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(addition(X1,antidomain(domain(X2))),X2)))) = antidomain(multiplication(X0,multiplication(addition(X1,antidomain(domain(X2))),domain(X2)))),
inference(forward_demodulation,[status(thm)],[f33,f13599]) ).
fof(f13770,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(addition(X1,c(X2)),X2)))) = antidomain(multiplication(X0,multiplication(addition(X1,antidomain(domain(X2))),domain(X2)))),
inference(forward_demodulation,[status(thm)],[f62,f13769]) ).
fof(f13771,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(addition(X1,c(X2)),X2)))) = antidomain(multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f225,f13770]) ).
fof(f13788,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,multiplication(domain(domain(X1)),X1)))) = antidomain(multiplication(X0,multiplication(domain(domain(X1)),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f33,f13603]) ).
fof(f13789,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,multiplication(antidomain(c(X1)),X1)))) = antidomain(multiplication(X0,multiplication(domain(domain(X1)),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f191,f13788]) ).
fof(f13790,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,multiplication(antidomain(c(X1)),X1)))) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f3965,f13789]) ).
fof(f13791,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)],[f37,f13604]) ).
fof(f13792,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)],[f37,f13791]) ).
fof(f13812,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)],[f33,f13611]) ).
fof(f13813,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)],[f38,f13812]) ).
fof(f13814,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)],[f8139,f13813]) ).
fof(f13815,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)],[f38,f13814]) ).
fof(f13816,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)],[f33,f13612]) ).
fof(f13817,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)],[f64,f13816]) ).
fof(f13825,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(X1,antidomain(c(X2)))))) = antidomain(multiplication(X0,multiplication(X1,antidomain(c(X2))))),
inference(forward_demodulation,[status(thm)],[f191,f13614]) ).
fof(f13826,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,multiplication(X1,antidomain(X2)))),antidomain(multiplication(X0,multiplication(X1,c(X2))))) = antidomain(multiplication(X0,multiplication(X1,c(X2)))),
inference(forward_demodulation,[status(thm)],[f316,f13615]) ).
fof(f13830,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f54,f13618]) ).
fof(f13831,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)],[f13620,f1348]) ).
fof(f13841,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)],[f13626,f3497]) ).
fof(f13842,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)],[f13628,f1348]) ).
fof(f13843,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)],[f13630,f6335]) ).
fof(f13844,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)],[f13632]) ).
fof(f13845,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)],[f13633]) ).
fof(f13846,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)],[f58,f13634]) ).
fof(f13847,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)],[f54,f13636]) ).
fof(f13848,plain,
! [X0,X1,X2] : zero = multiplication(domain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f57,f13847]) ).
fof(f13849,plain,
! [X0,X1,X2] : zero = domain_difference(multiplication(X0,multiplication(X1,domain(X2))),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f63,f13848]) ).
fof(f13850,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)],[f92,f13643]) ).
fof(f13851,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)],[f92,f13645]) ).
fof(f13852,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(trivial_equality_resolution,[status(thm)],[f13647]) ).
fof(f13853,plain,
! [X0] : forward_box(antidomain(c(X0)),c(c(X0))) = one,
inference(paramodulation,[status(thm)],[f12718,f13534]) ).
fof(f13856,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),c(backward_diamond(X0,c(X1)))) = one,
inference(paramodulation,[status(thm)],[f67,f13534]) ).
fof(f13857,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),c(forward_diamond(X0,c(X1)))) = one,
inference(paramodulation,[status(thm)],[f66,f13534]) ).
fof(f13859,plain,
! [X0] : forward_box(antidomain(c(X0)),c(antidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f493,f13534]) ).
fof(f13861,plain,
! [X0] : forward_box(c(c(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f12718,f13534]) ).
fof(f13864,plain,
! [X0,X1] : forward_box(c(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f67,f13534]) ).
fof(f13865,plain,
! [X0,X1] : forward_box(c(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f66,f13534]) ).
fof(f13867,plain,
! [X0] : forward_box(c(antidomain(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f493,f13534]) ).
fof(f13877,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f12718,f13853]) ).
fof(f13879,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f67,f13856]) ).
fof(f13880,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f66,f13857]) ).
fof(f13882,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f493,f13859]) ).
fof(f13883,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f12718,f13861]) ).
fof(f13886,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f67,f13864]) ).
fof(f13887,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f66,f13865]) ).
fof(f13888,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f493,f13867]) ).
fof(f13894,plain,
! [X0] : forward_box(antidomain(c(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f12718,f13538]) ).
fof(f13897,plain,
! [X0,X1] : forward_box(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))) = one,
inference(paramodulation,[status(thm)],[f67,f13538]) ).
fof(f13898,plain,
! [X0,X1] : forward_box(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))) = one,
inference(paramodulation,[status(thm)],[f66,f13538]) ).
fof(f13930,plain,
! [X0] : zero = antidomain(addition(one,X0)),
inference(paramodulation,[status(thm)],[f38,f2484]) ).
fof(f13945,plain,
! [X0,X1] : zero = multiplication(antidomain(coantidomain(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f561,f2484]) ).
fof(f13947,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(antidomain(multiplication(X0,multiplication(X1,domain(X2))))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f428,f2484]) ).
fof(f13948,plain,
! [X0,X1] : zero = multiplication(antidomain(antidomain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f404,f2484]) ).
fof(f13949,plain,
! [X0] : zero = multiplication(antidomain(c(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f434,f2484]) ).
fof(f13951,plain,
! [X0,X1,X2,X3] : zero = multiplication(antidomain(multiplication(addition(multiplication(X0,X1),X2),X3)),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f199,f2484]) ).
fof(f13952,plain,
! [X0,X1,X2,X3] : zero = multiplication(antidomain(addition(multiplication(addition(X0,X1),X2),X3)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f214,f2484]) ).
fof(f13953,plain,
! [X0,X1,X2,X3] : zero = multiplication(antidomain(addition(multiplication(X0,addition(X1,X2)),X3)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f165,f2484]) ).
fof(f13954,plain,
! [X0,X1,X2,X3] : zero = multiplication(antidomain(multiplication(addition(X0,multiplication(X1,X2)),X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f206,f2484]) ).
fof(f13955,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(addition(X0,X1),X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f196,f2484]) ).
fof(f13956,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,addition(X1,X2))),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f148,f2484]) ).
fof(f13957,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(addition(X0,X1),X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f41,f2484]) ).
fof(f13958,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,addition(X1,X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f40,f2484]) ).
fof(f13959,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(X0,addition(X1,X2))),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f98,f2484]) ).
fof(f13960,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(X0,addition(X1,X2))),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f2484]) ).
fof(f13978,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(addition(X0,one),X1)),X1),
inference(paramodulation,[status(thm)],[f227,f2484]) ).
fof(f13979,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(addition(one,X0),X1)),X1),
inference(paramodulation,[status(thm)],[f202,f2484]) ).
fof(f13980,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,addition(X1,one))),X0),
inference(paramodulation,[status(thm)],[f187,f2484]) ).
fof(f13981,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,addition(one,X1))),X0),
inference(paramodulation,[status(thm)],[f157,f2484]) ).
fof(f13983,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f966,f2484]) ).
fof(f13984,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f945,f2484]) ).
fof(f13986,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(X0,addition(X1,X2))),X2),
inference(paramodulation,[status(thm)],[f92,f2484]) ).
fof(f13987,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(X0,addition(X1,X2))),X1),
inference(paramodulation,[status(thm)],[f92,f2484]) ).
fof(f13989,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f33,f2484]) ).
fof(f13990,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f33,f2484]) ).
fof(f14010,plain,
! [X0,X1] : leq(antidomain(addition(addition(one,X0),X1)),zero),
inference(paramodulation,[status(thm)],[f2484,f2333]) ).
fof(f14011,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)],[f2484,f335]) ).
fof(f14013,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)],[f2484,f237]) ).
fof(f14015,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)],[f2484,f428]) ).
fof(f14016,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)],[f2484,f327]) ).
fof(f14017,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)],[f2484,f291]) ).
fof(f14018,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)],[f2484,f206]) ).
fof(f14019,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)],[f2484,f199]) ).
fof(f14024,plain,
! [X0,X1] : forward_diamond(antidomain(addition(domain(X0),X1)),X0) = domain(zero),
inference(paramodulation,[status(thm)],[f2484,f64]) ).
fof(f14026,plain,
! [X0,X1] : leq(antidomain(addition(star(X0),X1)),zero),
inference(paramodulation,[status(thm)],[f2484,f8048]) ).
fof(f14031,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)],[f2484,f428]) ).
fof(f14032,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0)))),
inference(paramodulation,[status(thm)],[f2484,f405]) ).
fof(f14033,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)],[f2484,f327]) ).
fof(f14034,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)],[f2484,f327]) ).
fof(f14035,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)],[f2484,f337]) ).
fof(f14036,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)],[f2484,f324]) ).
fof(f14037,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)],[f2484,f291]) ).
fof(f14039,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(addition(X1,X2))),X0),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f2484,f288]) ).
fof(f14042,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)],[f2484,f214]) ).
fof(f14043,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)],[f2484,f214]) ).
fof(f14045,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)],[f2484,f206]) ).
fof(f14046,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)],[f2484,f206]) ).
fof(f14048,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)],[f2484,f199]) ).
fof(f14049,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)],[f2484,f199]) ).
fof(f14050,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(addition(X0,X1)),X2),X0) = addition(multiplication(X2,X0),zero),
inference(paramodulation,[status(thm)],[f2484,f196]) ).
fof(f14051,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(addition(X1,X2))),X1) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2484,f196]) ).
fof(f14052,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)],[f2484,f165]) ).
fof(f14053,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)],[f2484,f165]) ).
fof(f14054,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,one)) = addition(antidomain(addition(X0,X1)),zero),
inference(paramodulation,[status(thm)],[f2484,f187]) ).
fof(f14055,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(one,X0)) = addition(antidomain(addition(X0,X1)),zero),
inference(paramodulation,[status(thm)],[f2484,f157]) ).
fof(f14056,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,X2)) = addition(multiplication(antidomain(addition(X0,X1)),X2),zero),
inference(paramodulation,[status(thm)],[f2484,f148]) ).
fof(f14057,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X2,X0)) = addition(zero,multiplication(antidomain(addition(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f2484,f148]) ).
fof(f14060,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)],[f2484,f561]) ).
fof(f14061,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)],[f2484,f404]) ).
fof(f14062,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)],[f2484,f53]) ).
fof(f14063,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(addition(X1,X2))),X0),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f2484,f51]) ).
fof(f14064,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(addition(X1,X2))),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f2484,f41]) ).
fof(f14065,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(addition(X0,X1)),X2),X0) = addition(zero,multiplication(X2,X0)),
inference(paramodulation,[status(thm)],[f2484,f41]) ).
fof(f14066,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X2,X0)) = addition(multiplication(antidomain(addition(X0,X1)),X2),zero),
inference(paramodulation,[status(thm)],[f2484,f40]) ).
fof(f14067,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,X2)) = addition(zero,multiplication(antidomain(addition(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f2484,f40]) ).
fof(f14068,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),multiplication(X0,X2)) = multiplication(zero,X2),
inference(paramodulation,[status(thm)],[f2484,f37]) ).
fof(f14075,plain,
! [X0,X1,X2] : zero = multiplication(domain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f57,f13947]) ).
fof(f14076,plain,
! [X0,X1,X2] : zero = domain_difference(multiplication(X0,multiplication(X1,domain(X2))),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f63,f14075]) ).
fof(f14077,plain,
! [X0,X1] : zero = multiplication(domain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f57,f13948]) ).
fof(f14078,plain,
! [X0,X1] : zero = domain_difference(multiplication(X0,domain(X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f63,f14077]) ).
fof(f14080,plain,
! [X0,X1] : leq(antidomain(addition(X0,addition(one,X1))),zero),
inference(forward_demodulation,[status(thm)],[f98,f14010]) ).
fof(f14081,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)],[f98,f14011]) ).
fof(f14082,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)],[f98,f14081]) ).
fof(f14083,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)],[f98,f14082]) ).
fof(f14084,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)],[f14083,f235]) ).
fof(f14088,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)],[f98,f14013]) ).
fof(f14089,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)],[f98,f14088]) ).
fof(f14090,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)],[f2484,f14089]) ).
fof(f14091,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)],[f98,f14090]) ).
fof(f14092,plain,
! [X0,X1,X2] :
( zero != zero
| leq(multiplication(antidomain(addition(X0,addition(X1,X2))),X1),zero) ),
inference(forward_demodulation,[status(thm)],[f2484,f14091]) ).
fof(f14093,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(addition(X0,addition(X1,X2))),X1),zero),
inference(trivial_equality_resolution,[status(thm)],[f14092]) ).
fof(f14098,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)],[f523,f14015]) ).
fof(f14099,plain,
! [X0,X1,X2] : one = antidomain(multiplication(antidomain(addition(multiplication(X0,X1),X2)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1315,f14098]) ).
fof(f14100,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)],[f75,f14016]) ).
fof(f14101,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)],[f75,f14017]) ).
fof(f14102,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)],[f35,f14018]) ).
fof(f14103,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)],[f75,f14019]) ).
fof(f14111,plain,
! [X0,X1] : forward_diamond(antidomain(addition(domain(X0),X1)),X0) = zero,
inference(forward_demodulation,[status(thm)],[f553,f14024]) ).
fof(f14116,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)],[f42,f14031]) ).
fof(f14117,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)],[f523,f14116]) ).
fof(f14118,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(antidomain(addition(X1,X2)),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1315,f14117]) ).
fof(f14119,plain,
! [X0,X1] : leq(one,antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f523,f14032]) ).
fof(f14120,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)],[f2484,f14033]) ).
fof(f14121,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)],[f42,f14034]) ).
fof(f14122,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)],[f75,f14121]) ).
fof(f14123,plain,
! [X0,X1] : leq(multiplication(antidomain(addition(X0,X1)),multiplication(X0,star(X0))),antidomain(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f14035,f235]) ).
fof(f14124,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),antidomain(addition(X1,X2)))
| ~ leq(X0,antidomain(addition(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f35,f14036]) ).
fof(f14125,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)],[f42,f14037]) ).
fof(f14126,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X2,antidomain(addition(X1,X3)))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f14125]) ).
fof(f14128,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(addition(X1,X2))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f35,f14039]) ).
fof(f14141,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)],[f92,f14042]) ).
fof(f14142,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)],[f75,f14141]) ).
fof(f14143,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)],[f75,f14043]) ).
fof(f14147,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)],[f42,f14045]) ).
fof(f14148,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,antidomain(addition(X2,X3)))),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f35,f14147]) ).
fof(f14149,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)],[f75,f14046]) ).
fof(f14152,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)],[f35,f14048]) ).
fof(f14153,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)],[f42,f14049]) ).
fof(f14154,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,antidomain(addition(X1,X2))),X3),X1) = multiplication(X3,X1),
inference(forward_demodulation,[status(thm)],[f75,f14153]) ).
fof(f14155,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(addition(X0,X1)),X2),X0) = multiplication(X2,X0),
inference(forward_demodulation,[status(thm)],[f35,f14050]) ).
fof(f14156,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(addition(X1,X2))),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f14051]) ).
fof(f14157,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)],[f92,f14052]) ).
fof(f14158,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)],[f75,f14157]) ).
fof(f14159,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)],[f75,f14053]) ).
fof(f14160,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,one)) = antidomain(addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f14054]) ).
fof(f14161,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(one,X0)) = antidomain(addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f35,f14055]) ).
fof(f14162,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,X2)) = multiplication(antidomain(addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f35,f14056]) ).
fof(f14163,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X2,X0)) = multiplication(antidomain(addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f14057]) ).
fof(f14166,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)],[f638,f14060]) ).
fof(f14167,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(antidomain(addition(X0,X1))),X0)),
inference(forward_demodulation,[status(thm)],[f1313,f14166]) ).
fof(f14168,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)],[f523,f14061]) ).
fof(f14169,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(addition(X0,X1)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1315,f14168]) ).
fof(f14170,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X1)),antidomain(addition(X1,X2)))
| ~ leq(X0,antidomain(addition(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f75,f14062]) ).
fof(f14171,plain,
! [X0,X1,X2] :
( leq(multiplication(star(antidomain(addition(X1,X2))),X0),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f14063]) ).
fof(f14172,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(addition(X1,X2))),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f14064]) ).
fof(f14173,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(addition(X0,X1)),X2),X0) = multiplication(X2,X0),
inference(forward_demodulation,[status(thm)],[f75,f14065]) ).
fof(f14174,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X2,X0)) = multiplication(antidomain(addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f35,f14066]) ).
fof(f14175,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,X2)) = multiplication(antidomain(addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f14067]) ).
fof(f14176,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),multiplication(X0,X2)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f14068]) ).
fof(f14208,plain,
! [X0] : zero = antidomain(addition(X0,one)),
inference(paramodulation,[status(thm)],[f966,f13930]) ).
fof(f14211,plain,
! [X0,X1] : zero = antidomain(addition(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f92,f13930]) ).
fof(f14212,plain,
! [X0,X1] : zero = antidomain(addition(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f92,f13930]) ).
fof(f14218,plain,
! [X0] : forward_box(c(addition(one,X0)),zero) = one,
inference(paramodulation,[status(thm)],[f13930,f13538]) ).
fof(f14219,plain,
! [X0] : leq(c(addition(one,X0)),zero),
inference(paramodulation,[status(thm)],[f13930,f12588]) ).
fof(f14220,plain,
! [X0] : c(addition(one,X0)) = multiplication(c(addition(one,X0)),zero),
inference(paramodulation,[status(thm)],[f13930,f2482]) ).
fof(f14226,plain,
! [X0,X1] : leq(domain_difference(X0,addition(one,X1)),zero),
inference(paramodulation,[status(thm)],[f13930,f6657]) ).
fof(f14242,plain,
! [X0,X1] : domain_difference(X0,addition(one,X1)) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f13930,f63]) ).
fof(f14243,plain,
! [X0] : addition(zero,domain(addition(one,X0))) = one,
inference(paramodulation,[status(thm)],[f13930,f504]) ).
fof(f14244,plain,
! [X0] : antidomain(c(addition(one,X0))) = c(zero),
inference(paramodulation,[status(thm)],[f13930,f493]) ).
fof(f14249,plain,
! [X0] : c(addition(one,X0)) = zero,
inference(forward_demodulation,[status(thm)],[f42,f14220]) ).
fof(f14264,plain,
! [X0,X1] : domain_difference(X0,addition(one,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f42,f14242]) ).
fof(f14265,plain,
! [X0] : domain(addition(one,X0)) = one,
inference(forward_demodulation,[status(thm)],[f75,f14243]) ).
fof(f14266,plain,
! [X0] : antidomain(c(addition(one,X0))) = one,
inference(forward_demodulation,[status(thm)],[f543,f14244]) ).
fof(f14269,plain,
! [X0] : addition(one,antidomain(multiplication(antidomain(X0),domain(X0)))) = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f523,f409]) ).
fof(f14270,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1315,f14269]) ).
fof(f14271,plain,
! [X0] : one = antidomain(multiplication(one,domain(multiplication(antidomain(X0),domain(X0))))),
inference(paramodulation,[status(thm)],[f14270,f14270]) ).
fof(f14275,plain,
! [X0] : one = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f62,f14270]) ).
fof(f14276,plain,
! [X0] : one = antidomain(multiplication(domain(X0),domain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f57,f14270]) ).
fof(f14282,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f64,f14270]) ).
fof(f14284,plain,
! [X0] : one = antidomain(multiplication(antidomain(domain(X0)),antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f191,f14270]) ).
fof(f14285,plain,
! [X0] : one = antidomain(multiplication(antidomain(antidomain(X0)),c(X0))),
inference(paramodulation,[status(thm)],[f316,f14270]) ).
fof(f14289,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f14270,f405]) ).
fof(f14290,plain,
! [X0] : addition(one,antidomain(multiplication(antidomain(X0),domain(domain(X0))))) = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f14270,f404]) ).
fof(f14294,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)],[f14270,f338]) ).
fof(f14295,plain,
! [X0] : addition(one,c(multiplication(antidomain(X0),domain(X0)))) = c(multiplication(antidomain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f14270,f434]) ).
fof(f14299,plain,
! [X0,X1] : leq(domain_difference(X0,multiplication(antidomain(X1),domain(X1))),one),
inference(paramodulation,[status(thm)],[f14270,f6657]) ).
fof(f14302,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(antidomain(X1),domain(X1))) = multiplication(X0,multiplication(antidomain(X1),domain(X1))),
inference(paramodulation,[status(thm)],[f14270,f225]) ).
fof(f14304,plain,
! [X0] : leq(one,c(multiplication(antidomain(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f14270,f4063]) ).
fof(f14305,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(antidomain(X1),domain(X1))) = multiplication(X0,multiplication(antidomain(X1),domain(X1))),
inference(paramodulation,[status(thm)],[f14270,f219]) ).
fof(f14309,plain,
! [X0,X1] : multiplication(one,addition(X0,multiplication(antidomain(X1),domain(X1)))) = multiplication(antidomain(multiplication(antidomain(X1),domain(X1))),X0),
inference(paramodulation,[status(thm)],[f14270,f181]) ).
fof(f14311,plain,
! [X0,X1] : multiplication(one,addition(multiplication(antidomain(X0),domain(X0)),X1)) = multiplication(antidomain(multiplication(antidomain(X0),domain(X0))),X1),
inference(paramodulation,[status(thm)],[f14270,f172]) ).
fof(f14313,plain,
! [X0,X1] : multiplication(one,multiplication(multiplication(antidomain(X0),domain(X0)),X1)) = zero,
inference(paramodulation,[status(thm)],[f14270,f131]) ).
fof(f14315,plain,
! [X0,X1] : domain_difference(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f14270,f63]) ).
fof(f14317,plain,
! [X0] : antidomain(c(multiplication(antidomain(X0),domain(X0)))) = c(one),
inference(paramodulation,[status(thm)],[f14270,f493]) ).
fof(f14318,plain,
! [X0] : domain(one) = c(multiplication(antidomain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f14270,f316]) ).
fof(f14319,plain,
! [X0] : domain(multiplication(antidomain(X0),domain(X0))) = antidomain(one),
inference(paramodulation,[status(thm)],[f14270,f57]) ).
fof(f14320,plain,
! [X0] : multiplication(one,multiplication(antidomain(X0),domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f14270,f54]) ).
fof(f14321,plain,
! [X0] : one = antidomain(domain(multiplication(antidomain(X0),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f39,f14271]) ).
fof(f14322,plain,
! [X0] : one = c(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f62,f14321]) ).
fof(f14327,plain,
! [X0] : one = antidomain(multiplication(c(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f14275]) ).
fof(f14328,plain,
! [X0] : one = antidomain(multiplication(domain(X0),c(X0))),
inference(forward_demodulation,[status(thm)],[f316,f14276]) ).
fof(f14336,plain,
! [X0] : one = antidomain(multiplication(c(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f14284]) ).
fof(f14337,plain,
! [X0] : one = antidomain(multiplication(domain(X0),c(X0))),
inference(forward_demodulation,[status(thm)],[f57,f14285]) ).
fof(f14343,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f191,f14289]) ).
fof(f14344,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f1315,f14290]) ).
fof(f14345,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f14344]) ).
fof(f14346,plain,
! [X0,X1] :
( leq(multiplication(X0,star(multiplication(antidomain(X1),domain(X1)))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f14270,f14294]) ).
fof(f14347,plain,
! [X0] : one = c(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1406,f14295]) ).
fof(f14358,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(antidomain(multiplication(antidomain(X1),domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f39,f14309]) ).
fof(f14359,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(one,X0),
inference(forward_demodulation,[status(thm)],[f14270,f14358]) ).
fof(f14360,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f39,f14359]) ).
fof(f14361,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = multiplication(antidomain(multiplication(antidomain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f39,f14311]) ).
fof(f14362,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = multiplication(one,X1),
inference(forward_demodulation,[status(thm)],[f14270,f14361]) ).
fof(f14363,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f39,f14362]) ).
fof(f14364,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),domain(X0)),X1) = zero,
inference(forward_demodulation,[status(thm)],[f39,f14313]) ).
fof(f14365,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f37,f14364]) ).
fof(f14366,plain,
! [X0,X1] : domain_difference(X0,multiplication(antidomain(X1),domain(X1))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f38,f14315]) ).
fof(f14367,plain,
! [X0] : antidomain(c(multiplication(antidomain(X0),domain(X0)))) = zero,
inference(forward_demodulation,[status(thm)],[f537,f14317]) ).
fof(f14368,plain,
! [X0] : one = c(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f516,f14318]) ).
fof(f14369,plain,
! [X0] : forward_diamond(antidomain(X0),X0) = antidomain(one),
inference(forward_demodulation,[status(thm)],[f64,f14319]) ).
fof(f14370,plain,
! [X0] : forward_diamond(antidomain(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f114,f14369]) ).
fof(f14371,plain,
! [X0] : multiplication(antidomain(X0),domain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f14320]) ).
fof(f14376,plain,
! [X0] : forward_diamond(one,multiplication(antidomain(X0),domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f14270,f14370]) ).
fof(f14381,plain,
! [X0] : forward_diamond(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f57,f14370]) ).
fof(f14385,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)],[f14370,f70]) ).
fof(f14398,plain,
! [X0] : antidomain(c(multiplication(antidomain(X0),domain(X0)))) = zero,
inference(forward_demodulation,[status(thm)],[f715,f14376]) ).
fof(f14403,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)],[f92,f14385]) ).
fof(f14404,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)],[f75,f14403]) ).
fof(f14405,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)],[f14370,f14404]) ).
fof(f14406,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)],[f75,f14405]) ).
fof(f14407,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(c(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)],[f62,f14406]) ).
fof(f14408,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(c(X1)),forward_diamond(star(c(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)],[f62,f14407]) ).
fof(f14409,plain,
! [X0,X1] :
( addition(domain(X1),addition(divergence(c(X1)),forward_diamond(star(c(X1)),domain(X0)))) = addition(divergence(c(X1)),forward_diamond(star(antidomain(domain(X1))),domain(X0)))
| addition(domain(X0),domain(X1)) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f62,f14408]) ).
fof(f14410,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)],[f62,f14409]) ).
fof(f14417,plain,
! [X0,X1] : zero = antidomain(addition(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f98,f14208]) ).
fof(f14418,plain,
! [X0,X1] : zero = antidomain(addition(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f34,f14208]) ).
fof(f14427,plain,
! [X0] : forward_box(c(addition(X0,one)),zero) = one,
inference(paramodulation,[status(thm)],[f14208,f13538]) ).
fof(f14428,plain,
! [X0] : leq(c(addition(X0,one)),zero),
inference(paramodulation,[status(thm)],[f14208,f12588]) ).
fof(f14429,plain,
! [X0] : c(addition(X0,one)) = multiplication(c(addition(X0,one)),zero),
inference(paramodulation,[status(thm)],[f14208,f2482]) ).
fof(f14435,plain,
! [X0,X1] : leq(domain_difference(X0,addition(X1,one)),zero),
inference(paramodulation,[status(thm)],[f14208,f6657]) ).
fof(f14451,plain,
! [X0,X1] : domain_difference(X0,addition(X1,one)) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f14208,f63]) ).
fof(f14452,plain,
! [X0] : addition(zero,domain(addition(X0,one))) = one,
inference(paramodulation,[status(thm)],[f14208,f504]) ).
fof(f14453,plain,
! [X0] : antidomain(c(addition(X0,one))) = c(zero),
inference(paramodulation,[status(thm)],[f14208,f493]) ).
fof(f14459,plain,
! [X0] : c(addition(X0,one)) = zero,
inference(forward_demodulation,[status(thm)],[f42,f14429]) ).
fof(f14474,plain,
! [X0,X1] : domain_difference(X0,addition(X1,one)) = zero,
inference(forward_demodulation,[status(thm)],[f42,f14451]) ).
fof(f14475,plain,
! [X0] : domain(addition(X0,one)) = one,
inference(forward_demodulation,[status(thm)],[f75,f14452]) ).
fof(f14476,plain,
! [X0] : antidomain(c(addition(X0,one))) = one,
inference(forward_demodulation,[status(thm)],[f543,f14453]) ).
fof(f14479,plain,
! [X0] : addition(one,antidomain(multiplication(X0,domain(coantidomain(X0))))) = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f523,f412]) ).
fof(f14480,plain,
! [X0] : one = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1315,f14479]) ).
fof(f14481,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f37,f14480]) ).
fof(f14486,plain,
! [X0] : one = antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f61,f14480]) ).
fof(f14490,plain,
! [X0] : leq(one,antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f14480,f405]) ).
fof(f14491,plain,
! [X0] : addition(one,antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))) = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f14480,f404]) ).
fof(f14492,plain,
! [X0] : forward_diamond(one,multiplication(X0,domain(coantidomain(X0)))) = zero,
inference(paramodulation,[status(thm)],[f14480,f14370]) ).
fof(f14493,plain,
! [X0] : one = antidomain(multiplication(one,domain(multiplication(X0,domain(coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f14480,f14270]) ).
fof(f14497,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)],[f14480,f338]) ).
fof(f14498,plain,
! [X0] : addition(one,c(multiplication(X0,domain(coantidomain(X0))))) = c(multiplication(X0,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f14480,f434]) ).
fof(f14502,plain,
! [X0,X1] : leq(domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))),one),
inference(paramodulation,[status(thm)],[f14480,f6657]) ).
fof(f14505,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,domain(coantidomain(X1)))) = multiplication(X0,multiplication(X1,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f14480,f225]) ).
fof(f14507,plain,
! [X0] : leq(one,c(multiplication(X0,domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f14480,f4063]) ).
fof(f14508,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,domain(coantidomain(X1)))) = multiplication(X0,multiplication(X1,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f14480,f219]) ).
fof(f14512,plain,
! [X0,X1] : multiplication(one,addition(X0,multiplication(X1,domain(coantidomain(X1))))) = multiplication(antidomain(multiplication(X1,domain(coantidomain(X1)))),X0),
inference(paramodulation,[status(thm)],[f14480,f181]) ).
fof(f14514,plain,
! [X0,X1] : multiplication(one,addition(multiplication(X0,domain(coantidomain(X0))),X1)) = multiplication(antidomain(multiplication(X0,domain(coantidomain(X0)))),X1),
inference(paramodulation,[status(thm)],[f14480,f172]) ).
fof(f14516,plain,
! [X0,X1] : multiplication(one,multiplication(multiplication(X0,domain(coantidomain(X0))),X1)) = zero,
inference(paramodulation,[status(thm)],[f14480,f131]) ).
fof(f14518,plain,
! [X0,X1] : domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f14480,f63]) ).
fof(f14520,plain,
! [X0] : antidomain(c(multiplication(X0,domain(coantidomain(X0))))) = c(one),
inference(paramodulation,[status(thm)],[f14480,f493]) ).
fof(f14521,plain,
! [X0] : domain(one) = c(multiplication(X0,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f14480,f316]) ).
fof(f14522,plain,
! [X0] : domain(multiplication(X0,domain(coantidomain(X0)))) = antidomain(one),
inference(paramodulation,[status(thm)],[f14480,f57]) ).
fof(f14523,plain,
! [X0] : multiplication(one,multiplication(X0,domain(coantidomain(X0)))) = zero,
inference(paramodulation,[status(thm)],[f14480,f54]) ).
fof(f14535,plain,
! [X0] : leq(one,antidomain(multiplication(X0,antidomain(c(coantidomain(X0)))))),
inference(forward_demodulation,[status(thm)],[f191,f14490]) ).
fof(f14536,plain,
! [X0] : one = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f1315,f14491]) ).
fof(f14537,plain,
! [X0] : one = antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f191,f14536]) ).
fof(f14538,plain,
! [X0] : antidomain(c(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(forward_demodulation,[status(thm)],[f715,f14492]) ).
fof(f14539,plain,
! [X0] : one = antidomain(domain(multiplication(X0,domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f39,f14493]) ).
fof(f14540,plain,
! [X0] : one = c(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f14539]) ).
fof(f14541,plain,
! [X0,X1] :
( leq(multiplication(X0,star(multiplication(X1,domain(coantidomain(X1))))),one)
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f14480,f14497]) ).
fof(f14542,plain,
! [X0] : one = c(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1406,f14498]) ).
fof(f14553,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(antidomain(multiplication(X1,domain(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f39,f14512]) ).
fof(f14554,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(one,X0),
inference(forward_demodulation,[status(thm)],[f14480,f14553]) ).
fof(f14555,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f39,f14554]) ).
fof(f14556,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = multiplication(antidomain(multiplication(X0,domain(coantidomain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f39,f14514]) ).
fof(f14557,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = multiplication(one,X1),
inference(forward_demodulation,[status(thm)],[f14480,f14556]) ).
fof(f14558,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = X1,
inference(forward_demodulation,[status(thm)],[f39,f14557]) ).
fof(f14559,plain,
! [X0,X1] : multiplication(multiplication(X0,domain(coantidomain(X0))),X1) = zero,
inference(forward_demodulation,[status(thm)],[f39,f14516]) ).
fof(f14560,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f37,f14559]) ).
fof(f14561,plain,
! [X0,X1] : domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f38,f14518]) ).
fof(f14562,plain,
! [X0] : antidomain(c(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(forward_demodulation,[status(thm)],[f537,f14520]) ).
fof(f14563,plain,
! [X0] : one = c(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f516,f14521]) ).
fof(f14564,plain,
! [X0] : forward_diamond(X0,coantidomain(X0)) = antidomain(one),
inference(forward_demodulation,[status(thm)],[f64,f14522]) ).
fof(f14565,plain,
! [X0] : forward_diamond(X0,coantidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f114,f14564]) ).
fof(f14566,plain,
! [X0] : multiplication(X0,domain(coantidomain(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f39,f14523]) ).
fof(f14572,plain,
! [X0] : forward_diamond(coantidomain(X0),codomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f61,f14565]) ).
fof(f14627,plain,
! [X0,X1] : c(addition(X0,addition(X1,one))) = zero,
inference(paramodulation,[status(thm)],[f92,f14249]) ).
fof(f14628,plain,
! [X0,X1] : c(addition(X0,addition(one,X1))) = zero,
inference(paramodulation,[status(thm)],[f92,f14249]) ).
fof(f14636,plain,
! [X0] : forward_box(antidomain(zero),addition(one,X0)) = one,
inference(paramodulation,[status(thm)],[f14249,f13113]) ).
fof(f14638,plain,
! [X0] : leq(antidomain(zero),domain(addition(one,X0))),
inference(paramodulation,[status(thm)],[f14249,f12944]) ).
fof(f14663,plain,
! [X0,X1] : backward_box(X0,addition(one,X1)) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f14249,f67]) ).
fof(f14664,plain,
! [X0,X1] : forward_box(X0,addition(one,X1)) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f14249,f66]) ).
fof(f14668,plain,
! [X0] : forward_box(one,addition(one,X0)) = one,
inference(forward_demodulation,[status(thm)],[f523,f14636]) ).
fof(f14669,plain,
! [X0] : leq(one,domain(addition(one,X0))),
inference(forward_demodulation,[status(thm)],[f523,f14638]) ).
fof(f14690,plain,
! [X0,X1] : backward_box(X0,addition(one,X1)) = c(zero),
inference(forward_demodulation,[status(thm)],[f749,f14663]) ).
fof(f14691,plain,
! [X0,X1] : backward_box(X0,addition(one,X1)) = one,
inference(forward_demodulation,[status(thm)],[f543,f14690]) ).
fof(f14692,plain,
! [X0,X1] : forward_box(X0,addition(one,X1)) = c(zero),
inference(forward_demodulation,[status(thm)],[f717,f14664]) ).
fof(f14693,plain,
! [X0,X1] : forward_box(X0,addition(one,X1)) = one,
inference(forward_demodulation,[status(thm)],[f543,f14692]) ).
fof(f14731,plain,
! [X0,X1] : domain(addition(X0,addition(X1,one))) = one,
inference(paramodulation,[status(thm)],[f92,f14265]) ).
fof(f14732,plain,
! [X0,X1] : domain(addition(X0,addition(one,X1))) = one,
inference(paramodulation,[status(thm)],[f92,f14265]) ).
fof(f14738,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)],[f14265,f428]) ).
fof(f14742,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,addition(one,X1))),antidomain(multiplication(X0,one))),
inference(paramodulation,[status(thm)],[f14265,f405]) ).
fof(f14756,plain,
! [X0,X1] : leq(domain_difference(addition(one,X0),X1),one),
inference(paramodulation,[status(thm)],[f14265,f3580]) ).
fof(f14762,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)],[f14265,f70]) ).
fof(f14763,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)],[f14265,f70]) ).
fof(f14764,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)],[f14265,f70]) ).
fof(f14765,plain,
! [X0,X1] : forward_diamond(X0,addition(one,X1)) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f14265,f64]) ).
fof(f14766,plain,
! [X0,X1] : domain_difference(addition(one,X0),X1) = multiplication(one,antidomain(X1)),
inference(paramodulation,[status(thm)],[f14265,f63]) ).
fof(f14769,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)],[f14265,f404]) ).
fof(f14773,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)],[f33,f14738]) ).
fof(f14774,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)],[f38,f14773]) ).
fof(f14775,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)],[f14265,f14774]) ).
fof(f14776,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)],[f38,f14775]) ).
fof(f14781,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,addition(one,X1))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f14742]) ).
fof(f14799,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)],[f92,f14762]) ).
fof(f14800,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)],[f14265,f14799]) ).
fof(f14801,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)],[f33,f14800]) ).
fof(f14802,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)],[f1420,f14801]) ).
fof(f14803,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)],[f14265,f14802]) ).
fof(f14804,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)],[f718,f14803]) ).
fof(f14805,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)],[f8139,f14804]) ).
fof(f14806,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)],[f92,f14805]) ).
fof(f14807,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)],[f14265,f14806]) ).
fof(f14808,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)],[f718,f14807]) ).
fof(f14809,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)],[f8139,f14808]) ).
fof(f14810,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)],[f33,f14809]) ).
fof(f14811,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)],[f1423,f14810]) ).
fof(f14812,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)],[f14265,f14763]) ).
fof(f14813,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)],[f718,f14812]) ).
fof(f14814,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)],[f14265,f14813]) ).
fof(f14815,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)],[f718,f14814]) ).
fof(f14816,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)],[f14265,f14815]) ).
fof(f14817,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)],[f14265,f14764]) ).
fof(f14818,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)],[f718,f14817]) ).
fof(f14819,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)],[f14265,f14818]) ).
fof(f14820,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)],[f718,f14819]) ).
fof(f14821,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)],[f14265,f14820]) ).
fof(f14822,plain,
! [X0,X1] : forward_diamond(X0,addition(one,X1)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f38,f14765]) ).
fof(f14823,plain,
! [X0,X1] : domain_difference(addition(one,X0),X1) = antidomain(X1),
inference(forward_demodulation,[status(thm)],[f39,f14766]) ).
fof(f14826,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)],[f33,f14769]) ).
fof(f14827,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(one,X1)))) = antidomain(multiplication(X0,domain(addition(one,X1)))),
inference(forward_demodulation,[status(thm)],[f38,f14826]) ).
fof(f14828,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(one,X1)))) = antidomain(multiplication(X0,one)),
inference(forward_demodulation,[status(thm)],[f14265,f14827]) ).
fof(f14829,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(one,X1)))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f38,f14828]) ).
fof(f14835,plain,
! [X0,X1] : c(addition(X0,addition(X1,one))) = zero,
inference(paramodulation,[status(thm)],[f98,f14459]) ).
fof(f14836,plain,
! [X0,X1] : c(addition(X0,addition(X1,one))) = zero,
inference(paramodulation,[status(thm)],[f34,f14459]) ).
fof(f14845,plain,
! [X0] : forward_box(antidomain(zero),addition(X0,one)) = one,
inference(paramodulation,[status(thm)],[f14459,f13113]) ).
fof(f14847,plain,
! [X0] : leq(antidomain(zero),domain(addition(X0,one))),
inference(paramodulation,[status(thm)],[f14459,f12944]) ).
fof(f14872,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f14459,f67]) ).
fof(f14873,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f14459,f66]) ).
fof(f14877,plain,
! [X0] : forward_box(one,addition(X0,one)) = one,
inference(forward_demodulation,[status(thm)],[f523,f14845]) ).
fof(f14878,plain,
! [X0] : leq(one,domain(addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f523,f14847]) ).
fof(f14899,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = c(zero),
inference(forward_demodulation,[status(thm)],[f749,f14872]) ).
fof(f14900,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = one,
inference(forward_demodulation,[status(thm)],[f543,f14899]) ).
fof(f14901,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = c(zero),
inference(forward_demodulation,[status(thm)],[f717,f14873]) ).
fof(f14902,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = one,
inference(forward_demodulation,[status(thm)],[f543,f14901]) ).
fof(f14908,plain,
! [X0,X1] : domain(addition(X0,addition(X1,one))) = one,
inference(paramodulation,[status(thm)],[f98,f14475]) ).
fof(f14909,plain,
! [X0,X1] : domain(addition(X0,addition(X1,one))) = one,
inference(paramodulation,[status(thm)],[f34,f14475]) ).
fof(f14916,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)],[f14475,f428]) ).
fof(f14917,plain,
! [X0,X1] : forward_box(X0,one) = forward_box(X0,addition(X1,one)),
inference(paramodulation,[status(thm)],[f14475,f13006]) ).
fof(f14918,plain,
! [X0,X1] : backward_box(X0,one) = backward_box(X0,addition(X1,one)),
inference(paramodulation,[status(thm)],[f14475,f13005]) ).
fof(f14920,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,addition(X1,one))),antidomain(multiplication(X0,one))),
inference(paramodulation,[status(thm)],[f14475,f405]) ).
fof(f14934,plain,
! [X0,X1] : leq(domain_difference(addition(X0,one),X1),one),
inference(paramodulation,[status(thm)],[f14475,f3580]) ).
fof(f14940,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)],[f14475,f70]) ).
fof(f14941,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)],[f14475,f70]) ).
fof(f14942,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)],[f14475,f70]) ).
fof(f14943,plain,
! [X0,X1] : forward_diamond(X0,addition(X1,one)) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f14475,f64]) ).
fof(f14944,plain,
! [X0,X1] : domain_difference(addition(X0,one),X1) = multiplication(one,antidomain(X1)),
inference(paramodulation,[status(thm)],[f14475,f63]) ).
fof(f14947,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)],[f14475,f404]) ).
fof(f14952,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)],[f33,f14916]) ).
fof(f14953,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)],[f38,f14952]) ).
fof(f14954,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)],[f14475,f14953]) ).
fof(f14955,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)],[f38,f14954]) ).
fof(f14956,plain,
! [X0,X1] : one = forward_box(X0,addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f774,f14917]) ).
fof(f14957,plain,
! [X0,X1] : one = backward_box(X0,addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f796,f14918]) ).
fof(f14960,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,addition(X1,one))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f38,f14920]) ).
fof(f14978,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)],[f92,f14940]) ).
fof(f14979,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)],[f14475,f14978]) ).
fof(f14980,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)],[f33,f14979]) ).
fof(f14981,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)],[f1420,f14980]) ).
fof(f14982,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)],[f14475,f14981]) ).
fof(f14983,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)],[f718,f14982]) ).
fof(f14984,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)],[f8139,f14983]) ).
fof(f14985,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)],[f92,f14984]) ).
fof(f14986,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)],[f14475,f14985]) ).
fof(f14987,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)],[f718,f14986]) ).
fof(f14988,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)],[f8139,f14987]) ).
fof(f14989,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)],[f33,f14988]) ).
fof(f14990,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)],[f1423,f14989]) ).
fof(f14991,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)],[f14475,f14941]) ).
fof(f14992,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)],[f718,f14991]) ).
fof(f14993,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)],[f14475,f14992]) ).
fof(f14994,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)],[f718,f14993]) ).
fof(f14995,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)],[f14475,f14994]) ).
fof(f14996,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)],[f14475,f14942]) ).
fof(f14997,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)],[f718,f14996]) ).
fof(f14998,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)],[f14475,f14997]) ).
fof(f14999,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)],[f718,f14998]) ).
fof(f15000,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)],[f14475,f14999]) ).
fof(f15001,plain,
! [X0,X1] : forward_diamond(X0,addition(X1,one)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f38,f14943]) ).
fof(f15002,plain,
! [X0,X1] : domain_difference(addition(X0,one),X1) = antidomain(X1),
inference(forward_demodulation,[status(thm)],[f39,f14944]) ).
fof(f15005,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)],[f33,f14947]) ).
fof(f15006,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(X1,one)))) = antidomain(multiplication(X0,domain(addition(X1,one)))),
inference(forward_demodulation,[status(thm)],[f38,f15005]) ).
fof(f15007,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(X1,one)))) = antidomain(multiplication(X0,one)),
inference(forward_demodulation,[status(thm)],[f14475,f15006]) ).
fof(f15008,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,addition(X1,one)))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f38,f15007]) ).
fof(f15050,plain,
! [X0,X1] : domain_difference(X0,addition(X1,one)) = zero,
inference(paramodulation,[status(thm)],[f966,f14264]) ).
fof(f15051,plain,
! [X0,X1] : domain_difference(X0,addition(X1,one)) = zero,
inference(paramodulation,[status(thm)],[f945,f14264]) ).
fof(f15053,plain,
! [X0,X1,X2] : domain_difference(X0,addition(X1,addition(X2,one))) = zero,
inference(paramodulation,[status(thm)],[f92,f14264]) ).
fof(f15054,plain,
! [X0,X1,X2] : domain_difference(X0,addition(X1,addition(one,X2))) = zero,
inference(paramodulation,[status(thm)],[f92,f14264]) ).
fof(f15056,plain,
! [X0,X1] : domain_difference(X0,addition(X1,one)) = zero,
inference(paramodulation,[status(thm)],[f33,f14264]) ).
fof(f15057,plain,
! [X0,X1] : domain_difference(X0,addition(X1,one)) = zero,
inference(paramodulation,[status(thm)],[f33,f14264]) ).
fof(f15076,plain,
! [X0] : multiplication(c(X0),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f62,f14371]) ).
fof(f15077,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f57,f14371]) ).
fof(f15085,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f64,f14371]) ).
fof(f15087,plain,
! [X0] : multiplication(antidomain(domain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f191,f14371]) ).
fof(f15088,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f316,f14371]) ).
fof(f15098,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(domain(X1)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(domain(X1))))),
inference(paramodulation,[status(thm)],[f14371,f428]) ).
fof(f15099,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f14371,f405]) ).
fof(f15100,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)],[f14371,f327]) ).
fof(f15101,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)],[f14371,f327]) ).
fof(f15102,plain,
! [X0] :
( leq(multiplication(antidomain(X0),multiplication(domain(X0),star(domain(X0)))),antidomain(X0))
| ~ leq(zero,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f14371,f337]) ).
fof(f15103,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(addition(X0,zero),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f14371,f324]) ).
fof(f15104,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)],[f14371,f291]) ).
fof(f15106,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),domain(X1))
| ~ leq(addition(X0,zero),domain(X1)) ),
inference(paramodulation,[status(thm)],[f14371,f288]) ).
fof(f15109,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)],[f14371,f214]) ).
fof(f15110,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)],[f14371,f214]) ).
fof(f15112,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)],[f14371,f206]) ).
fof(f15113,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)],[f14371,f206]) ).
fof(f15115,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)],[f14371,f199]) ).
fof(f15116,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)],[f14371,f199]) ).
fof(f15117,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = addition(multiplication(X1,domain(X0)),zero),
inference(paramodulation,[status(thm)],[f14371,f196]) ).
fof(f15118,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = addition(zero,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f14371,f196]) ).
fof(f15119,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)],[f14371,f165]) ).
fof(f15120,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)],[f14371,f165]) ).
fof(f15123,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f14371,f148]) ).
fof(f15124,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f14371,f148]) ).
fof(f15127,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),domain(X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f14371,f561]) ).
fof(f15128,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(domain(X0))))) = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f14371,f404]) ).
fof(f15129,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(addition(zero,X0),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f14371,f53]) ).
fof(f15130,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),domain(X1))
| ~ leq(addition(zero,X0),domain(X1)) ),
inference(paramodulation,[status(thm)],[f14371,f51]) ).
fof(f15131,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = addition(multiplication(X0,domain(X1)),zero),
inference(paramodulation,[status(thm)],[f14371,f41]) ).
fof(f15132,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = addition(zero,multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f14371,f41]) ).
fof(f15133,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f14371,f40]) ).
fof(f15134,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f14371,f40]) ).
fof(f15135,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f14371,f37]) ).
fof(f15140,plain,
! [X0] : multiplication(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f191,f15076]) ).
fof(f15141,plain,
! [X0] : multiplication(domain(X0),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f316,f15077]) ).
fof(f15144,plain,
! [X0] : multiplication(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f62,f15087]) ).
fof(f15145,plain,
! [X0] : multiplication(domain(X0),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f57,f15088]) ).
fof(f15160,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(antidomain(X1),domain(domain(X1)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f42,f15098]) ).
fof(f15161,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(antidomain(X1),domain(domain(X1)))))) = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f523,f15160]) ).
fof(f15162,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f1315,f15161]) ).
fof(f15163,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),antidomain(c(X1))))),
inference(forward_demodulation,[status(thm)],[f191,f15162]) ).
fof(f15164,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),domain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f523,f15099]) ).
fof(f15165,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f191,f15164]) ).
fof(f15166,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)],[f14371,f15100]) ).
fof(f15167,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)],[f42,f15101]) ).
fof(f15168,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)],[f75,f15167]) ).
fof(f15169,plain,
! [X0] : leq(multiplication(antidomain(X0),multiplication(domain(X0),star(domain(X0)))),antidomain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f15102,f235]) ).
fof(f15170,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f15103]) ).
fof(f15171,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)],[f42,f15104]) ).
fof(f15172,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,antidomain(X1))),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f15171]) ).
fof(f15174,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f15106]) ).
fof(f15187,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)],[f92,f15109]) ).
fof(f15188,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,domain(X2))) = addition(multiplication(addition(X1,antidomain(X2)),domain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f75,f15187]) ).
fof(f15189,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),X2) = addition(multiplication(addition(antidomain(X1),X0),domain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f15110]) ).
fof(f15193,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f42,f15112]) ).
fof(f15194,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),domain(X2)) = multiplication(X0,domain(X2)),
inference(forward_demodulation,[status(thm)],[f35,f15193]) ).
fof(f15195,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),domain(X0)) = multiplication(X1,multiplication(X2,domain(X0))),
inference(forward_demodulation,[status(thm)],[f75,f15113]) ).
fof(f15198,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),domain(X2)) = multiplication(X0,multiplication(X1,domain(X2))),
inference(forward_demodulation,[status(thm)],[f35,f15115]) ).
fof(f15199,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),domain(X1)) = addition(zero,multiplication(X2,domain(X1))),
inference(forward_demodulation,[status(thm)],[f42,f15116]) ).
fof(f15200,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),domain(X1)) = multiplication(X2,domain(X1)),
inference(forward_demodulation,[status(thm)],[f75,f15199]) ).
fof(f15201,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f15117]) ).
fof(f15202,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f75,f15118]) ).
fof(f15203,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)],[f92,f15119]) ).
fof(f15204,plain,
! [X0,X1,X2] : addition(X0,multiplication(antidomain(X1),X2)) = addition(multiplication(antidomain(X1),addition(X2,domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f75,f15203]) ).
fof(f15205,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),X2) = addition(multiplication(antidomain(X0),addition(domain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f15120]) ).
fof(f15211,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f15123]) ).
fof(f15212,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f15124]) ).
fof(f15215,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(antidomain(X0)),domain(X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f638,f15127]) ).
fof(f15216,plain,
! [X0] : one = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1313,f15215]) ).
fof(f15217,plain,
! [X0] : addition(one,antidomain(multiplication(antidomain(X0),domain(domain(X0))))) = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f523,f15128]) ).
fof(f15218,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f1315,f15217]) ).
fof(f15219,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f191,f15218]) ).
fof(f15220,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(X1))),antidomain(X1))
| ~ leq(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f15129]) ).
fof(f15221,plain,
! [X0,X1] :
( leq(multiplication(star(antidomain(X1)),X0),domain(X1))
| ~ leq(X0,domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f75,f15130]) ).
fof(f15222,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f35,f15131]) ).
fof(f15223,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f75,f15132]) ).
fof(f15224,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f35,f15133]) ).
fof(f15225,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f15134]) ).
fof(f15226,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f15135]) ).
fof(f15230,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f12715,f14381]) ).
fof(f15231,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f12714,f14381]) ).
fof(f15232,plain,
! [X0] : forward_diamond(c(X0),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f12643,f14381]) ).
fof(f15234,plain,
! [X0,X1] : forward_diamond(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f64,f14381]) ).
fof(f15239,plain,
! [X0] : forward_diamond(domain(multiplication(X0,domain(coantidomain(X0)))),one) = zero,
inference(paramodulation,[status(thm)],[f14480,f14381]) ).
fof(f15273,plain,
! [X0] : domain(domain(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(forward_demodulation,[status(thm)],[f718,f15239]) ).
fof(f15274,plain,
! [X0] : antidomain(c(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(forward_demodulation,[status(thm)],[f191,f15273]) ).
fof(f15283,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(resolution,[status(thm)],[f424,f47]) ).
fof(f15287,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),X1),
inference(paramodulation,[status(thm)],[f14480,f424]) ).
fof(f15288,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)],[f202,f424]) ).
fof(f15289,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)],[f219,f424]) ).
fof(f15290,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)],[f227,f424]) ).
fof(f15291,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)],[f225,f424]) ).
fof(f15292,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)],[f228,f424]) ).
fof(f15293,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)],[f221,f424]) ).
fof(f15296,plain,
! [X0,X1,X2] : addition(antidomain(zero),addition(antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),X2)) = addition(antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),X2),
inference(paramodulation,[status(thm)],[f1494,f424]) ).
fof(f15297,plain,
! [X0,X1] : addition(antidomain(zero),addition(antidomain(multiplication(c(X0),domain(domain(X0)))),X1)) = addition(antidomain(multiplication(c(X0),domain(domain(X0)))),X1),
inference(paramodulation,[status(thm)],[f192,f424]) ).
fof(f15299,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)],[f190,f424]) ).
fof(f15300,plain,
! [X0,X1] : addition(antidomain(domain(X0)),addition(antidomain(multiplication(domain(X0),domain(domain(X0)))),X1)) = addition(antidomain(multiplication(domain(X0),domain(domain(X0)))),X1),
inference(paramodulation,[status(thm)],[f2094,f424]) ).
fof(f15301,plain,
! [X0,X1,X2] : addition(antidomain(domain_difference(X0,X1)),addition(antidomain(multiplication(domain(X0),domain(antidomain(X1)))),X2)) = addition(antidomain(multiplication(domain(X0),domain(antidomain(X1)))),X2),
inference(paramodulation,[status(thm)],[f63,f424]) ).
fof(f15302,plain,
! [X0,X1] : addition(antidomain(X0),addition(antidomain(multiplication(domain(X0),domain(X0))),X1)) = addition(antidomain(multiplication(domain(X0),domain(X0))),X1),
inference(paramodulation,[status(thm)],[f3965,f424]) ).
fof(f15303,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)],[f37,f424]) ).
fof(f15304,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)],[f2484,f424]) ).
fof(f15305,plain,
! [X0,X1] : addition(antidomain(zero),addition(antidomain(multiplication(antidomain(X0),domain(domain(X0)))),X1)) = addition(antidomain(multiplication(antidomain(X0),domain(domain(X0)))),X1),
inference(paramodulation,[status(thm)],[f14371,f424]) ).
fof(f15306,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)],[f181,f424]) ).
fof(f15307,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)],[f172,f424]) ).
fof(f15308,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)],[f131,f424]) ).
fof(f15311,plain,
! [X0,X1] : addition(antidomain(X0),addition(antidomain(multiplication(one,domain(X0))),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(paramodulation,[status(thm)],[f39,f424]) ).
fof(f15312,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)],[f2178,f424]) ).
fof(f15313,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)],[f157,f424]) ).
fof(f15314,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)],[f176,f424]) ).
fof(f15315,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)],[f187,f424]) ).
fof(f15316,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)],[f185,f424]) ).
fof(f15317,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)],[f146,f424]) ).
fof(f15318,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)],[f139,f424]) ).
fof(f15322,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(domain(X1)))),X2)) = addition(antidomain(multiplication(X0,domain(X1))),addition(antidomain(multiplication(X0,domain(domain(X1)))),X2)),
inference(paramodulation,[status(thm)],[f424,f424]) ).
fof(f15323,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(domain(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,domain(domain(X1))))),
inference(paramodulation,[status(thm)],[f404,f424]) ).
fof(f15324,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),c(multiplication(X0,domain(X1)))) = addition(antidomain(multiplication(X0,domain(X1))),c(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f434,f424]) ).
fof(f15342,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)],[f227,f424]) ).
fof(f15343,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)],[f202,f424]) ).
fof(f15344,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)],[f187,f424]) ).
fof(f15345,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)],[f157,f424]) ).
fof(f15347,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)],[f966,f424]) ).
fof(f15348,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)],[f945,f424]) ).
fof(f15350,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)],[f92,f424]) ).
fof(f15351,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)],[f92,f424]) ).
fof(f15353,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)],[f33,f424]) ).
fof(f15354,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)],[f33,f424]) ).
fof(f15357,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(addition(antidomain(domain(X0)),X1),X0)),addition(antidomain(multiplication(X1,domain(X0))),X2)) = addition(antidomain(multiplication(addition(antidomain(domain(X0)),X1),domain(X0))),X2),
inference(paramodulation,[status(thm)],[f219,f424]) ).
fof(f15358,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(addition(X0,antidomain(domain(X1))),X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)) = addition(antidomain(multiplication(addition(X0,antidomain(domain(X1))),domain(X1))),X2),
inference(paramodulation,[status(thm)],[f225,f424]) ).
fof(f15361,plain,
! [X0,X1] : addition(antidomain(multiplication(domain(X0),X0)),addition(antidomain(domain(X0)),X1)) = addition(antidomain(multiplication(domain(X0),domain(X0))),X1),
inference(paramodulation,[status(thm)],[f2094,f424]) ).
fof(f15362,plain,
! [X0,X1] : addition(antidomain(multiplication(domain(domain(X0)),X0)),addition(antidomain(domain(X0)),X1)) = addition(antidomain(multiplication(domain(domain(X0)),domain(X0))),X1),
inference(paramodulation,[status(thm)],[f3965,f424]) ).
fof(f15363,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)],[f37,f424]) ).
fof(f15364,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)],[f2484,f424]) ).
fof(f15368,plain,
! [X0,X1] : addition(antidomain(multiplication(one,X0)),addition(antidomain(domain(X0)),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(paramodulation,[status(thm)],[f39,f424]) ).
fof(f15369,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)],[f14265,f424]) ).
fof(f15370,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)],[f14475,f424]) ).
fof(f15374,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)],[f8139,f424]) ).
fof(f15375,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)],[f64,f424]) ).
fof(f15377,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(antidomain(multiplication(X0,antidomain(c(X1)))),X2)) = addition(antidomain(multiplication(X0,domain(domain(X1)))),X2),
inference(paramodulation,[status(thm)],[f191,f424]) ).
fof(f15378,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,antidomain(X1))),addition(antidomain(multiplication(X0,c(X1))),X2)) = addition(antidomain(multiplication(X0,domain(antidomain(X1)))),X2),
inference(paramodulation,[status(thm)],[f316,f424]) ).
fof(f15387,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(antidomain(multiplication(X0,domain(X1))),X2)),antidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f424,f2484]) ).
fof(f15389,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)],[f424,f330]) ).
fof(f15395,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)],[f424,f335]) ).
fof(f15396,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)],[f424,f334]) ).
fof(f15397,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)],[f424,f297]) ).
fof(f15398,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)],[f424,f286]) ).
fof(f15399,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)],[f424,f285]) ).
fof(f15400,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)],[f424,f238]) ).
fof(f15401,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)],[f424,f237]) ).
fof(f15402,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)],[f424,f236]) ).
fof(f15403,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)],[f424,f228]) ).
fof(f15405,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)],[f424,f181]) ).
fof(f15407,plain,
! [X0,X1,X2,X3] : leq(antidomain(multiplication(X0,X1)),addition(X2,addition(antidomain(multiplication(X0,domain(X1))),X3))),
inference(paramodulation,[status(thm)],[f424,f1357]) ).
fof(f15410,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(paramodulation,[status(thm)],[f424,f1261]) ).
fof(f15412,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)],[f424,f98]) ).
fof(f15413,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)],[f424,f92]) ).
fof(f15414,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)],[f424,f92]) ).
fof(f15415,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)],[f424,f241]) ).
fof(f15416,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)],[f424,f47]) ).
fof(f15417,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)],[f424,f34]) ).
fof(f15421,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15287]) ).
fof(f15422,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15421]) ).
fof(f15433,plain,
! [X0,X1,X2] : addition(one,addition(antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),X2)) = addition(antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),X2),
inference(forward_demodulation,[status(thm)],[f523,f15296]) ).
fof(f15434,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(c(X0),domain(domain(X0)))),X1)) = addition(antidomain(multiplication(c(X0),domain(domain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f523,f15297]) ).
fof(f15435,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(c(X0),antidomain(c(X0)))),X1)) = addition(antidomain(multiplication(c(X0),domain(domain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15434]) ).
fof(f15436,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(c(X0),antidomain(c(X0)))),X1)) = addition(antidomain(multiplication(c(X0),antidomain(c(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15435]) ).
fof(f15443,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)],[f523,f15299]) ).
fof(f15444,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(multiplication(domain(X0),domain(domain(X0)))),X1)) = addition(antidomain(multiplication(domain(X0),domain(domain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f62,f15300]) ).
fof(f15445,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(multiplication(domain(X0),antidomain(c(X0)))),X1)) = addition(antidomain(multiplication(domain(X0),domain(domain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15444]) ).
fof(f15446,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(domain_difference(X0,c(X0))),X1)) = addition(antidomain(multiplication(domain(X0),domain(domain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f63,f15445]) ).
fof(f15447,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(domain_difference(X0,c(X0))),X1)) = addition(antidomain(multiplication(domain(X0),antidomain(c(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15446]) ).
fof(f15448,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(domain_difference(X0,c(X0))),X1)) = addition(antidomain(domain_difference(X0,c(X0))),X1),
inference(forward_demodulation,[status(thm)],[f63,f15447]) ).
fof(f15449,plain,
! [X0,X1,X2] : addition(antidomain(domain_difference(X0,X1)),addition(antidomain(multiplication(domain(X0),c(X1))),X2)) = addition(antidomain(multiplication(domain(X0),domain(antidomain(X1)))),X2),
inference(forward_demodulation,[status(thm)],[f316,f15301]) ).
fof(f15450,plain,
! [X0,X1,X2] : addition(antidomain(domain_difference(X0,X1)),addition(antidomain(multiplication(domain(X0),c(X1))),X2)) = addition(antidomain(multiplication(domain(X0),c(X1))),X2),
inference(forward_demodulation,[status(thm)],[f316,f15449]) ).
fof(f15451,plain,
! [X0,X1] : addition(antidomain(X0),addition(antidomain(domain(X0)),X1)) = addition(antidomain(multiplication(domain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f2094,f15302]) ).
fof(f15452,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(multiplication(domain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f62,f15451]) ).
fof(f15453,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f2094,f15452]) ).
fof(f15454,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f15453]) ).
fof(f15455,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)],[f37,f15303]) ).
fof(f15456,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)],[f37,f15455]) ).
fof(f15457,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)],[f523,f15304]) ).
fof(f15458,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(antidomain(X0),domain(domain(X0)))),X1)) = addition(antidomain(multiplication(antidomain(X0),domain(domain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f523,f15305]) ).
fof(f15459,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(antidomain(X0),antidomain(c(X0)))),X1)) = addition(antidomain(multiplication(antidomain(X0),domain(domain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15458]) ).
fof(f15460,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(antidomain(X0),antidomain(c(X0)))),X1)) = addition(antidomain(multiplication(antidomain(X0),antidomain(c(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15459]) ).
fof(f15461,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)],[f523,f15308]) ).
fof(f15474,plain,
! [X0,X1] : addition(antidomain(X0),addition(antidomain(domain(X0)),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f39,f15311]) ).
fof(f15475,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f62,f15474]) ).
fof(f15476,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f39,f15475]) ).
fof(f15477,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f15476]) ).
fof(f15478,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)],[f14265,f15313]) ).
fof(f15479,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)],[f92,f15478]) ).
fof(f15480,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)],[f38,f15479]) ).
fof(f15481,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)],[f14265,f15480]) ).
fof(f15482,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f38,f15481]) ).
fof(f15483,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)],[f14475,f15315]) ).
fof(f15484,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)],[f92,f15483]) ).
fof(f15485,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)],[f38,f15484]) ).
fof(f15486,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)],[f14475,f15485]) ).
fof(f15487,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(addition(X0,multiplication(X0,X2))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f38,f15486]) ).
fof(f15488,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)],[f523,f15317]) ).
fof(f15489,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)],[f523,f15318]) ).
fof(f15507,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,antidomain(c(X1)))),X2)) = addition(antidomain(multiplication(X0,domain(X1))),addition(antidomain(multiplication(X0,domain(domain(X1)))),X2)),
inference(forward_demodulation,[status(thm)],[f191,f15322]) ).
fof(f15508,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,antidomain(c(X1)))),X2)) = addition(antidomain(multiplication(X0,domain(domain(X1)))),X2),
inference(forward_demodulation,[status(thm)],[f424,f15507]) ).
fof(f15509,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,antidomain(c(X1)))),X2)) = addition(antidomain(multiplication(X0,antidomain(c(X1)))),X2),
inference(forward_demodulation,[status(thm)],[f191,f15508]) ).
fof(f15510,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(c(X1))))) = addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f191,f15323]) ).
fof(f15511,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(c(X1))))) = antidomain(multiplication(X0,domain(domain(X1)))),
inference(forward_demodulation,[status(thm)],[f404,f15510]) ).
fof(f15512,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(c(X1))))) = antidomain(multiplication(X0,antidomain(c(X1)))),
inference(forward_demodulation,[status(thm)],[f191,f15511]) ).
fof(f15513,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),c(multiplication(X0,domain(X1)))) = c(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f434,f15324]) ).
fof(f15532,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)],[f227,f15342]) ).
fof(f15533,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)],[f227,f15343]) ).
fof(f15534,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)],[f187,f15344]) ).
fof(f15535,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)],[f187,f15345]) ).
fof(f15537,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)],[f966,f15347]) ).
fof(f15538,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)],[f1266,f15348]) ).
fof(f15547,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(X2,antidomain(multiplication(addition(antidomain(domain(X1)),X0),X1)))) = addition(antidomain(multiplication(addition(antidomain(domain(X1)),X0),domain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f92,f15357]) ).
fof(f15548,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(X2,antidomain(multiplication(addition(c(X1),X0),X1)))) = addition(antidomain(multiplication(addition(antidomain(domain(X1)),X0),domain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f62,f15547]) ).
fof(f15549,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(X2,antidomain(multiplication(addition(c(X1),X0),X1)))) = addition(antidomain(multiplication(X0,domain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f219,f15548]) ).
fof(f15550,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(X2,antidomain(multiplication(addition(X0,antidomain(domain(X1))),X1)))) = addition(antidomain(multiplication(addition(X0,antidomain(domain(X1))),domain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f92,f15358]) ).
fof(f15551,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(X2,antidomain(multiplication(addition(X0,c(X1)),X1)))) = addition(antidomain(multiplication(addition(X0,antidomain(domain(X1))),domain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f62,f15550]) ).
fof(f15552,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(X2,antidomain(multiplication(addition(X0,c(X1)),X1)))) = addition(antidomain(multiplication(X0,domain(X1))),X2),
inference(forward_demodulation,[status(thm)],[f225,f15551]) ).
fof(f15566,plain,
! [X0,X1] : addition(antidomain(domain(X0)),addition(X1,antidomain(multiplication(domain(X0),X0)))) = addition(antidomain(multiplication(domain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f92,f15361]) ).
fof(f15567,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(domain(X0),X0)))) = addition(antidomain(multiplication(domain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f62,f15566]) ).
fof(f15568,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(X0))) = addition(antidomain(multiplication(domain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f3965,f15567]) ).
fof(f15569,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(multiplication(domain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f92,f15568]) ).
fof(f15570,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f2094,f15569]) ).
fof(f15571,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f15570]) ).
fof(f15572,plain,
! [X0,X1] : addition(antidomain(domain(X0)),addition(X1,antidomain(multiplication(domain(domain(X0)),X0)))) = addition(antidomain(multiplication(domain(domain(X0)),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f92,f15362]) ).
fof(f15573,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(domain(domain(X0)),X0)))) = addition(antidomain(multiplication(domain(domain(X0)),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f62,f15572]) ).
fof(f15574,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(antidomain(c(X0)),X0)))) = addition(antidomain(multiplication(domain(domain(X0)),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15573]) ).
fof(f15575,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(antidomain(c(X0)),X0)))) = addition(antidomain(domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f3965,f15574]) ).
fof(f15576,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(antidomain(c(X0)),X0)))) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f15575]) ).
fof(f15577,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)],[f37,f15363]) ).
fof(f15578,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)],[f37,f15577]) ).
fof(f15579,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)],[f92,f15364]) ).
fof(f15580,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)],[f523,f15579]) ).
fof(f15581,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)],[f2484,f15580]) ).
fof(f15582,plain,
! [X0,X1,X2] : addition(one,addition(X0,antidomain(multiplication(antidomain(addition(domain(X1),X2)),X1)))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f523,f15581]) ).
fof(f15602,plain,
! [X0,X1] : addition(antidomain(domain(X0)),addition(X1,antidomain(multiplication(one,X0)))) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f92,f15368]) ).
fof(f15603,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(one,X0)))) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f62,f15602]) ).
fof(f15604,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(X0))) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f39,f15603]) ).
fof(f15605,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f92,f15604]) ).
fof(f15606,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f39,f15605]) ).
fof(f15607,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f62,f15606]) ).
fof(f15608,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)],[f92,f15369]) ).
fof(f15609,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)],[f38,f15608]) ).
fof(f15610,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)],[f14265,f15609]) ).
fof(f15611,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,addition(one,X2))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f38,f15610]) ).
fof(f15612,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)],[f92,f15370]) ).
fof(f15613,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)],[f38,f15612]) ).
fof(f15614,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)],[f14475,f15613]) ).
fof(f15615,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,addition(X2,one))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f38,f15614]) ).
fof(f15622,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)],[f92,f15374]) ).
fof(f15623,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)],[f38,f15622]) ).
fof(f15624,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)],[f8139,f15623]) ).
fof(f15625,plain,
! [X0,X1,X2] : addition(antidomain(X0),addition(X1,antidomain(multiplication(X0,star(X2))))) = addition(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f38,f15624]) ).
fof(f15626,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)],[f92,f15375]) ).
fof(f15627,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)],[f64,f15626]) ).
fof(f15634,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,domain(X1))),addition(antidomain(multiplication(X0,antidomain(c(X1)))),X2)) = addition(antidomain(multiplication(X0,antidomain(c(X1)))),X2),
inference(forward_demodulation,[status(thm)],[f191,f15377]) ).
fof(f15635,plain,
! [X0,X1,X2] : addition(antidomain(multiplication(X0,antidomain(X1))),addition(antidomain(multiplication(X0,c(X1))),X2)) = addition(antidomain(multiplication(X0,c(X1))),X2),
inference(forward_demodulation,[status(thm)],[f316,f15378]) ).
fof(f15661,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)],[f15401]) ).
fof(f15662,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)],[f15402]) ).
fof(f15663,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,X1)),coantidomain(addition(antidomain(multiplication(X0,domain(X1))),X2))),
inference(forward_demodulation,[status(thm)],[f58,f15403]) ).
fof(f15664,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(antidomain(multiplication(X0,domain(X1))),X2)),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f54,f15405]) ).
fof(f15665,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)],[f98,f15412]) ).
fof(f15666,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)],[f92,f15665]) ).
fof(f15667,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)],[f98,f15666]) ).
fof(f15668,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)],[f98,f15413]) ).
fof(f15669,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)],[f98,f15414]) ).
fof(f15670,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)],[f92,f15669]) ).
fof(f15671,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)],[f424,f15670]) ).
fof(f15672,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(trivial_equality_resolution,[status(thm)],[f15416]) ).
fof(f15673,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)],[f98,f15417]) ).
fof(f15674,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)],[f98,f15673]) ).
fof(f15682,plain,
! [X0,X1,X2] : domain_difference(X0,addition(X1,addition(X2,one))) = zero,
inference(paramodulation,[status(thm)],[f98,f14474]) ).
fof(f15683,plain,
! [X0,X1,X2] : domain_difference(X0,addition(X1,addition(X2,one))) = zero,
inference(paramodulation,[status(thm)],[f34,f14474]) ).
fof(f15701,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f37,f14566]) ).
fof(f15706,plain,
! [X0] : multiplication(coantidomain(X0),domain(codomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f61,f14566]) ).
fof(f15714,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)],[f14566,f334]) ).
fof(f15715,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)],[f14566,f285]) ).
fof(f15716,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)],[f14566,f236]) ).
fof(f15719,plain,
! [X0] : backward_diamond(domain(coantidomain(codomain(X0))),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f14566,f65]) ).
fof(f15729,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f14566,f37]) ).
fof(f15741,plain,
! [X0,X1] : addition(antidomain(zero),addition(antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),X1),
inference(paramodulation,[status(thm)],[f14566,f424]) ).
fof(f15742,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(X1,domain(domain(coantidomain(X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(domain(coantidomain(X1)))))),
inference(paramodulation,[status(thm)],[f14566,f428]) ).
fof(f15743,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f14566,f405]) ).
fof(f15744,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)],[f14566,f327]) ).
fof(f15745,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)],[f14566,f327]) ).
fof(f15746,plain,
! [X0] :
( leq(multiplication(X0,multiplication(domain(coantidomain(X0)),star(domain(coantidomain(X0))))),X0)
| ~ leq(zero,X0) ),
inference(paramodulation,[status(thm)],[f14566,f337]) ).
fof(f15747,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(coantidomain(X1)))),X1)
| ~ leq(addition(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f14566,f324]) ).
fof(f15748,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)],[f14566,f291]) ).
fof(f15750,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),domain(coantidomain(X1)))
| ~ leq(addition(X0,zero),domain(coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f14566,f288]) ).
fof(f15753,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)],[f14566,f214]) ).
fof(f15754,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)],[f14566,f214]) ).
fof(f15755,plain,
! [X0] : multiplication(addition(X0,one),domain(coantidomain(X0))) = addition(domain(coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f14566,f227]) ).
fof(f15756,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)],[f14566,f206]) ).
fof(f15757,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)],[f14566,f206]) ).
fof(f15758,plain,
! [X0] : multiplication(addition(one,X0),domain(coantidomain(X0))) = addition(domain(coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f14566,f202]) ).
fof(f15759,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)],[f14566,f199]) ).
fof(f15760,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)],[f14566,f199]) ).
fof(f15761,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = addition(multiplication(X1,domain(coantidomain(X0))),zero),
inference(paramodulation,[status(thm)],[f14566,f196]) ).
fof(f15762,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = addition(zero,multiplication(X0,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f14566,f196]) ).
fof(f15763,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(X0,addition(X1,domain(coantidomain(X0)))),X2),
inference(paramodulation,[status(thm)],[f14566,f165]) ).
fof(f15764,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(domain(coantidomain(X0)),X1)),X2),
inference(paramodulation,[status(thm)],[f14566,f165]) ).
fof(f15767,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f14566,f148]) ).
fof(f15768,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f14566,f148]) ).
fof(f15771,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),domain(coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f14566,f561]) ).
fof(f15772,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))) = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f14566,f404]) ).
fof(f15773,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(coantidomain(X1)))),X1)
| ~ leq(addition(zero,X0),X1) ),
inference(paramodulation,[status(thm)],[f14566,f53]) ).
fof(f15774,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),domain(coantidomain(X1)))
| ~ leq(addition(zero,X0),domain(coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f14566,f51]) ).
fof(f15775,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = addition(multiplication(X0,domain(coantidomain(X1))),zero),
inference(paramodulation,[status(thm)],[f14566,f41]) ).
fof(f15776,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = addition(zero,multiplication(X1,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f14566,f41]) ).
fof(f15777,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f14566,f40]) ).
fof(f15778,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f14566,f40]) ).
fof(f15779,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f14566,f37]) ).
fof(f15784,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)],[f15714,f235]) ).
fof(f15785,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)],[f15715,f235]) ).
fof(f15786,plain,
! [X0] : backward_diamond(domain(coantidomain(codomain(X0))),X0) = zero,
inference(forward_demodulation,[status(thm)],[f678,f15719]) ).
fof(f15817,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),X1),
inference(forward_demodulation,[status(thm)],[f523,f15741]) ).
fof(f15818,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15817]) ).
fof(f15819,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),X1)) = addition(antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),X1),
inference(forward_demodulation,[status(thm)],[f191,f15818]) ).
fof(f15820,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(X1,domain(domain(coantidomain(X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(domain(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f42,f15742]) ).
fof(f15821,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(X1,domain(domain(coantidomain(X1))))))) = antidomain(multiplication(X0,multiplication(X1,domain(domain(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f523,f15820]) ).
fof(f15822,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(domain(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f1315,f15821]) ).
fof(f15823,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,antidomain(c(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f191,f15822]) ).
fof(f15824,plain,
! [X0] : leq(one,antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))),
inference(forward_demodulation,[status(thm)],[f523,f15743]) ).
fof(f15825,plain,
! [X0] : leq(one,antidomain(multiplication(X0,antidomain(c(coantidomain(X0)))))),
inference(forward_demodulation,[status(thm)],[f191,f15824]) ).
fof(f15826,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)],[f14566,f15744]) ).
fof(f15827,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)],[f42,f15745]) ).
fof(f15828,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(domain(coantidomain(X2)))),multiplication(X1,X2))
| ~ leq(X0,multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f75,f15827]) ).
fof(f15829,plain,
! [X0] : leq(multiplication(X0,multiplication(domain(coantidomain(X0)),star(domain(coantidomain(X0))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f15746,f235]) ).
fof(f15830,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(coantidomain(X1)))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f35,f15747]) ).
fof(f15831,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)],[f42,f15748]) ).
fof(f15832,plain,
! [X0,X1,X2] :
( leq(multiplication(star(multiplication(X2,X1)),X0),domain(coantidomain(X1)))
| ~ leq(X0,domain(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f75,f15831]) ).
fof(f15834,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),domain(coantidomain(X1)))
| ~ leq(X0,domain(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f35,f15750]) ).
fof(f15847,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)],[f92,f15753]) ).
fof(f15848,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)],[f75,f15847]) ).
fof(f15849,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)],[f75,f15754]) ).
fof(f15850,plain,
! [X0] : multiplication(addition(X0,one),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f15755]) ).
fof(f15851,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)],[f42,f15756]) ).
fof(f15852,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),domain(coantidomain(X2))) = multiplication(X0,domain(coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f35,f15851]) ).
fof(f15853,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)],[f75,f15757]) ).
fof(f15854,plain,
! [X0] : multiplication(addition(one,X0),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f15758]) ).
fof(f15855,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)],[f35,f15759]) ).
fof(f15856,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)],[f42,f15760]) ).
fof(f15857,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),domain(coantidomain(X1))) = multiplication(X2,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f75,f15856]) ).
fof(f15858,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = multiplication(X1,domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f15761]) ).
fof(f15859,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = multiplication(X0,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f75,f15762]) ).
fof(f15860,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)],[f92,f15763]) ).
fof(f15861,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,X2)) = addition(multiplication(X1,addition(X2,domain(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f75,f15860]) ).
fof(f15862,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),X2) = addition(multiplication(X0,addition(domain(coantidomain(X0)),X1)),X2),
inference(forward_demodulation,[status(thm)],[f75,f15764]) ).
fof(f15868,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f15767]) ).
fof(f15869,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f15768]) ).
fof(f15872,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(X0),domain(coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f638,f15771]) ).
fof(f15873,plain,
! [X0] : one = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1313,f15872]) ).
fof(f15874,plain,
! [X0] : addition(one,antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))) = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f523,f15772]) ).
fof(f15875,plain,
! [X0] : one = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f1315,f15874]) ).
fof(f15876,plain,
! [X0] : one = antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f191,f15875]) ).
fof(f15877,plain,
! [X0,X1] :
( leq(multiplication(X0,star(domain(coantidomain(X1)))),X1)
| ~ leq(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f75,f15773]) ).
fof(f15878,plain,
! [X0,X1] :
( leq(multiplication(star(X1),X0),domain(coantidomain(X1)))
| ~ leq(X0,domain(coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f75,f15774]) ).
fof(f15879,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = multiplication(X0,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f35,f15775]) ).
fof(f15880,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = multiplication(X1,domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f75,f15776]) ).
fof(f15881,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f35,f15777]) ).
fof(f15882,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f75,f15778]) ).
fof(f15883,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f43,f15779]) ).
fof(f15890,plain,
! [X0,X1] : forward_diamond(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f65,f14572]) ).
fof(f15945,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = one,
inference(paramodulation,[status(thm)],[f966,f14691]) ).
fof(f15946,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = one,
inference(paramodulation,[status(thm)],[f945,f14691]) ).
fof(f15948,plain,
! [X0,X1,X2] : backward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f92,f14691]) ).
fof(f15949,plain,
! [X0,X1,X2] : backward_box(X0,addition(X1,addition(one,X2))) = one,
inference(paramodulation,[status(thm)],[f92,f14691]) ).
fof(f15951,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = one,
inference(paramodulation,[status(thm)],[f33,f14691]) ).
fof(f15952,plain,
! [X0,X1] : backward_box(X0,addition(X1,one)) = one,
inference(paramodulation,[status(thm)],[f33,f14691]) ).
fof(f15972,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(c(backward_diamond(X0,c(X1))))) = one,
inference(paramodulation,[status(thm)],[f67,f514]) ).
fof(f15973,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(c(forward_diamond(X0,c(X1))))) = one,
inference(paramodulation,[status(thm)],[f66,f514]) ).
fof(f15982,plain,
! [X0,X1] : addition(c(backward_diamond(X0,c(X1))),antidomain(backward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f67,f514]) ).
fof(f15983,plain,
! [X0,X1] : addition(c(forward_diamond(X0,c(X1))),antidomain(forward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f66,f514]) ).
fof(f15989,plain,
! [X0] :
( leq(antidomain(c(X0)),c(X0))
| ~ leq(one,c(X0)) ),
inference(paramodulation,[status(thm)],[f514,f13227]) ).
fof(f15990,plain,
! [X0] :
( leq(multiplication(antidomain(c(X0)),star(c(X0))),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f514,f330]) ).
fof(f15996,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(antidomain(c(X1)),star(c(X1)))),X0)
| ~ leq(multiplication(X0,one),X0) ),
inference(paramodulation,[status(thm)],[f514,f335]) ).
fof(f15997,plain,
! [X0,X1] :
( leq(multiplication(antidomain(c(X1)),multiplication(X0,star(X0))),c(X1))
| ~ leq(multiplication(one,X0),c(X1)) ),
inference(paramodulation,[status(thm)],[f514,f334]) ).
fof(f15998,plain,
! [X0] :
( leq(multiplication(star(c(X0)),antidomain(c(X0))),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f514,f297]) ).
fof(f15999,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(c(X1)))),c(X1))
| ~ leq(multiplication(X0,one),c(X1)) ),
inference(paramodulation,[status(thm)],[f514,f286]) ).
fof(f16000,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),multiplication(antidomain(c(X1)),X0)),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(paramodulation,[status(thm)],[f514,f285]) ).
fof(f16001,plain,
! [X0,X1] :
( addition(X0,one) != antidomain(c(X1))
| leq(addition(X0,c(X1)),antidomain(c(X1))) ),
inference(paramodulation,[status(thm)],[f514,f238]) ).
fof(f16002,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,antidomain(c(X1)))
| leq(multiplication(X0,c(X1)),multiplication(X0,antidomain(c(X1)))) ),
inference(paramodulation,[status(thm)],[f514,f237]) ).
fof(f16003,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(antidomain(c(X0)),X1)
| leq(multiplication(c(X0),X1),multiplication(antidomain(c(X0)),X1)) ),
inference(paramodulation,[status(thm)],[f514,f236]) ).
fof(f16004,plain,
! [X0] : multiplication(one,coantidomain(antidomain(c(X0)))) = multiplication(c(X0),coantidomain(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f514,f228]) ).
fof(f16005,plain,
! [X0] : multiplication(one,coantidomain(c(X0))) = multiplication(antidomain(c(X0)),coantidomain(c(X0))),
inference(paramodulation,[status(thm)],[f514,f221]) ).
fof(f16007,plain,
! [X0] : multiplication(antidomain(c(X0)),one) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f514,f172]) ).
fof(f16013,plain,
! [X0,X1] : addition(antidomain(c(X0)),addition(c(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f514,f98]) ).
fof(f16014,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(c(X0)),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f514,f92]) ).
fof(f16015,plain,
! [X0,X1] : addition(X0,one) = addition(antidomain(c(X1)),addition(X0,c(X1))),
inference(paramodulation,[status(thm)],[f514,f92]) ).
fof(f16016,plain,
! [X0] :
( one != c(X0)
| leq(antidomain(c(X0)),c(X0)) ),
inference(paramodulation,[status(thm)],[f514,f241]) ).
fof(f16017,plain,
! [X0] :
( one != antidomain(c(X0))
| leq(c(X0),antidomain(c(X0))) ),
inference(paramodulation,[status(thm)],[f514,f47]) ).
fof(f16018,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(c(X0)),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f514,f34]) ).
fof(f16028,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f67,f15972]) ).
fof(f16029,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f66,f15973]) ).
fof(f16045,plain,
! [X0,X1] : addition(antidomain(backward_box(X0,X1)),c(backward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f33,f15982]) ).
fof(f16046,plain,
! [X0,X1] : addition(antidomain(backward_box(X0,X1)),backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f67,f16045]) ).
fof(f16047,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f33,f16046]) ).
fof(f16048,plain,
! [X0,X1] : addition(antidomain(forward_box(X0,X1)),c(forward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f33,f15983]) ).
fof(f16049,plain,
! [X0,X1] : addition(antidomain(forward_box(X0,X1)),forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f66,f16048]) ).
fof(f16050,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f33,f16049]) ).
fof(f16060,definition,
! [X0] :
( sQ43_spl
<=> leq(multiplication(antidomain(c(X0)),star(c(X0))),one) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f16061,plain,
! [X0] :
( ~ sQ43_spl
| leq(multiplication(antidomain(c(X0)),star(c(X0))),one) ),
inference(component_clause,[status(thm)],[f16060]) ).
fof(f16063,plain,
( sQ43_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15990,f8880,f16060]) ).
fof(f16076,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(antidomain(c(X1)),star(c(X1)))),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f38,f15996]) ).
fof(f16077,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(antidomain(c(X1)),star(c(X1)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[f16076,f234]) ).
fof(f16078,plain,
! [X0,X1] :
( leq(multiplication(antidomain(c(X1)),multiplication(X0,star(X0))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f15997]) ).
fof(f16079,definition,
! [X0] :
( sQ44_spl
<=> leq(multiplication(star(c(X0)),antidomain(c(X0))),one) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f16080,plain,
! [X0] :
( ~ sQ44_spl
| leq(multiplication(star(c(X0)),antidomain(c(X0))),one) ),
inference(component_clause,[status(thm)],[f16079]) ).
fof(f16082,plain,
( sQ44_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f15998,f8880,f16079]) ).
fof(f16083,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,antidomain(c(X1)))),c(X1))
| ~ leq(X0,c(X1)) ),
inference(forward_demodulation,[status(thm)],[f38,f15999]) ).
fof(f16084,plain,
! [X0,X1] :
( leq(multiplication(star(c(X1)),multiplication(antidomain(c(X1)),X0)),X0)
| ~ leq(X0,X0) ),
inference(forward_demodulation,[status(thm)],[f39,f16000]) ).
fof(f16085,plain,
! [X0,X1] : leq(multiplication(star(c(X0)),multiplication(antidomain(c(X0)),X1)),X1),
inference(forward_subsumption_resolution,[status(thm)],[f16084,f234]) ).
fof(f16086,plain,
! [X0,X1] :
( X0 != multiplication(X0,antidomain(c(X1)))
| leq(multiplication(X0,c(X1)),multiplication(X0,antidomain(c(X1)))) ),
inference(forward_demodulation,[status(thm)],[f38,f16002]) ).
fof(f16087,plain,
! [X0,X1] :
( X1 != multiplication(antidomain(c(X0)),X1)
| leq(multiplication(c(X0),X1),multiplication(antidomain(c(X0)),X1)) ),
inference(forward_demodulation,[status(thm)],[f39,f16003]) ).
fof(f16088,plain,
! [X0] : coantidomain(antidomain(c(X0))) = multiplication(c(X0),coantidomain(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f39,f16004]) ).
fof(f16089,plain,
! [X0] : coantidomain(c(X0)) = multiplication(antidomain(c(X0)),coantidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f39,f16005]) ).
fof(f16094,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f38,f16007]) ).
fof(f16097,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(c(X0)))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f92,f16013]) ).
fof(f16098,plain,
! [X0,X1] : addition(X0,one) = addition(c(X1),addition(antidomain(c(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f92,f16015]) ).
fof(f16131,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = one,
inference(paramodulation,[status(thm)],[f966,f14693]) ).
fof(f16132,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = one,
inference(paramodulation,[status(thm)],[f945,f14693]) ).
fof(f16134,plain,
! [X0,X1,X2] : forward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f92,f14693]) ).
fof(f16135,plain,
! [X0,X1,X2] : forward_box(X0,addition(X1,addition(one,X2))) = one,
inference(paramodulation,[status(thm)],[f92,f14693]) ).
fof(f16137,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = one,
inference(paramodulation,[status(thm)],[f33,f14693]) ).
fof(f16138,plain,
! [X0,X1] : forward_box(X0,addition(X1,one)) = one,
inference(paramodulation,[status(thm)],[f33,f14693]) ).
fof(f16156,plain,
! [X0,X1,X2] : backward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f98,f14900]) ).
fof(f16157,plain,
! [X0,X1,X2] : backward_box(X0,addition(X1,addition(X2,one))) = one,
inference(paramodulation,[status(thm)],[f34,f14900]) ).
fof(f16180,plain,
! [X0] :
( one != one
| leq(antidomain(addition(one,X0)),domain(addition(one,X0))) ),
inference(paramodulation,[status(thm)],[f14265,f512]) ).
fof(f16181,plain,
! [X0] :
( one != one
| leq(antidomain(addition(X0,one)),domain(addition(X0,one))) ),
inference(paramodulation,[status(thm)],[f14475,f512]) ).
fof(f16182,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(antidomain(forward_box(X0,X1)),domain(forward_box(X0,X1))) ),
inference(paramodulation,[status(thm)],[f12715,f512]) ).
fof(f16183,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(antidomain(backward_box(X0,X1)),domain(backward_box(X0,X1))) ),
inference(paramodulation,[status(thm)],[f12714,f512]) ).
fof(f16184,plain,
! [X0] :
( one != c(X0)
| leq(antidomain(c(X0)),domain(c(X0))) ),
inference(paramodulation,[status(thm)],[f12643,f512]) ).
fof(f16185,plain,
! [X0] :
( one != one
| leq(antidomain(star(X0)),domain(star(X0))) ),
inference(paramodulation,[status(thm)],[f8139,f512]) ).
fof(f16186,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(antidomain(multiplication(X0,domain(X1))),domain(multiplication(X0,domain(X1)))) ),
inference(paramodulation,[status(thm)],[f64,f512]) ).
fof(f16187,plain,
( one != zero
| leq(antidomain(zero),domain(zero)) ),
inference(paramodulation,[status(thm)],[f553,f512]) ).
fof(f16188,plain,
! [X0] :
( one != antidomain(c(X0))
| leq(antidomain(domain(X0)),domain(domain(X0))) ),
inference(paramodulation,[status(thm)],[f191,f512]) ).
fof(f16189,plain,
! [X0] :
( one != c(X0)
| leq(antidomain(antidomain(X0)),domain(antidomain(X0))) ),
inference(paramodulation,[status(thm)],[f316,f512]) ).
fof(f16190,plain,
( one != one
| leq(antidomain(one),domain(one)) ),
inference(paramodulation,[status(thm)],[f516,f512]) ).
fof(f16199,definition,
! [X0] :
( sQ45_spl
<=> leq(antidomain(addition(one,X0)),domain(addition(one,X0))) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f16202,plain,
( ~ sQ1_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f16180,f16199,f1463]) ).
fof(f16203,definition,
! [X0] :
( sQ46_spl
<=> leq(antidomain(addition(X0,one)),domain(addition(X0,one))) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f16206,plain,
( ~ sQ1_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f16181,f16203,f1463]) ).
fof(f16207,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(antidomain(forward_box(X0,X1)),forward_box(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f12715,f16182]) ).
fof(f16208,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(antidomain(backward_box(X0,X1)),backward_box(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f12714,f16183]) ).
fof(f16209,plain,
! [X0] :
( one != c(X0)
| leq(antidomain(c(X0)),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f12643,f16184]) ).
fof(f16210,definition,
! [X0] :
( sQ47_spl
<=> leq(antidomain(star(X0)),domain(star(X0))) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f16213,plain,
( ~ sQ1_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f16185,f16210,f1463]) ).
fof(f16214,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f64,f16186]) ).
fof(f16215,definition,
( sQ48_spl
<=> leq(antidomain(zero),domain(zero)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f16216,plain,
( ~ sQ48_spl
| leq(antidomain(zero),domain(zero)) ),
inference(component_clause,[status(thm)],[f16215]) ).
fof(f16218,definition,
( sQ49_spl
<=> one = zero ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f16221,plain,
( ~ sQ49_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f16187,f16215,f16218]) ).
fof(f16222,plain,
! [X0] :
( one != antidomain(c(X0))
| leq(c(X0),domain(domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f62,f16188]) ).
fof(f16223,plain,
! [X0] :
( one != antidomain(c(X0))
| leq(c(X0),antidomain(c(X0))) ),
inference(forward_demodulation,[status(thm)],[f191,f16222]) ).
fof(f16224,plain,
! [X0] :
( one != c(X0)
| leq(domain(X0),domain(antidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f57,f16189]) ).
fof(f16225,plain,
! [X0] :
( one != c(X0)
| leq(domain(X0),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f316,f16224]) ).
fof(f16226,definition,
( sQ50_spl
<=> leq(antidomain(one),domain(one)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f16229,plain,
( ~ sQ1_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f16190,f16226,f1463]) ).
fof(f16238,plain,
( ~ sQ48_spl
| leq(one,domain(zero)) ),
inference(forward_demodulation,[status(thm)],[f523,f16216]) ).
fof(f16239,plain,
( ~ sQ48_spl
| leq(one,zero) ),
inference(forward_demodulation,[status(thm)],[f553,f16238]) ).
fof(f16244,plain,
( ~ sQ48_spl
| addition(one,zero) = zero ),
inference(resolution,[status(thm)],[f16239,f46]) ).
fof(f16253,plain,
( ~ sQ48_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f35,f16244]) ).
fof(f16350,plain,
! [X0] :
( ~ sQ48_spl
| multiplication(zero,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f16253,f39]) ).
fof(f16751,plain,
! [X0] :
( ~ sQ48_spl
| zero = X0 ),
inference(paramodulation,[status(thm)],[f43,f16350]) ).
fof(f16853,plain,
! [X0,X1] :
( ~ sQ48_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f16751,f16751]) ).
fof(f16857,plain,
! [X0,X1] :
( ~ sQ48_spl
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f16751,f235]) ).
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
| sQ50_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE177+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n019.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 22:50:05 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.94/1.51 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.94/1.51 % SZS output start Saturation for theBenchmark
% See solution above
% 0.69/1.66 % Elapsed time: 1.294724 seconds
% 0.69/1.66 % CPU time: 8.967381 seconds
% 0.69/1.66 % Total memory used: 166.332 MB
% 0.69/1.66 % Net memory used: 156.700 MB
%------------------------------------------------------------------------------