%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE174+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 : n004.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 12:58:27 PM UTC 2026
% Result : Satisfiable 7.33s 1.50s
% 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,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,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(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f30,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f41,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f45,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)],[f14]) ).
fof(f46,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f47,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f48,plain,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f49,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)],[f18]) ).
fof(f50,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f51,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f52,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f53,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f54,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f55,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f56,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f57,plain,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f58,plain,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f59,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)],[f28]) ).
fof(f60,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)],[f59]) ).
fof(f65,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f31,f29]) ).
fof(f82,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f29,f30]) ).
fof(f84,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f32,f30]) ).
fof(f88,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f29,f30]) ).
fof(f90,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f32,f30]) ).
fof(f104,plain,
antidomain(one) = zero,
inference(paramodulation,[status(thm)],[f34,f44]) ).
fof(f111,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f44,f33]) ).
fof(f121,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f111]) ).
fof(f126,plain,
! [X0] : domain(antidomain(X0)) = antidomain(domain(X0)),
inference(paramodulation,[status(thm)],[f47,f47]) ).
fof(f127,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f104,f47]) ).
fof(f128,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f47,f44]) ).
fof(f129,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f33,f48]) ).
fof(f131,plain,
coantidomain(one) = zero,
inference(paramodulation,[status(thm)],[f35,f48]) ).
fof(f135,plain,
! [X0,X1] : multiplication(X0,multiplication(coantidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f48,f33]) ).
fof(f136,plain,
! [X0,X1] : multiplication(X0,multiplication(coantidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f135]) ).
fof(f138,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f29,f36]) ).
fof(f142,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f44,f36]) ).
fof(f145,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f48,f36]) ).
fof(f147,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f36]) ).
fof(f149,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f44,f36]) ).
fof(f152,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f48,f36]) ).
fof(f154,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f34,f36]) ).
fof(f155,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)],[f36,f30]) ).
fof(f162,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f142]) ).
fof(f166,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f145]) ).
fof(f171,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f149]) ).
fof(f175,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f152]) ).
fof(f177,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f154]) ).
fof(f178,plain,
! [X0] : codomain(coantidomain(X0)) = coantidomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f51,f51]) ).
fof(f179,plain,
codomain(one) = coantidomain(zero),
inference(paramodulation,[status(thm)],[f131,f51]) ).
fof(f180,plain,
! [X0] : multiplication(coantidomain(X0),codomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f51,f48]) ).
fof(f181,plain,
! [X0] : domain(domain(X0)) = antidomain(c(X0)),
inference(paramodulation,[status(thm)],[f52,f47]) ).
fof(f182,plain,
! [X0] : multiplication(c(X0),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f52,f44]) ).
fof(f186,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f29,f37]) ).
fof(f189,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)],[f33,f37]) ).
fof(f190,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f44,f37]) ).
fof(f192,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f37]) ).
fof(f193,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(zero,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f48,f37]) ).
fof(f196,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)],[f33,f37]) ).
fof(f197,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f44,f37]) ).
fof(f199,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f35,f37]) ).
fof(f200,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),zero),
inference(paramodulation,[status(thm)],[f48,f37]) ).
fof(f204,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)],[f37,f30]) ).
fof(f209,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f65,f190]) ).
fof(f211,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f65,f193]) ).
fof(f215,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f197]) ).
fof(f217,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f199]) ).
fof(f218,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f31,f200]) ).
fof(f224,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f43,f32]) ).
fof(f225,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f43,f65]) ).
fof(f226,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f37,f43]) ).
fof(f227,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f36,f43]) ).
fof(f228,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f30,f43]) ).
fof(f230,plain,
! [X0] :
( X0 != zero
| leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f31,f43]) ).
fof(f231,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f29,f43]) ).
fof(f236,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f47,f45]) ).
fof(f237,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f47,f236]) ).
fof(f238,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(resolution,[status(thm)],[f237,f43]) ).
fof(f239,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)],[f33,f237]) ).
fof(f240,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(X0)))) = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f44,f237]) ).
fof(f242,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(one,domain(X0)))) = antidomain(multiplication(one,domain(X0))),
inference(paramodulation,[status(thm)],[f35,f237]) ).
fof(f243,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(X0,domain(coantidomain(X0))))) = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f48,f237]) ).
fof(f250,plain,
! [X0] : addition(antidomain(multiplication(X0,one)),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,domain(one))),
inference(paramodulation,[status(thm)],[f127,f237]) ).
fof(f252,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)],[f237,f30]) ).
fof(f253,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)],[f33,f239]) ).
fof(f254,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)],[f33,f253]) ).
fof(f257,plain,
! [X0] : addition(antidomain(X0),antidomain(domain(X0))) = antidomain(multiplication(one,domain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f242]) ).
fof(f258,plain,
! [X0] : addition(antidomain(X0),c(X0)) = antidomain(multiplication(one,domain(X0))),
inference(forward_demodulation,[status(thm)],[f52,f257]) ).
fof(f259,plain,
! [X0] : addition(antidomain(X0),c(X0)) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f35,f258]) ).
fof(f260,plain,
! [X0] : addition(antidomain(X0),c(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f52,f259]) ).
fof(f277,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,domain(one))),
inference(forward_demodulation,[status(thm)],[f34,f250]) ).
fof(f278,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,antidomain(zero)))) = antidomain(multiplication(X0,antidomain(zero))),
inference(forward_demodulation,[status(thm)],[f127,f277]) ).
fof(f282,plain,
! [X0] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f29,f46]) ).
fof(f283,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f47,f282]) ).
fof(f284,plain,
! [X0] : addition(c(X0),domain(domain(X0))) = one,
inference(paramodulation,[status(thm)],[f52,f283]) ).
fof(f286,plain,
addition(zero,domain(one)) = one,
inference(paramodulation,[status(thm)],[f104,f283]) ).
fof(f287,plain,
addition(antidomain(one),antidomain(zero)) = one,
inference(paramodulation,[status(thm)],[f127,f283]) ).
fof(f288,plain,
! [X0] :
( one != domain(X0)
| leq(antidomain(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f283,f43]) ).
fof(f289,plain,
! [X0,X1] : addition(antidomain(X0),addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f283,f30]) ).
fof(f290,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f65,f286]) ).
fof(f291,plain,
addition(antidomain(zero),antidomain(one)) = one,
inference(forward_demodulation,[status(thm)],[f29,f287]) ).
fof(f292,plain,
addition(antidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f104,f291]) ).
fof(f293,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f31,f292]) ).
fof(f297,plain,
c(one) = antidomain(one),
inference(paramodulation,[status(thm)],[f290,f52]) ).
fof(f303,plain,
c(one) = zero,
inference(forward_demodulation,[status(thm)],[f104,f297]) ).
fof(f305,plain,
domain(zero) = antidomain(one),
inference(paramodulation,[status(thm)],[f293,f47]) ).
fof(f307,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f104,f305]) ).
fof(f308,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(forward_demodulation,[status(thm)],[f51,f49]) ).
fof(f309,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(codomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f51,f308]) ).
fof(f310,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(resolution,[status(thm)],[f309,f43]) ).
fof(f311,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)],[f33,f309]) ).
fof(f312,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),X0))) = coantidomain(multiplication(codomain(antidomain(X0)),X0)),
inference(paramodulation,[status(thm)],[f44,f309]) ).
fof(f313,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(zero),X0))) = coantidomain(multiplication(codomain(zero),X0)),
inference(paramodulation,[status(thm)],[f39,f309]) ).
fof(f314,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(one),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(paramodulation,[status(thm)],[f35,f309]) ).
fof(f315,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),coantidomain(X0)))) = coantidomain(multiplication(codomain(X0),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f48,f309]) ).
fof(f317,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(X0),one))) = coantidomain(multiplication(codomain(X0),one)),
inference(paramodulation,[status(thm)],[f34,f309]) ).
fof(f318,plain,
! [X0] : addition(coantidomain(multiplication(X0,coantidomain(codomain(X0)))),coantidomain(zero)) = coantidomain(multiplication(codomain(X0),coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f48,f309]) ).
fof(f320,plain,
! [X0] : addition(coantidomain(multiplication(X0,one)),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(paramodulation,[status(thm)],[f34,f309]) ).
fof(f321,plain,
! [X0] : addition(coantidomain(multiplication(one,X0)),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(paramodulation,[status(thm)],[f179,f309]) ).
fof(f322,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)],[f309,f43]) ).
fof(f323,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)],[f309,f30]) ).
fof(f324,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(forward_demodulation,[status(thm)],[f179,f314]) ).
fof(f325,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(coantidomain(zero),X0)),
inference(forward_demodulation,[status(thm)],[f179,f324]) ).
fof(f328,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f34,f317]) ).
fof(f329,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f328]) ).
fof(f330,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(X0,coantidomain(codomain(X0))))) = coantidomain(multiplication(codomain(X0),coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f29,f318]) ).
fof(f331,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(X0,coantidomain(codomain(X0))))) = coantidomain(zero),
inference(forward_demodulation,[status(thm)],[f48,f330]) ).
fof(f335,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,one))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f29,f320]) ).
fof(f336,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(X0)) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f34,f335]) ).
fof(f337,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f29,f336]) ).
fof(f338,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f337]) ).
fof(f339,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(codomain(one),X0)),
inference(forward_demodulation,[status(thm)],[f35,f321]) ).
fof(f340,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(coantidomain(zero),X0))) = coantidomain(multiplication(coantidomain(zero),X0)),
inference(forward_demodulation,[status(thm)],[f179,f339]) ).
fof(f341,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(trivial_equality_resolution,[status(thm)],[f322]) ).
fof(f345,plain,
c(zero) = antidomain(zero),
inference(paramodulation,[status(thm)],[f307,f52]) ).
fof(f352,plain,
c(zero) = one,
inference(forward_demodulation,[status(thm)],[f293,f345]) ).
fof(f353,plain,
! [X0] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f29,f50]) ).
fof(f354,plain,
! [X0] : addition(coantidomain(X0),codomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f51,f353]) ).
fof(f355,plain,
! [X0] : addition(codomain(X0),codomain(coantidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f51,f354]) ).
fof(f356,plain,
addition(zero,codomain(one)) = one,
inference(paramodulation,[status(thm)],[f131,f354]) ).
fof(f357,plain,
addition(coantidomain(one),coantidomain(zero)) = one,
inference(paramodulation,[status(thm)],[f179,f354]) ).
fof(f358,plain,
! [X0] :
( one != codomain(X0)
| leq(coantidomain(X0),codomain(X0)) ),
inference(paramodulation,[status(thm)],[f354,f43]) ).
fof(f359,plain,
! [X0,X1] : addition(coantidomain(X0),addition(codomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f354,f30]) ).
fof(f360,plain,
codomain(one) = one,
inference(forward_demodulation,[status(thm)],[f65,f356]) ).
fof(f361,plain,
addition(coantidomain(zero),coantidomain(one)) = one,
inference(forward_demodulation,[status(thm)],[f29,f357]) ).
fof(f362,plain,
addition(coantidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f131,f361]) ).
fof(f363,plain,
coantidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f31,f362]) ).
fof(f373,plain,
codomain(zero) = coantidomain(one),
inference(paramodulation,[status(thm)],[f363,f51]) ).
fof(f375,plain,
codomain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f131,f373]) ).
fof(f384,plain,
! [X0] : domain_difference(zero,X0) = multiplication(zero,antidomain(X0)),
inference(paramodulation,[status(thm)],[f307,f53]) ).
fof(f385,plain,
! [X0] : domain_difference(one,X0) = multiplication(one,antidomain(X0)),
inference(paramodulation,[status(thm)],[f290,f53]) ).
fof(f386,plain,
! [X0] : domain_difference(X0,zero) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f293,f53]) ).
fof(f387,plain,
! [X0,X1] : domain_difference(X0,domain(X1)) = multiplication(domain(X0),c(X1)),
inference(paramodulation,[status(thm)],[f52,f53]) ).
fof(f388,plain,
! [X0,X1] : domain_difference(X0,antidomain(X1)) = multiplication(domain(X0),domain(X1)),
inference(paramodulation,[status(thm)],[f47,f53]) ).
fof(f389,plain,
! [X0] : domain_difference(X0,one) = multiplication(domain(X0),zero),
inference(paramodulation,[status(thm)],[f104,f53]) ).
fof(f390,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)],[f53,f309]) ).
fof(f391,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)],[f53,f237]) ).
fof(f392,plain,
! [X0,X1,X2] : multiplication(addition(X0,domain(X1)),antidomain(X2)) = addition(multiplication(X0,antidomain(X2)),domain_difference(X1,X2)),
inference(paramodulation,[status(thm)],[f53,f37]) ).
fof(f393,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),X1),antidomain(X2)) = addition(domain_difference(X0,X2),multiplication(X1,antidomain(X2))),
inference(paramodulation,[status(thm)],[f53,f37]) ).
fof(f394,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(X1,antidomain(X2))) = addition(multiplication(domain(X0),X1),domain_difference(X0,X2)),
inference(paramodulation,[status(thm)],[f53,f36]) ).
fof(f395,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(antidomain(X1),X2)) = addition(domain_difference(X0,X1),multiplication(domain(X0),X2)),
inference(paramodulation,[status(thm)],[f53,f36]) ).
fof(f396,plain,
! [X0,X1,X2] : multiplication(domain(X0),multiplication(antidomain(X1),X2)) = multiplication(domain_difference(X0,X1),X2),
inference(paramodulation,[status(thm)],[f53,f33]) ).
fof(f397,plain,
! [X0] : domain_difference(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f39,f384]) ).
fof(f398,plain,
! [X0] : domain_difference(one,X0) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f385]) ).
fof(f399,plain,
! [X0] : domain_difference(X0,zero) = domain(X0),
inference(forward_demodulation,[status(thm)],[f34,f386]) ).
fof(f400,plain,
! [X0] : domain_difference(X0,one) = zero,
inference(forward_demodulation,[status(thm)],[f38,f389]) ).
fof(f438,plain,
! [X0,X1,X2] : forward_diamond(multiplication(X0,X1),X2) = domain(multiplication(X0,multiplication(X1,domain(X2)))),
inference(paramodulation,[status(thm)],[f33,f54]) ).
fof(f439,plain,
! [X0] : forward_diamond(antidomain(domain(X0)),X0) = domain(zero),
inference(paramodulation,[status(thm)],[f44,f54]) ).
fof(f440,plain,
! [X0] : forward_diamond(zero,X0) = domain(zero),
inference(paramodulation,[status(thm)],[f39,f54]) ).
fof(f441,plain,
! [X0] : forward_diamond(one,X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f35,f54]) ).
fof(f442,plain,
! [X0,X1,X2] : forward_diamond(X0,multiplication(X1,domain(X2))) = domain(multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f54,f54]) ).
fof(f443,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f307,f54]) ).
fof(f444,plain,
! [X0] : forward_diamond(X0,one) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f290,f54]) ).
fof(f445,plain,
! [X0,X1,X2] : domain_difference(multiplication(X0,domain(X1)),X2) = multiplication(forward_diamond(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f54,f53]) ).
fof(f446,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f54,f283]) ).
fof(f447,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)],[f54,f237]) ).
fof(f448,plain,
! [X0,X1] : c(multiplication(X0,domain(X1))) = antidomain(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f54,f52]) ).
fof(f449,plain,
! [X0] : forward_diamond(c(X0),X0) = domain(zero),
inference(forward_demodulation,[status(thm)],[f52,f439]) ).
fof(f450,plain,
! [X0] : forward_diamond(c(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f307,f449]) ).
fof(f451,plain,
! [X0] : forward_diamond(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f307,f440]) ).
fof(f452,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f38,f443]) ).
fof(f453,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f307,f452]) ).
fof(f454,plain,
! [X0] : forward_diamond(X0,one) = domain(X0),
inference(forward_demodulation,[status(thm)],[f34,f444]) ).
fof(f455,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f29,f446]) ).
fof(f456,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)],[f29,f447]) ).
fof(f457,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)],[f54,f456]) ).
fof(f476,plain,
! [X0] : backward_diamond(coantidomain(codomain(X0)),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f48,f55]) ).
fof(f477,plain,
! [X0] : backward_diamond(zero,X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f38,f55]) ).
fof(f478,plain,
! [X0] : backward_diamond(one,X0) = codomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f34,f55]) ).
fof(f479,plain,
! [X0,X1,X2] : backward_diamond(X0,multiplication(codomain(X1),X2)) = codomain(multiplication(backward_diamond(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f55,f55]) ).
fof(f480,plain,
! [X0] : backward_diamond(X0,zero) = codomain(multiplication(zero,X0)),
inference(paramodulation,[status(thm)],[f375,f55]) ).
fof(f481,plain,
! [X0] : backward_diamond(X0,one) = codomain(multiplication(one,X0)),
inference(paramodulation,[status(thm)],[f360,f55]) ).
fof(f482,plain,
! [X0,X1] : addition(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = one,
inference(paramodulation,[status(thm)],[f55,f354]) ).
fof(f483,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)],[f55,f309]) ).
fof(f484,plain,
! [X0] : backward_diamond(coantidomain(codomain(X0)),X0) = zero,
inference(forward_demodulation,[status(thm)],[f375,f476]) ).
fof(f485,plain,
! [X0] : backward_diamond(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f375,f477]) ).
fof(f486,plain,
! [X0] : backward_diamond(X0,zero) = codomain(zero),
inference(forward_demodulation,[status(thm)],[f39,f480]) ).
fof(f487,plain,
! [X0] : backward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f375,f486]) ).
fof(f488,plain,
! [X0] : backward_diamond(X0,one) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f481]) ).
fof(f489,plain,
! [X0,X1] : addition(backward_diamond(X0,X1),coantidomain(multiplication(codomain(X1),X0))) = one,
inference(forward_demodulation,[status(thm)],[f29,f482]) ).
fof(f490,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)],[f29,f483]) ).
fof(f491,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)],[f33,f490]) ).
fof(f492,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)],[f55,f491]) ).
fof(f507,plain,
! [X0] : forward_box(c(c(X0)),X0) = c(zero),
inference(paramodulation,[status(thm)],[f450,f56]) ).
fof(f508,plain,
! [X0] : forward_box(zero,X0) = c(zero),
inference(paramodulation,[status(thm)],[f451,f56]) ).
fof(f509,plain,
! [X0,X1,X2] : forward_box(X0,forward_diamond(X1,c(X2))) = c(forward_diamond(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f56,f56]) ).
fof(f510,plain,
! [X0] : forward_box(X0,zero) = c(forward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f352,f56]) ).
fof(f511,plain,
! [X0] : forward_box(X0,one) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f303,f56]) ).
fof(f512,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f56,f450]) ).
fof(f513,plain,
! [X0] : forward_box(c(c(X0)),X0) = one,
inference(forward_demodulation,[status(thm)],[f352,f507]) ).
fof(f514,plain,
! [X0] : forward_box(zero,X0) = one,
inference(forward_demodulation,[status(thm)],[f352,f508]) ).
fof(f515,plain,
! [X0] : forward_box(X0,zero) = c(domain(X0)),
inference(forward_demodulation,[status(thm)],[f454,f510]) ).
fof(f516,plain,
! [X0] : forward_box(X0,one) = c(zero),
inference(forward_demodulation,[status(thm)],[f453,f511]) ).
fof(f517,plain,
! [X0] : forward_box(X0,one) = one,
inference(forward_demodulation,[status(thm)],[f352,f516]) ).
fof(f520,plain,
zero = divergence(zero),
inference(paramodulation,[status(thm)],[f451,f58]) ).
fof(f526,plain,
! [X0] : backward_box(zero,X0) = c(zero),
inference(paramodulation,[status(thm)],[f485,f57]) ).
fof(f527,plain,
! [X0,X1,X2] : backward_box(X0,backward_diamond(X1,c(X2))) = c(backward_diamond(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f57,f57]) ).
fof(f528,plain,
! [X0,X1,X2] : backward_box(X0,forward_diamond(X1,c(X2))) = c(backward_diamond(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f529,plain,
! [X0] : backward_box(X0,zero) = c(backward_diamond(X0,one)),
inference(paramodulation,[status(thm)],[f352,f57]) ).
fof(f530,plain,
! [X0] : backward_box(X0,one) = c(backward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f303,f57]) ).
fof(f531,plain,
! [X0,X1,X2] : forward_box(X0,backward_diamond(X1,c(X2))) = c(forward_diamond(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f57,f56]) ).
fof(f532,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f57,f450]) ).
fof(f533,plain,
! [X0] : backward_box(zero,X0) = one,
inference(forward_demodulation,[status(thm)],[f352,f526]) ).
fof(f534,plain,
! [X0] : backward_box(X0,zero) = c(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f488,f529]) ).
fof(f535,plain,
! [X0] : backward_box(X0,one) = c(zero),
inference(forward_demodulation,[status(thm)],[f487,f530]) ).
fof(f536,plain,
! [X0] : backward_box(X0,one) = one,
inference(forward_demodulation,[status(thm)],[f352,f535]) ).
fof(f542,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)],[f309,f231]) ).
fof(f543,plain,
! [X0] :
( one != coantidomain(X0)
| leq(codomain(X0),coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f354,f231]) ).
fof(f544,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)],[f237,f231]) ).
fof(f545,plain,
! [X0] :
( one != antidomain(X0)
| leq(domain(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f283,f231]) ).
fof(f546,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f37,f231]) ).
fof(f547,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f36,f231]) ).
fof(f548,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f30,f231]) ).
fof(f556,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)],[f54,f60]) ).
fof(f558,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)],[f290,f60]) ).
fof(f559,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)],[f29,f60]) ).
fof(f560,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)],[f29,f60]) ).
fof(f561,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)],[f450,f60]) ).
fof(f562,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)],[f451,f60]) ).
fof(f563,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)],[f54,f60]) ).
fof(f565,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)],[f290,f60]) ).
fof(f566,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)],[f54,f60]) ).
fof(f567,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)],[f307,f60]) ).
fof(f568,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)],[f290,f60]) ).
fof(f569,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)],[f54,f556]) ).
fof(f570,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)],[f54,f569]) ).
fof(f571,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)],[f54,f570]) ).
fof(f580,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)],[f290,f558]) ).
fof(f581,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(domain(X0),domain(X1))) != addition(forward_diamond(X0,domain(one)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f454,f580]) ).
fof(f582,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(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f290,f581]) ).
fof(f583,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(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f454,f582]) ).
fof(f584,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)],[f290,f583]) ).
fof(f585,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)],[f65,f561]) ).
fof(f586,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)],[f450,f585]) ).
fof(f587,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)],[f65,f586]) ).
fof(f588,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)],[f65,f562]) ).
fof(f589,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)],[f451,f588]) ).
fof(f590,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)],[f65,f589]) ).
fof(f591,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)],[f520,f590]) ).
fof(f592,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)],[f65,f591]) ).
fof(f593,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)],[f520,f592]) ).
fof(f594,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)],[f65,f593]) ).
fof(f595,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)],[f54,f563]) ).
fof(f596,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)],[f54,f595]) ).
fof(f597,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)],[f54,f596]) ).
fof(f606,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)],[f290,f565]) ).
fof(f607,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(domain(X0),domain(X1))) != addition(forward_diamond(X0,domain(one)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f454,f606]) ).
fof(f608,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(domain(X0),domain(X1))) != addition(forward_diamond(X0,one),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f290,f607]) ).
fof(f609,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(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f454,f608]) ).
fof(f610,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)],[f290,f609]) ).
fof(f611,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)],[f54,f566]) ).
fof(f612,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)],[f54,f611]) ).
fof(f613,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)],[f54,f612]) ).
fof(f614,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)],[f31,f567]) ).
fof(f615,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)],[f29,f614]) ).
fof(f616,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)],[f307,f615]) ).
fof(f617,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)],[f65,f616]) ).
fof(f618,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)],[f307,f617]) ).
fof(f619,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)],[f453,f618]) ).
fof(f620,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)],[f31,f619]) ).
fof(f621,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)],[f307,f620]) ).
fof(f622,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)],[f453,f621]) ).
fof(f623,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)],[f31,f622]) ).
fof(f624,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)],[f29,f568]) ).
fof(f625,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)],[f29,f624]) ).
fof(f626,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)],[f290,f625]) ).
fof(f627,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)],[f290,f626]) ).
fof(f628,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),domain(star(X1)))) = 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)],[f454,f627]) ).
fof(f629,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),domain(star(X1)))) = 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)],[f290,f628]) ).
fof(f630,plain,
! [X0,X1] :
( addition(domain(X0),addition(divergence(X1),domain(star(X1)))) = addition(divergence(X1),domain(star(X1)))
| addition(domain(X0),addition(one,forward_diamond(X1,domain(X0)))) != addition(one,forward_diamond(X1,domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f454,f629]) ).
fof(f631,plain,
! [X0] : domain(antidomain(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f52,f126]) ).
fof(f633,plain,
! [X0] : domain(c(X0)) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f52,f631]) ).
fof(f634,plain,
! [X0] : domain(domain(X0)) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f47,f631]) ).
fof(f636,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)],[f631,f60]) ).
fof(f637,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)],[f631,f60]) ).
fof(f638,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)],[f631,f60]) ).
fof(f639,plain,
! [X0,X1] : forward_diamond(X0,antidomain(X1)) = domain(multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f631,f54]) ).
fof(f640,plain,
! [X0,X1] : domain_difference(antidomain(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f631,f53]) ).
fof(f641,plain,
! [X0] : addition(antidomain(antidomain(X0)),c(X0)) = one,
inference(paramodulation,[status(thm)],[f631,f283]) ).
fof(f642,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))) = antidomain(multiplication(X0,domain(antidomain(X1)))),
inference(paramodulation,[status(thm)],[f631,f237]) ).
fof(f646,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)],[f631,f636]) ).
fof(f647,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)],[f631,f646]) ).
fof(f648,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)],[f631,f647]) ).
fof(f649,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)],[f631,f637]) ).
fof(f650,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)],[f631,f649]) ).
fof(f651,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)],[f631,f650]) ).
fof(f652,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)],[f631,f638]) ).
fof(f653,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)],[f631,f652]) ).
fof(f654,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)],[f631,f653]) ).
fof(f655,plain,
! [X0] : addition(c(X0),antidomain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f29,f641]) ).
fof(f656,plain,
! [X0] : addition(c(X0),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f47,f655]) ).
fof(f657,plain,
! [X0] : addition(domain(X0),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f29,f656]) ).
fof(f658,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))) = antidomain(multiplication(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f631,f642]) ).
fof(f659,plain,
! [X0] : domain_difference(X0,X0) = zero,
inference(forward_demodulation,[status(thm)],[f53,f128]) ).
fof(f673,plain,
! [X0,X1] : backward_diamond(X0,coantidomain(X1)) = codomain(multiplication(coantidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f178,f55]) ).
fof(f674,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(codomain(X0))) = one,
inference(paramodulation,[status(thm)],[f178,f354]) ).
fof(f675,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)],[f178,f309]) ).
fof(f681,plain,
! [X0] : addition(codomain(X0),coantidomain(codomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f51,f674]) ).
fof(f682,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)],[f178,f675]) ).
fof(f683,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f30,f82]) ).
fof(f687,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f29,f82]) ).
fof(f688,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f29,f82]) ).
fof(f689,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(addition(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f32,f82]) ).
fof(f690,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)],[f309,f82]) ).
fof(f691,plain,
! [X0,X1] : addition(X0,one) = addition(codomain(X1),addition(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f354,f82]) ).
fof(f692,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)],[f237,f82]) ).
fof(f693,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f283,f82]) ).
fof(f694,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)],[f37,f82]) ).
fof(f695,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)],[f36,f82]) ).
fof(f696,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f30,f82]) ).
fof(f698,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X2),addition(X0,X3)),
inference(paramodulation,[status(thm)],[f82,f82]) ).
fof(f699,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X3,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f82,f82]) ).
fof(f701,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f29,f82]) ).
fof(f702,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f29,f82]) ).
fof(f703,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f32,f82]) ).
fof(f704,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f30,f82]) ).
fof(f710,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f32,f82]) ).
fof(f711,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)],[f309,f82]) ).
fof(f712,plain,
! [X0,X1] : addition(coantidomain(X0),addition(codomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f354,f82]) ).
fof(f713,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)],[f237,f82]) ).
fof(f714,plain,
! [X0,X1] : addition(antidomain(X0),addition(domain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f283,f82]) ).
fof(f715,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)],[f37,f82]) ).
fof(f716,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)],[f36,f82]) ).
fof(f717,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(X3,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f30,f82]) ).
fof(f719,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f82,f82]) ).
fof(f720,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f82,f82]) ).
fof(f722,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f82]) ).
fof(f723,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f82]) ).
fof(f724,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f32,f82]) ).
fof(f725,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)],[f82,f60]) ).
fof(f726,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f82,f30]) ).
fof(f728,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f82,f231]) ).
fof(f729,plain,
! [X0,X1,X2] :
( addition(X2,addition(X0,X1)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f82,f43]) ).
fof(f730,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X2,addition(X0,X1)),X3),
inference(paramodulation,[status(thm)],[f82,f30]) ).
fof(f731,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f82,f29]) ).
fof(f732,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f82,f29]) ).
fof(f733,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f82,f32]) ).
fof(f734,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f82,f30]) ).
fof(f736,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f82,f231]) ).
fof(f737,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f82,f43]) ).
fof(f738,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X1,addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f82,f30]) ).
fof(f741,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f82,f32]) ).
fof(f742,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f30,f683]) ).
fof(f744,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,addition(X1,X0))),
inference(forward_demodulation,[status(thm)],[f30,f689]) ).
fof(f745,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)],[f82,f690]) ).
fof(f746,plain,
! [X0,X1] : addition(X0,one) = addition(coantidomain(X1),addition(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f691]) ).
fof(f747,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)],[f82,f692]) ).
fof(f748,plain,
! [X0,X1] : addition(X0,one) = addition(antidomain(X1),addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f693]) ).
fof(f750,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f30,f698]) ).
fof(f751,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f30,f699]) ).
fof(f752,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f30,f717]) ).
fof(f754,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f30,f719]) ).
fof(f755,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f30,f720]) ).
fof(f757,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f30,f726]) ).
fof(f759,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,addition(X0,X1)),X3),
inference(forward_demodulation,[status(thm)],[f30,f730]) ).
fof(f760,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(addition(X0,X1),X3)),
inference(forward_demodulation,[status(thm)],[f30,f759]) ).
fof(f761,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f30,f760]) ).
fof(f762,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f30,f733]) ).
fof(f763,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f30,f738]) ).
fof(f764,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(addition(X2,X0),X3)),
inference(forward_demodulation,[status(thm)],[f30,f763]) ).
fof(f765,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f30,f764]) ).
fof(f771,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f55,f180]) ).
fof(f774,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0)))) = coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0))),
inference(paramodulation,[status(thm)],[f180,f309]) ).
fof(f775,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))) = antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f180,f237]) ).
fof(f776,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = addition(multiplication(X0,codomain(X1)),zero),
inference(paramodulation,[status(thm)],[f180,f37]) ).
fof(f777,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = addition(zero,multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f180,f37]) ).
fof(f778,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f180,f36]) ).
fof(f779,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = addition(zero,multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f180,f36]) ).
fof(f780,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f180,f33]) ).
fof(f786,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0)))) = coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0))),
inference(forward_demodulation,[status(thm)],[f363,f774]) ).
fof(f787,plain,
! [X0] : addition(one,coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0)))) = coantidomain(multiplication(codomain(coantidomain(X0)),codomain(X0))),
inference(forward_demodulation,[status(thm)],[f178,f786]) ).
fof(f788,plain,
! [X0] : addition(one,coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0)))) = coantidomain(multiplication(coantidomain(codomain(X0)),codomain(X0))),
inference(forward_demodulation,[status(thm)],[f178,f787]) ).
fof(f789,plain,
! [X0] : addition(one,antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))) = antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f293,f775]) ).
fof(f790,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f31,f776]) ).
fof(f791,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f65,f777]) ).
fof(f792,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f778]) ).
fof(f793,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f779]) ).
fof(f794,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f780]) ).
fof(f795,plain,
! [X0] : domain(antidomain(c(X0))) = antidomain(c(domain(X0))),
inference(paramodulation,[status(thm)],[f181,f181]) ).
fof(f796,plain,
! [X0] : domain(c(X0)) = antidomain(c(antidomain(X0))),
inference(paramodulation,[status(thm)],[f631,f181]) ).
fof(f797,plain,
! [X0,X1] : domain(forward_diamond(X0,X1)) = antidomain(c(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f54,f181]) ).
fof(f800,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)],[f181,f60]) ).
fof(f801,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)],[f181,f60]) ).
fof(f802,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)],[f181,f60]) ).
fof(f803,plain,
! [X0,X1] : forward_diamond(X0,domain(X1)) = domain(multiplication(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f181,f54]) ).
fof(f804,plain,
! [X0,X1] : domain_difference(domain(X0),X1) = multiplication(antidomain(c(X0)),antidomain(X1)),
inference(paramodulation,[status(thm)],[f181,f53]) ).
fof(f805,plain,
! [X0] : addition(antidomain(domain(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f181,f283]) ).
fof(f806,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)],[f181,f237]) ).
fof(f808,plain,
! [X0] : c(c(X0)) = antidomain(c(domain(X0))),
inference(forward_demodulation,[status(thm)],[f631,f795]) ).
fof(f813,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)],[f181,f800]) ).
fof(f814,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)],[f181,f813]) ).
fof(f815,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)],[f181,f814]) ).
fof(f816,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)],[f181,f801]) ).
fof(f817,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)],[f181,f816]) ).
fof(f818,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)],[f181,f817]) ).
fof(f819,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)],[f181,f802]) ).
fof(f820,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)],[f181,f819]) ).
fof(f821,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)],[f181,f820]) ).
fof(f822,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f52,f805]) ).
fof(f823,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)],[f181,f806]) ).
fof(f826,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f57,f182]) ).
fof(f827,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f56,f182]) ).
fof(f830,plain,
! [X0] : multiplication(c(domain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f181,f182]) ).
fof(f831,plain,
! [X0] : multiplication(c(antidomain(X0)),c(X0)) = zero,
inference(paramodulation,[status(thm)],[f631,f182]) ).
fof(f832,plain,
! [X0,X1] : multiplication(c(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f54,f182]) ).
fof(f836,plain,
! [X0] : addition(antidomain(multiplication(c(X0),X0)),antidomain(zero)) = antidomain(multiplication(c(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f182,f237]) ).
fof(f837,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(c(X0)),domain(X0)))) = coantidomain(multiplication(codomain(c(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f182,f309]) ).
fof(f838,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),domain(domain(X0))))) = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f182,f237]) ).
fof(f839,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = addition(multiplication(X0,domain(X1)),zero),
inference(paramodulation,[status(thm)],[f182,f37]) ).
fof(f840,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = addition(zero,multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f182,f37]) ).
fof(f841,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f182,f36]) ).
fof(f842,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f182,f36]) ).
fof(f843,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f182,f33]) ).
fof(f848,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(c(X0),X0))) = antidomain(multiplication(c(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f836]) ).
fof(f849,plain,
! [X0] : addition(one,antidomain(multiplication(c(X0),X0))) = antidomain(multiplication(c(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f293,f848]) ).
fof(f850,plain,
! [X0] : addition(one,antidomain(multiplication(c(X0),X0))) = antidomain(zero),
inference(forward_demodulation,[status(thm)],[f182,f849]) ).
fof(f851,plain,
! [X0] : addition(one,antidomain(multiplication(c(X0),X0))) = one,
inference(forward_demodulation,[status(thm)],[f293,f850]) ).
fof(f852,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(c(X0)),domain(X0)))) = coantidomain(multiplication(codomain(c(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f363,f837]) ).
fof(f853,plain,
! [X0] : addition(one,antidomain(multiplication(c(X0),domain(domain(X0))))) = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f293,f838]) ).
fof(f854,plain,
! [X0] : addition(one,antidomain(multiplication(c(X0),antidomain(c(X0))))) = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f181,f853]) ).
fof(f855,plain,
! [X0] : addition(one,antidomain(multiplication(c(X0),antidomain(c(X0))))) = antidomain(multiplication(c(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f181,f854]) ).
fof(f856,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f31,f839]) ).
fof(f857,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f65,f840]) ).
fof(f858,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f841]) ).
fof(f859,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f842]) ).
fof(f860,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f843]) ).
fof(f863,plain,
! [X0] : forward_diamond(one,X0) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f181,f441]) ).
fof(f864,plain,
divergence(one) = antidomain(c(divergence(one))),
inference(paramodulation,[status(thm)],[f58,f863]) ).
fof(f867,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)],[f863,f60]) ).
fof(f868,plain,
antidomain(c(divergence(one))) = divergence(one),
inference(paramodulation,[status(thm)],[f863,f58]) ).
fof(f869,plain,
! [X0] : forward_box(one,X0) = c(antidomain(c(c(X0)))),
inference(paramodulation,[status(thm)],[f863,f56]) ).
fof(f875,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(antidomain(c(domain(X0))),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f863,f867]) ).
fof(f882,plain,
! [X0] : backward_diamond(coantidomain(coantidomain(codomain(X0))),coantidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f178,f484]) ).
fof(f883,plain,
! [X0,X1] : backward_diamond(coantidomain(backward_diamond(X0,X1)),multiplication(codomain(X1),X0)) = zero,
inference(paramodulation,[status(thm)],[f55,f484]) ).
fof(f886,plain,
! [X0] : backward_box(coantidomain(codomain(c(X0))),X0) = c(zero),
inference(paramodulation,[status(thm)],[f484,f57]) ).
fof(f893,plain,
! [X0] : backward_diamond(codomain(codomain(X0)),coantidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f51,f882]) ).
fof(f897,plain,
! [X0] : backward_box(coantidomain(codomain(c(X0))),X0) = one,
inference(forward_demodulation,[status(thm)],[f352,f886]) ).
fof(f903,plain,
! [X0] : backward_box(one,X0) = c(codomain(codomain(c(X0)))),
inference(paramodulation,[status(thm)],[f478,f57]) ).
fof(f910,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X0,X1),X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f30,f84]) ).
fof(f912,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f82,f84]) ).
fof(f913,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f30,f84]) ).
fof(f916,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f82,f84]) ).
fof(f923,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X2,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f30,f84]) ).
fof(f926,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X2),addition(X1,addition(X2,X0)))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f82,f84]) ).
fof(f927,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X2),addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f82,f84]) ).
fof(f929,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f29,f84]) ).
fof(f930,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f29,f84]) ).
fof(f932,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X0,X1),X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f84,f30]) ).
fof(f934,plain,
! [X0,X1] : addition(X0,addition(addition(X1,X0),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f84,f82]) ).
fof(f935,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,addition(X0,X1)),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f84,f82]) ).
fof(f936,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,addition(X1,X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f84,f82]) ).
fof(f937,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,addition(X1,X0)),X1) ),
inference(paramodulation,[status(thm)],[f84,f231]) ).
fof(f938,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X1,addition(X0,X1))
| leq(X0,addition(X1,addition(X0,X1))) ),
inference(paramodulation,[status(thm)],[f84,f43]) ).
fof(f939,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,addition(X0,X1)),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f84,f30]) ).
fof(f940,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)],[f30,f910]) ).
fof(f941,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)],[f30,f940]) ).
fof(f944,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f30,f912]) ).
fof(f960,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)],[f30,f923]) ).
fof(f961,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)],[f30,f960]) ).
fof(f966,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)],[f30,f926]) ).
fof(f967,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)],[f30,f927]) ).
fof(f970,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)],[f30,f932]) ).
fof(f971,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)],[f30,f970]) ).
fof(f974,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f30,f934]) ).
fof(f975,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f30,f935]) ).
fof(f976,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f30,f975]) ).
fof(f977,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(addition(X1,X2),addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f30,f936]) ).
fof(f978,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,addition(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f30,f977]) ).
fof(f979,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f30,f939]) ).
fof(f980,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f30,f979]) ).
fof(f981,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f30,f980]) ).
fof(f983,plain,
! [X0,X1] : forward_box(c(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f57,f513]) ).
fof(f984,plain,
! [X0,X1] : forward_box(c(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f56,f513]) ).
fof(f1005,plain,
! [X0] : forward_box(X0,zero) = domain(c(X0)),
inference(backward_demodulation,[status(thm)],[f633,f515]) ).
fof(f1006,plain,
! [X0] : domain(c(domain(X0))) = c(antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f181,f633]) ).
fof(f1007,plain,
! [X0] : domain(c(antidomain(X0))) = c(c(X0)),
inference(paramodulation,[status(thm)],[f631,f633]) ).
fof(f1008,plain,
! [X0,X1] : domain(c(multiplication(X0,domain(X1)))) = c(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f54,f633]) ).
fof(f1011,plain,
! [X0] : forward_box(c(domain(c(X0))),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f633,f513]) ).
fof(f1013,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = c(backward_diamond(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f633,f57]) ).
fof(f1014,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = c(forward_diamond(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f633,f56]) ).
fof(f1015,plain,
! [X0] : forward_diamond(domain(c(X0)),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f633,f450]) ).
fof(f1016,plain,
! [X0] : domain(domain(c(X0))) = c(antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f633,f1006]) ).
fof(f1017,plain,
! [X0] : antidomain(c(c(X0))) = c(antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f181,f1016]) ).
fof(f1022,plain,
! [X0] : forward_box(domain(c(c(X0))),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f633,f1011]) ).
fof(f1025,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f30,f88]) ).
fof(f1026,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X1,X0),X2)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f84,f88]) ).
fof(f1027,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f82,f88]) ).
fof(f1028,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f82,f88]) ).
fof(f1030,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f88]) ).
fof(f1031,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f88]) ).
fof(f1032,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f32,f88]) ).
fof(f1033,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)],[f309,f88]) ).
fof(f1034,plain,
! [X0,X1] : addition(codomain(X0),addition(coantidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f354,f88]) ).
fof(f1035,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)],[f237,f88]) ).
fof(f1036,plain,
! [X0,X1] : addition(domain(X0),addition(antidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f283,f88]) ).
fof(f1037,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)],[f37,f88]) ).
fof(f1038,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)],[f36,f88]) ).
fof(f1039,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X2,addition(X1,X0)),X3),
inference(paramodulation,[status(thm)],[f88,f88]) ).
fof(f1042,plain,
! [X0,X1,X2] : addition(addition(X0,addition(X1,X0)),addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f84,f88]) ).
fof(f1043,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f82,f88]) ).
fof(f1044,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X1,addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f82,f88]) ).
fof(f1049,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f88,f30]) ).
fof(f1050,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(addition(X1,X0),X2)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f88,f84]) ).
fof(f1051,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,addition(X2,X1))))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f88,f84]) ).
fof(f1052,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f88,f82]) ).
fof(f1053,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f88,f82]) ).
fof(f1055,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X2,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f88,f84]) ).
fof(f1056,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(X3,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f88,f82]) ).
fof(f1057,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f88,f82]) ).
fof(f1058,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f88,f231]) ).
fof(f1059,plain,
! [X0,X1,X2] :
( addition(X1,addition(X0,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f88,f43]) ).
fof(f1060,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X1,addition(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f88,f30]) ).
fof(f1061,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f88,f29]) ).
fof(f1062,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f88,f29]) ).
fof(f1063,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f88,f32]) ).
fof(f1064,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)],[f88,f1026]) ).
fof(f1065,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)],[f88,f1064]) ).
fof(f1066,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f88,f1028]) ).
fof(f1068,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)],[f82,f1033]) ).
fof(f1069,plain,
! [X0,X1] : addition(coantidomain(X0),addition(X1,codomain(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f82,f1034]) ).
fof(f1070,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)],[f82,f1035]) ).
fof(f1071,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,domain(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f82,f1036]) ).
fof(f1072,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f88,f1039]) ).
fof(f1073,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,X0),addition(X1,X3)),
inference(forward_demodulation,[status(thm)],[f88,f1072]) ).
fof(f1074,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X0,addition(X2,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f88,f1073]) ).
fof(f1077,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f88,f1042]) ).
fof(f1078,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f1077]) ).
fof(f1079,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1078]) ).
fof(f1080,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f88,f1043]) ).
fof(f1081,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,X2),addition(X1,X3)),
inference(forward_demodulation,[status(thm)],[f88,f1080]) ).
fof(f1082,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f88,f1081]) ).
fof(f1083,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f88,f1044]) ).
fof(f1084,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,X1),addition(X0,X3)),
inference(forward_demodulation,[status(thm)],[f88,f1083]) ).
fof(f1085,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f88,f1084]) ).
fof(f1086,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)],[f88,f1050]) ).
fof(f1087,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)],[f88,f1086]) ).
fof(f1088,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f88,f1053]) ).
fof(f1090,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)],[f88,f1055]) ).
fof(f1091,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)],[f88,f1090]) ).
fof(f1092,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f88,f1056]) ).
fof(f1093,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f88,f1060]) ).
fof(f1094,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X2),addition(X0,X3)),
inference(forward_demodulation,[status(thm)],[f88,f1093]) ).
fof(f1095,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X1,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f88,f1094]) ).
fof(f1096,plain,
! [X0] : antidomain(c(X0)) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f181,f634]) ).
fof(f1101,plain,
! [X0] : forward_box(c(antidomain(c(X0))),antidomain(X0)) = one,
inference(paramodulation,[status(thm)],[f1096,f513]) ).
fof(f1103,plain,
! [X0,X1] : backward_box(X0,antidomain(X1)) = c(backward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f1096,f57]) ).
fof(f1104,plain,
! [X0,X1] : forward_box(X0,antidomain(X1)) = c(forward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f1096,f56]) ).
fof(f1105,plain,
! [X0] : forward_diamond(antidomain(c(X0)),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f1096,f450]) ).
fof(f1113,plain,
! [X0] : forward_box(antidomain(c(c(X0))),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f1096,f1101]) ).
fof(f1116,plain,
! [X0] : addition(c(X0),c(antidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f631,f657]) ).
fof(f1117,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),c(multiplication(X0,domain(X1)))) = one,
inference(paramodulation,[status(thm)],[f54,f657]) ).
fof(f1120,plain,
! [X0] : addition(domain(antidomain(X0)),antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f1096,f657]) ).
fof(f1122,plain,
! [X0,X1] : addition(domain(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f57,f657]) ).
fof(f1123,plain,
! [X0,X1] : addition(domain(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f56,f657]) ).
fof(f1126,plain,
! [X0,X1] : addition(c(X0),addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f657,f88]) ).
fof(f1128,plain,
! [X0,X1] : addition(domain(X0),addition(c(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f657,f82]) ).
fof(f1129,plain,
! [X0,X1] : addition(X0,one) = addition(c(X1),addition(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f657,f82]) ).
fof(f1130,plain,
! [X0] :
( one != domain(X0)
| leq(c(X0),domain(X0)) ),
inference(paramodulation,[status(thm)],[f657,f231]) ).
fof(f1131,plain,
! [X0] :
( one != c(X0)
| leq(domain(X0),c(X0)) ),
inference(paramodulation,[status(thm)],[f657,f43]) ).
fof(f1132,plain,
! [X0,X1] : addition(domain(X0),addition(c(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f657,f30]) ).
fof(f1134,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f1096,f1116]) ).
fof(f1137,plain,
! [X0] : addition(antidomain(c(X0)),domain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f29,f1120]) ).
fof(f1138,plain,
! [X0] : addition(antidomain(c(X0)),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f631,f1137]) ).
fof(f1139,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f29,f1138]) ).
fof(f1141,plain,
! [X0,X1] : addition(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f29,f1122]) ).
fof(f1142,plain,
! [X0,X1] : addition(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f29,f1123]) ).
fof(f1146,plain,
! [X0,X1] : addition(domain(X0),addition(X1,c(X0))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f82,f1126]) ).
fof(f1150,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1129]) ).
fof(f1163,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f90,f43]) ).
fof(f1164,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f88,f90]) ).
fof(f1165,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f30,f90]) ).
fof(f1168,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f82,f90]) ).
fof(f1170,plain,
! [X0] : addition(domain(X0),one) = addition(domain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f657,f90]) ).
fof(f1172,plain,
! [X0] : addition(coantidomain(X0),one) = addition(coantidomain(X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f354,f90]) ).
fof(f1174,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f283,f90]) ).
fof(f1177,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f88,f90]) ).
fof(f1178,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f30,f90]) ).
fof(f1182,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f82,f90]) ).
fof(f1183,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f82,f90]) ).
fof(f1188,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f90,f88]) ).
fof(f1189,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f90,f30]) ).
fof(f1197,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f90,f82]) ).
fof(f1198,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f90,f82]) ).
fof(f1199,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f90,f231]) ).
fof(f1201,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f90,f30]) ).
fof(f1202,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f1164]) ).
fof(f1203,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1202]) ).
fof(f1204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f88,f1165]) ).
fof(f1205,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f90,f1204]) ).
fof(f1206,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1205]) ).
fof(f1210,plain,
! [X0] : addition(one,domain(X0)) = addition(domain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f29,f1170]) ).
fof(f1211,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f657,f1210]) ).
fof(f1212,plain,
! [X0] : addition(one,coantidomain(X0)) = addition(coantidomain(X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f29,f1172]) ).
fof(f1213,plain,
! [X0] : addition(one,coantidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f354,f1212]) ).
fof(f1214,plain,
! [X0] : addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f29,f1174]) ).
fof(f1215,plain,
! [X0] : addition(one,antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f283,f1214]) ).
fof(f1220,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f1177]) ).
fof(f1221,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1220]) ).
fof(f1222,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f1178]) ).
fof(f1223,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f90,f1222]) ).
fof(f1224,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1223]) ).
fof(f1227,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f1188]) ).
fof(f1228,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1227]) ).
fof(f1229,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f88,f1189]) ).
fof(f1230,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f90,f1229]) ).
fof(f1231,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1230]) ).
fof(f1238,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f88,f1197]) ).
fof(f1239,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f1198]) ).
fof(f1241,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f88,f1201]) ).
fof(f1242,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1241]) ).
fof(f1244,plain,
! [X0] : leq(domain(X0),one),
inference(paramodulation,[status(thm)],[f657,f1163]) ).
fof(f1245,plain,
! [X0,X1] : leq(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(paramodulation,[status(thm)],[f309,f1163]) ).
fof(f1246,plain,
! [X0] : leq(coantidomain(X0),one),
inference(paramodulation,[status(thm)],[f354,f1163]) ).
fof(f1247,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f237,f1163]) ).
fof(f1248,plain,
! [X0] : leq(antidomain(X0),one),
inference(paramodulation,[status(thm)],[f283,f1163]) ).
fof(f1249,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f37,f1163]) ).
fof(f1250,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f1163]) ).
fof(f1251,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f88,f1163]) ).
fof(f1252,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f30,f1163]) ).
fof(f1256,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f82,f1163]) ).
fof(f1257,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f82,f1163]) ).
fof(f1259,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f1163]) ).
fof(f1264,plain,
! [X0] : leq(c(X0),one),
inference(paramodulation,[status(thm)],[f631,f1244]) ).
fof(f1265,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),one),
inference(paramodulation,[status(thm)],[f54,f1244]) ).
fof(f1271,plain,
! [X0] : leq(codomain(X0),one),
inference(paramodulation,[status(thm)],[f51,f1246]) ).
fof(f1286,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f37,f1259]) ).
fof(f1287,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f36,f1259]) ).
fof(f1291,plain,
! [X0,X1] : leq(addition(X0,addition(X1,X0)),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f84,f1259]) ).
fof(f1293,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f82,f1259]) ).
fof(f1294,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f82,f1259]) ).
fof(f1299,plain,
! [X0] : addition(c(X0),one) = one,
inference(resolution,[status(thm)],[f1264,f42]) ).
fof(f1302,plain,
! [X0,X1] : leq(backward_box(X0,X1),one),
inference(paramodulation,[status(thm)],[f57,f1264]) ).
fof(f1303,plain,
! [X0,X1] : leq(forward_box(X0,X1),one),
inference(paramodulation,[status(thm)],[f56,f1264]) ).
fof(f1306,plain,
! [X0] : addition(one,c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f29,f1299]) ).
fof(f1307,plain,
! [X0] : addition(codomain(X0),one) = one,
inference(resolution,[status(thm)],[f1271,f42]) ).
fof(f1309,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),one),
inference(paramodulation,[status(thm)],[f55,f1271]) ).
fof(f1312,plain,
! [X0] : addition(one,codomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f29,f1307]) ).
fof(f1313,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1265,f42]) ).
fof(f1317,plain,
! [X0] : leq(divergence(X0),one),
inference(paramodulation,[status(thm)],[f58,f1265]) ).
fof(f1320,plain,
! [X0,X1] : addition(one,forward_diamond(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f29,f1313]) ).
fof(f1321,plain,
! [X0] : addition(divergence(X0),one) = one,
inference(resolution,[status(thm)],[f1317,f42]) ).
fof(f1323,plain,
! [X0] : addition(one,divergence(X0)) = one,
inference(forward_demodulation,[status(thm)],[f29,f1321]) ).
fof(f1326,plain,
! [X0,X1] : multiplication(c(X0),multiplication(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f52,f121]) ).
fof(f1327,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f47,f121]) ).
fof(f1331,plain,
! [X0,X1] : multiplication(antidomain(domain(X0)),domain_difference(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f53,f121]) ).
fof(f1332,plain,
! [X0,X1,X2] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,multiplication(X1,X2))) = zero,
inference(paramodulation,[status(thm)],[f33,f121]) ).
fof(f1340,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)],[f121,f309]) ).
fof(f1341,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)],[f121,f237]) ).
fof(f1342,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f121,f37]) ).
fof(f1343,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = addition(zero,multiplication(X1,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f121,f37]) ).
fof(f1344,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f121,f36]) ).
fof(f1345,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = addition(zero,multiplication(antidomain(X0),X2)),
inference(paramodulation,[status(thm)],[f121,f36]) ).
fof(f1349,plain,
! [X0,X1] : multiplication(c(X0),domain_difference(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f52,f1331]) ).
fof(f1351,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)],[f363,f1340]) ).
fof(f1352,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)],[f293,f1341]) ).
fof(f1353,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f31,f1342]) ).
fof(f1354,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f65,f1343]) ).
fof(f1355,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f1344]) ).
fof(f1356,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = multiplication(antidomain(X0),X2),
inference(forward_demodulation,[status(thm)],[f65,f1345]) ).
fof(f1359,plain,
! [X0,X1] : addition(backward_box(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1302,f42]) ).
fof(f1363,plain,
! [X0,X1] : addition(one,backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f29,f1359]) ).
fof(f1364,plain,
! [X0,X1] : addition(forward_box(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1303,f42]) ).
fof(f1369,plain,
! [X0,X1] : addition(one,forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f29,f1364]) ).
fof(f1370,plain,
! [X0,X1] : addition(backward_diamond(X0,X1),one) = one,
inference(resolution,[status(thm)],[f1309,f42]) ).
fof(f1376,plain,
! [X0,X1] : addition(one,backward_diamond(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f29,f1370]) ).
fof(f1378,plain,
! [X0] : addition(one,antidomain(c(X0))) = one,
inference(paramodulation,[status(thm)],[f181,f1211]) ).
fof(f1386,plain,
! [X0,X1] : addition(domain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1211,f88]) ).
fof(f1388,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1211,f82]) ).
fof(f1389,plain,
! [X0,X1] : addition(X0,one) = addition(domain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1211,f82]) ).
fof(f1390,plain,
! [X0] :
( one != one
| leq(domain(X0),one) ),
inference(paramodulation,[status(thm)],[f1211,f231]) ).
fof(f1391,plain,
! [X0] :
( one != domain(X0)
| leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f1211,f43]) ).
fof(f1392,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1211,f30]) ).
fof(f1394,plain,
! [X0,X1] : addition(one,addition(X0,domain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1386]) ).
fof(f1396,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1389]) ).
fof(f1397,definition,
! [X0] :
( sQ0_spl
<=> leq(domain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1400,definition,
( sQ1_spl
<=> one = one ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1402,plain,
( sQ1_spl
| one != one ),
inference(component_clause,[status(thm)],[f1400]) ).
fof(f1403,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1390,f1397,f1400]) ).
fof(f1405,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(multiplication(X0,X1),X2))))) = zero,
inference(paramodulation,[status(thm)],[f33,f129]) ).
fof(f1409,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(paramodulation,[status(thm)],[f33,f129]) ).
fof(f1414,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),coantidomain(domain_difference(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f53,f129]) ).
fof(f1415,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2))))) = zero,
inference(paramodulation,[status(thm)],[f33,f129]) ).
fof(f1424,plain,
! [X0,X1] : backward_diamond(multiplication(X0,coantidomain(multiplication(codomain(X1),X0))),X1) = codomain(zero),
inference(paramodulation,[status(thm)],[f129,f55]) ).
fof(f1425,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,multiplication(X1,coantidomain(multiplication(codomain(X0),X1))))),coantidomain(zero)) = coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(codomain(X0),X1))))),
inference(paramodulation,[status(thm)],[f129,f309]) ).
fof(f1426,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(multiplication(X0,X1),X2))))) = zero,
inference(paramodulation,[status(thm)],[f129,f33]) ).
fof(f1431,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)],[f129,f309]) ).
fof(f1432,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)],[f129,f237]) ).
fof(f1433,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)],[f129,f37]) ).
fof(f1434,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)],[f129,f37]) ).
fof(f1435,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f129,f36]) ).
fof(f1436,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = addition(zero,multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f129,f36]) ).
fof(f1437,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(zero,X2),
inference(paramodulation,[status(thm)],[f129,f33]) ).
fof(f1439,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f33,f1405]) ).
fof(f1446,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f33,f1415]) ).
fof(f1456,plain,
! [X0,X1] : backward_diamond(multiplication(X0,coantidomain(multiplication(codomain(X1),X0))),X1) = zero,
inference(forward_demodulation,[status(thm)],[f375,f1424]) ).
fof(f1457,plain,
! [X0,X1] : addition(coantidomain(zero),coantidomain(multiplication(X0,multiplication(X1,coantidomain(multiplication(codomain(X0),X1)))))) = coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(codomain(X0),X1))))),
inference(forward_demodulation,[status(thm)],[f29,f1425]) ).
fof(f1458,plain,
! [X0,X1] : addition(one,coantidomain(multiplication(X0,multiplication(X1,coantidomain(multiplication(codomain(X0),X1)))))) = coantidomain(multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(codomain(X0),X1))))),
inference(forward_demodulation,[status(thm)],[f363,f1457]) ).
fof(f1459,plain,
! [X0,X1] : addition(one,coantidomain(multiplication(X0,multiplication(X1,coantidomain(multiplication(codomain(X0),X1)))))) = coantidomain(zero),
inference(forward_demodulation,[status(thm)],[f129,f1458]) ).
fof(f1460,plain,
! [X0,X1] : addition(one,coantidomain(multiplication(X0,multiplication(X1,coantidomain(multiplication(codomain(X0),X1)))))) = one,
inference(forward_demodulation,[status(thm)],[f363,f1459]) ).
fof(f1461,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,coantidomain(multiplication(X0,multiplication(X1,X2)))))) = zero,
inference(forward_demodulation,[status(thm)],[f33,f1426]) ).
fof(f1463,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)],[f363,f1431]) ).
fof(f1464,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)],[f293,f1432]) ).
fof(f1465,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)],[f31,f1433]) ).
fof(f1466,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)],[f65,f1434]) ).
fof(f1467,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f1435]) ).
fof(f1468,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f65,f1436]) ).
fof(f1469,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = multiplication(zero,X2),
inference(forward_demodulation,[status(thm)],[f33,f1437]) ).
fof(f1470,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(forward_demodulation,[status(thm)],[f39,f1469]) ).
fof(f1478,plain,
! [X0,X1] : addition(coantidomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1213,f88]) ).
fof(f1480,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1213,f82]) ).
fof(f1481,plain,
! [X0,X1] : addition(X0,one) = addition(coantidomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1213,f82]) ).
fof(f1482,plain,
! [X0] :
( one != one
| leq(coantidomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1213,f231]) ).
fof(f1483,plain,
! [X0] :
( one != coantidomain(X0)
| leq(one,coantidomain(X0)) ),
inference(paramodulation,[status(thm)],[f1213,f43]) ).
fof(f1484,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1213,f30]) ).
fof(f1486,plain,
! [X0,X1] : addition(one,addition(X0,coantidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1478]) ).
fof(f1488,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1481]) ).
fof(f1489,definition,
! [X0] :
( sQ2_spl
<=> leq(coantidomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1492,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1482,f1489,f1400]) ).
fof(f1493,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1402]) ).
fof(f1494,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1493]) ).
fof(f1503,plain,
! [X0,X1] : addition(antidomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1215,f88]) ).
fof(f1505,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1215,f82]) ).
fof(f1506,plain,
! [X0,X1] : addition(X0,one) = addition(antidomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1215,f82]) ).
fof(f1507,plain,
! [X0] :
( one != one
| leq(antidomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1215,f231]) ).
fof(f1508,plain,
! [X0] :
( one != antidomain(X0)
| leq(one,antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f1215,f43]) ).
fof(f1509,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1215,f30]) ).
fof(f1511,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1503]) ).
fof(f1513,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1506]) ).
fof(f1514,definition,
! [X0] :
( sQ3_spl
<=> leq(antidomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1517,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f1507,f1514,f1400]) ).
fof(f1528,plain,
! [X0,X1] : addition(c(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1306,f88]) ).
fof(f1530,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1306,f82]) ).
fof(f1531,plain,
! [X0,X1] : addition(X0,one) = addition(c(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1306,f82]) ).
fof(f1532,plain,
! [X0] :
( one != one
| leq(c(X0),one) ),
inference(paramodulation,[status(thm)],[f1306,f231]) ).
fof(f1533,plain,
! [X0] :
( one != c(X0)
| leq(one,c(X0)) ),
inference(paramodulation,[status(thm)],[f1306,f43]) ).
fof(f1534,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1306,f30]) ).
fof(f1536,plain,
! [X0,X1] : addition(one,addition(X0,c(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1528]) ).
fof(f1538,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1531]) ).
fof(f1539,definition,
! [X0] :
( sQ4_spl
<=> leq(c(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1542,plain,
( ~ sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1532,f1539,f1400]) ).
fof(f1551,plain,
! [X0,X1] : addition(codomain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1312,f88]) ).
fof(f1553,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1312,f82]) ).
fof(f1554,plain,
! [X0,X1] : addition(X0,one) = addition(codomain(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1312,f82]) ).
fof(f1555,plain,
! [X0] :
( one != one
| leq(codomain(X0),one) ),
inference(paramodulation,[status(thm)],[f1312,f231]) ).
fof(f1556,plain,
! [X0] :
( one != codomain(X0)
| leq(one,codomain(X0)) ),
inference(paramodulation,[status(thm)],[f1312,f43]) ).
fof(f1557,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1312,f30]) ).
fof(f1559,plain,
! [X0,X1] : addition(one,addition(X0,codomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1551]) ).
fof(f1561,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1554]) ).
fof(f1562,definition,
! [X0] :
( sQ5_spl
<=> leq(codomain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1565,plain,
( ~ sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1555,f1562,f1400]) ).
fof(f1567,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(paramodulation,[status(thm)],[f33,f136]) ).
fof(f1578,plain,
! [X0,X1] : multiplication(coantidomain(X0),multiplication(codomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f51,f136]) ).
fof(f1580,plain,
! [X0,X1] : backward_diamond(multiplication(coantidomain(codomain(X0)),X1),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f136,f55]) ).
fof(f1582,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(coantidomain(multiplication(X0,X1)),X2))) = zero,
inference(paramodulation,[status(thm)],[f136,f33]) ).
fof(f1588,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)],[f136,f309]) ).
fof(f1589,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)],[f136,f237]) ).
fof(f1590,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = addition(multiplication(X0,multiplication(coantidomain(X1),X2)),zero),
inference(paramodulation,[status(thm)],[f136,f37]) ).
fof(f1591,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = addition(zero,multiplication(X1,multiplication(coantidomain(X0),X2))),
inference(paramodulation,[status(thm)],[f136,f37]) ).
fof(f1592,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f136,f36]) ).
fof(f1593,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = addition(zero,multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f136,f36]) ).
fof(f1598,plain,
! [X0,X1] : backward_diamond(multiplication(coantidomain(codomain(X0)),X1),X0) = zero,
inference(forward_demodulation,[status(thm)],[f375,f1580]) ).
fof(f1605,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)],[f363,f1588]) ).
fof(f1606,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(X0),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f1213,f1605]) ).
fof(f1607,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)],[f293,f1589]) ).
fof(f1608,plain,
! [X0,X1] : one = antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f1215,f1607]) ).
fof(f1609,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f31,f1590]) ).
fof(f1610,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f65,f1591]) ).
fof(f1611,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f1592]) ).
fof(f1612,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f65,f1593]) ).
fof(f1620,plain,
! [X0,X1] : addition(divergence(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1323,f88]) ).
fof(f1622,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f1323,f82]) ).
fof(f1623,plain,
! [X0,X1] : addition(X0,one) = addition(divergence(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1323,f82]) ).
fof(f1624,plain,
! [X0] :
( one != one
| leq(divergence(X0),one) ),
inference(paramodulation,[status(thm)],[f1323,f231]) ).
fof(f1625,plain,
! [X0] :
( one != divergence(X0)
| leq(one,divergence(X0)) ),
inference(paramodulation,[status(thm)],[f1323,f43]) ).
fof(f1626,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f1323,f30]) ).
fof(f1628,plain,
! [X0,X1] : addition(one,addition(X0,divergence(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1620]) ).
fof(f1630,plain,
! [X0,X1] : addition(X0,one) = addition(one,addition(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1623]) ).
fof(f1631,definition,
! [X0] :
( sQ6_spl
<=> leq(divergence(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1634,plain,
( ~ sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1624,f1631,f1400]) ).
fof(f1636,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f36,f138]) ).
fof(f1640,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f182,f138]) ).
fof(f1641,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = addition(zero,multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f180,f138]) ).
fof(f1642,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(X1,antidomain(X2))) = addition(domain_difference(X0,X2),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f53,f138]) ).
fof(f1643,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)],[f33,f138]) ).
fof(f1644,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f121,f138]) ).
fof(f1645,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f44,f138]) ).
fof(f1648,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f136,f138]) ).
fof(f1649,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f129,f138]) ).
fof(f1650,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f48,f138]) ).
fof(f1652,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f138]) ).
fof(f1653,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f182,f138]) ).
fof(f1654,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f180,f138]) ).
fof(f1655,plain,
! [X0,X1,X2] : multiplication(domain(X0),addition(antidomain(X1),X2)) = addition(multiplication(domain(X0),X2),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f53,f138]) ).
fof(f1656,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)],[f33,f138]) ).
fof(f1657,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = addition(multiplication(antidomain(X0),X2),zero),
inference(paramodulation,[status(thm)],[f121,f138]) ).
fof(f1658,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f44,f138]) ).
fof(f1661,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f136,f138]) ).
fof(f1662,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f129,f138]) ).
fof(f1663,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f48,f138]) ).
fof(f1665,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f34,f138]) ).
fof(f1667,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f138,f36]) ).
fof(f1668,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f138,f1259]) ).
fof(f1669,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f138,f1163]) ).
fof(f1670,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,addition(X2,X1))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f138,f90]) ).
fof(f1671,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)],[f138,f88]) ).
fof(f1673,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)],[f138,f82]) ).
fof(f1674,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)],[f138,f82]) ).
fof(f1675,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f138,f231]) ).
fof(f1676,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f138,f43]) ).
fof(f1677,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)],[f138,f30]) ).
fof(f1682,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f1640]) ).
fof(f1683,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f1641]) ).
fof(f1684,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)],[f33,f1643]) ).
fof(f1685,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)],[f33,f1684]) ).
fof(f1686,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)],[f138,f1685]) ).
fof(f1687,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f138,f1686]) ).
fof(f1688,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,multiplication(X0,X2))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f1644]) ).
fof(f1689,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f1645]) ).
fof(f1694,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(coantidomain(X0),X2))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f1648]) ).
fof(f1695,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,coantidomain(multiplication(X0,X2))))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f1649]) ).
fof(f1696,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f1650]) ).
fof(f1698,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f1653]) ).
fof(f1699,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f1654]) ).
fof(f1700,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)],[f33,f1656]) ).
fof(f1701,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)],[f33,f1700]) ).
fof(f1702,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)],[f138,f1701]) ).
fof(f1703,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f138,f1702]) ).
fof(f1704,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(multiplication(X0,X1),X2)) = multiplication(antidomain(X0),X2),
inference(forward_demodulation,[status(thm)],[f31,f1657]) ).
fof(f1705,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f1658]) ).
fof(f1710,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f31,f1661]) ).
fof(f1711,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),X2)) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f31,f1662]) ).
fof(f1712,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f1663]) ).
fof(f1714,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f1665]) ).
fof(f1716,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,X2),X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f138,f1670]) ).
fof(f1717,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,X1))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f1716]) ).
fof(f1718,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,X1))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f138,f1717]) ).
fof(f1724,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f1256,f42]) ).
fof(f1725,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f88,f1256]) ).
fof(f1726,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f30,f1256]) ).
fof(f1735,plain,
! [X0,X1] : leq(divergence(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1323,f1256]) ).
fof(f1736,plain,
! [X0,X1] : leq(codomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1312,f1256]) ).
fof(f1737,plain,
! [X0,X1] : leq(c(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1306,f1256]) ).
fof(f1738,plain,
! [X0,X1] : leq(antidomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1215,f1256]) ).
fof(f1739,plain,
! [X0,X1] : leq(coantidomain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1213,f1256]) ).
fof(f1740,plain,
! [X0,X1] : leq(domain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1211,f1256]) ).
fof(f1746,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f138,f1256]) ).
fof(f1747,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f37,f1256]) ).
fof(f1748,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f36,f1256]) ).
fof(f1749,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f88,f1256]) ).
fof(f1750,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f30,f1256]) ).
fof(f1752,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X0)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f84,f1256]) ).
fof(f1754,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f82,f1256]) ).
fof(f1755,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X1,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f82,f1256]) ).
fof(f1762,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f1257,f42]) ).
fof(f1763,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f88,f1257]) ).
fof(f1764,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f30,f1257]) ).
fof(f1780,plain,
! [X0,X1,X2] : leq(coantidomain(multiplication(X0,X1)),addition(X2,coantidomain(multiplication(codomain(X0),X1)))),
inference(paramodulation,[status(thm)],[f309,f1257]) ).
fof(f1782,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(X2,antidomain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f237,f1257]) ).
fof(f1784,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f138,f1257]) ).
fof(f1785,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f37,f1257]) ).
fof(f1786,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f36,f1257]) ).
fof(f1787,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X1,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f88,f1257]) ).
fof(f1788,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f30,f1257]) ).
fof(f1792,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f82,f1257]) ).
fof(f1793,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f82,f1257]) ).
fof(f1808,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1320,f1256]) ).
fof(f1812,plain,
! [X0,X1,X2] : addition(forward_diamond(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1320,f88]) ).
fof(f1814,plain,
! [X0,X1,X2] : addition(one,addition(forward_diamond(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1320,f82]) ).
fof(f1815,plain,
! [X0,X1,X2] : addition(X0,one) = addition(forward_diamond(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1320,f82]) ).
fof(f1816,plain,
! [X0,X1] :
( one != one
| leq(forward_diamond(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1320,f231]) ).
fof(f1817,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(one,forward_diamond(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1320,f43]) ).
fof(f1818,plain,
! [X0,X1,X2] : addition(one,addition(forward_diamond(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1320,f30]) ).
fof(f1820,plain,
! [X0,X1,X2] : addition(one,addition(X0,forward_diamond(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1812]) ).
fof(f1822,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1815]) ).
fof(f1823,definition,
! [X0,X1] :
( sQ7_spl
<=> leq(forward_diamond(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1826,plain,
( ~ sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1816,f1823,f1400]) ).
fof(f1832,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1363,f1256]) ).
fof(f1836,plain,
! [X0,X1,X2] : addition(backward_box(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1363,f88]) ).
fof(f1838,plain,
! [X0,X1,X2] : addition(one,addition(backward_box(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1363,f82]) ).
fof(f1839,plain,
! [X0,X1,X2] : addition(X0,one) = addition(backward_box(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1363,f82]) ).
fof(f1840,plain,
! [X0,X1] :
( one != one
| leq(backward_box(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1363,f231]) ).
fof(f1841,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(one,backward_box(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1363,f43]) ).
fof(f1842,plain,
! [X0,X1,X2] : addition(one,addition(backward_box(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1363,f30]) ).
fof(f1844,plain,
! [X0,X1,X2] : addition(one,addition(X0,backward_box(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1836]) ).
fof(f1846,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1839]) ).
fof(f1847,definition,
! [X0,X1] :
( sQ8_spl
<=> leq(backward_box(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1850,plain,
( ~ sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f1840,f1847,f1400]) ).
fof(f1857,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1369,f1256]) ).
fof(f1861,plain,
! [X0,X1,X2] : addition(forward_box(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1369,f88]) ).
fof(f1863,plain,
! [X0,X1,X2] : addition(one,addition(forward_box(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1369,f82]) ).
fof(f1864,plain,
! [X0,X1,X2] : addition(X0,one) = addition(forward_box(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1369,f82]) ).
fof(f1865,plain,
! [X0,X1] :
( one != one
| leq(forward_box(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1369,f231]) ).
fof(f1866,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(one,forward_box(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1369,f43]) ).
fof(f1867,plain,
! [X0,X1,X2] : addition(one,addition(forward_box(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1369,f30]) ).
fof(f1869,plain,
! [X0,X1,X2] : addition(one,addition(X0,forward_box(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1861]) ).
fof(f1871,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1864]) ).
fof(f1872,definition,
! [X0,X1] :
( sQ9_spl
<=> leq(forward_box(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1875,plain,
( ~ sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1865,f1872,f1400]) ).
fof(f1883,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f1376,f1256]) ).
fof(f1887,plain,
! [X0,X1,X2] : addition(backward_diamond(X0,X1),addition(one,X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1376,f88]) ).
fof(f1889,plain,
! [X0,X1,X2] : addition(one,addition(backward_diamond(X0,X1),X2)) = addition(X2,one),
inference(paramodulation,[status(thm)],[f1376,f82]) ).
fof(f1890,plain,
! [X0,X1,X2] : addition(X0,one) = addition(backward_diamond(X1,X2),addition(X0,one)),
inference(paramodulation,[status(thm)],[f1376,f82]) ).
fof(f1891,plain,
! [X0,X1] :
( one != one
| leq(backward_diamond(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f1376,f231]) ).
fof(f1892,plain,
! [X0,X1] :
( one != backward_diamond(X0,X1)
| leq(one,backward_diamond(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1376,f43]) ).
fof(f1893,plain,
! [X0,X1,X2] : addition(one,addition(backward_diamond(X0,X1),X2)) = addition(one,X2),
inference(paramodulation,[status(thm)],[f1376,f30]) ).
fof(f1895,plain,
! [X0,X1,X2] : addition(one,addition(X0,backward_diamond(X1,X2))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f1887]) ).
fof(f1897,plain,
! [X0,X1,X2] : addition(X0,one) = addition(one,addition(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f82,f1890]) ).
fof(f1898,definition,
! [X0,X1] :
( sQ10_spl
<=> leq(backward_diamond(X0,X1),one) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1901,plain,
( ~ sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f1891,f1898,f1400]) ).
fof(f1903,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(antidomain(domain(X0)),X1),
inference(paramodulation,[status(thm)],[f52,f162]) ).
fof(f1904,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(antidomain(antidomain(X0)),X1),
inference(paramodulation,[status(thm)],[f47,f162]) ).
fof(f1916,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f657,f162]) ).
fof(f1918,plain,
! [X0] : multiplication(antidomain(coantidomain(X0)),one) = multiplication(antidomain(coantidomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f354,f162]) ).
fof(f1920,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),one) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f283,f162]) ).
fof(f1921,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)],[f138,f162]) ).
fof(f1922,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)],[f37,f162]) ).
fof(f1923,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)],[f36,f162]) ).
fof(f1924,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X1,addition(X0,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f88,f162]) ).
fof(f1925,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,addition(X1,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f30,f162]) ).
fof(f1927,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),addition(X1,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f84,f162]) ).
fof(f1929,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(paramodulation,[status(thm)],[f82,f162]) ).
fof(f1930,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f82,f162]) ).
fof(f1932,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(paramodulation,[status(thm)],[f29,f162]) ).
fof(f1933,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(paramodulation,[status(thm)],[f29,f162]) ).
fof(f1935,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)],[f162,f138]) ).
fof(f1936,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)],[f162,f138]) ).
fof(f1937,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X0,X1),coantidomain(multiplication(antidomain(X0),X1)))) = zero,
inference(paramodulation,[status(thm)],[f162,f129]) ).
fof(f1939,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)],[f162,f309]) ).
fof(f1940,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)],[f162,f237]) ).
fof(f1941,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)],[f162,f37]) ).
fof(f1942,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)],[f162,f37]) ).
fof(f1943,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)],[f162,f36]) ).
fof(f1944,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)],[f162,f36]) ).
fof(f1945,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X0,X1),X2)) = multiplication(multiplication(antidomain(X0),X1),X2),
inference(paramodulation,[status(thm)],[f162,f33]) ).
fof(f1949,plain,
! [X0,X1] : multiplication(c(X0),addition(domain(X0),X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f52,f1903]) ).
fof(f1950,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f47,f1904]) ).
fof(f1973,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f34,f1916]) ).
fof(f1974,plain,
! [X0] : c(X0) = multiplication(antidomain(domain(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f52,f1973]) ).
fof(f1975,plain,
! [X0] : c(X0) = multiplication(c(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f52,f1974]) ).
fof(f1976,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(antidomain(coantidomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f1918]) ).
fof(f1977,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f1920]) ).
fof(f1978,plain,
! [X0] : domain(X0) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f47,f1977]) ).
fof(f1979,plain,
! [X0] : domain(X0) = multiplication(domain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f47,f1978]) ).
fof(f1980,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f162,f1927]) ).
fof(f1982,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)],[f88,f1935]) ).
fof(f1983,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f138,f1982]) ).
fof(f1984,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f138,f1936]) ).
fof(f1985,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)],[f29,f1941]) ).
fof(f1986,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f138,f1943]) ).
fof(f1987,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)],[f88,f1944]) ).
fof(f1988,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X0,X2))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f138,f1987]) ).
fof(f1989,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X0,X1),X2)) = multiplication(antidomain(X0),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f1945]) ).
fof(f1990,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f33,f166]) ).
fof(f1994,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,codomain(X0)),
inference(paramodulation,[status(thm)],[f354,f166]) ).
fof(f1995,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,addition(X1,addition(coantidomain(X0),X1))),
inference(paramodulation,[status(thm)],[f84,f166]) ).
fof(f1997,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f82,f166]) ).
fof(f1998,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f82,f166]) ).
fof(f2000,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f29,f166]) ).
fof(f2001,plain,
! [X0,X1] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f29,f166]) ).
fof(f2004,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(codomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(paramodulation,[status(thm)],[f51,f166]) ).
fof(f2007,plain,
! [X0,X1] : backward_diamond(addition(coantidomain(codomain(X0)),X1),X0) = codomain(multiplication(codomain(X0),X1)),
inference(paramodulation,[status(thm)],[f166,f55]) ).
fof(f2008,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)],[f166,f309]) ).
fof(f2009,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f166,f33]) ).
fof(f2012,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f166,f138]) ).
fof(f2013,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f166,f138]) ).
fof(f2014,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f166,f129]) ).
fof(f2016,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)],[f166,f309]) ).
fof(f2017,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)],[f166,f237]) ).
fof(f2018,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)],[f166,f37]) ).
fof(f2019,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)],[f166,f37]) ).
fof(f2020,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f166,f36]) ).
fof(f2021,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(coantidomain(X0),X1),X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f166,f36]) ).
fof(f2022,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f166,f33]) ).
fof(f2023,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f1990]) ).
fof(f2026,plain,
! [X0] : X0 = multiplication(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f1994]) ).
fof(f2027,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,addition(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f166,f1995]) ).
fof(f2032,plain,
! [X0,X1] : backward_diamond(addition(coantidomain(codomain(X0)),X1),X0) = backward_diamond(X1,X0),
inference(forward_demodulation,[status(thm)],[f55,f2007]) ).
fof(f2033,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)],[f29,f2008]) ).
fof(f2034,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)],[f166,f2033]) ).
fof(f2035,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(coantidomain(multiplication(X0,X1)),X2))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f2009]) ).
fof(f2038,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f88,f2012]) ).
fof(f2039,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f138,f2038]) ).
fof(f2040,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f138,f2013]) ).
fof(f2041,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)],[f29,f2018]) ).
fof(f2042,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f138,f2020]) ).
fof(f2043,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f2021]) ).
fof(f2044,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(coantidomain(X0),X2))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f138,f2043]) ).
fof(f2045,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(coantidomain(X0),X1),X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f2022]) ).
fof(f2047,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,multiplication(X1,codomain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f33,f2026]) ).
fof(f2050,plain,
! [X0] : coantidomain(X0) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f178,f2026]) ).
fof(f2051,plain,
! [X0,X1] : multiplication(codomain(X0),X1) = multiplication(multiplication(codomain(X0),X1),backward_diamond(X1,X0)),
inference(paramodulation,[status(thm)],[f55,f2026]) ).
fof(f2055,plain,
! [X0] : backward_diamond(codomain(codomain(X0)),X0) = codomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f2026,f55]) ).
fof(f2056,plain,
! [X0] : addition(coantidomain(multiplication(X0,codomain(codomain(X0)))),coantidomain(codomain(X0))) = coantidomain(multiplication(codomain(X0),codomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f2026,f309]) ).
fof(f2057,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,codomain(multiplication(X0,X1)))) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f2026,f33]) ).
fof(f2060,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f2026,f138]) ).
fof(f2061,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2026,f138]) ).
fof(f2062,plain,
! [X0] : multiplication(X0,multiplication(codomain(X0),coantidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f2026,f129]) ).
fof(f2064,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(X0),codomain(X0)))) = coantidomain(multiplication(codomain(X0),codomain(X0))),
inference(paramodulation,[status(thm)],[f2026,f309]) ).
fof(f2065,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(X0,domain(codomain(X0))))) = antidomain(multiplication(X0,domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f2026,f237]) ).
fof(f2066,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(multiplication(X0,codomain(X1)),X1),
inference(paramodulation,[status(thm)],[f2026,f37]) ).
fof(f2067,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(X0,multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f2026,f37]) ).
fof(f2068,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f2026,f36]) ).
fof(f2069,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2026,f36]) ).
fof(f2070,plain,
! [X0,X1] : multiplication(X0,multiplication(codomain(X0),X1)) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f2026,f33]) ).
fof(f2072,plain,
! [X0,X1] : multiplication(codomain(X0),X1) = multiplication(codomain(X0),multiplication(X1,backward_diamond(X1,X0))),
inference(forward_demodulation,[status(thm)],[f33,f2051]) ).
fof(f2073,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,codomain(codomain(X0))))) = coantidomain(multiplication(codomain(X0),codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f29,f2056]) ).
fof(f2074,plain,
! [X0] : addition(coantidomain(codomain(X0)),coantidomain(multiplication(X0,codomain(codomain(X0))))) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f2026,f2073]) ).
fof(f2075,plain,
! [X0,X1] : multiplication(X0,addition(codomain(X0),X1)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f2060]) ).
fof(f2076,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(X1,multiplication(X0,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f29,f2066]) ).
fof(f2077,plain,
! [X0,X1] : multiplication(X0,addition(X1,codomain(X0))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f2068]) ).
fof(f2078,plain,
! [X0,X1] : addition(divergence(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1735,f42]) ).
fof(f2080,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f88,f1735]) ).
fof(f2081,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f30,f1735]) ).
fof(f2083,plain,
! [X0,X1] : leq(divergence(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f29,f1735]) ).
fof(f2086,plain,
! [X0,X1] : addition(one,addition(divergence(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f82,f2078]) ).
fof(f2087,plain,
! [X0,X1] : addition(codomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1736,f42]) ).
fof(f2088,plain,
! [X0,X1] : leq(coantidomain(codomain(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f178,f1736]) ).
fof(f2089,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f55,f1736]) ).
fof(f2092,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f88,f1736]) ).
fof(f2093,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f30,f1736]) ).
fof(f2095,plain,
! [X0,X1] : leq(codomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f29,f1736]) ).
fof(f2098,plain,
! [X0,X1] : addition(one,addition(codomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f82,f2087]) ).
fof(f2102,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,backward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f1376,f147]) ).
fof(f2103,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f1369,f147]) ).
fof(f2104,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f1363,f147]) ).
fof(f2105,plain,
! [X0,X1,X2] : multiplication(X0,one) = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f1320,f147]) ).
fof(f2106,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,divergence(X1))),
inference(paramodulation,[status(thm)],[f1323,f147]) ).
fof(f2107,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f1312,f147]) ).
fof(f2108,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f1306,f147]) ).
fof(f2109,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f1215,f147]) ).
fof(f2110,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f1213,f147]) ).
fof(f2111,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f1211,f147]) ).
fof(f2112,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(X1,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f84,f147]) ).
fof(f2113,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f90,f147]) ).
fof(f2114,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f82,f147]) ).
fof(f2115,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f82,f147]) ).
fof(f2117,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f29,f147]) ).
fof(f2118,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f29,f147]) ).
fof(f2120,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(one,X1)) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f37,f147]) ).
fof(f2121,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X1,addition(X0,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f88,f147]) ).
fof(f2122,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f30,f147]) ).
fof(f2126,plain,
! [X0,X1] : multiplication(domain(X0),addition(one,antidomain(X1))) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f53,f147]) ).
fof(f2127,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(one,X2)) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f33,f147]) ).
fof(f2128,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X0,X1))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f162,f147]) ).
fof(f2129,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f121,f147]) ).
fof(f2130,plain,
! [X0] : multiplication(antidomain(X0),addition(one,X0)) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f44,f147]) ).
fof(f2133,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(coantidomain(X0),X1))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f166,f147]) ).
fof(f2134,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f136,f147]) ).
fof(f2135,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f129,f147]) ).
fof(f2141,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(one,X1),X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f147,f138]) ).
fof(f2142,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(addition(X0,multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f147,f138]) ).
fof(f2143,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(addition(X0,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f147,f129]) ).
fof(f2145,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)],[f147,f309]) ).
fof(f2146,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)],[f147,f237]) ).
fof(f2147,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)],[f147,f37]) ).
fof(f2148,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)],[f147,f37]) ).
fof(f2149,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f147,f36]) ).
fof(f2150,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(one,X1),X2)) = addition(addition(X0,multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f147,f36]) ).
fof(f2151,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(one,X1),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f147,f33]) ).
fof(f2153,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(paramodulation,[status(thm)],[f147,f37]) ).
fof(f2154,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),X2))) = multiplication(addition(X1,X0),addition(one,X2)),
inference(paramodulation,[status(thm)],[f147,f88]) ).
fof(f2155,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),X2))) = multiplication(addition(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f147,f30]) ).
fof(f2157,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f147,f1257]) ).
fof(f2158,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f147,f1256]) ).
fof(f2159,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f147,f1259]) ).
fof(f2160,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f147,f1163]) ).
fof(f2161,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f147,f90]) ).
fof(f2162,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f147,f88]) ).
fof(f2163,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,X1),multiplication(X0,addition(one,X1)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f147,f84]) ).
fof(f2164,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(X2,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f147,f82]) ).
fof(f2165,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(one,X2))) = addition(multiplication(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f147,f82]) ).
fof(f2166,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != X0
| leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f147,f231]) ).
fof(f2167,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != multiplication(X0,X1)
| leq(X0,multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f147,f43]) ).
fof(f2168,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f147,f30]) ).
fof(f2170,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_diamond(X1,X2))),
inference(forward_demodulation,[status(thm)],[f34,f2102]) ).
fof(f2171,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(forward_demodulation,[status(thm)],[f34,f2103]) ).
fof(f2172,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(forward_demodulation,[status(thm)],[f34,f2104]) ).
fof(f2173,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(forward_demodulation,[status(thm)],[f34,f2105]) ).
fof(f2174,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,divergence(X1))),
inference(forward_demodulation,[status(thm)],[f34,f2106]) ).
fof(f2175,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f34,f2107]) ).
fof(f2176,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f34,f2108]) ).
fof(f2177,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f34,f2109]) ).
fof(f2178,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f34,f2110]) ).
fof(f2179,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f34,f2111]) ).
fof(f2184,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f33,f2120]) ).
fof(f2189,plain,
! [X0,X1] : multiplication(domain(X0),one) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1215,f2126]) ).
fof(f2190,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f34,f2189]) ).
fof(f2191,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)],[f33,f2127]) ).
fof(f2192,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = multiplication(X0,addition(multiplication(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f138,f2191]) ).
fof(f2193,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = multiplication(X0,addition(X1,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f29,f2192]) ).
fof(f2194,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X0,X1))) = multiplication(antidomain(X0),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f147,f2128]) ).
fof(f2195,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f31,f2129]) ).
fof(f2196,plain,
! [X0] : multiplication(antidomain(X0),addition(one,X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f31,f2130]) ).
fof(f2201,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = X0,
inference(forward_demodulation,[status(thm)],[f31,f2134]) ).
fof(f2202,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f31,f2135]) ).
fof(f2210,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)],[f88,f2141]) ).
fof(f2211,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)],[f82,f2210]) ).
fof(f2212,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f2211]) ).
fof(f2213,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)],[f88,f2142]) ).
fof(f2214,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)],[f82,f2213]) ).
fof(f2215,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f2214]) ).
fof(f2217,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)],[f88,f2148]) ).
fof(f2218,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)],[f82,f2217]) ).
fof(f2219,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)],[f82,f2149]) ).
fof(f2220,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f138,f2219]) ).
fof(f2221,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)],[f88,f2150]) ).
fof(f2222,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)],[f88,f2221]) ).
fof(f2223,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)],[f82,f2222]) ).
fof(f2224,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f138,f2223]) ).
fof(f2226,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f33,f2153]) ).
fof(f2228,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(one,X2)),X1),
inference(forward_demodulation,[status(thm)],[f82,f2162]) ).
fof(f2229,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(addition(one,X1),X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f138,f2163]) ).
fof(f2230,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,addition(one,X1)))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f88,f2229]) ).
fof(f2231,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(one,X2))) = addition(X1,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f82,f2165]) ).
fof(f2232,plain,
! [X0,X1] : addition(c(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1737,f42]) ).
fof(f2233,plain,
! [X0,X1] : leq(antidomain(c(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f1096,f1737]) ).
fof(f2234,plain,
! [X0,X1] : leq(domain(c(X0)),addition(X1,one)),
inference(paramodulation,[status(thm)],[f633,f1737]) ).
fof(f2235,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f57,f1737]) ).
fof(f2236,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f56,f1737]) ).
fof(f2239,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f88,f1737]) ).
fof(f2240,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f30,f1737]) ).
fof(f2242,plain,
! [X0,X1] : leq(c(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f29,f1737]) ).
fof(f2245,plain,
! [X0,X1] : addition(one,addition(c(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f82,f2232]) ).
fof(f2246,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1738,f42]) ).
fof(f2251,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f88,f1738]) ).
fof(f2252,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f30,f1738]) ).
fof(f2254,plain,
! [X0,X1] : leq(antidomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f29,f1738]) ).
fof(f2257,plain,
! [X0,X1] : addition(one,addition(antidomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f82,f2246]) ).
fof(f2258,plain,
! [X0,X1] : addition(coantidomain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1739,f42]) ).
fof(f2262,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f88,f1739]) ).
fof(f2263,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f30,f1739]) ).
fof(f2265,plain,
! [X0,X1] : leq(coantidomain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f29,f1739]) ).
fof(f2268,plain,
! [X0,X1] : addition(one,addition(coantidomain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f82,f2258]) ).
fof(f2269,plain,
! [X0,X1] : addition(domain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f1740,f42]) ).
fof(f2272,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f54,f1740]) ).
fof(f2275,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f88,f1740]) ).
fof(f2276,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f30,f1740]) ).
fof(f2278,plain,
! [X0,X1] : leq(domain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f29,f1740]) ).
fof(f2281,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(X1,one),
inference(forward_demodulation,[status(thm)],[f82,f2269]) ).
fof(f2285,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(antidomain(domain(X0)),X1),
inference(paramodulation,[status(thm)],[f52,f171]) ).
fof(f2286,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(antidomain(antidomain(X0)),X1),
inference(paramodulation,[status(thm)],[f47,f171]) ).
fof(f2298,plain,
! [X0] : multiplication(antidomain(c(X0)),one) = multiplication(antidomain(c(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f657,f171]) ).
fof(f2299,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)],[f309,f171]) ).
fof(f2300,plain,
! [X0] : multiplication(antidomain(codomain(X0)),one) = multiplication(antidomain(codomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f354,f171]) ).
fof(f2301,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)],[f237,f171]) ).
fof(f2302,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f283,f171]) ).
fof(f2303,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)],[f138,f171]) ).
fof(f2304,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)],[f37,f171]) ).
fof(f2305,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)],[f36,f171]) ).
fof(f2306,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f88,f171]) ).
fof(f2307,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(paramodulation,[status(thm)],[f30,f171]) ).
fof(f2309,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(one,X1))) = multiplication(antidomain(multiplication(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f147,f171]) ).
fof(f2310,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)],[f84,f171]) ).
fof(f2311,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,X1)) = multiplication(antidomain(addition(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f90,f171]) ).
fof(f2312,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X0,addition(X1,X2))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f82,f171]) ).
fof(f2313,plain,
! [X0,X1,X2] : multiplication(antidomain(addition(X0,X1)),addition(X1,addition(X2,X0))) = multiplication(antidomain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f82,f171]) ).
fof(f2320,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X1,X0))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f171,f147]) ).
fof(f2322,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)],[f171,f138]) ).
fof(f2323,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,X0),coantidomain(multiplication(antidomain(X0),X1)))) = zero,
inference(paramodulation,[status(thm)],[f171,f129]) ).
fof(f2325,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)],[f171,f309]) ).
fof(f2326,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)],[f171,f237]) ).
fof(f2327,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)],[f171,f37]) ).
fof(f2328,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)],[f171,f37]) ).
fof(f2329,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)],[f171,f36]) ).
fof(f2330,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)],[f171,f36]) ).
fof(f2331,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X1,X0),X2)) = multiplication(multiplication(antidomain(X0),X1),X2),
inference(paramodulation,[status(thm)],[f171,f33]) ).
fof(f2336,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,domain(X0))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f52,f2285]) ).
fof(f2337,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f47,f2286]) ).
fof(f2340,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f2298]) ).
fof(f2341,plain,
! [X0,X1] : zero = multiplication(antidomain(coantidomain(multiplication(codomain(X0),X1))),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f44,f2299]) ).
fof(f2342,plain,
! [X0] : antidomain(codomain(X0)) = multiplication(antidomain(codomain(X0)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f2300]) ).
fof(f2343,plain,
! [X0,X1] : zero = multiplication(antidomain(antidomain(multiplication(X0,domain(X1)))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f44,f2301]) ).
fof(f2344,plain,
! [X0,X1] : zero = multiplication(domain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f47,f2343]) ).
fof(f2345,plain,
! [X0,X1] : zero = domain_difference(multiplication(X0,domain(X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f53,f2344]) ).
fof(f2346,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f2302]) ).
fof(f2347,plain,
! [X0] : c(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f2346]) ).
fof(f2348,plain,
! [X0] : c(X0) = multiplication(c(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f2347]) ).
fof(f2350,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X0),
inference(forward_demodulation,[status(thm)],[f44,f2311]) ).
fof(f2352,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,addition(X1,X0))) = multiplication(antidomain(X0),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f147,f2320]) ).
fof(f2355,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f138,f2322]) ).
fof(f2356,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)],[f29,f2327]) ).
fof(f2357,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,addition(X2,X0))) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f138,f2329]) ).
fof(f2358,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)],[f88,f2330]) ).
fof(f2359,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,X2)) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f162,f2358]) ).
fof(f2360,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),addition(X1,X2)) = multiplication(antidomain(X0),addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f138,f2359]) ).
fof(f2361,plain,
! [X0,X1,X2] : multiplication(antidomain(X0),multiplication(addition(X1,X0),X2)) = multiplication(antidomain(X0),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f2331]) ).
fof(f2362,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f33,f175]) ).
fof(f2369,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)],[f309,f175]) ).
fof(f2370,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f88,f175]) ).
fof(f2371,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f30,f175]) ).
fof(f2377,plain,
! [X0,X1] : multiplication(coantidomain(X0),addition(X1,codomain(X0))) = multiplication(coantidomain(X0),X1),
inference(paramodulation,[status(thm)],[f51,f175]) ).
fof(f2380,plain,
! [X0,X1] : backward_diamond(addition(X0,coantidomain(codomain(X1))),X1) = codomain(multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f175,f55]) ).
fof(f2381,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)],[f175,f309]) ).
fof(f2382,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f175,f33]) ).
fof(f2388,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,coantidomain(X0)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f175,f147]) ).
fof(f2390,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f175,f138]) ).
fof(f2391,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f175,f129]) ).
fof(f2393,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)],[f175,f309]) ).
fof(f2394,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)],[f175,f237]) ).
fof(f2395,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)],[f175,f37]) ).
fof(f2396,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)],[f175,f37]) ).
fof(f2397,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f175,f36]) ).
fof(f2399,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f175,f33]) ).
fof(f2400,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f2362]) ).
fof(f2406,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)],[f33,f2369]) ).
fof(f2407,plain,
! [X0,X1] : zero = multiplication(multiplication(codomain(X0),X1),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f129,f2406]) ).
fof(f2408,plain,
! [X0,X1] : zero = multiplication(codomain(X0),multiplication(X1,coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f33,f2407]) ).
fof(f2413,plain,
! [X0,X1] : backward_diamond(addition(X0,coantidomain(codomain(X1))),X1) = backward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f55,f2380]) ).
fof(f2414,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)],[f29,f2381]) ).
fof(f2415,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)],[f175,f2414]) ).
fof(f2416,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,coantidomain(multiplication(X0,X1))))) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f2382]) ).
fof(f2424,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f138,f2390]) ).
fof(f2425,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)],[f29,f2395]) ).
fof(f2426,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,coantidomain(X0)))) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f138,f2397]) ).
fof(f2429,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,coantidomain(X0)),X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f2399]) ).
fof(f2435,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f88,f177]) ).
fof(f2436,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f30,f177]) ).
fof(f2441,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(X1,one)) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f37,f177]) ).
fof(f2442,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X1,addition(X0,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f88,f177]) ).
fof(f2443,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f30,f177]) ).
fof(f2445,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = multiplication(X0,addition(one,X1)),
inference(paramodulation,[status(thm)],[f147,f177]) ).
fof(f2448,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X1),one)) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f53,f177]) ).
fof(f2449,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(X2,one)) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f33,f177]) ).
fof(f2451,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(addition(X0,X1),one)) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f162,f177]) ).
fof(f2452,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(multiplication(X0,X1),one)) = addition(antidomain(X0),zero),
inference(paramodulation,[status(thm)],[f121,f177]) ).
fof(f2457,plain,
! [X0,X1] : multiplication(X0,addition(addition(X1,one),one)) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f177,f177]) ).
fof(f2459,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(coantidomain(X0),X1),one)) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f136,f177]) ).
fof(f2460,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X1,coantidomain(multiplication(X0,X1))),one)) = addition(X0,zero),
inference(paramodulation,[status(thm)],[f129,f177]) ).
fof(f2468,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f177,f147]) ).
fof(f2469,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,one),X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f177,f138]) ).
fof(f2470,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(addition(X0,multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f177,f138]) ).
fof(f2471,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(addition(X0,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f177,f129]) ).
fof(f2473,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)],[f177,f309]) ).
fof(f2474,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)],[f177,f237]) ).
fof(f2475,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)],[f177,f37]) ).
fof(f2476,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)],[f177,f37]) ).
fof(f2477,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f177,f36]) ).
fof(f2479,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,one),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f177,f33]) ).
fof(f2481,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(paramodulation,[status(thm)],[f177,f37]) ).
fof(f2482,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),X2))) = multiplication(addition(X1,X0),addition(X2,one)),
inference(paramodulation,[status(thm)],[f177,f88]) ).
fof(f2483,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),X2))) = multiplication(addition(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f177,f30]) ).
fof(f2484,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = multiplication(X0,addition(X1,one)),
inference(paramodulation,[status(thm)],[f177,f147]) ).
fof(f2485,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,addition(X1,one))) = multiplication(antidomain(multiplication(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f177,f171]) ).
fof(f2487,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f177,f1257]) ).
fof(f2488,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f177,f1256]) ).
fof(f2489,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f177,f1259]) ).
fof(f2490,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f177,f1163]) ).
fof(f2491,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f177,f90]) ).
fof(f2492,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f177,f88]) ).
fof(f2493,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,X1),multiplication(X0,addition(X1,one)))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f177,f84]) ).
fof(f2494,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(X2,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f177,f82]) ).
fof(f2495,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(X2,one))) = addition(multiplication(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f177,f82]) ).
fof(f2496,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != X0
| leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f177,f231]) ).
fof(f2497,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != multiplication(X0,X1)
| leq(X0,multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f177,f43]) ).
fof(f2498,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f177,f30]) ).
fof(f2507,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f33,f2441]) ).
fof(f2514,plain,
! [X0,X1] : multiplication(domain(X0),addition(one,antidomain(X1))) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f2448]) ).
fof(f2515,plain,
! [X0,X1] : multiplication(domain(X0),one) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1215,f2514]) ).
fof(f2516,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f34,f2515]) ).
fof(f2517,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)],[f33,f2449]) ).
fof(f2518,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = multiplication(X0,addition(multiplication(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f138,f2517]) ).
fof(f2519,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = multiplication(X0,addition(X1,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f29,f2518]) ).
fof(f2522,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,addition(X0,one))) = addition(antidomain(X0),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f88,f2451]) ).
fof(f2523,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,addition(X0,one))) = multiplication(antidomain(X0),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f177,f2522]) ).
fof(f2524,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = addition(antidomain(X0),zero),
inference(forward_demodulation,[status(thm)],[f29,f2452]) ).
fof(f2525,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,multiplication(X0,X1))) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f31,f2524]) ).
fof(f2537,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f2457]) ).
fof(f2538,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f90,f2537]) ).
fof(f2541,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = addition(X0,zero),
inference(forward_demodulation,[status(thm)],[f29,f2459]) ).
fof(f2542,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(coantidomain(X0),X1))) = X0,
inference(forward_demodulation,[status(thm)],[f31,f2541]) ).
fof(f2543,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = addition(X0,zero),
inference(forward_demodulation,[status(thm)],[f29,f2460]) ).
fof(f2544,plain,
! [X0,X1] : multiplication(X0,addition(one,multiplication(X1,coantidomain(multiplication(X0,X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f31,f2543]) ).
fof(f2555,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f90,f2468]) ).
fof(f2556,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)],[f88,f2469]) ).
fof(f2557,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)],[f82,f2556]) ).
fof(f2558,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f2557]) ).
fof(f2559,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)],[f88,f2470]) ).
fof(f2560,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)],[f82,f2559]) ).
fof(f2561,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f2560]) ).
fof(f2563,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)],[f88,f2476]) ).
fof(f2564,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)],[f82,f2563]) ).
fof(f2565,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)],[f82,f2477]) ).
fof(f2566,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f138,f2565]) ).
fof(f2572,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f33,f2481]) ).
fof(f2574,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,one)),X1),
inference(forward_demodulation,[status(thm)],[f82,f2492]) ).
fof(f2575,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(addition(X1,one),X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f138,f2493]) ).
fof(f2576,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,addition(X1,X1)))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f88,f2575]) ).
fof(f2577,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f32,f2576]) ).
fof(f2578,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(X2,one))) = addition(X1,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f82,f2495]) ).
fof(f2579,plain,
! [X0,X1] : addition(divergence(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2083,f42]) ).
fof(f2593,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f82,f2083]) ).
fof(f2594,plain,
! [X0,X1,X2] : leq(divergence(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f82,f2083]) ).
fof(f2599,plain,
! [X0,X1] : addition(one,addition(X0,divergence(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f2579]) ).
fof(f2600,plain,
! [X0,X1] : addition(codomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2095,f42]) ).
fof(f2601,plain,
! [X0,X1] : leq(coantidomain(codomain(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f178,f2095]) ).
fof(f2602,plain,
! [X0,X1,X2] : leq(backward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f55,f2095]) ).
fof(f2617,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f82,f2095]) ).
fof(f2618,plain,
! [X0,X1,X2] : leq(codomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f82,f2095]) ).
fof(f2623,plain,
! [X0,X1] : addition(one,addition(X0,codomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f2600]) ).
fof(f2626,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)],[f82,f155]) ).
fof(f2627,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)],[f82,f155]) ).
fof(f2630,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)],[f182,f155]) ).
fof(f2631,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)],[f180,f155]) ).
fof(f2632,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)],[f53,f155]) ).
fof(f2633,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)],[f33,f155]) ).
fof(f2635,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)],[f162,f155]) ).
fof(f2636,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)],[f121,f155]) ).
fof(f2640,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(codomain(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f2026,f155]) ).
fof(f2641,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)],[f147,f155]) ).
fof(f2642,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)],[f166,f155]) ).
fof(f2643,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)],[f177,f155]) ).
fof(f2645,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)],[f136,f155]) ).
fof(f2646,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)],[f129,f155]) ).
fof(f2649,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f34,f155]) ).
fof(f2650,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)],[f155,f155]) ).
fof(f2651,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)],[f138,f155]) ).
fof(f2652,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)],[f37,f155]) ).
fof(f2653,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)],[f36,f155]) ).
fof(f2654,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)],[f177,f155]) ).
fof(f2655,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)],[f147,f155]) ).
fof(f2656,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)],[f84,f155]) ).
fof(f2657,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)],[f90,f155]) ).
fof(f2658,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)],[f82,f155]) ).
fof(f2659,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)],[f82,f155]) ).
fof(f2660,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f31,f155]) ).
fof(f2661,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)],[f29,f155]) ).
fof(f2662,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)],[f29,f155]) ).
fof(f2663,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f32,f155]) ).
fof(f2664,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)],[f182,f155]) ).
fof(f2665,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)],[f180,f155]) ).
fof(f2666,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)],[f53,f155]) ).
fof(f2667,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)],[f33,f155]) ).
fof(f2668,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)],[f171,f155]) ).
fof(f2669,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)],[f162,f155]) ).
fof(f2670,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)],[f121,f155]) ).
fof(f2674,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,codomain(X0))),X2),
inference(paramodulation,[status(thm)],[f2026,f155]) ).
fof(f2675,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)],[f147,f155]) ).
fof(f2676,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)],[f166,f155]) ).
fof(f2677,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)],[f177,f155]) ).
fof(f2678,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)],[f175,f155]) ).
fof(f2679,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)],[f136,f155]) ).
fof(f2680,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)],[f129,f155]) ).
fof(f2683,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f34,f155]) ).
fof(f2685,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(X0,addition(X2,X1)),X3)),
inference(paramodulation,[status(thm)],[f155,f1257]) ).
fof(f2689,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)],[f155,f82]) ).
fof(f2690,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)],[f155,f82]) ).
fof(f2691,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)],[f155,f171]) ).
fof(f2692,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)],[f155,f162]) ).
fof(f2693,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(X0,addition(X1,X3)),X4))),
inference(paramodulation,[status(thm)],[f155,f1257]) ).
fof(f2694,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)],[f155,f1256]) ).
fof(f2695,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(X0,addition(X3,X1)),X2)),
inference(paramodulation,[status(thm)],[f155,f1259]) ).
fof(f2696,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(X0,addition(X1,X2)),X3)),
inference(paramodulation,[status(thm)],[f155,f1163]) ).
fof(f2698,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)],[f155,f88]) ).
fof(f2699,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)],[f155,f84]) ).
fof(f2700,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)],[f155,f82]) ).
fof(f2701,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)],[f155,f82]) ).
fof(f2702,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)],[f155,f231]) ).
fof(f2703,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)],[f155,f43]) ).
fof(f2704,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)],[f155,f30]) ).
fof(f2712,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,addition(X3,X2)),X0),
inference(forward_demodulation,[status(thm)],[f138,f2627]) ).
fof(f2717,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),X2) = addition(multiplication(c(X0),addition(domain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f2630]) ).
fof(f2718,plain,
! [X0,X1,X2] : addition(multiplication(coantidomain(X0),X1),X2) = addition(multiplication(coantidomain(X0),addition(codomain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f2631]) ).
fof(f2719,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)],[f33,f2633]) ).
fof(f2720,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)],[f155,f2719]) ).
fof(f2721,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)],[f138,f2720]) ).
fof(f2722,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)],[f33,f2721]) ).
fof(f2725,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)],[f155,f2635]) ).
fof(f2726,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)],[f88,f2725]) ).
fof(f2727,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)],[f65,f2636]) ).
fof(f2735,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)],[f88,f2641]) ).
fof(f2736,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)],[f82,f2735]) ).
fof(f2737,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)],[f88,f2736]) ).
fof(f2738,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)],[f138,f2737]) ).
fof(f2739,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)],[f88,f2738]) ).
fof(f2740,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)],[f155,f2642]) ).
fof(f2741,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)],[f88,f2740]) ).
fof(f2742,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)],[f88,f2643]) ).
fof(f2743,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)],[f82,f2742]) ).
fof(f2744,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)],[f88,f2743]) ).
fof(f2745,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)],[f138,f2744]) ).
fof(f2746,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)],[f88,f2745]) ).
fof(f2749,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)],[f65,f2645]) ).
fof(f2750,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)],[f65,f2646]) ).
fof(f2753,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)],[f155,f2650]) ).
fof(f2754,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)],[f155,f2753]) ).
fof(f2755,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)],[f88,f2754]) ).
fof(f2756,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)],[f138,f2651]) ).
fof(f2757,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)],[f88,f2756]) ).
fof(f2758,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = multiplication(X0,addition(X2,addition(X3,X1))),
inference(forward_demodulation,[status(thm)],[f138,f2757]) ).
fof(f2759,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)],[f138,f2653]) ).
fof(f2760,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)],[f88,f2759]) ).
fof(f2761,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = multiplication(X0,addition(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f138,f2760]) ).
fof(f2762,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)],[f33,f2654]) ).
fof(f2763,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)],[f138,f2762]) ).
fof(f2764,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)],[f33,f2763]) ).
fof(f2765,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)],[f138,f2764]) ).
fof(f2766,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)],[f82,f2765]) ).
fof(f2767,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)],[f33,f2655]) ).
fof(f2768,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)],[f138,f2767]) ).
fof(f2769,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)],[f33,f2768]) ).
fof(f2770,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)],[f138,f2769]) ).
fof(f2771,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)],[f82,f2770]) ).
fof(f2772,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)],[f155,f2656]) ).
fof(f2773,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)],[f155,f2657]) ).
fof(f2774,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)],[f155,f2773]) ).
fof(f2775,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)],[f88,f2774]) ).
fof(f2776,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),zero),
inference(forward_demodulation,[status(thm)],[f138,f2660]) ).
fof(f2777,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f31,f2776]) ).
fof(f2778,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f138,f2663]) ).
fof(f2779,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f2778]) ).
fof(f2780,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)],[f82,f2664]) ).
fof(f2781,plain,
! [X0,X1,X2] : addition(X0,multiplication(c(X1),X2)) = addition(multiplication(c(X1),addition(X2,domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f65,f2780]) ).
fof(f2782,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)],[f82,f2665]) ).
fof(f2783,plain,
! [X0,X1,X2] : addition(X0,multiplication(coantidomain(X1),X2)) = addition(multiplication(coantidomain(X1),addition(X2,codomain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f65,f2782]) ).
fof(f2784,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)],[f33,f2667]) ).
fof(f2785,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)],[f155,f2784]) ).
fof(f2786,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)],[f138,f2785]) ).
fof(f2787,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)],[f33,f2786]) ).
fof(f2788,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)],[f155,f2668]) ).
fof(f2789,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)],[f155,f2669]) ).
fof(f2790,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)],[f82,f2670]) ).
fof(f2791,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)],[f65,f2790]) ).
fof(f2802,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,codomain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f82,f2674]) ).
fof(f2803,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)],[f88,f2675]) ).
fof(f2804,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)],[f155,f2803]) ).
fof(f2805,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)],[f82,f2804]) ).
fof(f2806,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)],[f155,f2676]) ).
fof(f2807,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)],[f88,f2677]) ).
fof(f2808,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)],[f155,f2807]) ).
fof(f2809,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)],[f82,f2808]) ).
fof(f2810,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)],[f155,f2678]) ).
fof(f2811,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)],[f82,f2679]) ).
fof(f2812,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)],[f65,f2811]) ).
fof(f2813,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)],[f82,f2680]) ).
fof(f2814,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)],[f65,f2813]) ).
fof(f2821,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,X2))) = addition(multiplication(X0,addition(X2,one)),X1),
inference(forward_demodulation,[status(thm)],[f82,f2683]) ).
fof(f2830,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f2690]) ).
fof(f2833,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)],[f88,f2698]) ).
fof(f2834,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)],[f155,f2833]) ).
fof(f2835,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)],[f88,f2834]) ).
fof(f2836,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)],[f88,f2699]) ).
fof(f2837,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)],[f155,f2836]) ).
fof(f2838,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)],[f155,f2837]) ).
fof(f2839,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)],[f88,f2700]) ).
fof(f2840,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)],[f88,f2701]) ).
fof(f2841,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)],[f88,f2704]) ).
fof(f2842,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)],[f88,f2841]) ).
fof(f2847,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),X0),
inference(resolution,[status(thm)],[f2174,f231]) ).
fof(f2850,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),divergence(X2)))),
inference(paramodulation,[status(thm)],[f88,f2174]) ).
fof(f2851,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),divergence(X2)))),
inference(paramodulation,[status(thm)],[f30,f2174]) ).
fof(f2865,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)],[f2174,f155]) ).
fof(f2866,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),divergence(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2174,f88]) ).
fof(f2867,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),divergence(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2174,f30]) ).
fof(f2874,plain,
! [X0,X1,X2] : leq(multiplication(X0,divergence(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2174,f1256]) ).
fof(f2878,plain,
! [X0,X1,X2] : addition(multiplication(X0,divergence(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2174,f88]) ).
fof(f2880,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,divergence(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2174,f82]) ).
fof(f2881,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,divergence(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2174,f82]) ).
fof(f2883,plain,
! [X0,X1] :
( X0 != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(paramodulation,[status(thm)],[f2174,f43]) ).
fof(f2884,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,divergence(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2174,f30]) ).
fof(f2896,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)],[f138,f2865]) ).
fof(f2897,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)],[f33,f2896]) ).
fof(f2898,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)],[f138,f2897]) ).
fof(f2899,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)],[f82,f2898]) ).
fof(f2905,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,divergence(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f2878]) ).
fof(f2907,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,divergence(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f82,f2881]) ).
fof(f2910,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,divergence(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f2847]) ).
fof(f2917,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),X0),
inference(resolution,[status(thm)],[f2175,f231]) ).
fof(f2920,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),codomain(X2)))),
inference(paramodulation,[status(thm)],[f88,f2175]) ).
fof(f2921,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),codomain(X2)))),
inference(paramodulation,[status(thm)],[f30,f2175]) ).
fof(f2931,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,coantidomain(codomain(X1)))),
inference(paramodulation,[status(thm)],[f178,f2175]) ).
fof(f2932,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f55,f2175]) ).
fof(f2940,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)],[f2175,f155]) ).
fof(f2941,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),codomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2175,f88]) ).
fof(f2942,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),codomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2175,f30]) ).
fof(f2949,plain,
! [X0,X1,X2] : leq(multiplication(X0,codomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2175,f1256]) ).
fof(f2953,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2175,f88]) ).
fof(f2955,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,codomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2175,f82]) ).
fof(f2956,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,codomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2175,f82]) ).
fof(f2958,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f2175,f43]) ).
fof(f2959,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,codomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2175,f30]) ).
fof(f2972,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)],[f138,f2940]) ).
fof(f2973,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)],[f33,f2972]) ).
fof(f2974,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)],[f138,f2973]) ).
fof(f2975,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)],[f82,f2974]) ).
fof(f2981,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,codomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f2953]) ).
fof(f2983,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,codomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f82,f2956]) ).
fof(f2987,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,codomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f2917]) ).
fof(f2992,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(codomain(X1))),X0),
inference(paramodulation,[status(thm)],[f178,f2917]) ).
fof(f2993,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f55,f2917]) ).
fof(f2999,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),X0),
inference(resolution,[status(thm)],[f2176,f231]) ).
fof(f3002,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),c(X2)))),
inference(paramodulation,[status(thm)],[f88,f2176]) ).
fof(f3003,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),c(X2)))),
inference(paramodulation,[status(thm)],[f30,f2176]) ).
fof(f3011,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f1096,f2176]) ).
fof(f3012,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,domain(c(X1)))),
inference(paramodulation,[status(thm)],[f633,f2176]) ).
fof(f3013,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f57,f2176]) ).
fof(f3014,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f56,f2176]) ).
fof(f3022,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)],[f2176,f155]) ).
fof(f3023,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),c(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2176,f88]) ).
fof(f3024,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),c(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2176,f30]) ).
fof(f3031,plain,
! [X0,X1,X2] : leq(multiplication(X0,c(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2176,f1256]) ).
fof(f3035,plain,
! [X0,X1,X2] : addition(multiplication(X0,c(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2176,f88]) ).
fof(f3037,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,c(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2176,f82]) ).
fof(f3038,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,c(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2176,f82]) ).
fof(f3040,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f2176,f43]) ).
fof(f3041,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,c(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2176,f30]) ).
fof(f3054,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)],[f138,f3022]) ).
fof(f3055,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)],[f33,f3054]) ).
fof(f3056,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)],[f138,f3055]) ).
fof(f3057,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)],[f82,f3056]) ).
fof(f3063,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,c(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f3035]) ).
fof(f3065,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,c(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f82,f3038]) ).
fof(f3068,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,c(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f2999]) ).
fof(f3072,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(c(X1))),X0),
inference(paramodulation,[status(thm)],[f1096,f2999]) ).
fof(f3073,plain,
! [X0,X1] : leq(multiplication(X0,domain(c(X1))),X0),
inference(paramodulation,[status(thm)],[f633,f2999]) ).
fof(f3074,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f57,f2999]) ).
fof(f3075,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f56,f2999]) ).
fof(f3082,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f37,f186]) ).
fof(f3087,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(paramodulation,[status(thm)],[f177,f186]) ).
fof(f3088,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(paramodulation,[status(thm)],[f147,f186]) ).
fof(f3092,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = addition(zero,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f182,f186]) ).
fof(f3093,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = addition(zero,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f180,f186]) ).
fof(f3094,plain,
! [X0,X1,X2] : multiplication(addition(X0,domain(X1)),antidomain(X2)) = addition(domain_difference(X1,X2),multiplication(X0,antidomain(X2))),
inference(paramodulation,[status(thm)],[f53,f186]) ).
fof(f3095,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,f186]) ).
fof(f3096,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)],[f171,f186]) ).
fof(f3097,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)],[f162,f186]) ).
fof(f3098,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = addition(zero,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f121,f186]) ).
fof(f3099,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f44,f186]) ).
fof(f3101,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f35,f186]) ).
fof(f3102,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X1)) = addition(X1,multiplication(X0,codomain(X1))),
inference(paramodulation,[status(thm)],[f2026,f186]) ).
fof(f3103,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)],[f147,f186]) ).
fof(f3104,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)],[f166,f186]) ).
fof(f3105,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)],[f177,f186]) ).
fof(f3106,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)],[f175,f186]) ).
fof(f3107,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = addition(zero,multiplication(X0,multiplication(coantidomain(X1),X2))),
inference(paramodulation,[status(thm)],[f136,f186]) ).
fof(f3108,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)],[f129,f186]) ).
fof(f3109,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(zero,multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f48,f186]) ).
fof(f3112,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = addition(multiplication(X1,domain(X0)),zero),
inference(paramodulation,[status(thm)],[f182,f186]) ).
fof(f3113,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = addition(multiplication(X1,codomain(X0)),zero),
inference(paramodulation,[status(thm)],[f180,f186]) ).
fof(f3114,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),X1),antidomain(X2)) = addition(multiplication(X1,antidomain(X2)),domain_difference(X0,X2)),
inference(paramodulation,[status(thm)],[f53,f186]) ).
fof(f3115,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,f186]) ).
fof(f3116,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)],[f171,f186]) ).
fof(f3117,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)],[f162,f186]) ).
fof(f3118,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = addition(multiplication(X1,multiplication(X0,X2)),zero),
inference(paramodulation,[status(thm)],[f121,f186]) ).
fof(f3119,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(multiplication(X1,X0),zero),
inference(paramodulation,[status(thm)],[f44,f186]) ).
fof(f3121,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f35,f186]) ).
fof(f3122,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(multiplication(X1,codomain(X0)),X0),
inference(paramodulation,[status(thm)],[f2026,f186]) ).
fof(f3123,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)],[f147,f186]) ).
fof(f3124,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)],[f166,f186]) ).
fof(f3125,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)],[f177,f186]) ).
fof(f3126,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)],[f175,f186]) ).
fof(f3127,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = addition(multiplication(X1,multiplication(coantidomain(X0),X2)),zero),
inference(paramodulation,[status(thm)],[f136,f186]) ).
fof(f3128,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)],[f129,f186]) ).
fof(f3129,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(multiplication(X1,coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f48,f186]) ).
fof(f3133,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f186,f37]) ).
fof(f3135,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)],[f186,f155]) ).
fof(f3139,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(X1,one)) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f186,f177]) ).
fof(f3140,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(one,X1)) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f186,f147]) ).
fof(f3141,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)],[f186,f171]) ).
fof(f3142,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)],[f186,f162]) ).
fof(f3143,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f186,f1257]) ).
fof(f3144,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f186,f1256]) ).
fof(f3145,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f186,f1259]) ).
fof(f3146,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f186,f1163]) ).
fof(f3147,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(addition(X2,X0),X1)) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f186,f90]) ).
fof(f3148,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)],[f186,f88]) ).
fof(f3150,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)],[f186,f82]) ).
fof(f3151,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)],[f186,f82]) ).
fof(f3152,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f186,f231]) ).
fof(f3153,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f186,f43]) ).
fof(f3154,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)],[f186,f30]) ).
fof(f3163,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(forward_demodulation,[status(thm)],[f29,f3087]) ).
fof(f3164,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f33,f3163]) ).
fof(f3165,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f29,f3088]) ).
fof(f3166,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f33,f3165]) ).
fof(f3167,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f65,f3092]) ).
fof(f3168,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f65,f3093]) ).
fof(f3169,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f65,f3098]) ).
fof(f3170,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f3099]) ).
fof(f3172,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)],[f88,f3103]) ).
fof(f3173,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)],[f82,f3172]) ).
fof(f3174,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)],[f88,f3105]) ).
fof(f3175,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)],[f82,f3174]) ).
fof(f3176,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f65,f3107]) ).
fof(f3177,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)],[f65,f3108]) ).
fof(f3178,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f65,f3109]) ).
fof(f3183,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f31,f3112]) ).
fof(f3184,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f31,f3113]) ).
fof(f3185,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)],[f29,f3116]) ).
fof(f3186,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)],[f29,f3117]) ).
fof(f3187,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f31,f3118]) ).
fof(f3188,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f31,f3119]) ).
fof(f3190,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f3121]) ).
fof(f3191,plain,
! [X0,X1] : multiplication(addition(X0,X1),codomain(X0)) = addition(X0,multiplication(X1,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f3122]) ).
fof(f3192,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)],[f29,f3124]) ).
fof(f3193,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)],[f29,f3126]) ).
fof(f3194,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f31,f3127]) ).
fof(f3195,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)],[f31,f3128]) ).
fof(f3196,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f31,f3129]) ).
fof(f3206,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f33,f3139]) ).
fof(f3207,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f29,f3206]) ).
fof(f3208,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f33,f3140]) ).
fof(f3209,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f29,f3208]) ).
fof(f3210,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,X1),X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f186,f3147]) ).
fof(f3211,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X0)),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f3210]) ).
fof(f3212,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f186,f3211]) ).
fof(f3218,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),X0),
inference(resolution,[status(thm)],[f2177,f231]) ).
fof(f3222,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),antidomain(X2)))),
inference(paramodulation,[status(thm)],[f88,f2177]) ).
fof(f3223,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),antidomain(X2)))),
inference(paramodulation,[status(thm)],[f30,f2177]) ).
fof(f3227,plain,
! [X0,X1] : domain(X0) = addition(domain(X0),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f53,f2177]) ).
fof(f3242,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)],[f2177,f155]) ).
fof(f3243,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),antidomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2177,f88]) ).
fof(f3244,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),antidomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2177,f30]) ).
fof(f3251,plain,
! [X0,X1,X2] : leq(multiplication(X0,antidomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2177,f1256]) ).
fof(f3255,plain,
! [X0,X1,X2] : addition(multiplication(X0,antidomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2177,f88]) ).
fof(f3257,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,antidomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2177,f82]) ).
fof(f3258,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,antidomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2177,f82]) ).
fof(f3260,plain,
! [X0,X1] :
( X0 != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f2177,f43]) ).
fof(f3261,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,antidomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2177,f30]) ).
fof(f3278,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)],[f138,f3242]) ).
fof(f3279,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)],[f33,f3278]) ).
fof(f3280,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)],[f138,f3279]) ).
fof(f3281,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)],[f82,f3280]) ).
fof(f3287,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,antidomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f3255]) ).
fof(f3289,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,antidomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f82,f3258]) ).
fof(f3292,plain,
! [X0,X1] : leq(domain_difference(X0,X1),domain(X0)),
inference(paramodulation,[status(thm)],[f53,f3218]) ).
fof(f3293,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,antidomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f3218]) ).
fof(f3299,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),X0),
inference(paramodulation,[status(thm)],[f47,f3218]) ).
fof(f3305,plain,
! [X0,X1] : addition(domain_difference(X0,X1),domain(X0)) = domain(X0),
inference(resolution,[status(thm)],[f3292,f42]) ).
fof(f3311,plain,
! [X0,X1] : leq(domain_difference(domain(X0),X1),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f181,f3292]) ).
fof(f3312,plain,
! [X0,X1] : leq(domain_difference(antidomain(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f631,f3292]) ).
fof(f3313,plain,
! [X0,X1,X2] : leq(domain_difference(multiplication(X0,domain(X1)),X2),forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f54,f3292]) ).
fof(f3316,plain,
! [X0,X1] : addition(domain(X0),domain_difference(X0,X1)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f29,f3305]) ).
fof(f3323,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,domain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f3299]) ).
fof(f3329,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f54,f3299]) ).
fof(f3336,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),X0),
inference(resolution,[status(thm)],[f2178,f231]) ).
fof(f3340,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),coantidomain(X2)))),
inference(paramodulation,[status(thm)],[f88,f2178]) ).
fof(f3341,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),coantidomain(X2)))),
inference(paramodulation,[status(thm)],[f30,f2178]) ).
fof(f3359,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)],[f2178,f155]) ).
fof(f3360,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),coantidomain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2178,f88]) ).
fof(f3361,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),coantidomain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2178,f30]) ).
fof(f3368,plain,
! [X0,X1,X2] : leq(multiplication(X0,coantidomain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2178,f1256]) ).
fof(f3372,plain,
! [X0,X1,X2] : addition(multiplication(X0,coantidomain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2178,f88]) ).
fof(f3374,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,coantidomain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2178,f82]) ).
fof(f3375,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,coantidomain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2178,f82]) ).
fof(f3377,plain,
! [X0,X1] :
( X0 != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f2178,f43]) ).
fof(f3378,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,coantidomain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2178,f30]) ).
fof(f3393,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)],[f138,f3359]) ).
fof(f3394,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)],[f33,f3393]) ).
fof(f3395,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)],[f138,f3394]) ).
fof(f3396,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)],[f82,f3395]) ).
fof(f3402,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,coantidomain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f3372]) ).
fof(f3404,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,coantidomain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f82,f3375]) ).
fof(f3407,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,coantidomain(X2))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f3336]) ).
fof(f3418,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f138,f189]) ).
fof(f3419,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f36,f189]) ).
fof(f3425,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)],[f177,f189]) ).
fof(f3426,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)],[f147,f189]) ).
fof(f3427,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)],[f29,f189]) ).
fof(f3428,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)],[f29,f189]) ).
fof(f3429,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)],[f33,f189]) ).
fof(f3431,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(antidomain(multiplication(X0,X1)),X0),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f44,f189]) ).
fof(f3435,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)],[f129,f189]) ).
fof(f3436,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)],[f182,f189]) ).
fof(f3437,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)],[f180,f189]) ).
fof(f3438,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)],[f53,f189]) ).
fof(f3439,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)],[f33,f189]) ).
fof(f3440,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)],[f171,f189]) ).
fof(f3441,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)],[f162,f189]) ).
fof(f3442,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)],[f121,f189]) ).
fof(f3443,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = addition(multiplication(X0,zero),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f44,f189]) ).
fof(f3446,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),codomain(X1)) = addition(multiplication(X0,X1),multiplication(X2,codomain(X1))),
inference(paramodulation,[status(thm)],[f2026,f189]) ).
fof(f3447,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)],[f147,f189]) ).
fof(f3448,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)],[f166,f189]) ).
fof(f3449,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)],[f177,f189]) ).
fof(f3450,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)],[f175,f189]) ).
fof(f3451,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)],[f136,f189]) ).
fof(f3452,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)],[f129,f189]) ).
fof(f3453,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = addition(multiplication(X0,zero),multiplication(X2,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f48,f189]) ).
fof(f3456,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)],[f182,f189]) ).
fof(f3457,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)],[f180,f189]) ).
fof(f3458,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)],[f53,f189]) ).
fof(f3459,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)],[f33,f189]) ).
fof(f3460,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)],[f171,f189]) ).
fof(f3461,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)],[f162,f189]) ).
fof(f3462,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)],[f121,f189]) ).
fof(f3463,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f44,f189]) ).
fof(f3465,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f35,f189]) ).
fof(f3466,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),codomain(X2)) = addition(multiplication(X0,multiplication(X1,codomain(X2))),X2),
inference(paramodulation,[status(thm)],[f2026,f189]) ).
fof(f3467,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)],[f147,f189]) ).
fof(f3468,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)],[f166,f189]) ).
fof(f3469,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)],[f177,f189]) ).
fof(f3470,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)],[f175,f189]) ).
fof(f3471,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)],[f136,f189]) ).
fof(f3472,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)],[f129,f189]) ).
fof(f3473,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X2)) = addition(multiplication(X0,multiplication(X1,coantidomain(X2))),zero),
inference(paramodulation,[status(thm)],[f48,f189]) ).
fof(f3476,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(multiplication(X0,X2),X0),X1),
inference(paramodulation,[status(thm)],[f189,f138]) ).
fof(f3477,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,X2),X2)) = multiplication(addition(multiplication(X0,X1),X0),X2),
inference(paramodulation,[status(thm)],[f189,f36]) ).
fof(f3478,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)],[f189,f155]) ).
fof(f3484,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)],[f189,f177]) ).
fof(f3485,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)],[f189,f147]) ).
fof(f3486,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)],[f189,f171]) ).
fof(f3487,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)],[f189,f162]) ).
fof(f3488,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)],[f189,f1257]) ).
fof(f3489,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(multiplication(X3,X4),X0),X1))),
inference(paramodulation,[status(thm)],[f189,f1256]) ).
fof(f3490,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(multiplication(X2,X3),X0),X1)),
inference(paramodulation,[status(thm)],[f189,f1259]) ).
fof(f3491,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f189,f1163]) ).
fof(f3493,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)],[f189,f88]) ).
fof(f3495,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)],[f189,f82]) ).
fof(f3496,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)],[f189,f82]) ).
fof(f3497,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)],[f189,f231]) ).
fof(f3498,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)],[f189,f43]) ).
fof(f3499,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)],[f189,f30]) ).
fof(f3500,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)],[f189,f29]) ).
fof(f3501,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)],[f189,f29]) ).
fof(f3502,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f29,f3418]) ).
fof(f3503,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f29,f3419]) ).
fof(f3504,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f29,f3503]) ).
fof(f3520,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)],[f138,f3425]) ).
fof(f3521,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)],[f33,f3520]) ).
fof(f3522,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)],[f29,f3521]) ).
fof(f3523,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)],[f33,f3522]) ).
fof(f3524,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)],[f33,f3523]) ).
fof(f3525,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)],[f138,f3426]) ).
fof(f3526,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)],[f33,f3525]) ).
fof(f3527,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)],[f29,f3526]) ).
fof(f3528,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)],[f33,f3527]) ).
fof(f3529,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)],[f33,f3528]) ).
fof(f3530,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)],[f33,f3429]) ).
fof(f3533,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(antidomain(multiplication(X0,X1)),X0),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f65,f3431]) ).
fof(f3539,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)],[f65,f3435]) ).
fof(f3540,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),domain(X1)) = addition(zero,multiplication(X2,domain(X1))),
inference(forward_demodulation,[status(thm)],[f38,f3436]) ).
fof(f3541,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),domain(X1)) = multiplication(X2,domain(X1)),
inference(forward_demodulation,[status(thm)],[f65,f3540]) ).
fof(f3542,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,coantidomain(X1)),X2),codomain(X1)) = addition(zero,multiplication(X2,codomain(X1))),
inference(forward_demodulation,[status(thm)],[f38,f3437]) ).
fof(f3543,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,coantidomain(X1)),X2),codomain(X1)) = multiplication(X2,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f65,f3542]) ).
fof(f3544,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)],[f38,f3442]) ).
fof(f3545,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)],[f65,f3544]) ).
fof(f3546,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f38,f3443]) ).
fof(f3547,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f65,f3546]) ).
fof(f3552,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)],[f38,f3451]) ).
fof(f3553,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)],[f65,f3552]) ).
fof(f3554,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)],[f38,f3452]) ).
fof(f3555,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)],[f65,f3554]) ).
fof(f3556,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = addition(zero,multiplication(X2,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f38,f3453]) ).
fof(f3557,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f65,f3556]) ).
fof(f3561,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),domain(X2)) = multiplication(X0,multiplication(X1,domain(X2))),
inference(forward_demodulation,[status(thm)],[f31,f3456]) ).
fof(f3562,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),coantidomain(X2)),codomain(X2)) = multiplication(X0,multiplication(X1,codomain(X2))),
inference(forward_demodulation,[status(thm)],[f31,f3457]) ).
fof(f3563,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)],[f29,f3460]) ).
fof(f3564,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)],[f29,f3461]) ).
fof(f3565,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)],[f31,f3462]) ).
fof(f3566,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),X2) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f31,f3463]) ).
fof(f3569,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(forward_demodulation,[status(thm)],[f29,f3465]) ).
fof(f3570,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f29,f3569]) ).
fof(f3571,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)],[f29,f3466]) ).
fof(f3572,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)],[f29,f3468]) ).
fof(f3573,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)],[f29,f3470]) ).
fof(f3574,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)],[f31,f3471]) ).
fof(f3575,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)],[f31,f3472]) ).
fof(f3576,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),coantidomain(X2)) = multiplication(X0,multiplication(X1,coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f31,f3473]) ).
fof(f3581,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f29,f3476]) ).
fof(f3582,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(multiplication(X0,X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f29,f3477]) ).
fof(f3583,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f29,f3582]) ).
fof(f3599,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)],[f33,f3484]) ).
fof(f3600,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)],[f33,f3599]) ).
fof(f3601,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)],[f138,f3600]) ).
fof(f3602,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)],[f33,f3601]) ).
fof(f3603,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)],[f29,f3602]) ).
fof(f3604,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)],[f33,f3485]) ).
fof(f3605,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)],[f33,f3604]) ).
fof(f3606,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)],[f138,f3605]) ).
fof(f3607,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)],[f33,f3606]) ).
fof(f3608,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)],[f29,f3607]) ).
fof(f3621,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(addition(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f88,f2179]) ).
fof(f3622,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(addition(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f30,f2179]) ).
fof(f3633,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_diamond(X1,X2))),
inference(paramodulation,[status(thm)],[f54,f2179]) ).
fof(f3643,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)],[f2179,f155]) ).
fof(f3644,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),domain(X2)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2179,f88]) ).
fof(f3645,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),domain(X2)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2179,f30]) ).
fof(f3652,plain,
! [X0,X1,X2] : leq(multiplication(X0,domain(X1)),addition(X2,X0)),
inference(paramodulation,[status(thm)],[f2179,f1256]) ).
fof(f3656,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),addition(X0,X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2179,f88]) ).
fof(f3658,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,domain(X1)),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f2179,f82]) ).
fof(f3659,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(X1,domain(X2)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2179,f82]) ).
fof(f3661,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f2179,f43]) ).
fof(f3662,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,domain(X1)),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f2179,f30]) ).
fof(f3685,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)],[f138,f3643]) ).
fof(f3686,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)],[f33,f3685]) ).
fof(f3687,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)],[f138,f3686]) ).
fof(f3688,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)],[f82,f3687]) ).
fof(f3694,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,domain(X2)))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f3656]) ).
fof(f3696,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(X1,domain(X2)),X0)),
inference(forward_demodulation,[status(thm)],[f82,f3659]) ).
fof(f3698,plain,
! [X0,X1] : addition(c(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2242,f42]) ).
fof(f3699,plain,
! [X0,X1] : leq(antidomain(c(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f1096,f2242]) ).
fof(f3700,plain,
! [X0,X1] : leq(domain(c(X0)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f633,f2242]) ).
fof(f3701,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f57,f2242]) ).
fof(f3702,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f56,f2242]) ).
fof(f3723,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f82,f2242]) ).
fof(f3724,plain,
! [X0,X1,X2] : leq(c(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f82,f2242]) ).
fof(f3729,plain,
! [X0,X1] : addition(one,addition(X0,c(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f3698]) ).
fof(f3733,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f283,f209]) ).
fof(f3734,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),domain(X1)),X0),
inference(paramodulation,[status(thm)],[f2179,f209]) ).
fof(f3735,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),coantidomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2178,f209]) ).
fof(f3736,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),antidomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2177,f209]) ).
fof(f3737,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),c(X1)),X0),
inference(paramodulation,[status(thm)],[f2176,f209]) ).
fof(f3738,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),codomain(X1)),X0),
inference(paramodulation,[status(thm)],[f2175,f209]) ).
fof(f3739,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(multiplication(antidomain(X0),divergence(X1)),X0),
inference(paramodulation,[status(thm)],[f2174,f209]) ).
fof(f3740,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),addition(X1,one)),X0) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f177,f209]) ).
fof(f3741,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),addition(one,X1)),X0) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f147,f209]) ).
fof(f3742,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(addition(X1,addition(antidomain(X0),X1)),X0),
inference(paramodulation,[status(thm)],[f84,f209]) ).
fof(f3744,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f82,f209]) ).
fof(f3745,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f82,f209]) ).
fof(f3747,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f29,f209]) ).
fof(f3748,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f29,f209]) ).
fof(f3751,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(paramodulation,[status(thm)],[f52,f209]) ).
fof(f3752,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(paramodulation,[status(thm)],[f47,f209]) ).
fof(f3754,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(antidomain(antidomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f209,f3218]) ).
fof(f3755,plain,
! [X0,X1] : addition(antidomain(antidomain(X0)),X1) = addition(addition(antidomain(antidomain(X0)),X1),multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f209,f2177]) ).
fof(f3756,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),addition(antidomain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f209,f2999]) ).
fof(f3757,plain,
! [X0,X1] : addition(antidomain(c(X0)),X1) = addition(addition(antidomain(c(X0)),X1),multiplication(X1,c(X0))),
inference(paramodulation,[status(thm)],[f209,f2176]) ).
fof(f3758,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),addition(antidomain(divergence(X1)),X0)),
inference(paramodulation,[status(thm)],[f209,f2847]) ).
fof(f3759,plain,
! [X0,X1] : addition(antidomain(divergence(X0)),X1) = addition(addition(antidomain(divergence(X0)),X1),multiplication(X1,divergence(X0))),
inference(paramodulation,[status(thm)],[f209,f2174]) ).
fof(f3760,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),addition(antidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f209,f2917]) ).
fof(f3761,plain,
! [X0,X1] : addition(antidomain(codomain(X0)),X1) = addition(addition(antidomain(codomain(X0)),X1),multiplication(X1,codomain(X0))),
inference(paramodulation,[status(thm)],[f209,f2175]) ).
fof(f3762,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)],[f209,f189]) ).
fof(f3763,plain,
! [X0,X1] : addition(antidomain(domain(X0)),X1) = addition(addition(antidomain(domain(X0)),X1),multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f209,f2179]) ).
fof(f3764,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(antidomain(domain(X1)),X0)),
inference(paramodulation,[status(thm)],[f209,f3299]) ).
fof(f3765,plain,
! [X0,X1] : forward_diamond(addition(antidomain(domain(X0)),X1),X0) = domain(multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f209,f54]) ).
fof(f3766,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)],[f209,f237]) ).
fof(f3767,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(antidomain(coantidomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f209,f3336]) ).
fof(f3768,plain,
! [X0,X1] : addition(antidomain(coantidomain(X0)),X1) = addition(addition(antidomain(coantidomain(X0)),X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f209,f2178]) ).
fof(f3771,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)],[f209,f189]) ).
fof(f3772,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)],[f209,f189]) ).
fof(f3773,plain,
! [X0,X1,X2] : multiplication(addition(addition(antidomain(X0),X1),X2),X0) = addition(multiplication(X2,X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f209,f186]) ).
fof(f3774,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f209,f186]) ).
fof(f3775,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)],[f209,f155]) ).
fof(f3776,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)],[f209,f155]) ).
fof(f3777,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(X0,one)) = addition(addition(antidomain(X0),X1),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f209,f177]) ).
fof(f3778,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(one,X0)) = addition(addition(antidomain(X0),X1),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f209,f147]) ).
fof(f3779,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)],[f209,f138]) ).
fof(f3780,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)],[f209,f138]) ).
fof(f3781,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),multiplication(X0,coantidomain(multiplication(X1,X0)))) = zero,
inference(paramodulation,[status(thm)],[f209,f129]) ).
fof(f3782,plain,
! [X0,X1] : multiplication(antidomain(addition(antidomain(X0),X1)),multiplication(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f209,f121]) ).
fof(f3783,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)],[f209,f309]) ).
fof(f3784,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)],[f209,f237]) ).
fof(f3785,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f209,f37]) ).
fof(f3786,plain,
! [X0,X1,X2] : multiplication(addition(addition(antidomain(X0),X1),X2),X0) = addition(multiplication(X1,X0),multiplication(X2,X0)),
inference(paramodulation,[status(thm)],[f209,f37]) ).
fof(f3787,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)],[f209,f36]) ).
fof(f3788,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)],[f209,f36]) ).
fof(f3789,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(multiplication(X1,X0),X2),
inference(paramodulation,[status(thm)],[f209,f33]) ).
fof(f3792,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f35,f3733]) ).
fof(f3793,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),domain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f44,f3734]) ).
fof(f3794,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f33,f3793]) ).
fof(f3795,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),coantidomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f44,f3735]) ).
fof(f3796,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f33,f3795]) ).
fof(f3797,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),antidomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f44,f3736]) ).
fof(f3798,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f33,f3797]) ).
fof(f3799,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),c(X1)),X0),
inference(forward_demodulation,[status(thm)],[f44,f3737]) ).
fof(f3800,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f33,f3799]) ).
fof(f3801,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),codomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f44,f3738]) ).
fof(f3802,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f33,f3801]) ).
fof(f3803,plain,
! [X0,X1] : zero = multiplication(multiplication(antidomain(X0),divergence(X1)),X0),
inference(forward_demodulation,[status(thm)],[f44,f3739]) ).
fof(f3804,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f33,f3803]) ).
fof(f3805,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(forward_demodulation,[status(thm)],[f33,f3740]) ).
fof(f3806,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f33,f3805]) ).
fof(f3807,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(multiplication(antidomain(X0),X1),X0),
inference(forward_demodulation,[status(thm)],[f33,f3741]) ).
fof(f3808,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f33,f3807]) ).
fof(f3809,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,addition(antidomain(X1),X0)),X1),
inference(forward_demodulation,[status(thm)],[f209,f3742]) ).
fof(f3814,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f47,f3754]) ).
fof(f3815,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(addition(antidomain(antidomain(X0)),X1),multiplication(X1,antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f47,f3755]) ).
fof(f3816,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(X1,addition(antidomain(antidomain(X0)),multiplication(X1,antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f3815]) ).
fof(f3817,plain,
! [X0,X1] : addition(domain(X0),X1) = addition(X1,addition(domain(X0),multiplication(X1,antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f47,f3816]) ).
fof(f3818,plain,
! [X0,X1] : addition(antidomain(c(X0)),X1) = addition(X1,addition(antidomain(c(X0)),multiplication(X1,c(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f3757]) ).
fof(f3819,plain,
! [X0,X1] : addition(antidomain(divergence(X0)),X1) = addition(X1,addition(antidomain(divergence(X0)),multiplication(X1,divergence(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f3759]) ).
fof(f3820,plain,
! [X0,X1] : addition(antidomain(codomain(X0)),X1) = addition(X1,addition(antidomain(codomain(X0)),multiplication(X1,codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f3761]) ).
fof(f3821,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)],[f189,f3762]) ).
fof(f3822,plain,
! [X0,X1] : addition(c(X0),X1) = addition(addition(antidomain(domain(X0)),X1),multiplication(X1,domain(X0))),
inference(forward_demodulation,[status(thm)],[f52,f3763]) ).
fof(f3823,plain,
! [X0,X1] : addition(c(X0),X1) = addition(X1,addition(antidomain(domain(X0)),multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f3822]) ).
fof(f3824,plain,
! [X0,X1] : addition(c(X0),X1) = addition(X1,addition(c(X0),multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f52,f3823]) ).
fof(f3825,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f52,f3764]) ).
fof(f3826,plain,
! [X0,X1] : forward_diamond(addition(c(X0),X1),X0) = domain(multiplication(X1,domain(X0))),
inference(forward_demodulation,[status(thm)],[f52,f3765]) ).
fof(f3827,plain,
! [X0,X1] : forward_diamond(addition(c(X0),X1),X0) = forward_diamond(X1,X0),
inference(forward_demodulation,[status(thm)],[f54,f3826]) ).
fof(f3828,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)],[f29,f3766]) ).
fof(f3829,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)],[f52,f3828]) ).
fof(f3830,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)],[f209,f3829]) ).
fof(f3831,plain,
! [X0,X1] : addition(antidomain(coantidomain(X0)),X1) = addition(X1,addition(antidomain(coantidomain(X0)),multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f3768]) ).
fof(f3834,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)],[f189,f3771]) ).
fof(f3835,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)],[f189,f3772]) ).
fof(f3836,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f88,f3773]) ).
fof(f3837,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f186,f3836]) ).
fof(f3838,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f186,f3774]) ).
fof(f3839,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)],[f82,f3775]) ).
fof(f3840,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(X0,one)) = addition(X1,addition(antidomain(X0),multiplication(X1,X0))),
inference(forward_demodulation,[status(thm)],[f88,f3777]) ).
fof(f3841,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),addition(one,X0)) = addition(X1,addition(antidomain(X0),multiplication(X1,X0))),
inference(forward_demodulation,[status(thm)],[f88,f3778]) ).
fof(f3842,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)],[f29,f3779]) ).
fof(f3843,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f186,f3785]) ).
fof(f3844,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f88,f3786]) ).
fof(f3845,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(antidomain(X1),X2)),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f186,f3844]) ).
fof(f3846,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)],[f29,f3787]) ).
fof(f3847,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),X1),multiplication(X0,X2)) = multiplication(X1,multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f33,f3789]) ).
fof(f3849,plain,
! [X0] : antidomain(X0) = domain_difference(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f53,f3792]) ).
fof(f3852,plain,
! [X0] : domain(X0) = multiplication(antidomain(c(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f181,f3792]) ).
fof(f3853,plain,
! [X0] : antidomain(X0) = multiplication(c(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f631,f3792]) ).
fof(f3854,plain,
! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(forward_diamond(X0,X1),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f54,f3792]) ).
fof(f3858,plain,
! [X0] : leq(antidomain(X0),domain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f3792,f3218]) ).
fof(f3859,plain,
! [X0] : domain(antidomain(X0)) = addition(domain(antidomain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f3792,f2177]) ).
fof(f3860,plain,
! [X0] : leq(c(X0),domain(c(X0))),
inference(paramodulation,[status(thm)],[f3792,f2999]) ).
fof(f3861,plain,
! [X0] : domain(c(X0)) = addition(domain(c(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f3792,f2176]) ).
fof(f3862,plain,
! [X0] : leq(divergence(X0),domain(divergence(X0))),
inference(paramodulation,[status(thm)],[f3792,f2847]) ).
fof(f3863,plain,
! [X0] : domain(divergence(X0)) = addition(domain(divergence(X0)),divergence(X0)),
inference(paramodulation,[status(thm)],[f3792,f2174]) ).
fof(f3864,plain,
! [X0] : leq(codomain(X0),domain(codomain(X0))),
inference(paramodulation,[status(thm)],[f3792,f2917]) ).
fof(f3865,plain,
! [X0] : domain(codomain(X0)) = addition(domain(codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f3792,f2175]) ).
fof(f3866,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)],[f3792,f189]) ).
fof(f3867,plain,
! [X0] : domain(domain(X0)) = addition(domain(domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f3792,f2179]) ).
fof(f3868,plain,
! [X0] : leq(domain(X0),domain(domain(X0))),
inference(paramodulation,[status(thm)],[f3792,f3299]) ).
fof(f3869,plain,
! [X0] : forward_diamond(domain(domain(X0)),X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f3792,f54]) ).
fof(f3870,plain,
! [X0] : addition(antidomain(multiplication(domain(domain(X0)),X0)),antidomain(domain(X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f3792,f237]) ).
fof(f3871,plain,
! [X0] : leq(coantidomain(X0),domain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f3792,f3336]) ).
fof(f3872,plain,
! [X0] : domain(coantidomain(X0)) = addition(domain(coantidomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f3792,f2178]) ).
fof(f3875,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f3792,f189]) ).
fof(f3876,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),X1) = addition(multiplication(X0,X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f3792,f189]) ).
fof(f3877,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f3792,f186]) ).
fof(f3878,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f3792,f186]) ).
fof(f3879,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),addition(X0,X2)) = addition(multiplication(domain(X0),addition(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f3792,f155]) ).
fof(f3880,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X0),X1),X2)) = addition(multiplication(domain(X0),addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f3792,f155]) ).
fof(f3881,plain,
! [X0] : multiplication(domain(X0),addition(X0,one)) = addition(domain(X0),X0),
inference(paramodulation,[status(thm)],[f3792,f177]) ).
fof(f3882,plain,
! [X0] : multiplication(domain(X0),addition(one,X0)) = addition(domain(X0),X0),
inference(paramodulation,[status(thm)],[f3792,f147]) ).
fof(f3883,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(multiplication(domain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f3792,f138]) ).
fof(f3884,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(X0,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f3792,f138]) ).
fof(f3886,plain,
! [X0] : multiplication(antidomain(domain(X0)),X0) = zero,
inference(paramodulation,[status(thm)],[f3792,f121]) ).
fof(f3887,plain,
! [X0] : addition(coantidomain(X0),coantidomain(multiplication(codomain(domain(X0)),X0))) = coantidomain(multiplication(codomain(domain(X0)),X0)),
inference(paramodulation,[status(thm)],[f3792,f309]) ).
fof(f3888,plain,
! [X0] : addition(antidomain(X0),antidomain(multiplication(domain(X0),domain(X0)))) = antidomain(multiplication(domain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f3792,f237]) ).
fof(f3889,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f3792,f37]) ).
fof(f3890,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f3792,f37]) ).
fof(f3891,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(multiplication(domain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f3792,f36]) ).
fof(f3892,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f3792,f36]) ).
fof(f3893,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(X0,X1)) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f3792,f33]) ).
fof(f3895,plain,
! [X0] : leq(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f631,f3858]) ).
fof(f3896,plain,
! [X0] : c(X0) = addition(domain(antidomain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f631,f3859]) ).
fof(f3897,plain,
! [X0] : c(X0) = addition(antidomain(X0),domain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f3896]) ).
fof(f3898,plain,
! [X0] : c(X0) = addition(antidomain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f631,f3897]) ).
fof(f3899,plain,
! [X0] : domain(c(X0)) = addition(c(X0),domain(c(X0))),
inference(forward_demodulation,[status(thm)],[f29,f3861]) ).
fof(f3900,plain,
! [X0] : domain(divergence(X0)) = addition(divergence(X0),domain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f29,f3863]) ).
fof(f3901,plain,
! [X0] : domain(codomain(X0)) = addition(codomain(X0),domain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f3865]) ).
fof(f3902,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(domain(multiplication(X0,X1)),X0),X2),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f186,f3866]) ).
fof(f3903,plain,
! [X0] : antidomain(c(X0)) = addition(domain(domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f181,f3867]) ).
fof(f3904,plain,
! [X0] : antidomain(c(X0)) = addition(domain(X0),domain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f3903]) ).
fof(f3905,plain,
! [X0] : antidomain(c(X0)) = addition(domain(X0),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f181,f3904]) ).
fof(f3906,plain,
! [X0] : leq(domain(X0),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f181,f3868]) ).
fof(f3907,plain,
! [X0] : forward_diamond(antidomain(c(X0)),X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f181,f3869]) ).
fof(f3908,plain,
! [X0] : forward_diamond(antidomain(c(X0)),X0) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f181,f3907]) ).
fof(f3909,plain,
! [X0] : addition(antidomain(domain(X0)),antidomain(multiplication(domain(domain(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f3870]) ).
fof(f3910,plain,
! [X0] : addition(c(X0),antidomain(multiplication(domain(domain(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f52,f3909]) ).
fof(f3911,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = antidomain(multiplication(domain(domain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f181,f3910]) ).
fof(f3912,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f3792,f3911]) ).
fof(f3913,plain,
! [X0] : addition(c(X0),antidomain(multiplication(antidomain(c(X0)),X0))) = c(X0),
inference(forward_demodulation,[status(thm)],[f52,f3912]) ).
fof(f3914,plain,
! [X0] : domain(coantidomain(X0)) = addition(coantidomain(X0),domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f3872]) ).
fof(f3915,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f29,f3875]) ).
fof(f3916,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),X1) = multiplication(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f186,f3876]) ).
fof(f3917,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f29,f3877]) ).
fof(f3918,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)],[f82,f3879]) ).
fof(f3919,plain,
! [X0] : multiplication(domain(X0),addition(X0,one)) = addition(X0,domain(X0)),
inference(forward_demodulation,[status(thm)],[f29,f3881]) ).
fof(f3920,plain,
! [X0] : multiplication(domain(X0),addition(one,X0)) = addition(X0,domain(X0)),
inference(forward_demodulation,[status(thm)],[f29,f3882]) ).
fof(f3921,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f29,f3883]) ).
fof(f3923,plain,
! [X0] : multiplication(c(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f52,f3886]) ).
fof(f3924,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f3889]) ).
fof(f3925,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(X0,multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f29,f3891]) ).
fof(f3926,plain,
! [X0] : addition(antidomain(X0),c(X0)) = c(X0),
inference(resolution,[status(thm)],[f3895,f42]) ).
fof(f3933,plain,
! [X0,X1] : leq(antidomain(backward_diamond(X0,c(X1))),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f57,f3895]) ).
fof(f3934,plain,
! [X0,X1] : leq(antidomain(forward_diamond(X0,c(X1))),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f56,f3895]) ).
fof(f3948,plain,
! [X0] : multiplication(antidomain(c(X0)),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f1096,f3923]) ).
fof(f3949,plain,
! [X0] : multiplication(domain(c(X0)),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f633,f3923]) ).
fof(f3950,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f57,f3923]) ).
fof(f3951,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f56,f3923]) ).
fof(f3962,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(c(multiplication(X0,X1)),X0),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f3923,f189]) ).
fof(f3965,plain,
! [X0] : forward_diamond(c(domain(X0)),X0) = domain(zero),
inference(paramodulation,[status(thm)],[f3923,f54]) ).
fof(f3971,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),X2) = addition(multiplication(X0,multiplication(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f3923,f189]) ).
fof(f3972,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = addition(multiplication(X0,zero),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f3923,f189]) ).
fof(f3973,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = addition(multiplication(X1,X0),zero),
inference(paramodulation,[status(thm)],[f3923,f186]) ).
fof(f3974,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f3923,f186]) ).
fof(f3975,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(zero,X2)) = addition(multiplication(c(X0),addition(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f3923,f155]) ).
fof(f3976,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(c(X0),X1),X2)) = addition(multiplication(c(X0),addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f3923,f155]) ).
fof(f3977,plain,
! [X0] : multiplication(c(X0),addition(X0,one)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f3923,f177]) ).
fof(f3978,plain,
! [X0] : multiplication(c(X0),addition(one,X0)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f3923,f147]) ).
fof(f3979,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f3923,f138]) ).
fof(f3980,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f3923,f138]) ).
fof(f3983,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(c(X0)),X0))) = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(paramodulation,[status(thm)],[f3923,f309]) ).
fof(f3985,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f3923,f37]) ).
fof(f3986,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f3923,f37]) ).
fof(f3987,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f3923,f36]) ).
fof(f3988,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f3923,f36]) ).
fof(f3989,plain,
! [X0,X1] : multiplication(c(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f3923,f33]) ).
fof(f3994,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(c(multiplication(X0,X1)),X0),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f65,f3962]) ).
fof(f3998,plain,
! [X0] : forward_diamond(domain(c(X0)),X0) = domain(zero),
inference(forward_demodulation,[status(thm)],[f633,f3965]) ).
fof(f3999,plain,
! [X0] : forward_diamond(domain(c(X0)),X0) = zero,
inference(forward_demodulation,[status(thm)],[f307,f3998]) ).
fof(f4004,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),c(X2)),X2) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f31,f3971]) ).
fof(f4005,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(forward_demodulation,[status(thm)],[f38,f3972]) ).
fof(f4006,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,c(X1)),X2),X1) = multiplication(X2,X1),
inference(forward_demodulation,[status(thm)],[f65,f4005]) ).
fof(f4007,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f31,f3973]) ).
fof(f4008,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f3974]) ).
fof(f4009,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)],[f82,f3975]) ).
fof(f4010,plain,
! [X0,X1,X2] : addition(X0,multiplication(c(X1),X2)) = addition(multiplication(c(X1),addition(X2,X1)),X0),
inference(forward_demodulation,[status(thm)],[f65,f4009]) ).
fof(f4011,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),X2) = addition(multiplication(c(X0),addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f3976]) ).
fof(f4012,plain,
! [X0] : multiplication(c(X0),addition(X0,one)) = c(X0),
inference(forward_demodulation,[status(thm)],[f31,f3977]) ).
fof(f4013,plain,
! [X0] : multiplication(c(X0),addition(one,X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f31,f3978]) ).
fof(f4014,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f3979]) ).
fof(f4015,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f3980]) ).
fof(f4018,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(c(X0)),X0))) = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f363,f3983]) ).
fof(f4019,plain,
! [X0] : one = coantidomain(multiplication(codomain(c(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f1213,f4018]) ).
fof(f4023,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f3985]) ).
fof(f4024,plain,
! [X0,X1] : multiplication(addition(c(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f65,f3986]) ).
fof(f4025,plain,
! [X0,X1] : multiplication(c(X0),addition(X1,X0)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f3987]) ).
fof(f4026,plain,
! [X0,X1] : multiplication(c(X0),addition(X0,X1)) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f3988]) ).
fof(f4027,plain,
! [X0,X1] : multiplication(c(X0),multiplication(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f3989]) ).
fof(f4031,plain,
! [X0] : antidomain(domain(X0)) = domain_difference(c(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f52,f3849]) ).
fof(f4032,plain,
! [X0] : antidomain(antidomain(X0)) = domain_difference(domain(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f47,f3849]) ).
fof(f4041,plain,
! [X0] : c(X0) = domain_difference(c(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f4031]) ).
fof(f4042,plain,
! [X0] : domain(X0) = domain_difference(domain(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f47,f4032]) ).
fof(f4050,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1376,f192]) ).
fof(f4051,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1369,f192]) ).
fof(f4052,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1363,f192]) ).
fof(f4053,plain,
! [X0,X1,X2] : multiplication(one,X0) = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1320,f192]) ).
fof(f4054,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(divergence(X1),X0)),
inference(paramodulation,[status(thm)],[f1323,f192]) ).
fof(f4055,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1312,f192]) ).
fof(f4056,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(c(X1),X0)),
inference(paramodulation,[status(thm)],[f1306,f192]) ).
fof(f4057,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1215,f192]) ).
fof(f4058,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(coantidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f1213,f192]) ).
fof(f4059,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f1211,f192]) ).
fof(f4066,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(X0,addition(one,X0)),X1)),
inference(paramodulation,[status(thm)],[f84,f192]) ).
fof(f4067,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f90,f192]) ).
fof(f4068,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f82,f192]) ).
fof(f4069,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f82,f192]) ).
fof(f4071,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f29,f192]) ).
fof(f4072,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f29,f192]) ).
fof(f4074,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f138,f192]) ).
fof(f4075,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f192]) ).
fof(f4076,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X2,addition(X1,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f88,f192]) ).
fof(f4077,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X1,addition(X2,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f30,f192]) ).
fof(f4085,plain,
! [X0] : multiplication(addition(one,X0),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f177,f192]) ).
fof(f4086,plain,
! [X0] : multiplication(addition(one,X0),X0) = multiplication(X0,addition(one,X0)),
inference(paramodulation,[status(thm)],[f147,f192]) ).
fof(f4088,plain,
! [X0,X1] : multiplication(addition(one,addition(antidomain(X0),X1)),X0) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f209,f192]) ).
fof(f4092,plain,
! [X0,X1] : multiplication(addition(one,domain(X0)),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f53,f192]) ).
fof(f4094,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f33,f192]) ).
fof(f4095,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f171,f192]) ).
fof(f4096,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f162,f192]) ).
fof(f4101,plain,
! [X0] : multiplication(addition(one,X0),codomain(X0)) = addition(codomain(X0),X0),
inference(paramodulation,[status(thm)],[f2026,f192]) ).
fof(f4102,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(addition(one,X1),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f147,f192]) ).
fof(f4103,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(coantidomain(X0),X1)) = addition(addition(coantidomain(X0),X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f166,f192]) ).
fof(f4104,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(addition(X1,one),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f177,f192]) ).
fof(f4105,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,coantidomain(X0))) = addition(addition(X1,coantidomain(X0)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f175,f192]) ).
fof(f4106,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(coantidomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f136,f192]) ).
fof(f4107,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)],[f129,f192]) ).
fof(f4108,plain,
! [X0] : multiplication(addition(one,X0),coantidomain(X0)) = addition(coantidomain(X0),zero),
inference(paramodulation,[status(thm)],[f48,f192]) ).
fof(f4111,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)],[f192,f189]) ).
fof(f4112,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)],[f192,f189]) ).
fof(f4113,plain,
! [X0,X1,X2] : multiplication(addition(addition(one,X0),X1),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f192,f186]) ).
fof(f4114,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(addition(X2,multiplication(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f192,f186]) ).
fof(f4115,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)],[f192,f155]) ).
fof(f4116,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)],[f192,f155]) ).
fof(f4117,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(addition(one,X0),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f177]) ).
fof(f4118,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(addition(one,X0),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f147]) ).
fof(f4119,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)],[f192,f138]) ).
fof(f4120,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)],[f192,f138]) ).
fof(f4121,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(addition(X1,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f192,f129]) ).
fof(f4122,plain,
! [X0,X1] : multiplication(antidomain(addition(one,X0)),addition(X1,multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f192,f121]) ).
fof(f4123,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)],[f192,f309]) ).
fof(f4124,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)],[f192,f237]) ).
fof(f4125,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f192,f37]) ).
fof(f4126,plain,
! [X0,X1,X2] : multiplication(addition(addition(one,X0),X1),X2) = addition(addition(X2,multiplication(X0,X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f192,f37]) ).
fof(f4127,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)],[f192,f36]) ).
fof(f4128,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)],[f192,f36]) ).
fof(f4129,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f192,f33]) ).
fof(f4130,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f192,f166]) ).
fof(f4132,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X0,X1),X1)) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f192,f138]) ).
fof(f4133,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f192,f36]) ).
fof(f4134,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)],[f192,f155]) ).
fof(f4135,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X1,X0)))) = multiplication(addition(one,X2),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f192,f88]) ).
fof(f4136,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X0,X1)))) = multiplication(addition(one,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f192,f30]) ).
fof(f4143,plain,
! [X0] : multiplication(X0,addition(X0,one)) = multiplication(addition(one,X0),X0),
inference(paramodulation,[status(thm)],[f192,f177]) ).
fof(f4144,plain,
! [X0] : multiplication(X0,addition(one,X0)) = multiplication(addition(one,X0),X0),
inference(paramodulation,[status(thm)],[f192,f147]) ).
fof(f4145,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(one,X0),X1)) = multiplication(antidomain(multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f192,f171]) ).
fof(f4146,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(one,X1),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f192,f162]) ).
fof(f4147,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(one,X2),X0))),
inference(paramodulation,[status(thm)],[f192,f1257]) ).
fof(f4148,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(one,X0),X1))),
inference(paramodulation,[status(thm)],[f192,f1256]) ).
fof(f4149,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f192,f1259]) ).
fof(f4150,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f192,f1163]) ).
fof(f4151,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f192,f90]) ).
fof(f4152,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(one,X0),X1),X2),
inference(paramodulation,[status(thm)],[f192,f88]) ).
fof(f4153,plain,
! [X0,X1] : addition(X0,addition(multiplication(X1,X0),multiplication(addition(one,X1),X0))) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f192,f84]) ).
fof(f4154,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(X2,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f192,f82]) ).
fof(f4155,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(one,X1),X2)) = addition(multiplication(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f192,f82]) ).
fof(f4156,plain,
! [X0,X1] :
( multiplication(addition(one,X0),X1) != X1
| leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f192,f231]) ).
fof(f4157,plain,
! [X0,X1] :
( multiplication(addition(one,X1),X0) != multiplication(X1,X0)
| leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f192,f43]) ).
fof(f4158,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(one,X1),X0),X2),
inference(paramodulation,[status(thm)],[f192,f30]) ).
fof(f4160,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4050]) ).
fof(f4161,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4051]) ).
fof(f4162,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4052]) ).
fof(f4163,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4053]) ).
fof(f4164,plain,
! [X0,X1] : X0 = addition(X0,multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4054]) ).
fof(f4165,plain,
! [X0,X1] : X0 = addition(X0,multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4055]) ).
fof(f4166,plain,
! [X0,X1] : X0 = addition(X0,multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4056]) ).
fof(f4167,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4057]) ).
fof(f4168,plain,
! [X0,X1] : X0 = addition(X0,multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4058]) ).
fof(f4169,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4059]) ).
fof(f4192,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f29,f4074]) ).
fof(f4207,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1211,f4092]) ).
fof(f4208,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f4207]) ).
fof(f4211,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f1215,f4095]) ).
fof(f4212,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f4211]) ).
fof(f4213,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f88,f4212]) ).
fof(f4214,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1215,f4096]) ).
fof(f4215,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f4214]) ).
fof(f4216,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f4215]) ).
fof(f4225,plain,
! [X0] : multiplication(addition(one,X0),codomain(X0)) = addition(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f29,f4101]) ).
fof(f4226,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(X1,addition(one,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f4102]) ).
fof(f4227,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(coantidomain(X0),X1)) = addition(X1,addition(coantidomain(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f4103]) ).
fof(f4228,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(one,addition(X1,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f4104]) ).
fof(f4229,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,coantidomain(X0))) = addition(coantidomain(X0),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f4105]) ).
fof(f4230,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(coantidomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f4106]) ).
fof(f4231,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f31,f4107]) ).
fof(f4232,plain,
! [X0] : multiplication(addition(one,X0),coantidomain(X0)) = coantidomain(X0),
inference(forward_demodulation,[status(thm)],[f31,f4108]) ).
fof(f4234,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)],[f82,f4111]) ).
fof(f4235,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)],[f82,f4234]) ).
fof(f4236,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)],[f88,f4113]) ).
fof(f4237,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)],[f82,f4236]) ).
fof(f4238,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f4237]) ).
fof(f4239,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)],[f88,f4114]) ).
fof(f4240,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)],[f82,f4239]) ).
fof(f4241,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f4240]) ).
fof(f4242,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)],[f88,f4115]) ).
fof(f4243,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)],[f82,f4242]) ).
fof(f4244,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)],[f88,f4116]) ).
fof(f4245,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)],[f82,f4244]) ).
fof(f4246,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)],[f88,f4245]) ).
fof(f4247,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(X0,addition(one,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f4117]) ).
fof(f4248,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(X0,addition(one,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f4118]) ).
fof(f4249,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)],[f88,f4120]) ).
fof(f4250,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)],[f82,f4249]) ).
fof(f4251,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)],[f82,f4125]) ).
fof(f4252,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f186,f4251]) ).
fof(f4253,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)],[f88,f4126]) ).
fof(f4254,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)],[f88,f4253]) ).
fof(f4255,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)],[f82,f4254]) ).
fof(f4256,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f186,f4255]) ).
fof(f4257,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)],[f88,f4128]) ).
fof(f4258,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)],[f82,f4257]) ).
fof(f4266,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f4132]) ).
fof(f4273,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(one,X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f82,f4152]) ).
fof(f4274,plain,
! [X0,X1] : addition(X0,multiplication(addition(addition(one,X1),X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f186,f4153]) ).
fof(f4275,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,addition(one,X1)),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f4274]) ).
fof(f4276,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(one,X1),X2)) = addition(X2,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f82,f4155]) ).
fof(f4277,plain,
! [X0,X1] : addition(antidomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2254,f42]) ).
fof(f4300,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f82,f2254]) ).
fof(f4301,plain,
! [X0,X1,X2] : leq(antidomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f82,f2254]) ).
fof(f4306,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f4277]) ).
fof(f4317,plain,
! [X0] : multiplication(one,coantidomain(domain(X0))) = multiplication(c(X0),coantidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f657,f211]) ).
fof(f4319,plain,
! [X0] : multiplication(one,coantidomain(coantidomain(X0))) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f354,f211]) ).
fof(f4321,plain,
! [X0] : multiplication(one,coantidomain(antidomain(X0))) = multiplication(domain(X0),coantidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f283,f211]) ).
fof(f4322,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)],[f189,f211]) ).
fof(f4323,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)],[f155,f211]) ).
fof(f4324,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)],[f186,f211]) ).
fof(f4325,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)],[f138,f211]) ).
fof(f4326,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)],[f37,f211]) ).
fof(f4327,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)],[f36,f211]) ).
fof(f4328,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X1,X0))) = multiplication(X2,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f88,f211]) ).
fof(f4329,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X0,X1))) = multiplication(X2,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f30,f211]) ).
fof(f4331,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,domain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2179,f211]) ).
fof(f4332,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,coantidomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2178,f211]) ).
fof(f4333,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,antidomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2177,f211]) ).
fof(f4334,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,c(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2176,f211]) ).
fof(f4335,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,codomain(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2175,f211]) ).
fof(f4336,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(multiplication(X0,divergence(X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2174,f211]) ).
fof(f4338,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(X1,one)),coantidomain(X0)) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f177,f211]) ).
fof(f4339,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(one,X1)),coantidomain(X0)) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f147,f211]) ).
fof(f4340,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(addition(X1,addition(X0,X1)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f84,f211]) ).
fof(f4342,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f82,f211]) ).
fof(f4343,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(paramodulation,[status(thm)],[f82,f211]) ).
fof(f4345,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(paramodulation,[status(thm)],[f29,f211]) ).
fof(f4346,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(paramodulation,[status(thm)],[f29,f211]) ).
fof(f4349,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,coantidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f51,f211]) ).
fof(f4351,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f211,f3336]) ).
fof(f4352,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f211,f2178]) ).
fof(f4353,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X0)) = addition(coantidomain(X0),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f211,f192]) ).
fof(f4354,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)],[f211,f189]) ).
fof(f4355,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)],[f211,f189]) ).
fof(f4356,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)],[f211,f186]) ).
fof(f4357,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)],[f211,f186]) ).
fof(f4358,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)],[f211,f155]) ).
fof(f4359,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)],[f211,f155]) ).
fof(f4360,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(coantidomain(X0),one)) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f211,f177]) ).
fof(f4361,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,coantidomain(X0))) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f211,f147]) ).
fof(f4362,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)],[f211,f138]) ).
fof(f4363,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)],[f211,f138]) ).
fof(f4364,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),coantidomain(multiplication(X1,coantidomain(X0))))) = zero,
inference(paramodulation,[status(thm)],[f211,f129]) ).
fof(f4365,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),multiplication(X1,coantidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f211,f121]) ).
fof(f4366,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)],[f211,f309]) ).
fof(f4367,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)],[f211,f237]) ).
fof(f4368,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)],[f211,f37]) ).
fof(f4369,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)],[f211,f37]) ).
fof(f4370,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)],[f211,f36]) ).
fof(f4371,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)],[f211,f36]) ).
fof(f4372,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(multiplication(X1,coantidomain(X0)),X2),
inference(paramodulation,[status(thm)],[f211,f33]) ).
fof(f4403,plain,
! [X0] : coantidomain(domain(X0)) = multiplication(c(X0),coantidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4317]) ).
fof(f4404,plain,
! [X0] : coantidomain(coantidomain(X0)) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4319]) ).
fof(f4405,plain,
! [X0] : codomain(X0) = multiplication(codomain(X0),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f51,f4404]) ).
fof(f4406,plain,
! [X0] : codomain(X0) = multiplication(codomain(X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f51,f4405]) ).
fof(f4407,plain,
! [X0] : coantidomain(antidomain(X0)) = multiplication(domain(X0),coantidomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f4321]) ).
fof(f4408,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)],[f33,f4322]) ).
fof(f4409,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)],[f33,f4408]) ).
fof(f4410,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)],[f33,f4324]) ).
fof(f4411,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)],[f33,f4410]) ).
fof(f4412,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)],[f33,f4325]) ).
fof(f4413,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)],[f33,f4412]) ).
fof(f4414,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)],[f33,f4326]) ).
fof(f4415,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)],[f33,f4414]) ).
fof(f4416,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)],[f33,f4327]) ).
fof(f4417,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)],[f33,f4416]) ).
fof(f4418,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,domain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f4331]) ).
fof(f4419,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4418]) ).
fof(f4420,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,coantidomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f4332]) ).
fof(f4421,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4420]) ).
fof(f4422,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,antidomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f4333]) ).
fof(f4423,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4422]) ).
fof(f4424,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,c(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f4334]) ).
fof(f4425,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4424]) ).
fof(f4426,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,codomain(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f4335]) ).
fof(f4427,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4426]) ).
fof(f4428,plain,
! [X0,X1] : zero = multiplication(multiplication(X0,divergence(X1)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f4336]) ).
fof(f4429,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4428]) ).
fof(f4437,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f4338]) ).
fof(f4438,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4437]) ).
fof(f4439,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(multiplication(X0,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f4339]) ).
fof(f4440,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f33,f4439]) ).
fof(f4441,plain,
! [X0,X1] : multiplication(X0,coantidomain(X1)) = multiplication(addition(X0,addition(X1,X0)),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f211,f4340]) ).
fof(f4446,plain,
! [X0,X1] : multiplication(addition(coantidomain(X0),X1),codomain(X0)) = multiplication(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f51,f4349]) ).
fof(f4451,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f4352]) ).
fof(f4452,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X0)) = multiplication(addition(one,X1),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f192,f4353]) ).
fof(f4453,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)],[f189,f4354]) ).
fof(f4454,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)],[f189,f4355]) ).
fof(f4455,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)],[f88,f4356]) ).
fof(f4456,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X0,X2),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f186,f4455]) ).
fof(f4457,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X0,X2),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f186,f4357]) ).
fof(f4458,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)],[f82,f4358]) ).
fof(f4459,plain,
! [X0,X1] : multiplication(addition(X0,X1),addition(one,coantidomain(X0))) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f4360]) ).
fof(f4460,plain,
! [X0,X1] : multiplication(addition(X0,X1),one) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f1213,f4459]) ).
fof(f4461,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f34,f4460]) ).
fof(f4462,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f4461]) ).
fof(f4463,plain,
! [X0,X1] : multiplication(addition(X0,X1),one) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f1213,f4361]) ).
fof(f4464,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(X1,coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f34,f4463]) ).
fof(f4465,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f88,f4464]) ).
fof(f4466,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)],[f29,f4362]) ).
fof(f4467,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f186,f4368]) ).
fof(f4468,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)],[f88,f4369]) ).
fof(f4469,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X1)) = multiplication(addition(X2,X0),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f186,f4468]) ).
fof(f4470,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)],[f29,f4370]) ).
fof(f4471,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X0),X2)) = multiplication(X1,multiplication(coantidomain(X0),X2)),
inference(forward_demodulation,[status(thm)],[f33,f4372]) ).
fof(f4472,plain,
! [X0,X1] : addition(coantidomain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2265,f42]) ).
fof(f4494,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f82,f2265]) ).
fof(f4495,plain,
! [X0,X1,X2] : leq(coantidomain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f82,f2265]) ).
fof(f4500,plain,
! [X0,X1] : addition(one,addition(X0,coantidomain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f4472]) ).
fof(f4501,plain,
! [X0,X1] : addition(domain(X0),addition(one,X1)) = addition(one,X1),
inference(resolution,[status(thm)],[f2278,f42]) ).
fof(f4504,plain,
! [X0,X1,X2] : leq(forward_diamond(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f54,f2278]) ).
fof(f4525,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f82,f2278]) ).
fof(f4526,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f82,f2278]) ).
fof(f4531,plain,
! [X0,X1] : addition(one,addition(X0,domain(X1))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f82,f4501]) ).
fof(f4532,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f138,f196]) ).
fof(f4533,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f196]) ).
fof(f4534,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(addition(one,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f192,f196]) ).
fof(f4535,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)],[f177,f196]) ).
fof(f4536,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)],[f147,f196]) ).
fof(f4537,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)],[f29,f196]) ).
fof(f4538,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)],[f29,f196]) ).
fof(f4539,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)],[f192,f196]) ).
fof(f4540,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)],[f209,f196]) ).
fof(f4541,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)],[f211,f196]) ).
fof(f4542,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)],[f182,f196]) ).
fof(f4543,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),X0) = addition(zero,multiplication(X1,multiplication(X2,X0))),
inference(paramodulation,[status(thm)],[f3923,f196]) ).
fof(f4544,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)],[f180,f196]) ).
fof(f4545,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)],[f53,f196]) ).
fof(f4546,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),multiplication(X1,X2)),X0) = addition(X0,multiplication(X1,multiplication(X2,X0))),
inference(paramodulation,[status(thm)],[f3792,f196]) ).
fof(f4547,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)],[f33,f196]) ).
fof(f4548,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)],[f171,f196]) ).
fof(f4549,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)],[f162,f196]) ).
fof(f4550,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)],[f121,f196]) ).
fof(f4553,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f35,f196]) ).
fof(f4554,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),codomain(X0)) = addition(X0,multiplication(X1,multiplication(X2,codomain(X0)))),
inference(paramodulation,[status(thm)],[f2026,f196]) ).
fof(f4555,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)],[f147,f196]) ).
fof(f4556,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)],[f166,f196]) ).
fof(f4557,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)],[f177,f196]) ).
fof(f4558,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)],[f175,f196]) ).
fof(f4559,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)],[f136,f196]) ).
fof(f4560,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)],[f129,f196]) ).
fof(f4564,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)],[f209,f196]) ).
fof(f4565,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(c(multiplication(X1,X2)),X1)),X2) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f3923,f196]) ).
fof(f4566,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)],[f3792,f196]) ).
fof(f4567,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)],[f33,f196]) ).
fof(f4569,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(antidomain(multiplication(X1,X2)),X1)),X2) = addition(multiplication(X0,X2),zero),
inference(paramodulation,[status(thm)],[f44,f196]) ).
fof(f4573,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)],[f129,f196]) ).
fof(f4574,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)],[f192,f196]) ).
fof(f4575,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)],[f209,f196]) ).
fof(f4576,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)],[f211,f196]) ).
fof(f4577,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)],[f182,f196]) ).
fof(f4578,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f3923,f196]) ).
fof(f4579,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)],[f180,f196]) ).
fof(f4580,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)],[f53,f196]) ).
fof(f4581,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f3792,f196]) ).
fof(f4582,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)],[f33,f196]) ).
fof(f4583,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)],[f171,f196]) ).
fof(f4584,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)],[f162,f196]) ).
fof(f4585,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)],[f121,f196]) ).
fof(f4586,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f44,f196]) ).
fof(f4589,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),codomain(X2)) = addition(multiplication(X0,codomain(X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f2026,f196]) ).
fof(f4590,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)],[f147,f196]) ).
fof(f4591,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)],[f166,f196]) ).
fof(f4592,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)],[f177,f196]) ).
fof(f4593,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)],[f175,f196]) ).
fof(f4594,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)],[f136,f196]) ).
fof(f4595,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)],[f129,f196]) ).
fof(f4596,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f48,f196]) ).
fof(f4599,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,X2),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f196,f138]) ).
fof(f4600,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(paramodulation,[status(thm)],[f196,f36]) ).
fof(f4601,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)],[f196,f155]) ).
fof(f4602,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f196,f192]) ).
fof(f4603,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)],[f196,f177]) ).
fof(f4604,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)],[f196,f147]) ).
fof(f4605,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)],[f196,f211]) ).
fof(f4606,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)],[f196,f171]) ).
fof(f4607,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)],[f196,f162]) ).
fof(f4608,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,multiplication(X3,X4)),X1))),
inference(paramodulation,[status(thm)],[f196,f1257]) ).
fof(f4609,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)],[f196,f1256]) ).
fof(f4610,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f196,f1259]) ).
fof(f4611,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(X0,multiplication(X2,X3)),X1)),
inference(paramodulation,[status(thm)],[f196,f1163]) ).
fof(f4612,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)],[f196,f90]) ).
fof(f4613,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)],[f196,f88]) ).
fof(f4614,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)],[f196,f84]) ).
fof(f4615,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)],[f196,f82]) ).
fof(f4616,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)],[f196,f82]) ).
fof(f4617,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)],[f196,f231]) ).
fof(f4618,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)],[f196,f43]) ).
fof(f4619,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)],[f196,f30]) ).
fof(f4620,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)],[f196,f29]) ).
fof(f4621,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)],[f196,f29]) ).
fof(f4622,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f29,f4532]) ).
fof(f4623,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)],[f33,f4535]) ).
fof(f4624,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)],[f33,f4623]) ).
fof(f4625,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)],[f29,f4624]) ).
fof(f4626,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)],[f33,f4536]) ).
fof(f4627,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,f4626]) ).
fof(f4628,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)],[f88,f4539]) ).
fof(f4629,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)],[f88,f4628]) ).
fof(f4630,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)],[f82,f4629]) ).
fof(f4631,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)],[f189,f4630]) ).
fof(f4632,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)],[f88,f4540]) ).
fof(f4633,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)],[f196,f4632]) ).
fof(f4634,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)],[f88,f4541]) ).
fof(f4635,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)],[f196,f4634]) ).
fof(f4636,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),domain(X0)) = multiplication(X1,multiplication(X2,domain(X0))),
inference(forward_demodulation,[status(thm)],[f65,f4542]) ).
fof(f4637,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),multiplication(X1,X2)),X0) = multiplication(X1,multiplication(X2,X0)),
inference(forward_demodulation,[status(thm)],[f65,f4543]) ).
fof(f4638,plain,
! [X0,X1,X2] : multiplication(addition(coantidomain(X0),multiplication(X1,X2)),codomain(X0)) = multiplication(X1,multiplication(X2,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f65,f4544]) ).
fof(f4639,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)],[f65,f4550]) ).
fof(f4644,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)],[f88,f4555]) ).
fof(f4645,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)],[f82,f4644]) ).
fof(f4646,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)],[f88,f4557]) ).
fof(f4647,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)],[f82,f4646]) ).
fof(f4648,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)],[f65,f4559]) ).
fof(f4649,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)],[f65,f4560]) ).
fof(f4656,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)],[f196,f4564]) ).
fof(f4657,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(c(multiplication(X1,X2)),X1)),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f31,f4565]) ).
fof(f4658,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(domain(multiplication(X1,X2)),X1)),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f186,f4566]) ).
fof(f4659,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)],[f33,f4567]) ).
fof(f4662,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(antidomain(multiplication(X1,X2)),X1)),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f31,f4569]) ).
fof(f4668,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)],[f31,f4573]) ).
fof(f4669,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)],[f196,f4575]) ).
fof(f4670,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)],[f196,f4576]) ).
fof(f4671,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f38,f4577]) ).
fof(f4672,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),domain(X2)) = multiplication(X0,domain(X2)),
inference(forward_demodulation,[status(thm)],[f31,f4671]) ).
fof(f4673,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = addition(multiplication(X0,X2),zero),
inference(forward_demodulation,[status(thm)],[f38,f4578]) ).
fof(f4674,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,c(X2))),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f31,f4673]) ).
fof(f4675,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,coantidomain(X2))),codomain(X2)) = addition(multiplication(X0,codomain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f38,f4579]) ).
fof(f4676,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,coantidomain(X2))),codomain(X2)) = multiplication(X0,codomain(X2)),
inference(forward_demodulation,[status(thm)],[f31,f4675]) ).
fof(f4677,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f186,f4581]) ).
fof(f4678,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)],[f38,f4585]) ).
fof(f4679,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)],[f31,f4678]) ).
fof(f4680,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),zero),
inference(forward_demodulation,[status(thm)],[f38,f4586]) ).
fof(f4681,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),X2) = multiplication(X0,X2),
inference(forward_demodulation,[status(thm)],[f31,f4680]) ).
fof(f4686,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)],[f38,f4594]) ).
fof(f4687,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)],[f31,f4686]) ).
fof(f4688,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)],[f38,f4595]) ).
fof(f4689,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)],[f31,f4688]) ).
fof(f4690,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f38,f4596]) ).
fof(f4691,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),coantidomain(X2)) = multiplication(X0,coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f31,f4690]) ).
fof(f4695,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f29,f4599]) ).
fof(f4696,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)],[f33,f4603]) ).
fof(f4697,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)],[f29,f4696]) ).
fof(f4698,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)],[f33,f4697]) ).
fof(f4699,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,f4604]) ).
fof(f4700,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)],[f33,f4699]) ).
fof(f4701,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)],[f33,f4605]) ).
fof(f4702,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)],[f33,f4701]) ).
fof(f4703,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)],[f33,f4702]) ).
fof(f4704,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)],[f186,f4612]) ).
fof(f4705,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)],[f88,f4704]) ).
fof(f4706,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)],[f32,f4705]) ).
fof(f4707,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)],[f189,f4614]) ).
fof(f4708,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)],[f186,f4707]) ).
fof(f4709,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)],[f88,f4708]) ).
fof(f4710,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)],[f88,f4709]) ).
fof(f4711,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)],[f84,f4710]) ).
fof(f4712,plain,
! [X0,X1,X2] : addition(multiplication(X0,backward_diamond(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f2993,f42]) ).
fof(f4713,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(antidomain(backward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f209,f2993]) ).
fof(f4715,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f3792,f2993]) ).
fof(f4716,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,backward_diamond(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f2993]) ).
fof(f4725,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,backward_diamond(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f29,f4712]) ).
fof(f4729,plain,
! [X0,X1,X2] : addition(multiplication(X0,backward_box(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3074,f42]) ).
fof(f4730,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),addition(antidomain(backward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f209,f3074]) ).
fof(f4732,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f3792,f3074]) ).
fof(f4733,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,backward_box(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f3074]) ).
fof(f4740,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,backward_box(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f29,f4729]) ).
fof(f4743,plain,
! [X0,X1,X2] : addition(multiplication(X0,forward_box(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3075,f42]) ).
fof(f4744,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),addition(antidomain(forward_box(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f209,f3075]) ).
fof(f4746,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f3792,f3075]) ).
fof(f4747,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,forward_box(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f3075]) ).
fof(f4755,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,forward_box(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f29,f4743]) ).
fof(f4765,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)],[f237,f215]) ).
fof(f4766,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f88,f215]) ).
fof(f4767,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f30,f215]) ).
fof(f4773,plain,
! [X0,X1] : multiplication(addition(X0,c(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f52,f215]) ).
fof(f4774,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = multiplication(X0,antidomain(X1)),
inference(paramodulation,[status(thm)],[f47,f215]) ).
fof(f4779,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_box(X1,X2)),addition(X0,antidomain(forward_box(X1,X2)))),
inference(paramodulation,[status(thm)],[f215,f3075]) ).
fof(f4780,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_box(X1,X2)),addition(X0,antidomain(backward_box(X1,X2)))),
inference(paramodulation,[status(thm)],[f215,f3074]) ).
fof(f4781,plain,
! [X0,X1,X2] : leq(multiplication(X0,backward_diamond(X1,X2)),addition(X0,antidomain(backward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f215,f2993]) ).
fof(f4782,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(X0,antidomain(antidomain(X1)))),
inference(paramodulation,[status(thm)],[f215,f3218]) ).
fof(f4784,plain,
! [X0,X1] : leq(multiplication(X0,c(X1)),addition(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f215,f2999]) ).
fof(f4786,plain,
! [X0,X1] : leq(multiplication(X0,divergence(X1)),addition(X0,antidomain(divergence(X1)))),
inference(paramodulation,[status(thm)],[f215,f2847]) ).
fof(f4788,plain,
! [X0,X1] : leq(multiplication(X0,codomain(X1)),addition(X0,antidomain(codomain(X1)))),
inference(paramodulation,[status(thm)],[f215,f2917]) ).
fof(f4790,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)],[f215,f196]) ).
fof(f4791,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)],[f215,f189]) ).
fof(f4793,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(X0,antidomain(domain(X1)))),
inference(paramodulation,[status(thm)],[f215,f3299]) ).
fof(f4794,plain,
! [X0,X1] : forward_diamond(addition(X0,antidomain(domain(X1))),X1) = domain(multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f215,f54]) ).
fof(f4795,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)],[f215,f237]) ).
fof(f4796,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X0,antidomain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f215,f3336]) ).
fof(f4800,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)],[f215,f196]) ).
fof(f4802,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,antidomain(X1))),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f215,f192]) ).
fof(f4803,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)],[f215,f189]) ).
fof(f4804,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)],[f215,f189]) ).
fof(f4806,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f215,f186]) ).
fof(f4807,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)],[f215,f155]) ).
fof(f4808,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)],[f215,f155]) ).
fof(f4809,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(X1,one)) = addition(addition(X0,antidomain(X1)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f215,f177]) ).
fof(f4810,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(one,X1)) = addition(addition(X0,antidomain(X1)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f215,f147]) ).
fof(f4811,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)],[f215,f138]) ).
fof(f4812,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)],[f215,f138]) ).
fof(f4813,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(paramodulation,[status(thm)],[f215,f129]) ).
fof(f4814,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,antidomain(X1))),multiplication(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f215,f121]) ).
fof(f4815,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)],[f215,f309]) ).
fof(f4816,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)],[f215,f237]) ).
fof(f4817,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f215,f37]) ).
fof(f4819,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)],[f215,f36]) ).
fof(f4820,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)],[f215,f36]) ).
fof(f4821,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(paramodulation,[status(thm)],[f215,f33]) ).
fof(f4827,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f44,f4765]) ).
fof(f4835,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),addition(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f47,f4782]) ).
fof(f4846,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)],[f196,f4790]) ).
fof(f4847,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)],[f189,f4791]) ).
fof(f4852,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),addition(X0,c(X1))),
inference(forward_demodulation,[status(thm)],[f52,f4793]) ).
fof(f4853,plain,
! [X0,X1] : forward_diamond(addition(X0,c(X1)),X1) = domain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f52,f4794]) ).
fof(f4854,plain,
! [X0,X1] : forward_diamond(addition(X0,c(X1)),X1) = forward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f54,f4853]) ).
fof(f4855,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)],[f29,f4795]) ).
fof(f4856,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)],[f52,f4855]) ).
fof(f4857,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)],[f215,f4856]) ).
fof(f4862,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)],[f196,f4800]) ).
fof(f4865,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)],[f189,f4803]) ).
fof(f4866,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)],[f189,f4804]) ).
fof(f4869,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f186,f4806]) ).
fof(f4870,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)],[f82,f4807]) ).
fof(f4871,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(X1,one)) = addition(antidomain(X1),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f4809]) ).
fof(f4872,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),addition(one,X1)) = addition(antidomain(X1),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f4810]) ).
fof(f4873,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)],[f29,f4811]) ).
fof(f4874,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,antidomain(X2))),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f186,f4817]) ).
fof(f4877,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)],[f29,f4819]) ).
fof(f4878,plain,
! [X0,X1,X2] : multiplication(addition(X0,antidomain(X1)),multiplication(X1,X2)) = multiplication(X0,multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f33,f4821]) ).
fof(f4879,plain,
! [X0,X1,X2] : addition(multiplication(X0,forward_diamond(X1,X2)),X0) = X0,
inference(resolution,[status(thm)],[f3329,f42]) ).
fof(f4880,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(antidomain(forward_diamond(X1,X2)),X0)),
inference(paramodulation,[status(thm)],[f209,f3329]) ).
fof(f4881,plain,
! [X0,X1,X2] : leq(multiplication(X0,forward_diamond(X1,X2)),addition(X0,antidomain(forward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f215,f3329]) ).
fof(f4883,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),domain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f3792,f3329]) ).
fof(f4884,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,forward_diamond(X2,X3))),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f33,f3329]) ).
fof(f4894,plain,
! [X0,X1,X2] : addition(X0,multiplication(X0,forward_diamond(X1,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f29,f4879]) ).
fof(f4898,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(resolution,[status(thm)],[f3860,f42]) ).
fof(f4900,plain,
! [X0] : leq(domain(c(X0)),domain(c(domain(X0)))),
inference(paramodulation,[status(thm)],[f633,f3860]) ).
fof(f4901,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(c(backward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f57,f3860]) ).
fof(f4902,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(c(forward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f56,f3860]) ).
fof(f4906,plain,
! [X0] : leq(c(domain(X0)),domain(domain(c(X0)))),
inference(paramodulation,[status(thm)],[f633,f3860]) ).
fof(f4907,plain,
! [X0,X1] : leq(c(backward_diamond(X0,c(X1))),domain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f57,f3860]) ).
fof(f4908,plain,
! [X0,X1] : leq(c(forward_diamond(X0,c(X1))),domain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f56,f3860]) ).
fof(f4913,plain,
! [X0] : leq(domain(c(X0)),domain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f633,f4900]) ).
fof(f4914,plain,
! [X0] : leq(domain(c(X0)),antidomain(c(c(X0)))),
inference(forward_demodulation,[status(thm)],[f181,f4913]) ).
fof(f4915,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f57,f4901]) ).
fof(f4916,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f56,f4902]) ).
fof(f4923,plain,
! [X0] : leq(domain(c(X0)),domain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f633,f4906]) ).
fof(f4924,plain,
! [X0] : leq(domain(c(X0)),antidomain(c(c(X0)))),
inference(forward_demodulation,[status(thm)],[f181,f4923]) ).
fof(f4925,plain,
! [X0,X1] : leq(backward_box(X0,X1),domain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f57,f4907]) ).
fof(f4926,plain,
! [X0,X1] : leq(forward_box(X0,X1),domain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f56,f4908]) ).
fof(f4936,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f88,f217]) ).
fof(f4937,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f30,f217]) ).
fof(f4942,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f196,f217]) ).
fof(f4943,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f138,f217]) ).
fof(f4944,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f217]) ).
fof(f4945,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X2,addition(X1,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f88,f217]) ).
fof(f4946,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X1,addition(X2,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f30,f217]) ).
fof(f4954,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = multiplication(addition(one,X0),X1),
inference(paramodulation,[status(thm)],[f192,f217]) ).
fof(f4955,plain,
! [X0] : multiplication(addition(X0,one),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f177,f217]) ).
fof(f4956,plain,
! [X0] : multiplication(addition(X0,one),X0) = multiplication(X0,addition(one,X0)),
inference(paramodulation,[status(thm)],[f147,f217]) ).
fof(f4959,plain,
! [X0,X1] : multiplication(addition(addition(X0,one),one),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f217,f217]) ).
fof(f4961,plain,
! [X0,X1] : multiplication(addition(addition(X0,X1),one),coantidomain(X0)) = addition(coantidomain(X0),multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f211,f217]) ).
fof(f4965,plain,
! [X0,X1] : multiplication(addition(domain(X0),one),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f53,f217]) ).
fof(f4967,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f33,f217]) ).
fof(f4968,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),one),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f171,f217]) ).
fof(f4969,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),one),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f162,f217]) ).
fof(f4974,plain,
! [X0] : multiplication(addition(X0,one),codomain(X0)) = addition(codomain(X0),X0),
inference(paramodulation,[status(thm)],[f2026,f217]) ).
fof(f4975,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(addition(one,X1),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f147,f217]) ).
fof(f4976,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(coantidomain(X0),X1)) = addition(addition(coantidomain(X0),X1),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f166,f217]) ).
fof(f4977,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(addition(X1,one),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f177,f217]) ).
fof(f4978,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,coantidomain(X0))) = addition(addition(X1,coantidomain(X0)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f175,f217]) ).
fof(f4979,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(coantidomain(X0),X1)) = addition(multiplication(coantidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f136,f217]) ).
fof(f4980,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)],[f129,f217]) ).
fof(f4986,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)],[f217,f196]) ).
fof(f4987,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)],[f217,f196]) ).
fof(f4988,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f217,f192]) ).
fof(f4989,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)],[f217,f189]) ).
fof(f4990,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)],[f217,f189]) ).
fof(f4991,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f217,f186]) ).
fof(f4992,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(addition(X2,multiplication(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f217,f186]) ).
fof(f4993,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)],[f217,f155]) ).
fof(f4994,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)],[f217,f155]) ).
fof(f4995,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(addition(X0,one),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f217,f177]) ).
fof(f4996,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(addition(X0,one),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f217,f147]) ).
fof(f4997,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)],[f217,f138]) ).
fof(f4998,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)],[f217,f138]) ).
fof(f4999,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(addition(X1,multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f217,f129]) ).
fof(f5000,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,one)),addition(X1,multiplication(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f217,f121]) ).
fof(f5001,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)],[f217,f309]) ).
fof(f5002,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)],[f217,f237]) ).
fof(f5003,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f217,f37]) ).
fof(f5005,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)],[f217,f36]) ).
fof(f5006,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)],[f217,f36]) ).
fof(f5007,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f217,f33]) ).
fof(f5008,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(X0))) = multiplication(X0,multiplication(X1,coantidomain(X0))),
inference(paramodulation,[status(thm)],[f217,f166]) ).
fof(f5010,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(addition(X1,one),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f217,f196]) ).
fof(f5011,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X0,X1),X1)) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f217,f138]) ).
fof(f5012,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f217,f36]) ).
fof(f5013,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)],[f217,f155]) ).
fof(f5014,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X1,X0)))) = multiplication(addition(X2,one),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f217,f88]) ).
fof(f5015,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X0,X1)))) = multiplication(addition(X2,one),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f217,f30]) ).
fof(f5022,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = multiplication(addition(X0,one),X1),
inference(paramodulation,[status(thm)],[f217,f192]) ).
fof(f5023,plain,
! [X0] : multiplication(X0,addition(X0,one)) = multiplication(addition(X0,one),X0),
inference(paramodulation,[status(thm)],[f217,f177]) ).
fof(f5024,plain,
! [X0] : multiplication(X0,addition(one,X0)) = multiplication(addition(X0,one),X0),
inference(paramodulation,[status(thm)],[f217,f147]) ).
fof(f5026,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(addition(X0,one),X1)) = multiplication(antidomain(multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f217,f171]) ).
fof(f5027,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(addition(X1,one),X0)) = multiplication(antidomain(X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f217,f162]) ).
fof(f5028,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(X2,one),X0))),
inference(paramodulation,[status(thm)],[f217,f1257]) ).
fof(f5029,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,one),X1))),
inference(paramodulation,[status(thm)],[f217,f1256]) ).
fof(f5030,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f217,f1259]) ).
fof(f5031,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f217,f1163]) ).
fof(f5032,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f217,f90]) ).
fof(f5033,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),X2),
inference(paramodulation,[status(thm)],[f217,f88]) ).
fof(f5034,plain,
! [X0,X1] : addition(X0,addition(multiplication(X1,X0),multiplication(addition(X1,one),X0))) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f217,f84]) ).
fof(f5035,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(X2,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f217,f82]) ).
fof(f5036,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X1,one),X2)) = addition(multiplication(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f217,f82]) ).
fof(f5037,plain,
! [X0,X1] :
( multiplication(addition(X0,one),X1) != X1
| leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f217,f231]) ).
fof(f5038,plain,
! [X0,X1] :
( multiplication(addition(X1,one),X0) != multiplication(X1,X0)
| leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f217,f43]) ).
fof(f5039,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(X1,one),X0),X2),
inference(paramodulation,[status(thm)],[f217,f30]) ).
fof(f5048,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f29,f4943]) ).
fof(f5067,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f4959]) ).
fof(f5068,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f90,f5067]) ).
fof(f5071,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),coantidomain(X1)) = addition(coantidomain(X1),multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f88,f4961]) ).
fof(f5072,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),coantidomain(X1)) = multiplication(addition(X0,one),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f217,f5071]) ).
fof(f5082,plain,
! [X0,X1] : multiplication(addition(one,domain(X0)),antidomain(X1)) = addition(antidomain(X1),domain_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f4965]) ).
fof(f5083,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1211,f5082]) ).
fof(f5084,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f5083]) ).
fof(f5088,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f29,f4967]) ).
fof(f5089,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X1,X0)) = addition(addition(X1,X0),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f29,f4968]) ).
fof(f5090,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f1215,f5089]) ).
fof(f5091,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f35,f5090]) ).
fof(f5092,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f88,f5091]) ).
fof(f5093,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f29,f4969]) ).
fof(f5094,plain,
! [X0,X1] : multiplication(one,addition(X0,X1)) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1215,f5093]) ).
fof(f5095,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f35,f5094]) ).
fof(f5096,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f5095]) ).
fof(f5106,plain,
! [X0] : multiplication(addition(X0,one),codomain(X0)) = addition(X0,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f29,f4974]) ).
fof(f5107,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(X1,addition(one,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f4975]) ).
fof(f5108,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(coantidomain(X0),X1)) = addition(X1,addition(coantidomain(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f4976]) ).
fof(f5109,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(one,addition(X1,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f4977]) ).
fof(f5110,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,coantidomain(X0))) = addition(coantidomain(X0),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f4978]) ).
fof(f5111,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(coantidomain(X0),X1)) = multiplication(coantidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f4979]) ).
fof(f5112,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f31,f4980]) ).
fof(f5119,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)],[f88,f4987]) ).
fof(f5120,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)],[f88,f5119]) ).
fof(f5121,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)],[f82,f5120]) ).
fof(f5122,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)],[f189,f5121]) ).
fof(f5123,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,one)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f90,f4988]) ).
fof(f5124,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)],[f82,f4989]) ).
fof(f5125,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)],[f82,f5124]) ).
fof(f5126,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)],[f196,f5125]) ).
fof(f5127,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)],[f88,f4991]) ).
fof(f5128,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)],[f82,f5127]) ).
fof(f5129,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f5128]) ).
fof(f5130,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)],[f88,f4992]) ).
fof(f5131,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)],[f82,f5130]) ).
fof(f5132,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f5131]) ).
fof(f5133,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)],[f88,f4993]) ).
fof(f5134,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)],[f82,f5133]) ).
fof(f5135,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)],[f88,f4994]) ).
fof(f5136,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)],[f82,f5135]) ).
fof(f5137,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)],[f88,f5136]) ).
fof(f5138,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(one,addition(X0,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f4995]) ).
fof(f5139,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(one,addition(X0,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f4996]) ).
fof(f5140,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)],[f88,f4998]) ).
fof(f5141,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)],[f82,f5140]) ).
fof(f5142,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)],[f82,f5003]) ).
fof(f5143,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f186,f5142]) ).
fof(f5148,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)],[f88,f5006]) ).
fof(f5149,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)],[f82,f5148]) ).
fof(f5157,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f5011]) ).
fof(f5177,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,one),X0),X1),
inference(forward_demodulation,[status(thm)],[f82,f5033]) ).
fof(f5178,plain,
! [X0,X1] : addition(X0,multiplication(addition(addition(X1,one),X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f186,f5034]) ).
fof(f5179,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,addition(X1,X1)),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f5178]) ).
fof(f5180,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f32,f5179]) ).
fof(f5181,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X1,one),X2)) = addition(X2,addition(multiplication(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f82,f5036]) ).
fof(f5182,plain,
! [X0] : addition(divergence(X0),domain(divergence(X0))) = domain(divergence(X0)),
inference(resolution,[status(thm)],[f3862,f42]) ).
fof(f5189,plain,
! [X0] : addition(codomain(X0),domain(codomain(X0))) = domain(codomain(X0)),
inference(resolution,[status(thm)],[f3864,f42]) ).
fof(f5190,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(codomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f178,f3864]) ).
fof(f5191,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(codomain(multiplication(codomain(X1),X0)))),
inference(paramodulation,[status(thm)],[f55,f3864]) ).
fof(f5194,plain,
! [X0] : leq(codomain(coantidomain(X0)),domain(coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f178,f3864]) ).
fof(f5195,plain,
! [X0,X1] : leq(codomain(multiplication(codomain(X0),X1)),domain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f55,f3864]) ).
fof(f5198,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f178,f5190]) ).
fof(f5199,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f55,f5191]) ).
fof(f5204,plain,
! [X0] : leq(coantidomain(codomain(X0)),domain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f178,f5194]) ).
fof(f5205,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),domain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f55,f5195]) ).
fof(f5210,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(resolution,[status(thm)],[f3906,f42]) ).
fof(f5213,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),antidomain(c(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f54,f3906]) ).
fof(f5218,plain,
! [X0,X1] : leq(domain(backward_diamond(X0,c(X1))),antidomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f57,f3906]) ).
fof(f5219,plain,
! [X0,X1] : leq(domain(forward_diamond(X0,c(X1))),antidomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f56,f3906]) ).
fof(f5238,plain,
! [X0] : addition(coantidomain(X0),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(resolution,[status(thm)],[f3871,f42]) ).
fof(f5267,plain,
! [X0] : multiplication(one,coantidomain(c(X0))) = multiplication(domain(X0),coantidomain(c(X0))),
inference(paramodulation,[status(thm)],[f657,f218]) ).
fof(f5268,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)],[f309,f218]) ).
fof(f5269,plain,
! [X0] : multiplication(one,coantidomain(codomain(X0))) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f354,f218]) ).
fof(f5270,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)],[f237,f218]) ).
fof(f5271,plain,
! [X0] : multiplication(one,coantidomain(domain(X0))) = multiplication(antidomain(X0),coantidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f283,f218]) ).
fof(f5272,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)],[f189,f218]) ).
fof(f5273,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)],[f155,f218]) ).
fof(f5274,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)],[f196,f218]) ).
fof(f5275,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)],[f186,f218]) ).
fof(f5276,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)],[f138,f218]) ).
fof(f5277,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)],[f37,f218]) ).
fof(f5278,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)],[f36,f218]) ).
fof(f5279,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f88,f218]) ).
fof(f5280,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(paramodulation,[status(thm)],[f30,f218]) ).
fof(f5288,plain,
! [X0,X1] : multiplication(multiplication(addition(X0,one),X1),coantidomain(multiplication(X0,X1))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f217,f218]) ).
fof(f5289,plain,
! [X0,X1] : multiplication(multiplication(addition(one,X0),X1),coantidomain(multiplication(X0,X1))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f192,f218]) ).
fof(f5290,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(X1,one)),coantidomain(multiplication(X0,X1))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f177,f218]) ).
fof(f5291,plain,
! [X0,X1] : multiplication(multiplication(X0,addition(one,X1)),coantidomain(multiplication(X0,X1))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f147,f218]) ).
fof(f5292,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)],[f84,f218]) ).
fof(f5293,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X0,X1))) = multiplication(X0,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f90,f218]) ).
fof(f5294,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X0,X1))) = multiplication(X2,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f82,f218]) ).
fof(f5295,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(addition(X2,X0))) = multiplication(X1,coantidomain(addition(X2,X0))),
inference(paramodulation,[status(thm)],[f82,f218]) ).
fof(f5301,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,coantidomain(coantidomain(X1))),
inference(paramodulation,[status(thm)],[f51,f218]) ).
fof(f5305,plain,
! [X0,X1] : leq(multiplication(X0,coantidomain(X1)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f218,f3336]) ).
fof(f5308,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)],[f218,f196]) ).
fof(f5310,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X1)) = addition(coantidomain(X1),multiplication(X0,coantidomain(X1))),
inference(paramodulation,[status(thm)],[f218,f192]) ).
fof(f5311,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)],[f218,f189]) ).
fof(f5312,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)],[f218,f189]) ).
fof(f5314,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)],[f218,f186]) ).
fof(f5315,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)],[f218,f155]) ).
fof(f5316,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)],[f218,f155]) ).
fof(f5319,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)],[f218,f138]) ).
fof(f5320,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)],[f218,f138]) ).
fof(f5321,plain,
! [X0,X1] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),coantidomain(multiplication(X0,coantidomain(X1))))) = zero,
inference(paramodulation,[status(thm)],[f218,f129]) ).
fof(f5322,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),multiplication(X0,coantidomain(X1))) = zero,
inference(paramodulation,[status(thm)],[f218,f121]) ).
fof(f5323,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)],[f218,f309]) ).
fof(f5324,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)],[f218,f237]) ).
fof(f5325,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)],[f218,f37]) ).
fof(f5326,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)],[f218,f37]) ).
fof(f5327,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)],[f218,f36]) ).
fof(f5328,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)],[f218,f36]) ).
fof(f5329,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(multiplication(X0,coantidomain(X1)),X2),
inference(paramodulation,[status(thm)],[f218,f33]) ).
fof(f5331,plain,
! [X0] : coantidomain(c(X0)) = multiplication(domain(X0),coantidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f35,f5267]) ).
fof(f5332,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),coantidomain(coantidomain(multiplication(codomain(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f48,f5268]) ).
fof(f5333,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),codomain(multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f51,f5332]) ).
fof(f5334,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),backward_diamond(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f5333]) ).
fof(f5335,plain,
! [X0] : coantidomain(codomain(X0)) = multiplication(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f5269]) ).
fof(f5336,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),coantidomain(antidomain(multiplication(X0,domain(X1))))),
inference(forward_demodulation,[status(thm)],[f48,f5270]) ).
fof(f5337,plain,
! [X0] : coantidomain(domain(X0)) = multiplication(antidomain(X0),coantidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f35,f5271]) ).
fof(f5338,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)],[f33,f5272]) ).
fof(f5339,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)],[f33,f5338]) ).
fof(f5340,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)],[f33,f5339]) ).
fof(f5341,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)],[f33,f5273]) ).
fof(f5342,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)],[f33,f5274]) ).
fof(f5343,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)],[f33,f5342]) ).
fof(f5344,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)],[f33,f5275]) ).
fof(f5345,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)],[f33,f5344]) ).
fof(f5346,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)],[f33,f5276]) ).
fof(f5347,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)],[f33,f5346]) ).
fof(f5348,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)],[f33,f5277]) ).
fof(f5349,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)],[f33,f5348]) ).
fof(f5350,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)],[f33,f5278]) ).
fof(f5351,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)],[f33,f5350]) ).
fof(f5353,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f5288]) ).
fof(f5354,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,coantidomain(multiplication(X0,X1)))) = multiplication(X1,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f5289]) ).
fof(f5355,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(X1,one),coantidomain(multiplication(X0,X1)))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f5290]) ).
fof(f5356,plain,
! [X0,X1] : multiplication(X0,multiplication(addition(one,X1),coantidomain(multiplication(X0,X1)))) = multiplication(X0,coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f33,f5291]) ).
fof(f5357,plain,
! [X0,X1] : zero = multiplication(X0,coantidomain(addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f48,f5293]) ).
fof(f5361,plain,
! [X0,X1] : multiplication(addition(X0,coantidomain(X1)),codomain(X1)) = multiplication(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f51,f5301]) ).
fof(f5371,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)],[f196,f5308]) ).
fof(f5374,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X1)),coantidomain(X1)) = multiplication(addition(X0,one),coantidomain(X1)),
inference(forward_demodulation,[status(thm)],[f217,f5310]) ).
fof(f5375,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)],[f189,f5311]) ).
fof(f5376,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)],[f189,f5312]) ).
fof(f5379,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X0,X1),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f186,f5314]) ).
fof(f5380,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)],[f82,f5315]) ).
fof(f5390,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)],[f29,f5319]) ).
fof(f5391,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X2)),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f186,f5325]) ).
fof(f5392,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)],[f88,f5326]) ).
fof(f5393,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),coantidomain(X2)) = addition(multiplication(X0,coantidomain(X2)),multiplication(X1,coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f211,f5392]) ).
fof(f5394,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),coantidomain(X2)) = multiplication(addition(X1,X0),coantidomain(X2)),
inference(forward_demodulation,[status(thm)],[f186,f5393]) ).
fof(f5395,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)],[f29,f5327]) ).
fof(f5396,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),multiplication(coantidomain(X1),X2)) = multiplication(X0,multiplication(coantidomain(X1),X2)),
inference(forward_demodulation,[status(thm)],[f33,f5329]) ).
fof(f5400,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)],[f82,f204]) ).
fof(f5401,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)],[f82,f204]) ).
fof(f5404,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)],[f192,f204]) ).
fof(f5405,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)],[f209,f204]) ).
fof(f5406,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)],[f217,f204]) ).
fof(f5409,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)],[f211,f204]) ).
fof(f5410,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)],[f182,f204]) ).
fof(f5411,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(addition(c(X1),X0),X1),X2),
inference(paramodulation,[status(thm)],[f3923,f204]) ).
fof(f5412,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)],[f180,f204]) ).
fof(f5413,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)],[f53,f204]) ).
fof(f5414,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(domain(X0),X1),X0),X2),
inference(paramodulation,[status(thm)],[f3792,f204]) ).
fof(f5415,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)],[f33,f204]) ).
fof(f5416,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)],[f171,f204]) ).
fof(f5417,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)],[f162,f204]) ).
fof(f5418,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)],[f121,f204]) ).
fof(f5421,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(one,X1),X0),X2),
inference(paramodulation,[status(thm)],[f35,f204]) ).
fof(f5422,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,codomain(X0)),X2)) = addition(multiplication(addition(X0,X1),codomain(X0)),X2),
inference(paramodulation,[status(thm)],[f2026,f204]) ).
fof(f5423,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)],[f147,f204]) ).
fof(f5424,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)],[f166,f204]) ).
fof(f5425,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)],[f177,f204]) ).
fof(f5426,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)],[f175,f204]) ).
fof(f5427,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)],[f136,f204]) ).
fof(f5428,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)],[f129,f204]) ).
fof(f5433,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)],[f204,f204]) ).
fof(f5434,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)],[f155,f204]) ).
fof(f5435,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)],[f196,f204]) ).
fof(f5436,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)],[f186,f204]) ).
fof(f5437,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)],[f138,f204]) ).
fof(f5438,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)],[f37,f204]) ).
fof(f5439,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)],[f36,f204]) ).
fof(f5440,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)],[f2179,f204]) ).
fof(f5441,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)],[f2178,f204]) ).
fof(f5442,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)],[f2177,f204]) ).
fof(f5443,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)],[f2176,f204]) ).
fof(f5444,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)],[f2175,f204]) ).
fof(f5445,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)],[f2174,f204]) ).
fof(f5446,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)],[f217,f204]) ).
fof(f5447,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)],[f192,f204]) ).
fof(f5448,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)],[f177,f204]) ).
fof(f5449,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)],[f147,f204]) ).
fof(f5450,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)],[f84,f204]) ).
fof(f5451,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)],[f90,f204]) ).
fof(f5452,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)],[f82,f204]) ).
fof(f5453,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)],[f82,f204]) ).
fof(f5454,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),zero),
inference(paramodulation,[status(thm)],[f31,f204]) ).
fof(f5455,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)],[f29,f204]) ).
fof(f5456,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)],[f29,f204]) ).
fof(f5457,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f32,f204]) ).
fof(f5458,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)],[f192,f204]) ).
fof(f5459,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)],[f209,f204]) ).
fof(f5460,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)],[f217,f204]) ).
fof(f5461,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)],[f215,f204]) ).
fof(f5462,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)],[f218,f204]) ).
fof(f5463,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)],[f211,f204]) ).
fof(f5464,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)],[f182,f204]) ).
fof(f5465,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(addition(X0,c(X1)),X1),X2),
inference(paramodulation,[status(thm)],[f3923,f204]) ).
fof(f5466,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)],[f180,f204]) ).
fof(f5467,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)],[f53,f204]) ).
fof(f5468,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,domain(X1)),X1),X2),
inference(paramodulation,[status(thm)],[f3792,f204]) ).
fof(f5469,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)],[f33,f204]) ).
fof(f5470,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)],[f171,f204]) ).
fof(f5471,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)],[f162,f204]) ).
fof(f5472,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)],[f121,f204]) ).
fof(f5475,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),X2),
inference(paramodulation,[status(thm)],[f35,f204]) ).
fof(f5476,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),addition(X1,X2)) = addition(multiplication(addition(X0,X1),codomain(X1)),X2),
inference(paramodulation,[status(thm)],[f2026,f204]) ).
fof(f5477,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)],[f147,f204]) ).
fof(f5478,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)],[f166,f204]) ).
fof(f5479,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)],[f177,f204]) ).
fof(f5480,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)],[f175,f204]) ).
fof(f5481,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)],[f136,f204]) ).
fof(f5482,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)],[f129,f204]) ).
fof(f5487,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)],[f204,f155]) ).
fof(f5489,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(addition(X2,X0),X1),X3)),
inference(paramodulation,[status(thm)],[f204,f1257]) ).
fof(f5493,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)],[f204,f82]) ).
fof(f5494,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)],[f204,f82]) ).
fof(f5495,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)],[f204,f218]) ).
fof(f5496,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)],[f204,f211]) ).
fof(f5497,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)],[f204,f171]) ).
fof(f5498,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)],[f204,f162]) ).
fof(f5499,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(addition(X0,X3),X1),X4))),
inference(paramodulation,[status(thm)],[f204,f1257]) ).
fof(f5500,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)],[f204,f1256]) ).
fof(f5501,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(addition(X3,X0),X1),X2)),
inference(paramodulation,[status(thm)],[f204,f1259]) ).
fof(f5502,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f204,f1163]) ).
fof(f5504,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)],[f204,f88]) ).
fof(f5505,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)],[f204,f84]) ).
fof(f5506,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)],[f204,f82]) ).
fof(f5507,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)],[f204,f82]) ).
fof(f5508,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)],[f204,f231]) ).
fof(f5509,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)],[f204,f43]) ).
fof(f5510,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)],[f204,f30]) ).
fof(f5519,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(addition(X2,X1),X3),X0),
inference(forward_demodulation,[status(thm)],[f186,f5401]) ).
fof(f5524,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)],[f88,f5404]) ).
fof(f5525,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)],[f82,f5524]) ).
fof(f5526,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)],[f88,f5525]) ).
fof(f5527,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)],[f186,f5526]) ).
fof(f5528,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)],[f88,f5527]) ).
fof(f5529,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)],[f204,f5405]) ).
fof(f5530,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)],[f88,f5529]) ).
fof(f5531,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)],[f88,f5406]) ).
fof(f5532,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)],[f82,f5531]) ).
fof(f5533,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)],[f88,f5532]) ).
fof(f5534,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)],[f186,f5533]) ).
fof(f5535,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)],[f88,f5534]) ).
fof(f5540,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)],[f204,f5409]) ).
fof(f5541,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)],[f88,f5540]) ).
fof(f5542,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),X2) = addition(multiplication(addition(c(X1),X0),domain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f5410]) ).
fof(f5543,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),X2) = addition(multiplication(addition(c(X1),X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f65,f5411]) ).
fof(f5544,plain,
! [X0,X1,X2] : addition(multiplication(X0,codomain(X1)),X2) = addition(multiplication(addition(coantidomain(X1),X0),codomain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f5412]) ).
fof(f5545,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)],[f65,f5418]) ).
fof(f5548,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)],[f88,f5423]) ).
fof(f5549,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)],[f82,f5548]) ).
fof(f5550,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)],[f88,f5549]) ).
fof(f5551,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)],[f88,f5425]) ).
fof(f5552,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)],[f82,f5551]) ).
fof(f5553,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)],[f88,f5552]) ).
fof(f5554,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)],[f65,f5427]) ).
fof(f5555,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)],[f65,f5428]) ).
fof(f5565,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)],[f204,f5433]) ).
fof(f5566,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)],[f204,f5565]) ).
fof(f5567,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)],[f88,f5566]) ).
fof(f5568,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)],[f186,f5435]) ).
fof(f5569,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)],[f88,f5568]) ).
fof(f5570,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)],[f196,f5569]) ).
fof(f5571,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)],[f88,f5570]) ).
fof(f5572,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)],[f186,f5436]) ).
fof(f5573,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)],[f88,f5572]) ).
fof(f5574,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f186,f5573]) ).
fof(f5575,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)],[f186,f5438]) ).
fof(f5576,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)],[f88,f5575]) ).
fof(f5577,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f186,f5576]) ).
fof(f5578,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)],[f186,f5440]) ).
fof(f5579,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)],[f33,f5578]) ).
fof(f5580,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)],[f186,f5441]) ).
fof(f5581,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)],[f33,f5580]) ).
fof(f5582,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)],[f186,f5442]) ).
fof(f5583,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)],[f33,f5582]) ).
fof(f5584,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)],[f186,f5443]) ).
fof(f5585,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)],[f33,f5584]) ).
fof(f5586,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)],[f186,f5444]) ).
fof(f5587,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)],[f33,f5586]) ).
fof(f5588,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)],[f186,f5445]) ).
fof(f5589,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)],[f33,f5588]) ).
fof(f5590,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)],[f196,f5446]) ).
fof(f5591,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)],[f196,f5590]) ).
fof(f5592,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)],[f88,f5591]) ).
fof(f5593,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)],[f196,f5447]) ).
fof(f5594,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)],[f196,f5593]) ).
fof(f5595,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)],[f88,f5594]) ).
fof(f5596,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)],[f33,f5448]) ).
fof(f5597,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)],[f33,f5596]) ).
fof(f5598,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)],[f33,f5449]) ).
fof(f5599,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)],[f33,f5598]) ).
fof(f5600,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)],[f204,f5450]) ).
fof(f5601,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)],[f204,f5451]) ).
fof(f5602,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)],[f204,f5601]) ).
fof(f5603,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)],[f88,f5602]) ).
fof(f5604,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),zero),
inference(forward_demodulation,[status(thm)],[f186,f5454]) ).
fof(f5605,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f31,f5604]) ).
fof(f5606,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f186,f5457]) ).
fof(f5607,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f186,f5606]) ).
fof(f5608,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)],[f88,f5458]) ).
fof(f5609,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)],[f204,f5608]) ).
fof(f5610,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)],[f82,f5609]) ).
fof(f5611,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)],[f204,f5459]) ).
fof(f5612,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)],[f88,f5460]) ).
fof(f5613,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)],[f204,f5612]) ).
fof(f5614,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)],[f82,f5613]) ).
fof(f5615,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)],[f204,f5461]) ).
fof(f5616,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)],[f204,f5462]) ).
fof(f5617,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)],[f204,f5463]) ).
fof(f5618,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)],[f82,f5464]) ).
fof(f5619,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,domain(X2))) = addition(multiplication(addition(X1,c(X2)),domain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f65,f5618]) ).
fof(f5620,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,X2))) = addition(multiplication(addition(X1,c(X2)),X2),X0),
inference(forward_demodulation,[status(thm)],[f82,f5465]) ).
fof(f5621,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,X2)) = addition(multiplication(addition(X1,c(X2)),X2),X0),
inference(forward_demodulation,[status(thm)],[f65,f5620]) ).
fof(f5622,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)],[f82,f5466]) ).
fof(f5623,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,codomain(X2))) = addition(multiplication(addition(X1,coantidomain(X2)),codomain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f65,f5622]) ).
fof(f5624,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,domain(X0)),X0),X1),
inference(forward_demodulation,[status(thm)],[f82,f5468]) ).
fof(f5625,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)],[f82,f5470]) ).
fof(f5626,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)],[f82,f5471]) ).
fof(f5627,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)],[f82,f5472]) ).
fof(f5628,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)],[f65,f5627]) ).
fof(f5635,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,X0))) = addition(multiplication(addition(X2,one),X0),X1),
inference(forward_demodulation,[status(thm)],[f82,f5475]) ).
fof(f5636,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)],[f82,f5476]) ).
fof(f5637,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)],[f88,f5477]) ).
fof(f5638,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)],[f82,f5637]) ).
fof(f5639,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)],[f82,f5478]) ).
fof(f5640,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)],[f88,f5479]) ).
fof(f5641,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)],[f82,f5640]) ).
fof(f5642,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)],[f82,f5480]) ).
fof(f5643,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)],[f82,f5481]) ).
fof(f5644,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)],[f65,f5643]) ).
fof(f5645,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)],[f82,f5482]) ).
fof(f5646,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)],[f65,f5645]) ).
fof(f5666,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f5494]) ).
fof(f5667,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)],[f33,f5495]) ).
fof(f5670,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)],[f88,f5504]) ).
fof(f5671,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)],[f204,f5670]) ).
fof(f5672,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)],[f88,f5671]) ).
fof(f5673,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)],[f88,f5505]) ).
fof(f5674,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)],[f204,f5673]) ).
fof(f5675,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)],[f204,f5674]) ).
fof(f5676,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)],[f88,f5506]) ).
fof(f5677,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)],[f88,f5507]) ).
fof(f5678,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)],[f88,f5510]) ).
fof(f5679,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)],[f88,f5678]) ).
fof(f5687,plain,
! [X0] : forward_diamond(domain(antidomain(c(X0))),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f1096,f3999]) ).
fof(f5688,plain,
! [X0] : forward_diamond(domain(domain(c(X0))),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f633,f3999]) ).
fof(f5689,plain,
! [X0,X1] : forward_diamond(domain(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f57,f3999]) ).
fof(f5690,plain,
! [X0,X1] : forward_diamond(domain(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = zero,
inference(paramodulation,[status(thm)],[f56,f3999]) ).
fof(f5693,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)],[f3999,f60]) ).
fof(f5694,plain,
! [X0] : forward_box(domain(c(c(X0))),X0) = c(zero),
inference(paramodulation,[status(thm)],[f3999,f56]) ).
fof(f5704,plain,
! [X0] : forward_diamond(c(c(X0)),antidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f631,f5687]) ).
fof(f5705,plain,
! [X0] : forward_diamond(antidomain(c(c(X0))),domain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f181,f5688]) ).
fof(f5709,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)],[f82,f5693]) ).
fof(f5710,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)],[f65,f5709]) ).
fof(f5711,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)],[f3999,f5710]) ).
fof(f5712,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)],[f65,f5711]) ).
fof(f5713,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)],[f633,f5712]) ).
fof(f5714,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)],[f181,f5713]) ).
fof(f5715,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)],[f633,f5714]) ).
fof(f5716,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)],[f181,f5715]) ).
fof(f5717,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)],[f633,f5716]) ).
fof(f5718,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)],[f181,f5717]) ).
fof(f5719,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)],[f633,f5718]) ).
fof(f5720,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)],[f181,f5719]) ).
fof(f5721,plain,
! [X0] : forward_box(domain(c(c(X0))),X0) = one,
inference(forward_demodulation,[status(thm)],[f352,f5694]) ).
fof(f5726,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),X1),
inference(resolution,[status(thm)],[f4164,f231]) ).
fof(f5731,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(divergence(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f88,f4164]) ).
fof(f5732,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(divergence(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f30,f4164]) ).
fof(f5739,plain,
! [X0] : codomain(divergence(X0)) = addition(codomain(divergence(X0)),divergence(X0)),
inference(paramodulation,[status(thm)],[f2026,f4164]) ).
fof(f5740,plain,
! [X0,X1] : addition(coantidomain(divergence(X0)),X1) = addition(addition(coantidomain(divergence(X0)),X1),multiplication(divergence(X0),X1)),
inference(paramodulation,[status(thm)],[f166,f4164]) ).
fof(f5756,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4164,f166]) ).
fof(f5761,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)],[f4164,f204]) ).
fof(f5762,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)],[f4164,f155]) ).
fof(f5763,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4164,f88]) ).
fof(f5764,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4164,f30]) ).
fof(f5774,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(paramodulation,[status(thm)],[f4164,f162]) ).
fof(f5776,plain,
! [X0,X1,X2] : leq(multiplication(divergence(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4164,f1256]) ).
fof(f5780,plain,
! [X0,X1,X2] : addition(multiplication(divergence(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4164,f88]) ).
fof(f5782,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(divergence(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4164,f82]) ).
fof(f5783,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(divergence(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4164,f82]) ).
fof(f5785,plain,
! [X0,X1] :
( X0 != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4164,f43]) ).
fof(f5786,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(divergence(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4164,f30]) ).
fof(f5796,plain,
! [X0] : codomain(divergence(X0)) = addition(divergence(X0),codomain(divergence(X0))),
inference(forward_demodulation,[status(thm)],[f29,f5739]) ).
fof(f5797,plain,
! [X0,X1] : addition(coantidomain(divergence(X0)),X1) = addition(X1,addition(coantidomain(divergence(X0)),multiplication(divergence(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f5740]) ).
fof(f5806,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(divergence(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f48,f5756]) ).
fof(f5811,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)],[f186,f5761]) ).
fof(f5812,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)],[f196,f5811]) ).
fof(f5813,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)],[f88,f5812]) ).
fof(f5814,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)],[f138,f5762]) ).
fof(f5824,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(divergence(X1),X0)),
inference(forward_demodulation,[status(thm)],[f44,f5774]) ).
fof(f5826,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(divergence(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f5780]) ).
fof(f5828,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(divergence(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f5783]) ).
fof(f5831,plain,
! [X0] : leq(divergence(X0),codomain(divergence(X0))),
inference(paramodulation,[status(thm)],[f2026,f5726]) ).
fof(f5832,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),addition(coantidomain(divergence(X0)),X1)),
inference(paramodulation,[status(thm)],[f166,f5726]) ).
fof(f5833,plain,
! [X0,X1] : leq(multiplication(divergence(X0),X1),addition(X1,coantidomain(divergence(X0)))),
inference(paramodulation,[status(thm)],[f175,f5726]) ).
fof(f5842,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4165,f231]) ).
fof(f5847,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(codomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f88,f4165]) ).
fof(f5848,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(codomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f30,f4165]) ).
fof(f5855,plain,
! [X0] : codomain(codomain(X0)) = addition(codomain(codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f2026,f4165]) ).
fof(f5856,plain,
! [X0,X1] : addition(coantidomain(codomain(X0)),X1) = addition(addition(coantidomain(codomain(X0)),X1),multiplication(codomain(X0),X1)),
inference(paramodulation,[status(thm)],[f166,f4165]) ).
fof(f5863,plain,
! [X0,X1] : X0 = addition(X0,multiplication(coantidomain(codomain(X1)),X0)),
inference(paramodulation,[status(thm)],[f178,f4165]) ).
fof(f5864,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f55,f4165]) ).
fof(f5875,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4165,f166]) ).
fof(f5880,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)],[f4165,f204]) ).
fof(f5881,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)],[f4165,f155]) ).
fof(f5882,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4165,f88]) ).
fof(f5883,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4165,f30]) ).
fof(f5893,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4165,f162]) ).
fof(f5895,plain,
! [X0,X1,X2] : leq(multiplication(codomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4165,f1256]) ).
fof(f5899,plain,
! [X0,X1,X2] : addition(multiplication(codomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4165,f88]) ).
fof(f5901,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(codomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4165,f82]) ).
fof(f5902,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(codomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4165,f82]) ).
fof(f5904,plain,
! [X0,X1] :
( X0 != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4165,f43]) ).
fof(f5905,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(codomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4165,f30]) ).
fof(f5915,plain,
! [X0] : codomain(codomain(X0)) = addition(codomain(X0),codomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f5855]) ).
fof(f5916,plain,
! [X0,X1] : addition(coantidomain(codomain(X0)),X1) = addition(X1,addition(coantidomain(codomain(X0)),multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f5856]) ).
fof(f5926,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(codomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f48,f5875]) ).
fof(f5931,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)],[f186,f5880]) ).
fof(f5932,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)],[f196,f5931]) ).
fof(f5933,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)],[f88,f5932]) ).
fof(f5934,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)],[f138,f5881]) ).
fof(f5944,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(codomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f44,f5893]) ).
fof(f5946,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(codomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f5899]) ).
fof(f5948,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(codomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f5902]) ).
fof(f5951,plain,
! [X0] : leq(codomain(X0),codomain(codomain(X0))),
inference(paramodulation,[status(thm)],[f2026,f5842]) ).
fof(f5952,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),addition(coantidomain(codomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f166,f5842]) ).
fof(f5953,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),addition(X1,coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f175,f5842]) ).
fof(f5959,plain,
! [X0,X1] : leq(multiplication(coantidomain(codomain(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f178,f5842]) ).
fof(f5960,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f55,f5842]) ).
fof(f5966,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),X1),
inference(resolution,[status(thm)],[f4166,f231]) ).
fof(f5971,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(c(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f88,f4166]) ).
fof(f5972,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(c(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f30,f4166]) ).
fof(f5981,plain,
! [X0] : codomain(c(X0)) = addition(codomain(c(X0)),c(X0)),
inference(paramodulation,[status(thm)],[f2026,f4166]) ).
fof(f5982,plain,
! [X0,X1] : addition(coantidomain(c(X0)),X1) = addition(addition(coantidomain(c(X0)),X1),multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f166,f4166]) ).
fof(f5989,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f1096,f4166]) ).
fof(f5990,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(c(X1)),X0)),
inference(paramodulation,[status(thm)],[f633,f4166]) ).
fof(f5991,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f57,f4166]) ).
fof(f5992,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f56,f4166]) ).
fof(f6003,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4166,f166]) ).
fof(f6008,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)],[f4166,f204]) ).
fof(f6009,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)],[f4166,f155]) ).
fof(f6010,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4166,f88]) ).
fof(f6011,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4166,f30]) ).
fof(f6021,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(paramodulation,[status(thm)],[f4166,f162]) ).
fof(f6023,plain,
! [X0,X1,X2] : leq(multiplication(c(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4166,f1256]) ).
fof(f6027,plain,
! [X0,X1,X2] : addition(multiplication(c(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4166,f88]) ).
fof(f6029,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(c(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4166,f82]) ).
fof(f6030,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(c(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4166,f82]) ).
fof(f6032,plain,
! [X0,X1] :
( X0 != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4166,f43]) ).
fof(f6033,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(c(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4166,f30]) ).
fof(f6043,plain,
! [X0] : codomain(c(X0)) = addition(c(X0),codomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f29,f5981]) ).
fof(f6044,plain,
! [X0,X1] : addition(coantidomain(c(X0)),X1) = addition(X1,addition(coantidomain(c(X0)),multiplication(c(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f5982]) ).
fof(f6054,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(c(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f48,f6003]) ).
fof(f6059,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)],[f186,f6008]) ).
fof(f6060,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)],[f196,f6059]) ).
fof(f6061,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)],[f88,f6060]) ).
fof(f6062,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)],[f138,f6009]) ).
fof(f6072,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f44,f6021]) ).
fof(f6074,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(c(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f6027]) ).
fof(f6076,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(c(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f6030]) ).
fof(f6081,plain,
! [X0] : leq(c(X0),codomain(c(X0))),
inference(paramodulation,[status(thm)],[f2026,f5966]) ).
fof(f6082,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),addition(coantidomain(c(X0)),X1)),
inference(paramodulation,[status(thm)],[f166,f5966]) ).
fof(f6083,plain,
! [X0,X1] : leq(multiplication(c(X0),X1),addition(X1,coantidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f175,f5966]) ).
fof(f6089,plain,
! [X0,X1] : leq(multiplication(antidomain(c(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f1096,f5966]) ).
fof(f6090,plain,
! [X0,X1] : leq(multiplication(domain(c(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f633,f5966]) ).
fof(f6091,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f57,f5966]) ).
fof(f6092,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f56,f5966]) ).
fof(f6108,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)],[f2026,f226]) ).
fof(f6109,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)],[f166,f226]) ).
fof(f6110,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)],[f175,f226]) ).
fof(f6111,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)],[f136,f226]) ).
fof(f6112,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)],[f129,f226]) ).
fof(f6113,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)],[f48,f226]) ).
fof(f6116,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)],[f1376,f226]) ).
fof(f6117,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)],[f1369,f226]) ).
fof(f6118,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)],[f1363,f226]) ).
fof(f6119,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)],[f1320,f226]) ).
fof(f6120,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(divergence(X1),X0)
| leq(multiplication(one,X0),multiplication(divergence(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1323,f226]) ).
fof(f6121,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(codomain(X1),X0)
| leq(multiplication(one,X0),multiplication(codomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1312,f226]) ).
fof(f6122,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(c(X1),X0)
| leq(multiplication(one,X0),multiplication(c(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1306,f226]) ).
fof(f6123,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(antidomain(X1),X0)
| leq(multiplication(one,X0),multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1215,f226]) ).
fof(f6124,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(coantidomain(X1),X0)
| leq(multiplication(one,X0),multiplication(coantidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1213,f226]) ).
fof(f6125,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(domain(X1),X0)
| leq(multiplication(one,X0),multiplication(domain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1211,f226]) ).
fof(f6126,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(c(X0),X1)
| leq(multiplication(domain(X0),X1),multiplication(c(X0),X1)) ),
inference(paramodulation,[status(thm)],[f657,f226]) ).
fof(f6127,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)],[f309,f226]) ).
fof(f6128,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(codomain(X0),X1)
| leq(multiplication(coantidomain(X0),X1),multiplication(codomain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f354,f226]) ).
fof(f6129,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)],[f237,f226]) ).
fof(f6130,plain,
! [X0,X1] :
( multiplication(one,X1) != multiplication(domain(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(domain(X0),X1)) ),
inference(paramodulation,[status(thm)],[f283,f226]) ).
fof(f6131,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)],[f189,f226]) ).
fof(f6132,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)],[f204,f226]) ).
fof(f6133,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)],[f155,f226]) ).
fof(f6134,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)],[f196,f226]) ).
fof(f6135,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)],[f186,f226]) ).
fof(f6136,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)],[f138,f226]) ).
fof(f6138,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)],[f36,f226]) ).
fof(f6139,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)],[f88,f226]) ).
fof(f6140,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)],[f30,f226]) ).
fof(f6142,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)],[f4166,f226]) ).
fof(f6143,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)],[f4165,f226]) ).
fof(f6144,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)],[f4164,f226]) ).
fof(f6145,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)],[f2179,f226]) ).
fof(f6146,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)],[f2178,f226]) ).
fof(f6147,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)],[f2177,f226]) ).
fof(f6148,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)],[f2176,f226]) ).
fof(f6149,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)],[f2175,f226]) ).
fof(f6150,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)],[f2174,f226]) ).
fof(f6151,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)],[f217,f226]) ).
fof(f6152,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)],[f192,f226]) ).
fof(f6153,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)],[f177,f226]) ).
fof(f6154,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)],[f147,f226]) ).
fof(f6155,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)],[f84,f226]) ).
fof(f6156,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)],[f90,f226]) ).
fof(f6157,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)],[f82,f226]) ).
fof(f6158,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)],[f82,f226]) ).
fof(f6160,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f29,f226]) ).
fof(f6161,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f29,f226]) ).
fof(f6187,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)],[f35,f6116]) ).
fof(f6188,plain,
! [X0,X1,X2] :
( X0 != multiplication(backward_diamond(X1,X2),X0)
| leq(X0,multiplication(backward_diamond(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6187]) ).
fof(f6189,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)],[f35,f6117]) ).
fof(f6190,plain,
! [X0,X1,X2] :
( X0 != multiplication(forward_box(X1,X2),X0)
| leq(X0,multiplication(forward_box(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6189]) ).
fof(f6191,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)],[f35,f6118]) ).
fof(f6192,plain,
! [X0,X1,X2] :
( X0 != multiplication(backward_box(X1,X2),X0)
| leq(X0,multiplication(backward_box(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6191]) ).
fof(f6193,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)],[f35,f6119]) ).
fof(f6194,plain,
! [X0,X1,X2] :
( X0 != multiplication(forward_diamond(X1,X2),X0)
| leq(X0,multiplication(forward_diamond(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6193]) ).
fof(f6195,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6120]) ).
fof(f6196,plain,
! [X0,X1] :
( X0 != multiplication(divergence(X1),X0)
| leq(X0,multiplication(divergence(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6195]) ).
fof(f6197,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6121]) ).
fof(f6198,plain,
! [X0,X1] :
( X0 != multiplication(codomain(X1),X0)
| leq(X0,multiplication(codomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6197]) ).
fof(f6199,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6122]) ).
fof(f6200,plain,
! [X0,X1] :
( X0 != multiplication(c(X1),X0)
| leq(X0,multiplication(c(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6199]) ).
fof(f6201,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6123]) ).
fof(f6202,plain,
! [X0,X1] :
( X0 != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6201]) ).
fof(f6203,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6124]) ).
fof(f6204,plain,
! [X0,X1] :
( X0 != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6203]) ).
fof(f6205,plain,
! [X0,X1] :
( multiplication(one,X0) != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6125]) ).
fof(f6206,plain,
! [X0,X1] :
( X0 != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f6205]) ).
fof(f6207,plain,
! [X0,X1] :
( X1 != multiplication(c(X0),X1)
| leq(multiplication(domain(X0),X1),multiplication(c(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f6126]) ).
fof(f6208,plain,
! [X0,X1,X2] : leq(multiplication(coantidomain(multiplication(X0,X1)),X2),multiplication(coantidomain(multiplication(codomain(X0),X1)),X2)),
inference(trivial_equality_resolution,[status(thm)],[f6127]) ).
fof(f6209,plain,
! [X0,X1] :
( X1 != multiplication(codomain(X0),X1)
| leq(multiplication(coantidomain(X0),X1),multiplication(codomain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f6128]) ).
fof(f6210,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(multiplication(X0,X1)),X2),multiplication(antidomain(multiplication(X0,domain(X1))),X2)),
inference(trivial_equality_resolution,[status(thm)],[f6129]) ).
fof(f6211,plain,
! [X0,X1] :
( X1 != multiplication(domain(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(domain(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f6130]) ).
fof(f6212,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)],[f33,f6131]) ).
fof(f6213,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)],[f33,f6212]) ).
fof(f6214,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)],[f33,f6213]) ).
fof(f6215,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)],[f33,f6214]) ).
fof(f6216,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)],[f33,f6215]) ).
fof(f6217,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)],[f33,f6132]) ).
fof(f6218,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)],[f33,f6133]) ).
fof(f6219,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)],[f33,f6134]) ).
fof(f6220,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)],[f33,f6219]) ).
fof(f6221,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)],[f33,f6220]) ).
fof(f6222,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)],[f33,f6221]) ).
fof(f6223,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)],[f33,f6222]) ).
fof(f6224,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)],[f33,f6223]) ).
fof(f6225,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)],[f33,f6135]) ).
fof(f6226,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)],[f33,f6225]) ).
fof(f6227,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)],[f33,f6226]) ).
fof(f6228,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)],[f33,f6227]) ).
fof(f6229,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)],[f33,f6136]) ).
fof(f6230,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)],[f33,f6229]) ).
fof(f6231,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)],[f33,f6230]) ).
fof(f6232,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)],[f33,f6231]) ).
fof(f6237,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)],[f33,f6138]) ).
fof(f6238,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)],[f33,f6237]) ).
fof(f6239,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)],[f33,f6238]) ).
fof(f6240,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)],[f33,f6239]) ).
fof(f6243,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)],[f33,f6142]) ).
fof(f6244,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)],[f33,f6243]) ).
fof(f6245,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)],[f33,f6143]) ).
fof(f6246,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)],[f33,f6245]) ).
fof(f6247,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)],[f33,f6144]) ).
fof(f6248,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)],[f33,f6247]) ).
fof(f6249,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)],[f33,f6145]) ).
fof(f6250,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)],[f33,f6249]) ).
fof(f6251,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)],[f33,f6146]) ).
fof(f6252,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)],[f33,f6251]) ).
fof(f6253,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)],[f33,f6147]) ).
fof(f6254,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)],[f33,f6253]) ).
fof(f6255,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)],[f33,f6148]) ).
fof(f6256,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)],[f33,f6255]) ).
fof(f6257,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)],[f33,f6149]) ).
fof(f6258,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)],[f33,f6257]) ).
fof(f6259,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)],[f33,f6150]) ).
fof(f6260,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)],[f33,f6259]) ).
fof(f6261,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)],[f33,f6151]) ).
fof(f6262,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)],[f33,f6261]) ).
fof(f6263,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)],[f33,f6262]) ).
fof(f6264,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)],[f33,f6152]) ).
fof(f6265,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)],[f33,f6264]) ).
fof(f6266,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)],[f33,f6265]) ).
fof(f6267,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)],[f33,f6153]) ).
fof(f6268,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)],[f33,f6267]) ).
fof(f6269,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)],[f33,f6268]) ).
fof(f6270,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)],[f33,f6154]) ).
fof(f6271,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)],[f33,f6270]) ).
fof(f6272,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)],[f33,f6271]) ).
fof(f6273,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(trivial_equality_resolution,[status(thm)],[f6156]) ).
fof(f6277,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4167,f231]) ).
fof(f6282,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f88,f4167]) ).
fof(f6283,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(antidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f30,f4167]) ).
fof(f6291,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f162,f4167]) ).
fof(f6294,plain,
! [X0] : codomain(antidomain(X0)) = addition(codomain(antidomain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f2026,f4167]) ).
fof(f6295,plain,
! [X0,X1] : addition(coantidomain(antidomain(X0)),X1) = addition(addition(coantidomain(antidomain(X0)),X1),multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f166,f4167]) ).
fof(f6314,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4167,f166]) ).
fof(f6319,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)],[f4167,f204]) ).
fof(f6320,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)],[f4167,f155]) ).
fof(f6321,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4167,f88]) ).
fof(f6322,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4167,f30]) ).
fof(f6329,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)],[f4167,f226]) ).
fof(f6333,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4167,f162]) ).
fof(f6335,plain,
! [X0,X1,X2] : leq(multiplication(antidomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4167,f1256]) ).
fof(f6339,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4167,f88]) ).
fof(f6341,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(antidomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4167,f82]) ).
fof(f6342,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(antidomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4167,f82]) ).
fof(f6344,plain,
! [X0,X1] :
( X0 != multiplication(antidomain(X1),X0)
| leq(X0,multiplication(antidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4167,f43]) ).
fof(f6345,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(antidomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4167,f30]) ).
fof(f6357,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f6291]) ).
fof(f6358,plain,
! [X0] : codomain(antidomain(X0)) = addition(antidomain(X0),codomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f6294]) ).
fof(f6359,plain,
! [X0,X1] : addition(coantidomain(antidomain(X0)),X1) = addition(X1,addition(coantidomain(antidomain(X0)),multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f6295]) ).
fof(f6369,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f48,f6314]) ).
fof(f6374,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)],[f186,f6319]) ).
fof(f6375,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)],[f196,f6374]) ).
fof(f6376,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)],[f88,f6375]) ).
fof(f6377,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)],[f138,f6320]) ).
fof(f6384,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)],[f33,f6329]) ).
fof(f6385,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)],[f33,f6384]) ).
fof(f6389,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f44,f6333]) ).
fof(f6391,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(antidomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f6339]) ).
fof(f6393,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(antidomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f6342]) ).
fof(f6396,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f171,f6277]) ).
fof(f6397,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f162,f6277]) ).
fof(f6400,plain,
! [X0] : leq(antidomain(X0),codomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f2026,f6277]) ).
fof(f6401,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(coantidomain(antidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f166,f6277]) ).
fof(f6402,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),addition(X1,coantidomain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f175,f6277]) ).
fof(f6410,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),X1),
inference(paramodulation,[status(thm)],[f47,f6277]) ).
fof(f6419,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)],[f209,f227]) ).
fof(f6420,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)],[f215,f227]) ).
fof(f6421,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)],[f3923,f227]) ).
fof(f6422,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)],[f3792,f227]) ).
fof(f6423,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)],[f33,f227]) ).
fof(f6426,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)],[f44,f227]) ).
fof(f6433,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)],[f1376,f227]) ).
fof(f6434,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)],[f1369,f227]) ).
fof(f6435,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)],[f1363,f227]) ).
fof(f6436,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)],[f1320,f227]) ).
fof(f6437,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,divergence(X1))
| leq(multiplication(X0,one),multiplication(X0,divergence(X1))) ),
inference(paramodulation,[status(thm)],[f1323,f227]) ).
fof(f6438,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(multiplication(X0,one),multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f1312,f227]) ).
fof(f6439,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(multiplication(X0,one),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f1306,f227]) ).
fof(f6440,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,antidomain(X1))
| leq(multiplication(X0,one),multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f1215,f227]) ).
fof(f6441,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,coantidomain(X1))
| leq(multiplication(X0,one),multiplication(X0,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f1213,f227]) ).
fof(f6442,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(multiplication(X0,one),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f1211,f227]) ).
fof(f6443,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(multiplication(X0,domain(X1)),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f657,f227]) ).
fof(f6444,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)],[f309,f227]) ).
fof(f6445,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(multiplication(X0,coantidomain(X1)),multiplication(X0,codomain(X1))) ),
inference(paramodulation,[status(thm)],[f354,f227]) ).
fof(f6446,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)],[f237,f227]) ).
fof(f6447,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,domain(X1))) ),
inference(paramodulation,[status(thm)],[f283,f227]) ).
fof(f6448,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)],[f189,f227]) ).
fof(f6449,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)],[f204,f227]) ).
fof(f6450,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)],[f155,f227]) ).
fof(f6451,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)],[f196,f227]) ).
fof(f6452,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)],[f186,f227]) ).
fof(f6453,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)],[f138,f227]) ).
fof(f6454,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)],[f37,f227]) ).
fof(f6455,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)],[f36,f227]) ).
fof(f6456,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)],[f88,f227]) ).
fof(f6457,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)],[f30,f227]) ).
fof(f6459,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)],[f4167,f227]) ).
fof(f6460,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)],[f4166,f227]) ).
fof(f6461,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)],[f4165,f227]) ).
fof(f6462,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)],[f4164,f227]) ).
fof(f6463,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)],[f2179,f227]) ).
fof(f6464,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)],[f2178,f227]) ).
fof(f6465,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)],[f2177,f227]) ).
fof(f6466,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)],[f2176,f227]) ).
fof(f6467,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)],[f2175,f227]) ).
fof(f6468,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)],[f2174,f227]) ).
fof(f6469,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)],[f217,f227]) ).
fof(f6470,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)],[f192,f227]) ).
fof(f6471,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)],[f177,f227]) ).
fof(f6472,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)],[f147,f227]) ).
fof(f6473,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)],[f84,f227]) ).
fof(f6474,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)],[f90,f227]) ).
fof(f6475,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)],[f82,f227]) ).
fof(f6476,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)],[f82,f227]) ).
fof(f6478,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f29,f227]) ).
fof(f6479,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f29,f227]) ).
fof(f6487,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)],[f33,f6423]) ).
fof(f6488,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)],[f33,f6487]) ).
fof(f6489,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)],[f33,f6488]) ).
fof(f6508,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)],[f34,f6433]) ).
fof(f6509,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_diamond(X1,X2))
| leq(X0,multiplication(X0,backward_diamond(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f34,f6508]) ).
fof(f6510,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)],[f34,f6434]) ).
fof(f6511,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_box(X1,X2))
| leq(X0,multiplication(X0,forward_box(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f34,f6510]) ).
fof(f6512,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)],[f34,f6435]) ).
fof(f6513,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,backward_box(X1,X2))
| leq(X0,multiplication(X0,backward_box(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f34,f6512]) ).
fof(f6514,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)],[f34,f6436]) ).
fof(f6515,plain,
! [X0,X1,X2] :
( X0 != multiplication(X0,forward_diamond(X1,X2))
| leq(X0,multiplication(X0,forward_diamond(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f34,f6514]) ).
fof(f6516,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6437]) ).
fof(f6517,plain,
! [X0,X1] :
( X0 != multiplication(X0,divergence(X1))
| leq(X0,multiplication(X0,divergence(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6516]) ).
fof(f6518,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6438]) ).
fof(f6519,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(X0,multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6518]) ).
fof(f6520,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6439]) ).
fof(f6521,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(X0,multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6520]) ).
fof(f6522,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6440]) ).
fof(f6523,plain,
! [X0,X1] :
( X0 != multiplication(X0,antidomain(X1))
| leq(X0,multiplication(X0,antidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6522]) ).
fof(f6524,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6441]) ).
fof(f6525,plain,
! [X0,X1] :
( X0 != multiplication(X0,coantidomain(X1))
| leq(X0,multiplication(X0,coantidomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6524]) ).
fof(f6526,plain,
! [X0,X1] :
( multiplication(X0,one) != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6442]) ).
fof(f6527,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(X0,multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6526]) ).
fof(f6528,plain,
! [X0,X1] :
( X0 != multiplication(X0,c(X1))
| leq(multiplication(X0,domain(X1)),multiplication(X0,c(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6443]) ).
fof(f6529,plain,
! [X0,X1,X2] : leq(multiplication(X0,coantidomain(multiplication(X1,X2))),multiplication(X0,coantidomain(multiplication(codomain(X1),X2)))),
inference(trivial_equality_resolution,[status(thm)],[f6444]) ).
fof(f6530,plain,
! [X0,X1] :
( X0 != multiplication(X0,codomain(X1))
| leq(multiplication(X0,coantidomain(X1)),multiplication(X0,codomain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6445]) ).
fof(f6531,plain,
! [X0,X1,X2] : leq(multiplication(X0,antidomain(multiplication(X1,X2))),multiplication(X0,antidomain(multiplication(X1,domain(X2))))),
inference(trivial_equality_resolution,[status(thm)],[f6446]) ).
fof(f6532,plain,
! [X0,X1] :
( X0 != multiplication(X0,domain(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,domain(X1))) ),
inference(forward_demodulation,[status(thm)],[f34,f6447]) ).
fof(f6535,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(trivial_equality_resolution,[status(thm)],[f6474]) ).
fof(f6540,plain,
! [X0,X1] : leq(domain_difference(X0,X1),antidomain(X1)),
inference(paramodulation,[status(thm)],[f53,f6410]) ).
fof(f6542,plain,
! [X0] : leq(domain(X0),codomain(domain(X0))),
inference(paramodulation,[status(thm)],[f2026,f6410]) ).
fof(f6543,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),addition(coantidomain(domain(X0)),X1)),
inference(paramodulation,[status(thm)],[f166,f6410]) ).
fof(f6544,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),addition(X1,coantidomain(domain(X0)))),
inference(paramodulation,[status(thm)],[f175,f6410]) ).
fof(f6552,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f54,f6410]) ).
fof(f6558,plain,
! [X0,X1] : addition(domain_difference(X0,X1),antidomain(X1)) = antidomain(X1),
inference(resolution,[status(thm)],[f6540,f42]) ).
fof(f6566,plain,
! [X0,X1] : leq(domain_difference(X0,domain(X1)),c(X1)),
inference(paramodulation,[status(thm)],[f52,f6540]) ).
fof(f6567,plain,
! [X0,X1] : leq(domain_difference(X0,antidomain(X1)),domain(X1)),
inference(paramodulation,[status(thm)],[f47,f6540]) ).
fof(f6569,plain,
! [X0,X1] : addition(antidomain(X0),domain_difference(X1,X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f29,f6558]) ).
fof(f6574,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),X1),
inference(resolution,[status(thm)],[f4168,f231]) ).
fof(f6579,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(coantidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f88,f4168]) ).
fof(f6580,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f30,f4168]) ).
fof(f6588,plain,
! [X0] : codomain(coantidomain(X0)) = addition(codomain(coantidomain(X0)),coantidomain(X0)),
inference(paramodulation,[status(thm)],[f2026,f4168]) ).
fof(f6589,plain,
! [X0,X1] : addition(coantidomain(coantidomain(X0)),X1) = addition(addition(coantidomain(coantidomain(X0)),X1),multiplication(coantidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f166,f4168]) ).
fof(f6607,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4168,f166]) ).
fof(f6612,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)],[f4168,f204]) ).
fof(f6613,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)],[f4168,f155]) ).
fof(f6614,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4168,f88]) ).
fof(f6615,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4168,f30]) ).
fof(f6622,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)],[f4168,f227]) ).
fof(f6623,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)],[f4168,f226]) ).
fof(f6627,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f4168,f162]) ).
fof(f6629,plain,
! [X0,X1,X2] : leq(multiplication(coantidomain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4168,f1256]) ).
fof(f6633,plain,
! [X0,X1,X2] : addition(multiplication(coantidomain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4168,f88]) ).
fof(f6635,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(coantidomain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4168,f82]) ).
fof(f6636,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(coantidomain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4168,f82]) ).
fof(f6638,plain,
! [X0,X1] :
( X0 != multiplication(coantidomain(X1),X0)
| leq(X0,multiplication(coantidomain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4168,f43]) ).
fof(f6639,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(coantidomain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4168,f30]) ).
fof(f6649,plain,
! [X0] : coantidomain(codomain(X0)) = addition(codomain(coantidomain(X0)),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f178,f6588]) ).
fof(f6650,plain,
! [X0] : coantidomain(codomain(X0)) = addition(coantidomain(X0),codomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f6649]) ).
fof(f6651,plain,
! [X0] : coantidomain(codomain(X0)) = addition(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f178,f6650]) ).
fof(f6652,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(addition(coantidomain(coantidomain(X0)),X1),multiplication(coantidomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f51,f6589]) ).
fof(f6653,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(X1,addition(coantidomain(coantidomain(X0)),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f6652]) ).
fof(f6654,plain,
! [X0,X1] : addition(codomain(X0),X1) = addition(X1,addition(codomain(X0),multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f51,f6653]) ).
fof(f6670,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f48,f6607]) ).
fof(f6675,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)],[f186,f6612]) ).
fof(f6676,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)],[f196,f6675]) ).
fof(f6677,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)],[f88,f6676]) ).
fof(f6678,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)],[f138,f6613]) ).
fof(f6685,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)],[f33,f6623]) ).
fof(f6686,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)],[f33,f6685]) ).
fof(f6690,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f44,f6627]) ).
fof(f6692,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(coantidomain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f6633]) ).
fof(f6694,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(coantidomain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f6636]) ).
fof(f6697,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)],[f204,f228]) ).
fof(f6698,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)],[f155,f228]) ).
fof(f6699,plain,
! [X0,X1,X2,X3] :
( addition(X1,addition(X0,addition(X2,X3))) != X3
| leq(addition(addition(X0,X1),X2),X3) ),
inference(paramodulation,[status(thm)],[f88,f228]) ).
fof(f6700,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(addition(X0,X1),X2),X3) ),
inference(paramodulation,[status(thm)],[f30,f228]) ).
fof(f6704,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f82,f228]) ).
fof(f6706,plain,
! [X0,X1,X2] :
( addition(addition(X1,X2),X0) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f29,f228]) ).
fof(f6707,plain,
! [X0,X1,X2] :
( addition(addition(X1,X2),X0) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f29,f228]) ).
fof(f6708,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(addition(X0,X1),X0),X1) ),
inference(paramodulation,[status(thm)],[f32,f228]) ).
fof(f6709,plain,
! [X0,X1,X2] :
( addition(X0,one) != backward_diamond(X1,X2)
| leq(addition(X0,one),backward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1376,f228]) ).
fof(f6710,plain,
! [X0,X1,X2] :
( addition(X0,one) != forward_box(X1,X2)
| leq(addition(X0,one),forward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1369,f228]) ).
fof(f6711,plain,
! [X0,X1,X2] :
( addition(X0,one) != backward_box(X1,X2)
| leq(addition(X0,one),backward_box(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1363,f228]) ).
fof(f6712,plain,
! [X0,X1,X2] :
( addition(X0,one) != forward_diamond(X1,X2)
| leq(addition(X0,one),forward_diamond(X1,X2)) ),
inference(paramodulation,[status(thm)],[f1320,f228]) ).
fof(f6713,plain,
! [X0,X1] :
( addition(X0,one) != divergence(X1)
| leq(addition(X0,one),divergence(X1)) ),
inference(paramodulation,[status(thm)],[f1323,f228]) ).
fof(f6714,plain,
! [X0,X1] :
( addition(X0,one) != codomain(X1)
| leq(addition(X0,one),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f1312,f228]) ).
fof(f6715,plain,
! [X0,X1] :
( addition(X0,one) != c(X1)
| leq(addition(X0,one),c(X1)) ),
inference(paramodulation,[status(thm)],[f1306,f228]) ).
fof(f6716,plain,
! [X0,X1] :
( addition(X0,one) != antidomain(X1)
| leq(addition(X0,one),antidomain(X1)) ),
inference(paramodulation,[status(thm)],[f1215,f228]) ).
fof(f6717,plain,
! [X0,X1] :
( addition(X0,one) != coantidomain(X1)
| leq(addition(X0,one),coantidomain(X1)) ),
inference(paramodulation,[status(thm)],[f1213,f228]) ).
fof(f6718,plain,
! [X0,X1] :
( addition(X0,one) != domain(X1)
| leq(addition(X0,one),domain(X1)) ),
inference(paramodulation,[status(thm)],[f1211,f228]) ).
fof(f6719,plain,
! [X0,X1] :
( addition(X0,one) != c(X1)
| leq(addition(X0,domain(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f657,f228]) ).
fof(f6720,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)],[f309,f228]) ).
fof(f6721,plain,
! [X0,X1] :
( addition(X0,one) != codomain(X1)
| leq(addition(X0,coantidomain(X1)),codomain(X1)) ),
inference(paramodulation,[status(thm)],[f354,f228]) ).
fof(f6722,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)],[f237,f228]) ).
fof(f6723,plain,
! [X0,X1] :
( addition(X0,one) != domain(X1)
| leq(addition(X0,antidomain(X1)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f283,f228]) ).
fof(f6724,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)],[f189,f228]) ).
fof(f6725,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)],[f204,f228]) ).
fof(f6726,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)],[f155,f228]) ).
fof(f6727,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)],[f196,f228]) ).
fof(f6728,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)],[f186,f228]) ).
fof(f6729,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)],[f138,f228]) ).
fof(f6730,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)],[f37,f228]) ).
fof(f6731,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)],[f36,f228]) ).
fof(f6732,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X2,addition(X1,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(paramodulation,[status(thm)],[f88,f228]) ).
fof(f6733,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(paramodulation,[status(thm)],[f30,f228]) ).
fof(f6735,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(coantidomain(X2),X1)
| leq(addition(X0,X1),multiplication(coantidomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4168,f228]) ).
fof(f6736,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(antidomain(X2),X1)
| leq(addition(X0,X1),multiplication(antidomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4167,f228]) ).
fof(f6737,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(c(X2),X1)
| leq(addition(X0,X1),multiplication(c(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4166,f228]) ).
fof(f6738,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(codomain(X2),X1)
| leq(addition(X0,X1),multiplication(codomain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4165,f228]) ).
fof(f6739,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(divergence(X2),X1)
| leq(addition(X0,X1),multiplication(divergence(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4164,f228]) ).
fof(f6740,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,domain(X2))
| leq(addition(X0,X1),multiplication(X1,domain(X2))) ),
inference(paramodulation,[status(thm)],[f2179,f228]) ).
fof(f6741,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,coantidomain(X2))
| leq(addition(X0,X1),multiplication(X1,coantidomain(X2))) ),
inference(paramodulation,[status(thm)],[f2178,f228]) ).
fof(f6742,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,antidomain(X2))
| leq(addition(X0,X1),multiplication(X1,antidomain(X2))) ),
inference(paramodulation,[status(thm)],[f2177,f228]) ).
fof(f6743,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,c(X2))
| leq(addition(X0,X1),multiplication(X1,c(X2))) ),
inference(paramodulation,[status(thm)],[f2176,f228]) ).
fof(f6744,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,codomain(X2))
| leq(addition(X0,X1),multiplication(X1,codomain(X2))) ),
inference(paramodulation,[status(thm)],[f2175,f228]) ).
fof(f6745,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(X1,divergence(X2))
| leq(addition(X0,X1),multiplication(X1,divergence(X2))) ),
inference(paramodulation,[status(thm)],[f2174,f228]) ).
fof(f6746,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)],[f217,f228]) ).
fof(f6747,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)],[f192,f228]) ).
fof(f6748,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)],[f177,f228]) ).
fof(f6749,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)],[f147,f228]) ).
fof(f6750,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)],[f84,f228]) ).
fof(f6751,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X1,X2)
| leq(addition(X0,X1),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f90,f228]) ).
fof(f6752,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)],[f82,f228]) ).
fof(f6753,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)],[f82,f228]) ).
fof(f6755,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f29,f228]) ).
fof(f6756,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f29,f228]) ).
fof(f6757,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f32,f228]) ).
fof(f6758,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)],[f186,f6697]) ).
fof(f6759,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)],[f138,f6698]) ).
fof(f6760,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)],[f88,f6699]) ).
fof(f6761,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)],[f88,f6700]) ).
fof(f6765,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f88,f6706]) ).
fof(f6766,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f88,f6707]) ).
fof(f6767,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,addition(X1,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f88,f6708]) ).
fof(f6768,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f32,f6767]) ).
fof(f6772,plain,
! [X0] : leq(coantidomain(X0),codomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f2026,f6574]) ).
fof(f6773,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(coantidomain(coantidomain(X0)),X1)),
inference(paramodulation,[status(thm)],[f166,f6574]) ).
fof(f6774,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(X1,coantidomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f175,f6574]) ).
fof(f6784,plain,
! [X0] : leq(coantidomain(X0),coantidomain(codomain(X0))),
inference(forward_demodulation,[status(thm)],[f178,f6772]) ).
fof(f6785,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(codomain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f51,f6773]) ).
fof(f6786,plain,
! [X0,X1] : leq(multiplication(coantidomain(X0),X1),addition(X1,codomain(X0))),
inference(forward_demodulation,[status(thm)],[f51,f6774]) ).
fof(f6796,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(X0,multiplication(domain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f88,f4169]) ).
fof(f6797,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X0,addition(X1,multiplication(domain(X2),addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f30,f4169]) ).
fof(f6804,plain,
! [X0,X1] : antidomain(X0) = addition(antidomain(X0),domain_difference(X1,X0)),
inference(paramodulation,[status(thm)],[f53,f4169]) ).
fof(f6806,plain,
! [X0] : codomain(domain(X0)) = addition(codomain(domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f2026,f4169]) ).
fof(f6807,plain,
! [X0,X1] : addition(coantidomain(domain(X0)),X1) = addition(addition(coantidomain(domain(X0)),X1),multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f166,f4169]) ).
fof(f6816,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_diamond(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f54,f4169]) ).
fof(f6827,plain,
! [X0,X1] : multiplication(X0,coantidomain(X0)) = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f4169,f166]) ).
fof(f6832,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)],[f4169,f204]) ).
fof(f6833,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)],[f4169,f155]) ).
fof(f6834,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),addition(X1,X0)))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f4169,f88]) ).
fof(f6835,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),addition(X0,X1)))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f4169,f30]) ).
fof(f6842,plain,
! [X0,X1,X2] :
( addition(X0,X1) != multiplication(domain(X2),X1)
| leq(addition(X0,X1),multiplication(domain(X2),X1)) ),
inference(paramodulation,[status(thm)],[f4169,f228]) ).
fof(f6843,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)],[f4169,f227]) ).
fof(f6844,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)],[f4169,f226]) ).
fof(f6848,plain,
! [X0,X1] : multiplication(antidomain(X0),X0) = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f4169,f162]) ).
fof(f6850,plain,
! [X0,X1,X2] : leq(multiplication(domain(X0),X1),addition(X2,X1)),
inference(paramodulation,[status(thm)],[f4169,f1256]) ).
fof(f6854,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),addition(X1,X2)) = addition(X1,X2),
inference(paramodulation,[status(thm)],[f4169,f88]) ).
fof(f6856,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X1),X0),X2)) = addition(X2,X0),
inference(paramodulation,[status(thm)],[f4169,f82]) ).
fof(f6857,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(multiplication(domain(X2),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f4169,f82]) ).
fof(f6859,plain,
! [X0,X1] :
( X0 != multiplication(domain(X1),X0)
| leq(X0,multiplication(domain(X1),X0)) ),
inference(paramodulation,[status(thm)],[f4169,f43]) ).
fof(f6860,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(domain(X1),X0),X2)) = addition(X0,X2),
inference(paramodulation,[status(thm)],[f4169,f30]) ).
fof(f6870,plain,
! [X0] : codomain(domain(X0)) = addition(domain(X0),codomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f6806]) ).
fof(f6871,plain,
! [X0,X1] : addition(coantidomain(domain(X0)),X1) = addition(X1,addition(coantidomain(domain(X0)),multiplication(domain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f88,f6807]) ).
fof(f6881,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(domain(X1),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f48,f6827]) ).
fof(f6886,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)],[f186,f6832]) ).
fof(f6887,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)],[f196,f6886]) ).
fof(f6888,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)],[f88,f6887]) ).
fof(f6889,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)],[f138,f6833]) ).
fof(f6896,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)],[f33,f6844]) ).
fof(f6897,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)],[f33,f6896]) ).
fof(f6901,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f44,f6848]) ).
fof(f6903,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(domain(X2),X0))) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f82,f6854]) ).
fof(f6905,plain,
! [X0,X1,X2] : addition(X0,X1) = addition(X1,addition(multiplication(domain(X2),X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f6857]) ).
fof(f6908,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X1,X0))),antidomain(multiplication(addition(one,X1),domain(X0)))),
inference(paramodulation,[status(thm)],[f192,f238]) ).
fof(f6909,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(addition(antidomain(X1),X0),domain(X1)))),
inference(paramodulation,[status(thm)],[f209,f238]) ).
fof(f6910,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X1,X0))),antidomain(multiplication(addition(X1,one),domain(X0)))),
inference(paramodulation,[status(thm)],[f217,f238]) ).
fof(f6911,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(addition(X0,antidomain(X1)),domain(X1)))),
inference(paramodulation,[status(thm)],[f215,f238]) ).
fof(f6912,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,coantidomain(X1))),antidomain(multiplication(addition(X0,X1),domain(coantidomain(X1))))),
inference(paramodulation,[status(thm)],[f218,f238]) ).
fof(f6913,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,coantidomain(X1))),antidomain(multiplication(addition(X1,X0),domain(coantidomain(X1))))),
inference(paramodulation,[status(thm)],[f211,f238]) ).
fof(f6914,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(c(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f182,f238]) ).
fof(f6916,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))),
inference(paramodulation,[status(thm)],[f180,f238]) ).
fof(f6917,plain,
! [X0,X1] : leq(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),domain(antidomain(X1))))),
inference(paramodulation,[status(thm)],[f53,f238]) ).
fof(f6918,plain,
! [X0] : leq(antidomain(X0),antidomain(multiplication(domain(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f3792,f238]) ).
fof(f6919,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(multiplication(X0,X1),domain(X2)))),
inference(paramodulation,[status(thm)],[f33,f238]) ).
fof(f6920,plain,
! [X0,X1] : leq(antidomain(multiplication(antidomain(X0),X1)),antidomain(multiplication(antidomain(X0),domain(addition(X1,X0))))),
inference(paramodulation,[status(thm)],[f171,f238]) ).
fof(f6921,plain,
! [X0,X1] : leq(antidomain(multiplication(antidomain(X0),X1)),antidomain(multiplication(antidomain(X0),domain(addition(X0,X1))))),
inference(paramodulation,[status(thm)],[f162,f238]) ).
fof(f6922,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f121,f238]) ).
fof(f6923,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f44,f238]) ).
fof(f6926,plain,
! [X0] : leq(antidomain(X0),antidomain(multiplication(X0,domain(codomain(X0))))),
inference(paramodulation,[status(thm)],[f2026,f238]) ).
fof(f6927,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(one,X1))))),
inference(paramodulation,[status(thm)],[f147,f238]) ).
fof(f6928,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(addition(coantidomain(X0),X1))))),
inference(paramodulation,[status(thm)],[f166,f238]) ).
fof(f6929,plain,
! [X0,X1] : leq(antidomain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(X1,one))))),
inference(paramodulation,[status(thm)],[f177,f238]) ).
fof(f6930,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(addition(X1,coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f175,f238]) ).
fof(f6931,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1))))),
inference(paramodulation,[status(thm)],[f136,f238]) ).
fof(f6932,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1))))))),
inference(paramodulation,[status(thm)],[f129,f238]) ).
fof(f6933,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(X0,domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f48,f238]) ).
fof(f6936,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(antidomain(domain(X0)),X1),X0)),antidomain(multiplication(X1,domain(X0)))),
inference(paramodulation,[status(thm)],[f209,f238]) ).
fof(f6937,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,antidomain(domain(X1))),X1)),antidomain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f215,f238]) ).
fof(f6940,plain,
! [X0] : leq(antidomain(multiplication(domain(domain(X0)),X0)),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f3792,f238]) ).
fof(f6941,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(multiplication(X0,X1),X2)),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(paramodulation,[status(thm)],[f33,f238]) ).
fof(f6945,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,antidomain(c(X1))))),
inference(paramodulation,[status(thm)],[f181,f238]) ).
fof(f6946,plain,
! [X0,X1] : leq(antidomain(multiplication(X0,antidomain(X1))),antidomain(multiplication(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f631,f238]) ).
fof(f6947,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,forward_diamond(X1,X2)))),
inference(paramodulation,[status(thm)],[f54,f238]) ).
fof(f6950,plain,
! [X0] : leq(one,antidomain(multiplication(c(X0),domain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f293,f6914]) ).
fof(f6951,plain,
! [X0] : leq(one,antidomain(multiplication(c(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f181,f6950]) ).
fof(f6955,plain,
! [X0] : leq(one,antidomain(multiplication(coantidomain(X0),domain(codomain(X0))))),
inference(forward_demodulation,[status(thm)],[f293,f6916]) ).
fof(f6956,plain,
! [X0,X1] : leq(antidomain(domain_difference(X0,X1)),antidomain(multiplication(domain(X0),c(X1)))),
inference(forward_demodulation,[status(thm)],[f631,f6917]) ).
fof(f6957,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(forward_demodulation,[status(thm)],[f33,f6919]) ).
fof(f6958,plain,
! [X0,X1] : leq(one,antidomain(multiplication(antidomain(X0),domain(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f293,f6922]) ).
fof(f6959,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f293,f6923]) ).
fof(f6965,plain,
! [X0,X1] : leq(one,antidomain(multiplication(X0,domain(multiplication(coantidomain(X0),X1))))),
inference(forward_demodulation,[status(thm)],[f293,f6931]) ).
fof(f6966,plain,
! [X0,X1] : leq(one,antidomain(multiplication(X0,domain(multiplication(X1,coantidomain(multiplication(X0,X1))))))),
inference(forward_demodulation,[status(thm)],[f293,f6932]) ).
fof(f6967,plain,
! [X0] : leq(one,antidomain(multiplication(X0,domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f293,f6933]) ).
fof(f6974,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(c(X0),X1),X0)),antidomain(multiplication(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f52,f6936]) ).
fof(f6975,plain,
! [X0,X1] : leq(antidomain(multiplication(addition(X0,c(X1)),X1)),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f52,f6937]) ).
fof(f6981,plain,
! [X0] : leq(antidomain(multiplication(antidomain(c(X0)),X0)),antidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f181,f6940]) ).
fof(f6982,plain,
! [X0] : leq(antidomain(multiplication(antidomain(c(X0)),X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f52,f6981]) ).
fof(f6983,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(forward_demodulation,[status(thm)],[f33,f6941]) ).
fof(f6999,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(resolution,[status(thm)],[f254,f43]) ).
fof(f7000,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)],[f209,f254]) ).
fof(f7001,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)],[f215,f254]) ).
fof(f7002,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)],[f3923,f254]) ).
fof(f7003,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)],[f3792,f254]) ).
fof(f7004,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)],[f33,f254]) ).
fof(f7006,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)],[f44,f254]) ).
fof(f7010,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)],[f129,f254]) ).
fof(f7011,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)],[f192,f254]) ).
fof(f7012,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)],[f209,f254]) ).
fof(f7013,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)],[f217,f254]) ).
fof(f7014,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)],[f215,f254]) ).
fof(f7015,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)],[f218,f254]) ).
fof(f7016,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)],[f211,f254]) ).
fof(f7017,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)],[f182,f254]) ).
fof(f7019,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)],[f180,f254]) ).
fof(f7020,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)],[f53,f254]) ).
fof(f7021,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(domain(X1),domain(X1))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(X1)))),
inference(paramodulation,[status(thm)],[f3792,f254]) ).
fof(f7022,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)],[f33,f254]) ).
fof(f7023,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)],[f171,f254]) ).
fof(f7024,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)],[f162,f254]) ).
fof(f7025,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)],[f121,f254]) ).
fof(f7026,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)],[f44,f254]) ).
fof(f7029,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)],[f2026,f254]) ).
fof(f7030,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)],[f147,f254]) ).
fof(f7031,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)],[f166,f254]) ).
fof(f7032,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)],[f177,f254]) ).
fof(f7033,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)],[f175,f254]) ).
fof(f7034,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)],[f136,f254]) ).
fof(f7035,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)],[f129,f254]) ).
fof(f7036,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)],[f48,f254]) ).
fof(f7039,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)],[f209,f254]) ).
fof(f7040,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)],[f215,f254]) ).
fof(f7042,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)],[f3792,f254]) ).
fof(f7043,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)],[f33,f254]) ).
fof(f7049,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)],[f209,f254]) ).
fof(f7050,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)],[f215,f254]) ).
fof(f7053,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)],[f3792,f254]) ).
fof(f7054,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)],[f33,f254]) ).
fof(f7058,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)],[f181,f254]) ).
fof(f7059,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)],[f631,f254]) ).
fof(f7060,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)],[f54,f254]) ).
fof(f7064,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)],[f254,f215]) ).
fof(f7065,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)],[f254,f228]) ).
fof(f7066,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)],[f254,f227]) ).
fof(f7067,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)],[f254,f226]) ).
fof(f7068,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)],[f254,f218]) ).
fof(f7070,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)],[f254,f171]) ).
fof(f7072,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)],[f254,f1257]) ).
fof(f7075,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(paramodulation,[status(thm)],[f254,f1163]) ).
fof(f7077,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)],[f254,f88]) ).
fof(f7079,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)],[f254,f82]) ).
fof(f7080,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)],[f254,f82]) ).
fof(f7081,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)],[f254,f231]) ).
fof(f7082,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)],[f254,f43]) ).
fof(f7083,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)],[f254,f30]) ).
fof(f7084,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)],[f293,f7002]) ).
fof(f7085,plain,
! [X0,X1] : one = antidomain(multiplication(c(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1215,f7084]) ).
fof(f7086,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)],[f33,f7004]) ).
fof(f7087,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)],[f33,f7086]) ).
fof(f7091,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)],[f293,f7006]) ).
fof(f7092,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1215,f7091]) ).
fof(f7101,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)],[f293,f7010]) ).
fof(f7102,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f1215,f7101]) ).
fof(f7103,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)],[f38,f7017]) ).
fof(f7104,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)],[f293,f7103]) ).
fof(f7105,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(c(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f1215,f7104]) ).
fof(f7106,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(c(X1),antidomain(c(X1))))),
inference(forward_demodulation,[status(thm)],[f181,f7105]) ).
fof(f7112,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)],[f38,f7019]) ).
fof(f7113,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)],[f293,f7112]) ).
fof(f7114,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(coantidomain(X1),domain(codomain(X1))))),
inference(forward_demodulation,[status(thm)],[f1215,f7113]) ).
fof(f7115,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)],[f631,f7020]) ).
fof(f7116,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)],[f631,f7115]) ).
fof(f7117,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)],[f33,f7022]) ).
fof(f7118,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)],[f33,f7117]) ).
fof(f7119,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)],[f38,f7025]) ).
fof(f7120,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)],[f293,f7119]) ).
fof(f7121,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(multiplication(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f1215,f7120]) ).
fof(f7122,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)],[f38,f7026]) ).
fof(f7123,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)],[f293,f7122]) ).
fof(f7124,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(X1)))),
inference(forward_demodulation,[status(thm)],[f1215,f7123]) ).
fof(f7132,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)],[f38,f7034]) ).
fof(f7133,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)],[f293,f7132]) ).
fof(f7134,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(coantidomain(X1),X2))))),
inference(forward_demodulation,[status(thm)],[f1215,f7133]) ).
fof(f7135,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)],[f38,f7035]) ).
fof(f7136,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)],[f293,f7135]) ).
fof(f7137,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2))))))),
inference(forward_demodulation,[status(thm)],[f1215,f7136]) ).
fof(f7138,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)],[f38,f7036]) ).
fof(f7139,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)],[f293,f7138]) ).
fof(f7140,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(X1))))),
inference(forward_demodulation,[status(thm)],[f1215,f7139]) ).
fof(f7151,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)],[f29,f7039]) ).
fof(f7152,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)],[f209,f7151]) ).
fof(f7153,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)],[f29,f7040]) ).
fof(f7154,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)],[f215,f7153]) ).
fof(f7159,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)],[f29,f7042]) ).
fof(f7160,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)],[f54,f7159]) ).
fof(f7161,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)],[f3792,f7160]) ).
fof(f7162,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)],[f33,f7043]) ).
fof(f7163,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)],[f33,f7162]) ).
fof(f7184,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)],[f29,f7049]) ).
fof(f7185,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)],[f52,f7184]) ).
fof(f7186,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)],[f209,f7185]) ).
fof(f7187,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)],[f29,f7050]) ).
fof(f7188,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)],[f52,f7187]) ).
fof(f7189,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)],[f215,f7188]) ).
fof(f7202,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)],[f29,f7053]) ).
fof(f7203,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)],[f181,f7202]) ).
fof(f7204,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)],[f3792,f7203]) ).
fof(f7205,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)],[f33,f7054]) ).
fof(f7206,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)],[f33,f7205]) ).
fof(f7223,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)],[f181,f7058]) ).
fof(f7224,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)],[f631,f7059]) ).
fof(f7225,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)],[f29,f7060]) ).
fof(f7226,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)],[f54,f7225]) ).
fof(f7237,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,multiplication(X1,X2))),multiplication(X0,multiplication(X1,domain(X2)))),
inference(forward_demodulation,[status(thm)],[f44,f7064]) ).
fof(f7238,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)],[f7066]) ).
fof(f7239,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)],[f7067]) ).
fof(f7240,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)],[f48,f7068]) ).
fof(f7241,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)],[f44,f7070]) ).
fof(f7242,plain,
! [X0,X1,X2] : zero = multiplication(domain(multiplication(X0,multiplication(X1,domain(X2)))),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f47,f7241]) ).
fof(f7243,plain,
! [X0,X1,X2] : zero = domain_difference(multiplication(X0,multiplication(X1,domain(X2))),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f53,f7242]) ).
fof(f7244,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)],[f82,f7077]) ).
fof(f7245,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)],[f82,f7080]) ).
fof(f7246,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,domain(X2))))),
inference(trivial_equality_resolution,[status(thm)],[f7082]) ).
fof(f7247,plain,
! [X0] : addition(divergence(X0),codomain(divergence(X0))) = codomain(divergence(X0)),
inference(resolution,[status(thm)],[f5831,f42]) ).
fof(f7254,plain,
! [X0] : addition(one,antidomain(multiplication(antidomain(X0),domain(X0)))) = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f293,f240]) ).
fof(f7255,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1215,f7254]) ).
fof(f7256,plain,
! [X0] : one = antidomain(multiplication(one,domain(multiplication(antidomain(X0),domain(X0))))),
inference(paramodulation,[status(thm)],[f7255,f7255]) ).
fof(f7258,plain,
! [X0] : one = antidomain(multiplication(c(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f52,f7255]) ).
fof(f7259,plain,
! [X0] : one = antidomain(multiplication(domain(X0),domain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f47,f7255]) ).
fof(f7261,plain,
! [X0] : one = antidomain(multiplication(antidomain(domain(X0)),antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f181,f7255]) ).
fof(f7262,plain,
! [X0] : one = antidomain(multiplication(antidomain(antidomain(X0)),c(X0))),
inference(paramodulation,[status(thm)],[f631,f7255]) ).
fof(f7263,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f54,f7255]) ).
fof(f7268,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f7255,f238]) ).
fof(f7269,plain,
! [X0] : addition(one,antidomain(multiplication(antidomain(X0),domain(domain(X0))))) = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f7255,f237]) ).
fof(f7270,plain,
! [X0,X1] : leq(domain_difference(X0,multiplication(antidomain(X1),domain(X1))),one),
inference(paramodulation,[status(thm)],[f7255,f6540]) ).
fof(f7273,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(antidomain(X1),domain(X1))) = multiplication(X0,multiplication(antidomain(X1),domain(X1))),
inference(paramodulation,[status(thm)],[f7255,f215]) ).
fof(f7276,plain,
! [X0] : leq(one,c(multiplication(antidomain(X0),domain(X0)))),
inference(paramodulation,[status(thm)],[f7255,f3895]) ).
fof(f7277,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(antidomain(X1),domain(X1))) = multiplication(X0,multiplication(antidomain(X1),domain(X1))),
inference(paramodulation,[status(thm)],[f7255,f209]) ).
fof(f7280,plain,
! [X0,X1] : multiplication(one,addition(X0,multiplication(antidomain(X1),domain(X1)))) = multiplication(antidomain(multiplication(antidomain(X1),domain(X1))),X0),
inference(paramodulation,[status(thm)],[f7255,f171]) ).
fof(f7282,plain,
! [X0,X1] : multiplication(one,addition(multiplication(antidomain(X0),domain(X0)),X1)) = multiplication(antidomain(multiplication(antidomain(X0),domain(X0))),X1),
inference(paramodulation,[status(thm)],[f7255,f162]) ).
fof(f7284,plain,
! [X0,X1] : multiplication(one,multiplication(multiplication(antidomain(X0),domain(X0)),X1)) = zero,
inference(paramodulation,[status(thm)],[f7255,f121]) ).
fof(f7286,plain,
! [X0] : antidomain(c(multiplication(antidomain(X0),domain(X0)))) = c(one),
inference(paramodulation,[status(thm)],[f7255,f1096]) ).
fof(f7287,plain,
! [X0] : domain(one) = c(multiplication(antidomain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f7255,f631]) ).
fof(f7288,plain,
! [X0,X1] : domain_difference(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f7255,f53]) ).
fof(f7290,plain,
! [X0] : domain(multiplication(antidomain(X0),domain(X0))) = antidomain(one),
inference(paramodulation,[status(thm)],[f7255,f47]) ).
fof(f7291,plain,
! [X0] : multiplication(one,multiplication(antidomain(X0),domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f7255,f44]) ).
fof(f7292,plain,
! [X0] : one = antidomain(domain(multiplication(antidomain(X0),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f7256]) ).
fof(f7293,plain,
! [X0] : one = c(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f52,f7292]) ).
fof(f7296,plain,
! [X0] : one = antidomain(multiplication(c(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f181,f7258]) ).
fof(f7297,plain,
! [X0] : one = antidomain(multiplication(domain(X0),c(X0))),
inference(forward_demodulation,[status(thm)],[f631,f7259]) ).
fof(f7299,plain,
! [X0] : one = antidomain(multiplication(c(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f52,f7261]) ).
fof(f7300,plain,
! [X0] : one = antidomain(multiplication(domain(X0),c(X0))),
inference(forward_demodulation,[status(thm)],[f47,f7262]) ).
fof(f7307,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f181,f7268]) ).
fof(f7308,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f1215,f7269]) ).
fof(f7309,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f181,f7308]) ).
fof(f7316,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(antidomain(multiplication(antidomain(X1),domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f35,f7280]) ).
fof(f7317,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = multiplication(one,X0),
inference(forward_demodulation,[status(thm)],[f7255,f7316]) ).
fof(f7318,plain,
! [X0,X1] : addition(X0,multiplication(antidomain(X1),domain(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f7317]) ).
fof(f7319,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = multiplication(antidomain(multiplication(antidomain(X0),domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f35,f7282]) ).
fof(f7320,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = multiplication(one,X1),
inference(forward_demodulation,[status(thm)],[f7255,f7319]) ).
fof(f7321,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),domain(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f35,f7320]) ).
fof(f7322,plain,
! [X0,X1] : multiplication(multiplication(antidomain(X0),domain(X0)),X1) = zero,
inference(forward_demodulation,[status(thm)],[f35,f7284]) ).
fof(f7323,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f33,f7322]) ).
fof(f7324,plain,
! [X0] : antidomain(c(multiplication(antidomain(X0),domain(X0)))) = zero,
inference(forward_demodulation,[status(thm)],[f303,f7286]) ).
fof(f7325,plain,
! [X0] : one = c(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f290,f7287]) ).
fof(f7326,plain,
! [X0,X1] : domain_difference(X0,multiplication(antidomain(X1),domain(X1))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f34,f7288]) ).
fof(f7327,plain,
! [X0] : forward_diamond(antidomain(X0),X0) = antidomain(one),
inference(forward_demodulation,[status(thm)],[f54,f7290]) ).
fof(f7328,plain,
! [X0] : forward_diamond(antidomain(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f104,f7327]) ).
fof(f7329,plain,
! [X0] : multiplication(antidomain(X0),domain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f35,f7291]) ).
fof(f7333,plain,
! [X0] : forward_diamond(one,multiplication(antidomain(X0),domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f7255,f7328]) ).
fof(f7335,plain,
! [X0] : forward_diamond(c(X0),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f52,f7328]) ).
fof(f7336,plain,
! [X0] : forward_diamond(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f47,f7328]) ).
fof(f7338,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)],[f7328,f60]) ).
fof(f7339,plain,
! [X0] : forward_box(antidomain(c(X0)),X0) = c(zero),
inference(paramodulation,[status(thm)],[f7328,f56]) ).
fof(f7347,plain,
! [X0] : antidomain(c(multiplication(antidomain(X0),domain(X0)))) = zero,
inference(forward_demodulation,[status(thm)],[f863,f7333]) ).
fof(f7350,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)],[f82,f7338]) ).
fof(f7351,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)],[f65,f7350]) ).
fof(f7352,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)],[f7328,f7351]) ).
fof(f7353,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)],[f65,f7352]) ).
fof(f7354,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)],[f52,f7353]) ).
fof(f7355,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)],[f52,f7354]) ).
fof(f7356,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)],[f52,f7355]) ).
fof(f7357,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)],[f52,f7356]) ).
fof(f7358,plain,
! [X0] : forward_box(antidomain(c(X0)),X0) = one,
inference(forward_demodulation,[status(thm)],[f352,f7339]) ).
fof(f7361,plain,
! [X0] : addition(codomain(X0),codomain(codomain(X0))) = codomain(codomain(X0)),
inference(resolution,[status(thm)],[f5951,f42]) ).
fof(f7362,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(codomain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f178,f5951]) ).
fof(f7363,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(codomain(multiplication(codomain(X1),X0)))),
inference(paramodulation,[status(thm)],[f55,f5951]) ).
fof(f7366,plain,
! [X0] : leq(codomain(coantidomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f178,f5951]) ).
fof(f7367,plain,
! [X0,X1] : leq(codomain(multiplication(codomain(X0),X1)),codomain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f55,f5951]) ).
fof(f7370,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f178,f7362]) ).
fof(f7371,plain,
! [X0] : leq(coantidomain(codomain(X0)),coantidomain(codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f178,f7370]) ).
fof(f7372,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f55,f7363]) ).
fof(f7377,plain,
! [X0] : leq(coantidomain(codomain(X0)),codomain(coantidomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f178,f7366]) ).
fof(f7378,plain,
! [X0] : leq(coantidomain(codomain(X0)),coantidomain(codomain(codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f178,f7377]) ).
fof(f7379,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f55,f7367]) ).
fof(f7384,plain,
! [X0,X1,X2] : addition(multiplication(backward_diamond(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f5960,f42]) ).
fof(f7385,plain,
! [X0,X1] : leq(backward_diamond(X0,X1),codomain(backward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f2026,f5960]) ).
fof(f7386,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),addition(coantidomain(backward_diamond(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f166,f5960]) ).
fof(f7387,plain,
! [X0,X1,X2] : leq(multiplication(backward_diamond(X0,X1),X2),addition(X2,coantidomain(backward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f175,f5960]) ).
fof(f7398,plain,
! [X0,X1,X2] : addition(X0,multiplication(backward_diamond(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f29,f7384]) ).
fof(f7402,plain,
! [X0] : addition(c(X0),codomain(c(X0))) = codomain(c(X0)),
inference(resolution,[status(thm)],[f6081,f42]) ).
fof(f7403,plain,
! [X0] : leq(antidomain(c(X0)),codomain(c(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f1096,f6081]) ).
fof(f7404,plain,
! [X0] : leq(domain(c(X0)),codomain(c(domain(X0)))),
inference(paramodulation,[status(thm)],[f633,f6081]) ).
fof(f7405,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(c(backward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f57,f6081]) ).
fof(f7406,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(c(forward_diamond(X0,c(X1))))),
inference(paramodulation,[status(thm)],[f56,f6081]) ).
fof(f7409,plain,
! [X0] : leq(c(antidomain(X0)),codomain(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f1096,f6081]) ).
fof(f7410,plain,
! [X0] : leq(c(domain(X0)),codomain(domain(c(X0)))),
inference(paramodulation,[status(thm)],[f633,f6081]) ).
fof(f7411,plain,
! [X0,X1] : leq(c(backward_diamond(X0,c(X1))),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f57,f6081]) ).
fof(f7412,plain,
! [X0,X1] : leq(c(forward_diamond(X0,c(X1))),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f56,f6081]) ).
fof(f7415,plain,
! [X0] : leq(antidomain(c(X0)),codomain(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f1096,f7403]) ).
fof(f7416,plain,
! [X0] : leq(domain(c(X0)),codomain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f633,f7404]) ).
fof(f7417,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f57,f7405]) ).
fof(f7418,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f56,f7406]) ).
fof(f7423,plain,
! [X0] : leq(antidomain(c(X0)),codomain(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f1096,f7409]) ).
fof(f7424,plain,
! [X0] : leq(domain(c(X0)),codomain(domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f633,f7410]) ).
fof(f7425,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f57,f7411]) ).
fof(f7426,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f56,f7412]) ).
fof(f7432,plain,
! [X0] : addition(one,c(multiplication(antidomain(X0),domain(X0)))) = c(multiplication(antidomain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f7255,f260]) ).
fof(f7434,plain,
! [X0] : addition(c(X0),c(domain(X0))) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f52,f260]) ).
fof(f7435,plain,
! [X0] : addition(domain(X0),c(antidomain(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f47,f260]) ).
fof(f7437,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(c(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f1096,f260]) ).
fof(f7438,plain,
! [X0] : addition(antidomain(domain(X0)),domain(c(X0))) = c(domain(X0)),
inference(paramodulation,[status(thm)],[f633,f260]) ).
fof(f7439,plain,
! [X0,X1] : addition(antidomain(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f57,f260]) ).
fof(f7440,plain,
! [X0,X1] : addition(antidomain(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f56,f260]) ).
fof(f7444,plain,
! [X0,X1] :
( addition(X0,c(X1)) != c(X1)
| leq(addition(X0,antidomain(X1)),c(X1)) ),
inference(paramodulation,[status(thm)],[f260,f228]) ).
fof(f7445,plain,
! [X0,X1] :
( multiplication(X0,c(X1)) != multiplication(X0,c(X1))
| leq(multiplication(X0,antidomain(X1)),multiplication(X0,c(X1))) ),
inference(paramodulation,[status(thm)],[f260,f227]) ).
fof(f7446,plain,
! [X0,X1] :
( multiplication(c(X0),X1) != multiplication(c(X0),X1)
| leq(multiplication(antidomain(X0),X1),multiplication(c(X0),X1)) ),
inference(paramodulation,[status(thm)],[f260,f226]) ).
fof(f7447,plain,
! [X0] : multiplication(c(X0),coantidomain(c(X0))) = multiplication(antidomain(X0),coantidomain(c(X0))),
inference(paramodulation,[status(thm)],[f260,f218]) ).
fof(f7449,plain,
! [X0] : multiplication(antidomain(c(X0)),c(X0)) = multiplication(antidomain(c(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f260,f171]) ).
fof(f7451,plain,
! [X0,X1] : leq(antidomain(X0),addition(X1,c(X0))),
inference(paramodulation,[status(thm)],[f260,f1257]) ).
fof(f7456,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(X0),X1)) = addition(c(X0),X1),
inference(paramodulation,[status(thm)],[f260,f88]) ).
fof(f7458,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(X1,c(X0)),
inference(paramodulation,[status(thm)],[f260,f82]) ).
fof(f7459,plain,
! [X0,X1] : addition(X0,c(X1)) = addition(c(X1),addition(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f260,f82]) ).
fof(f7460,plain,
! [X0] :
( c(X0) != antidomain(X0)
| leq(c(X0),antidomain(X0)) ),
inference(paramodulation,[status(thm)],[f260,f231]) ).
fof(f7462,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(paramodulation,[status(thm)],[f260,f30]) ).
fof(f7463,plain,
! [X0] : one = c(multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1306,f7432]) ).
fof(f7465,plain,
! [X0] : addition(c(X0),domain(c(X0))) = c(domain(X0)),
inference(forward_demodulation,[status(thm)],[f633,f7434]) ).
fof(f7466,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(forward_demodulation,[status(thm)],[f633,f7465]) ).
fof(f7467,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f1096,f7435]) ).
fof(f7468,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f1096,f7467]) ).
fof(f7469,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f47,f7437]) ).
fof(f7470,plain,
! [X0] : addition(domain(X0),antidomain(c(X0))) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f1096,f7469]) ).
fof(f7471,plain,
! [X0] : addition(c(X0),domain(c(X0))) = c(domain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f7438]) ).
fof(f7472,plain,
! [X0] : addition(c(X0),domain(c(X0))) = domain(c(X0)),
inference(forward_demodulation,[status(thm)],[f633,f7471]) ).
fof(f7473,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)],[f29,f7439]) ).
fof(f7474,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_diamond(X0,c(X1)))) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f57,f7473]) ).
fof(f7475,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)],[f29,f7440]) ).
fof(f7476,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_diamond(X0,c(X1)))) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f56,f7475]) ).
fof(f7481,plain,
! [X0,X1] : leq(multiplication(X0,antidomain(X1)),multiplication(X0,c(X1))),
inference(trivial_equality_resolution,[status(thm)],[f7445]) ).
fof(f7482,plain,
! [X0,X1] : leq(multiplication(antidomain(X0),X1),multiplication(c(X0),X1)),
inference(trivial_equality_resolution,[status(thm)],[f7446]) ).
fof(f7483,plain,
! [X0] : zero = multiplication(antidomain(X0),coantidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f48,f7447]) ).
fof(f7484,plain,
! [X0] : zero = multiplication(antidomain(c(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f44,f7449]) ).
fof(f7485,plain,
! [X0,X1] : addition(antidomain(X0),addition(X1,c(X0))) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f82,f7456]) ).
fof(f7486,plain,
! [X0,X1] : addition(X0,c(X1)) = addition(antidomain(X1),addition(c(X1),X0)),
inference(forward_demodulation,[status(thm)],[f82,f7459]) ).
fof(f7488,plain,
! [X0,X1,X2] : addition(multiplication(backward_box(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6091,f42]) ).
fof(f7489,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f2026,f6091]) ).
fof(f7490,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),addition(coantidomain(backward_box(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f166,f6091]) ).
fof(f7491,plain,
! [X0,X1,X2] : leq(multiplication(backward_box(X0,X1),X2),addition(X2,coantidomain(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f175,f6091]) ).
fof(f7500,plain,
! [X0,X1,X2] : addition(X0,multiplication(backward_box(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f29,f7488]) ).
fof(f7503,plain,
! [X0,X1,X2] : addition(multiplication(forward_box(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6092,f42]) ).
fof(f7504,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f2026,f6092]) ).
fof(f7505,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),addition(coantidomain(forward_box(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f166,f6092]) ).
fof(f7506,plain,
! [X0,X1,X2] : leq(multiplication(forward_box(X0,X1),X2),addition(X2,coantidomain(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f175,f6092]) ).
fof(f7516,plain,
! [X0,X1,X2] : addition(X0,multiplication(forward_box(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f29,f7503]) ).
fof(f7520,plain,
! [X0] : addition(antidomain(X0),codomain(antidomain(X0))) = codomain(antidomain(X0)),
inference(resolution,[status(thm)],[f6400,f42]) ).
fof(f7547,plain,
! [X0] : addition(one,antidomain(multiplication(X0,domain(coantidomain(X0))))) = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f293,f243]) ).
fof(f7548,plain,
! [X0] : one = antidomain(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1215,f7547]) ).
fof(f7549,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1)))))),
inference(paramodulation,[status(thm)],[f33,f7548]) ).
fof(f7553,plain,
! [X0] : one = antidomain(multiplication(coantidomain(X0),domain(codomain(X0)))),
inference(paramodulation,[status(thm)],[f51,f7548]) ).
fof(f7557,plain,
! [X0] : leq(one,antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f7548,f238]) ).
fof(f7558,plain,
! [X0] : addition(one,antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))) = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f7548,f237]) ).
fof(f7561,plain,
! [X0] : addition(one,c(multiplication(X0,domain(coantidomain(X0))))) = c(multiplication(X0,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f7548,f260]) ).
fof(f7562,plain,
! [X0] : forward_diamond(one,multiplication(X0,domain(coantidomain(X0)))) = zero,
inference(paramodulation,[status(thm)],[f7548,f7328]) ).
fof(f7563,plain,
! [X0] : one = antidomain(multiplication(one,domain(multiplication(X0,domain(coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f7548,f7255]) ).
fof(f7564,plain,
! [X0,X1] : leq(domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))),one),
inference(paramodulation,[status(thm)],[f7548,f6540]) ).
fof(f7567,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X1,domain(coantidomain(X1)))) = multiplication(X0,multiplication(X1,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f7548,f215]) ).
fof(f7570,plain,
! [X0] : leq(one,c(multiplication(X0,domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f7548,f3895]) ).
fof(f7571,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X1,domain(coantidomain(X1)))) = multiplication(X0,multiplication(X1,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f7548,f209]) ).
fof(f7574,plain,
! [X0,X1] : multiplication(one,addition(X0,multiplication(X1,domain(coantidomain(X1))))) = multiplication(antidomain(multiplication(X1,domain(coantidomain(X1)))),X0),
inference(paramodulation,[status(thm)],[f7548,f171]) ).
fof(f7576,plain,
! [X0,X1] : multiplication(one,addition(multiplication(X0,domain(coantidomain(X0))),X1)) = multiplication(antidomain(multiplication(X0,domain(coantidomain(X0)))),X1),
inference(paramodulation,[status(thm)],[f7548,f162]) ).
fof(f7578,plain,
! [X0,X1] : multiplication(one,multiplication(multiplication(X0,domain(coantidomain(X0))),X1)) = zero,
inference(paramodulation,[status(thm)],[f7548,f121]) ).
fof(f7580,plain,
! [X0] : antidomain(c(multiplication(X0,domain(coantidomain(X0))))) = c(one),
inference(paramodulation,[status(thm)],[f7548,f1096]) ).
fof(f7581,plain,
! [X0] : domain(one) = c(multiplication(X0,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f7548,f631]) ).
fof(f7582,plain,
! [X0,X1] : domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f7548,f53]) ).
fof(f7584,plain,
! [X0] : domain(multiplication(X0,domain(coantidomain(X0)))) = antidomain(one),
inference(paramodulation,[status(thm)],[f7548,f47]) ).
fof(f7585,plain,
! [X0] : multiplication(one,multiplication(X0,domain(coantidomain(X0)))) = zero,
inference(paramodulation,[status(thm)],[f7548,f44]) ).
fof(f7595,plain,
! [X0] : leq(one,antidomain(multiplication(X0,antidomain(c(coantidomain(X0)))))),
inference(forward_demodulation,[status(thm)],[f181,f7557]) ).
fof(f7596,plain,
! [X0] : one = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f1215,f7558]) ).
fof(f7597,plain,
! [X0] : one = antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f181,f7596]) ).
fof(f7602,plain,
! [X0] : one = c(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1306,f7561]) ).
fof(f7603,plain,
! [X0] : antidomain(c(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(forward_demodulation,[status(thm)],[f863,f7562]) ).
fof(f7604,plain,
! [X0] : one = antidomain(domain(multiplication(X0,domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f35,f7563]) ).
fof(f7605,plain,
! [X0] : one = c(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f52,f7604]) ).
fof(f7612,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(antidomain(multiplication(X1,domain(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f35,f7574]) ).
fof(f7613,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = multiplication(one,X0),
inference(forward_demodulation,[status(thm)],[f7548,f7612]) ).
fof(f7614,plain,
! [X0,X1] : addition(X0,multiplication(X1,domain(coantidomain(X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f35,f7613]) ).
fof(f7615,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = multiplication(antidomain(multiplication(X0,domain(coantidomain(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f35,f7576]) ).
fof(f7616,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = multiplication(one,X1),
inference(forward_demodulation,[status(thm)],[f7548,f7615]) ).
fof(f7617,plain,
! [X0,X1] : addition(multiplication(X0,domain(coantidomain(X0))),X1) = X1,
inference(forward_demodulation,[status(thm)],[f35,f7616]) ).
fof(f7618,plain,
! [X0,X1] : multiplication(multiplication(X0,domain(coantidomain(X0))),X1) = zero,
inference(forward_demodulation,[status(thm)],[f35,f7578]) ).
fof(f7619,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f33,f7618]) ).
fof(f7620,plain,
! [X0] : antidomain(c(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(forward_demodulation,[status(thm)],[f303,f7580]) ).
fof(f7621,plain,
! [X0] : one = c(multiplication(X0,domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f290,f7581]) ).
fof(f7622,plain,
! [X0,X1] : domain_difference(X0,multiplication(X1,domain(coantidomain(X1)))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f34,f7582]) ).
fof(f7623,plain,
! [X0] : forward_diamond(X0,coantidomain(X0)) = antidomain(one),
inference(forward_demodulation,[status(thm)],[f54,f7584]) ).
fof(f7624,plain,
! [X0] : forward_diamond(X0,coantidomain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f104,f7623]) ).
fof(f7625,plain,
! [X0] : multiplication(X0,domain(coantidomain(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f35,f7585]) ).
fof(f7630,plain,
! [X0] : forward_diamond(coantidomain(X0),codomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f51,f7624]) ).
fof(f7645,plain,
! [X0] : addition(domain(X0),codomain(domain(X0))) = codomain(domain(X0)),
inference(resolution,[status(thm)],[f6542,f42]) ).
fof(f7648,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(domain(multiplication(X0,domain(X1))))),
inference(paramodulation,[status(thm)],[f54,f6542]) ).
fof(f7653,plain,
! [X0,X1] : leq(domain(multiplication(X0,domain(X1))),codomain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f54,f6542]) ).
fof(f7658,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f54,f7648]) ).
fof(f7665,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(forward_demodulation,[status(thm)],[f54,f7653]) ).
fof(f7670,plain,
! [X0,X1,X2] : addition(multiplication(forward_diamond(X0,X1),X2),X2) = X2,
inference(resolution,[status(thm)],[f6552,f42]) ).
fof(f7671,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),codomain(forward_diamond(X0,X1))),
inference(paramodulation,[status(thm)],[f2026,f6552]) ).
fof(f7672,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),addition(coantidomain(forward_diamond(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f166,f6552]) ).
fof(f7673,plain,
! [X0,X1,X2] : leq(multiplication(forward_diamond(X0,X1),X2),addition(X2,coantidomain(forward_diamond(X0,X1)))),
inference(paramodulation,[status(thm)],[f175,f6552]) ).
fof(f7688,plain,
! [X0,X1,X2] : addition(X0,multiplication(forward_diamond(X1,X2),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f29,f7670]) ).
fof(f7699,plain,
! [X0] : addition(coantidomain(X0),coantidomain(codomain(X0))) = coantidomain(codomain(X0)),
inference(resolution,[status(thm)],[f6784,f42]) ).
fof(f7704,plain,
! [X0,X1] : leq(coantidomain(multiplication(codomain(X0),X1)),coantidomain(backward_diamond(X1,X0))),
inference(paramodulation,[status(thm)],[f55,f6784]) ).
fof(f7723,plain,
! [X0] : multiplication(c(X0),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f52,f7329]) ).
fof(f7724,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f47,f7329]) ).
fof(f7726,plain,
! [X0] : multiplication(antidomain(domain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f181,f7329]) ).
fof(f7728,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f54,f7329]) ).
fof(f7739,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)],[f7329,f254]) ).
fof(f7740,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(domain(X0))))),
inference(paramodulation,[status(thm)],[f7329,f238]) ).
fof(f7741,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)],[f7329,f204]) ).
fof(f7742,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)],[f7329,f204]) ).
fof(f7744,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)],[f7329,f196]) ).
fof(f7745,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)],[f7329,f196]) ).
fof(f7747,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)],[f7329,f189]) ).
fof(f7748,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)],[f7329,f189]) ).
fof(f7749,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = addition(multiplication(X1,domain(X0)),zero),
inference(paramodulation,[status(thm)],[f7329,f186]) ).
fof(f7750,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = addition(zero,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f7329,f186]) ).
fof(f7751,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)],[f7329,f155]) ).
fof(f7752,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)],[f7329,f155]) ).
fof(f7755,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f7329,f138]) ).
fof(f7756,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f7329,f138]) ).
fof(f7759,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),domain(X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(paramodulation,[status(thm)],[f7329,f309]) ).
fof(f7760,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(antidomain(X0),domain(domain(X0))))) = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(paramodulation,[status(thm)],[f7329,f237]) ).
fof(f7761,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = addition(multiplication(X0,domain(X1)),zero),
inference(paramodulation,[status(thm)],[f7329,f37]) ).
fof(f7762,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = addition(zero,multiplication(X1,domain(X0))),
inference(paramodulation,[status(thm)],[f7329,f37]) ).
fof(f7763,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f7329,f36]) ).
fof(f7764,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f7329,f36]) ).
fof(f7765,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f7329,f33]) ).
fof(f7770,plain,
! [X0] : multiplication(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f181,f7723]) ).
fof(f7771,plain,
! [X0] : multiplication(domain(X0),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f631,f7724]) ).
fof(f7772,plain,
! [X0] : multiplication(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f52,f7726]) ).
fof(f7788,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)],[f38,f7739]) ).
fof(f7789,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)],[f293,f7788]) ).
fof(f7790,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),domain(domain(X1))))),
inference(forward_demodulation,[status(thm)],[f1215,f7789]) ).
fof(f7791,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(antidomain(X1),antidomain(c(X1))))),
inference(forward_demodulation,[status(thm)],[f181,f7790]) ).
fof(f7792,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),domain(domain(X0))))),
inference(forward_demodulation,[status(thm)],[f293,f7740]) ).
fof(f7793,plain,
! [X0] : leq(one,antidomain(multiplication(antidomain(X0),antidomain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f181,f7792]) ).
fof(f7794,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)],[f82,f7741]) ).
fof(f7795,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,domain(X2))) = addition(multiplication(addition(X1,antidomain(X2)),domain(X2)),X0),
inference(forward_demodulation,[status(thm)],[f65,f7794]) ).
fof(f7796,plain,
! [X0,X1,X2] : addition(multiplication(X0,domain(X1)),X2) = addition(multiplication(addition(antidomain(X1),X0),domain(X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f7742]) ).
fof(f7800,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),domain(X2)) = addition(multiplication(X0,domain(X2)),zero),
inference(forward_demodulation,[status(thm)],[f38,f7744]) ).
fof(f7801,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,antidomain(X2))),domain(X2)) = multiplication(X0,domain(X2)),
inference(forward_demodulation,[status(thm)],[f31,f7800]) ).
fof(f7802,plain,
! [X0,X1,X2] : multiplication(addition(antidomain(X0),multiplication(X1,X2)),domain(X0)) = multiplication(X1,multiplication(X2,domain(X0))),
inference(forward_demodulation,[status(thm)],[f65,f7745]) ).
fof(f7805,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),antidomain(X2)),domain(X2)) = multiplication(X0,multiplication(X1,domain(X2))),
inference(forward_demodulation,[status(thm)],[f31,f7747]) ).
fof(f7806,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),domain(X1)) = addition(zero,multiplication(X2,domain(X1))),
inference(forward_demodulation,[status(thm)],[f38,f7748]) ).
fof(f7807,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,antidomain(X1)),X2),domain(X1)) = multiplication(X2,domain(X1)),
inference(forward_demodulation,[status(thm)],[f65,f7806]) ).
fof(f7808,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f31,f7749]) ).
fof(f7809,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f65,f7750]) ).
fof(f7810,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)],[f82,f7751]) ).
fof(f7811,plain,
! [X0,X1,X2] : addition(X0,multiplication(antidomain(X1),X2)) = addition(multiplication(antidomain(X1),addition(X2,domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f65,f7810]) ).
fof(f7812,plain,
! [X0,X1,X2] : addition(multiplication(antidomain(X0),X1),X2) = addition(multiplication(antidomain(X0),addition(domain(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f7752]) ).
fof(f7818,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f7755]) ).
fof(f7819,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f7756]) ).
fof(f7822,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(antidomain(X0)),domain(X0)))) = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f363,f7759]) ).
fof(f7823,plain,
! [X0] : one = coantidomain(multiplication(codomain(antidomain(X0)),domain(X0))),
inference(forward_demodulation,[status(thm)],[f1213,f7822]) ).
fof(f7824,plain,
! [X0] : addition(one,antidomain(multiplication(antidomain(X0),domain(domain(X0))))) = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f293,f7760]) ).
fof(f7825,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),domain(domain(X0)))),
inference(forward_demodulation,[status(thm)],[f1215,f7824]) ).
fof(f7826,plain,
! [X0] : one = antidomain(multiplication(antidomain(X0),antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f181,f7825]) ).
fof(f7827,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),domain(X1)) = multiplication(X0,domain(X1)),
inference(forward_demodulation,[status(thm)],[f31,f7761]) ).
fof(f7828,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),domain(X0)) = multiplication(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f65,f7762]) ).
fof(f7829,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,domain(X0))) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f7763]) ).
fof(f7830,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(domain(X0),X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f7764]) ).
fof(f7831,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(domain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f7765]) ).
fof(f7834,plain,
! [X0] : forward_diamond(domain(c(X0)),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f633,f7335]) ).
fof(f7835,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),domain(backward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f57,f7335]) ).
fof(f7836,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),domain(forward_diamond(X0,c(X1)))) = zero,
inference(paramodulation,[status(thm)],[f56,f7335]) ).
fof(f7839,plain,
! [X0] : forward_diamond(c(domain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f181,f7335]) ).
fof(f7841,plain,
! [X0,X1] : forward_diamond(c(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f54,f7335]) ).
fof(f7844,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)],[f7335,f60]) ).
fof(f7851,plain,
! [X0] : forward_diamond(domain(c(X0)),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f181,f7834]) ).
fof(f7856,plain,
! [X0] : forward_diamond(domain(c(X0)),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f633,f7839]) ).
fof(f7858,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)],[f82,f7844]) ).
fof(f7859,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)],[f65,f7858]) ).
fof(f7860,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)],[f7335,f7859]) ).
fof(f7861,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)],[f65,f7860]) ).
fof(f7867,plain,
! [X0,X1] : forward_diamond(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f54,f7336]) ).
fof(f7870,plain,
! [X0] : forward_diamond(domain(multiplication(X0,domain(coantidomain(X0)))),one) = zero,
inference(paramodulation,[status(thm)],[f7548,f7336]) ).
fof(f7886,plain,
! [X0] : domain(domain(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(forward_demodulation,[status(thm)],[f454,f7870]) ).
fof(f7887,plain,
! [X0] : antidomain(c(multiplication(X0,domain(coantidomain(X0))))) = zero,
inference(forward_demodulation,[status(thm)],[f181,f7886]) ).
fof(f7901,plain,
! [X0] : forward_box(antidomain(antidomain(c(X0))),antidomain(X0)) = one,
inference(paramodulation,[status(thm)],[f1096,f7358]) ).
fof(f7902,plain,
! [X0] : forward_box(antidomain(domain(c(X0))),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f633,f7358]) ).
fof(f7903,plain,
! [X0,X1] : forward_box(antidomain(backward_box(X0,X1)),backward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f57,f7358]) ).
fof(f7904,plain,
! [X0,X1] : forward_box(antidomain(forward_box(X0,X1)),forward_diamond(X0,c(X1))) = one,
inference(paramodulation,[status(thm)],[f56,f7358]) ).
fof(f7917,plain,
! [X0] : forward_box(domain(c(X0)),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f47,f7901]) ).
fof(f7918,plain,
! [X0] : forward_box(c(c(X0)),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f52,f7902]) ).
fof(f7931,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f33,f7625]) ).
fof(f7935,plain,
! [X0] : multiplication(coantidomain(X0),domain(codomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f51,f7625]) ).
fof(f7943,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)],[f7625,f226]) ).
fof(f7953,plain,
! [X0] : backward_diamond(domain(coantidomain(codomain(X0))),X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f7625,f55]) ).
fof(f7955,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,domain(coantidomain(multiplication(X0,X1))))) = zero,
inference(paramodulation,[status(thm)],[f7625,f33]) ).
fof(f7966,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)],[f7625,f254]) ).
fof(f7967,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))),
inference(paramodulation,[status(thm)],[f7625,f238]) ).
fof(f7968,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)],[f7625,f204]) ).
fof(f7969,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)],[f7625,f204]) ).
fof(f7970,plain,
! [X0] : multiplication(addition(X0,one),domain(coantidomain(X0))) = addition(domain(coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f7625,f217]) ).
fof(f7971,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)],[f7625,f196]) ).
fof(f7972,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)],[f7625,f196]) ).
fof(f7973,plain,
! [X0] : multiplication(addition(one,X0),domain(coantidomain(X0))) = addition(domain(coantidomain(X0)),zero),
inference(paramodulation,[status(thm)],[f7625,f192]) ).
fof(f7974,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)],[f7625,f189]) ).
fof(f7975,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)],[f7625,f189]) ).
fof(f7976,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = addition(multiplication(X1,domain(coantidomain(X0))),zero),
inference(paramodulation,[status(thm)],[f7625,f186]) ).
fof(f7977,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = addition(zero,multiplication(X0,domain(coantidomain(X1)))),
inference(paramodulation,[status(thm)],[f7625,f186]) ).
fof(f7978,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(zero,X2)) = addition(multiplication(X0,addition(X1,domain(coantidomain(X0)))),X2),
inference(paramodulation,[status(thm)],[f7625,f155]) ).
fof(f7979,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(domain(coantidomain(X0)),X1)),X2),
inference(paramodulation,[status(thm)],[f7625,f155]) ).
fof(f7982,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f7625,f138]) ).
fof(f7983,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f7625,f138]) ).
fof(f7986,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),domain(coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f7625,f309]) ).
fof(f7987,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))) = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f7625,f237]) ).
fof(f7988,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = addition(multiplication(X0,domain(coantidomain(X1))),zero),
inference(paramodulation,[status(thm)],[f7625,f37]) ).
fof(f7989,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = addition(zero,multiplication(X1,domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f7625,f37]) ).
fof(f7990,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f7625,f36]) ).
fof(f7991,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = addition(zero,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f7625,f36]) ).
fof(f7992,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f7625,f33]) ).
fof(f7999,plain,
! [X0] : backward_diamond(domain(coantidomain(codomain(X0))),X0) = zero,
inference(forward_demodulation,[status(thm)],[f375,f7953]) ).
fof(f8019,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)],[f38,f7966]) ).
fof(f8020,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)],[f293,f8019]) ).
fof(f8021,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,domain(domain(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f1215,f8020]) ).
fof(f8022,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(X1,antidomain(c(coantidomain(X1)))))),
inference(forward_demodulation,[status(thm)],[f181,f8021]) ).
fof(f8023,plain,
! [X0] : leq(one,antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))),
inference(forward_demodulation,[status(thm)],[f293,f7967]) ).
fof(f8024,plain,
! [X0] : leq(one,antidomain(multiplication(X0,antidomain(c(coantidomain(X0)))))),
inference(forward_demodulation,[status(thm)],[f181,f8023]) ).
fof(f8025,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)],[f82,f7968]) ).
fof(f8026,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)],[f65,f8025]) ).
fof(f8027,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)],[f65,f7969]) ).
fof(f8028,plain,
! [X0] : multiplication(addition(X0,one),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f31,f7970]) ).
fof(f8029,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)],[f38,f7971]) ).
fof(f8030,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X2)),domain(coantidomain(X2))) = multiplication(X0,domain(coantidomain(X2))),
inference(forward_demodulation,[status(thm)],[f31,f8029]) ).
fof(f8031,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)],[f65,f7972]) ).
fof(f8032,plain,
! [X0] : multiplication(addition(one,X0),domain(coantidomain(X0))) = domain(coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f31,f7973]) ).
fof(f8033,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)],[f31,f7974]) ).
fof(f8034,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)],[f38,f7975]) ).
fof(f8035,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),domain(coantidomain(X1))) = multiplication(X2,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f65,f8034]) ).
fof(f8036,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = multiplication(X1,domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f31,f7976]) ).
fof(f8037,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = multiplication(X0,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f65,f7977]) ).
fof(f8038,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)],[f82,f7978]) ).
fof(f8039,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,X2)) = addition(multiplication(X1,addition(X2,domain(coantidomain(X1)))),X0),
inference(forward_demodulation,[status(thm)],[f65,f8038]) ).
fof(f8040,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),X2) = addition(multiplication(X0,addition(domain(coantidomain(X0)),X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f7979]) ).
fof(f8046,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f7982]) ).
fof(f8047,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f7983]) ).
fof(f8050,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(X0),domain(coantidomain(X0))))) = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f363,f7986]) ).
fof(f8051,plain,
! [X0] : one = coantidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f1213,f8050]) ).
fof(f8052,plain,
! [X0] : addition(one,antidomain(multiplication(X0,domain(domain(coantidomain(X0)))))) = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f293,f7987]) ).
fof(f8053,plain,
! [X0] : one = antidomain(multiplication(X0,domain(domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f1215,f8052]) ).
fof(f8054,plain,
! [X0] : one = antidomain(multiplication(X0,antidomain(c(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f181,f8053]) ).
fof(f8055,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X1))) = multiplication(X0,domain(coantidomain(X1))),
inference(forward_demodulation,[status(thm)],[f31,f7988]) ).
fof(f8056,plain,
! [X0,X1] : multiplication(addition(X0,X1),domain(coantidomain(X0))) = multiplication(X1,domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f65,f7989]) ).
fof(f8057,plain,
! [X0,X1] : multiplication(X0,addition(X1,domain(coantidomain(X0)))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f7990]) ).
fof(f8058,plain,
! [X0,X1] : multiplication(X0,addition(domain(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f65,f7991]) ).
fof(f8059,plain,
! [X0,X1] : multiplication(X0,multiplication(domain(coantidomain(X0)),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f7992]) ).
fof(f8065,plain,
! [X0,X1] : forward_diamond(coantidomain(multiplication(codomain(X0),X1)),backward_diamond(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f55,f7630]) ).
fof(f8084,plain,
! [X0] : multiplication(c(X0),c(antidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f631,f7771]) ).
fof(f8085,plain,
! [X0,X1] : multiplication(forward_diamond(X0,X1),c(multiplication(X0,domain(X1)))) = zero,
inference(paramodulation,[status(thm)],[f54,f7771]) ).
fof(f8088,plain,
! [X0] : multiplication(domain(antidomain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f1096,f7771]) ).
fof(f8090,plain,
! [X0,X1] : multiplication(domain(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f57,f7771]) ).
fof(f8091,plain,
! [X0,X1] : multiplication(domain(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f56,f7771]) ).
fof(f8098,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,zero)),antidomain(multiplication(X0,multiplication(domain(X1),domain(c(X1)))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(c(X1))))),
inference(paramodulation,[status(thm)],[f7771,f254]) ).
fof(f8099,plain,
! [X0] : leq(antidomain(zero),antidomain(multiplication(domain(X0),domain(c(X0))))),
inference(paramodulation,[status(thm)],[f7771,f238]) ).
fof(f8100,plain,
! [X0,X1,X2] : addition(multiplication(X0,c(X1)),addition(zero,X2)) = addition(multiplication(addition(X0,domain(X1)),c(X1)),X2),
inference(paramodulation,[status(thm)],[f7771,f204]) ).
fof(f8101,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(X0,c(X1)),X2)) = addition(multiplication(addition(domain(X1),X0),c(X1)),X2),
inference(paramodulation,[status(thm)],[f7771,f204]) ).
fof(f8103,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),c(X2)) = addition(multiplication(X0,c(X2)),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f7771,f196]) ).
fof(f8104,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),multiplication(X1,X2)),c(X0)) = addition(zero,multiplication(X1,multiplication(X2,c(X0)))),
inference(paramodulation,[status(thm)],[f7771,f196]) ).
fof(f8106,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),c(X2)) = addition(multiplication(X0,multiplication(X1,c(X2))),zero),
inference(paramodulation,[status(thm)],[f7771,f189]) ).
fof(f8107,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),c(X1)) = addition(multiplication(X0,zero),multiplication(X2,c(X1))),
inference(paramodulation,[status(thm)],[f7771,f189]) ).
fof(f8108,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),c(X0)) = addition(multiplication(X1,c(X0)),zero),
inference(paramodulation,[status(thm)],[f7771,f186]) ).
fof(f8109,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),c(X1)) = addition(zero,multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f7771,f186]) ).
fof(f8110,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),addition(zero,X2)) = addition(multiplication(domain(X0),addition(X1,c(X0))),X2),
inference(paramodulation,[status(thm)],[f7771,f155]) ).
fof(f8111,plain,
! [X0,X1,X2] : addition(zero,addition(multiplication(domain(X0),X1),X2)) = addition(multiplication(domain(X0),addition(c(X0),X1)),X2),
inference(paramodulation,[status(thm)],[f7771,f155]) ).
fof(f8114,plain,
! [X0,X1] : multiplication(domain(X0),addition(c(X0),X1)) = addition(multiplication(domain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f7771,f138]) ).
fof(f8115,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,c(X0))) = addition(zero,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f7771,f138]) ).
fof(f8118,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(domain(X0)),c(X0)))) = coantidomain(multiplication(codomain(domain(X0)),c(X0))),
inference(paramodulation,[status(thm)],[f7771,f309]) ).
fof(f8119,plain,
! [X0] : addition(antidomain(zero),antidomain(multiplication(domain(X0),domain(c(X0))))) = antidomain(multiplication(domain(X0),domain(c(X0)))),
inference(paramodulation,[status(thm)],[f7771,f237]) ).
fof(f8120,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),c(X1)) = addition(multiplication(X0,c(X1)),zero),
inference(paramodulation,[status(thm)],[f7771,f37]) ).
fof(f8121,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),c(X0)) = addition(zero,multiplication(X1,c(X0))),
inference(paramodulation,[status(thm)],[f7771,f37]) ).
fof(f8122,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,c(X0))) = addition(multiplication(domain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f7771,f36]) ).
fof(f8123,plain,
! [X0,X1] : multiplication(domain(X0),addition(c(X0),X1)) = addition(zero,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f7771,f36]) ).
fof(f8124,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(c(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f7771,f33]) ).
fof(f8127,plain,
! [X0] : multiplication(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f1096,f8084]) ).
fof(f8129,plain,
! [X0] : domain_difference(antidomain(X0),c(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f53,f8088]) ).
fof(f8132,plain,
! [X0,X1] : addition(antidomain(zero),antidomain(multiplication(X0,multiplication(domain(X1),domain(c(X1)))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(c(X1))))),
inference(forward_demodulation,[status(thm)],[f38,f8098]) ).
fof(f8133,plain,
! [X0,X1] : addition(one,antidomain(multiplication(X0,multiplication(domain(X1),domain(c(X1)))))) = antidomain(multiplication(X0,multiplication(domain(X1),domain(c(X1))))),
inference(forward_demodulation,[status(thm)],[f293,f8132]) ).
fof(f8134,plain,
! [X0,X1] : one = antidomain(multiplication(X0,multiplication(domain(X1),domain(c(X1))))),
inference(forward_demodulation,[status(thm)],[f1215,f8133]) ).
fof(f8135,plain,
! [X0] : leq(one,antidomain(multiplication(domain(X0),domain(c(X0))))),
inference(forward_demodulation,[status(thm)],[f293,f8099]) ).
fof(f8136,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(X1,c(X2)))) = addition(multiplication(addition(X1,domain(X2)),c(X2)),X0),
inference(forward_demodulation,[status(thm)],[f82,f8100]) ).
fof(f8137,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,c(X2))) = addition(multiplication(addition(X1,domain(X2)),c(X2)),X0),
inference(forward_demodulation,[status(thm)],[f65,f8136]) ).
fof(f8138,plain,
! [X0,X1,X2] : addition(multiplication(X0,c(X1)),X2) = addition(multiplication(addition(domain(X1),X0),c(X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f8101]) ).
fof(f8142,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),c(X2)) = addition(multiplication(X0,c(X2)),zero),
inference(forward_demodulation,[status(thm)],[f38,f8103]) ).
fof(f8143,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,domain(X2))),c(X2)) = multiplication(X0,c(X2)),
inference(forward_demodulation,[status(thm)],[f31,f8142]) ).
fof(f8144,plain,
! [X0,X1,X2] : multiplication(addition(domain(X0),multiplication(X1,X2)),c(X0)) = multiplication(X1,multiplication(X2,c(X0))),
inference(forward_demodulation,[status(thm)],[f65,f8104]) ).
fof(f8147,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),domain(X2)),c(X2)) = multiplication(X0,multiplication(X1,c(X2))),
inference(forward_demodulation,[status(thm)],[f31,f8106]) ).
fof(f8148,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),c(X1)) = addition(zero,multiplication(X2,c(X1))),
inference(forward_demodulation,[status(thm)],[f38,f8107]) ).
fof(f8149,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,domain(X1)),X2),c(X1)) = multiplication(X2,c(X1)),
inference(forward_demodulation,[status(thm)],[f65,f8148]) ).
fof(f8150,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),c(X0)) = multiplication(X1,c(X0)),
inference(forward_demodulation,[status(thm)],[f31,f8108]) ).
fof(f8151,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),c(X1)) = multiplication(X0,c(X1)),
inference(forward_demodulation,[status(thm)],[f65,f8109]) ).
fof(f8152,plain,
! [X0,X1,X2] : addition(zero,addition(X0,multiplication(domain(X1),X2))) = addition(multiplication(domain(X1),addition(X2,c(X1))),X0),
inference(forward_demodulation,[status(thm)],[f82,f8110]) ).
fof(f8153,plain,
! [X0,X1,X2] : addition(X0,multiplication(domain(X1),X2)) = addition(multiplication(domain(X1),addition(X2,c(X1))),X0),
inference(forward_demodulation,[status(thm)],[f65,f8152]) ).
fof(f8154,plain,
! [X0,X1,X2] : addition(multiplication(domain(X0),X1),X2) = addition(multiplication(domain(X0),addition(c(X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f65,f8111]) ).
fof(f8160,plain,
! [X0,X1] : multiplication(domain(X0),addition(c(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f8114]) ).
fof(f8161,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,c(X0))) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f8115]) ).
fof(f8164,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(domain(X0)),c(X0)))) = coantidomain(multiplication(codomain(domain(X0)),c(X0))),
inference(forward_demodulation,[status(thm)],[f363,f8118]) ).
fof(f8165,plain,
! [X0] : one = coantidomain(multiplication(codomain(domain(X0)),c(X0))),
inference(forward_demodulation,[status(thm)],[f1213,f8164]) ).
fof(f8166,plain,
! [X0] : addition(one,antidomain(multiplication(domain(X0),domain(c(X0))))) = antidomain(multiplication(domain(X0),domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f293,f8119]) ).
fof(f8167,plain,
! [X0] : one = antidomain(multiplication(domain(X0),domain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f1215,f8166]) ).
fof(f8168,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),c(X1)) = multiplication(X0,c(X1)),
inference(forward_demodulation,[status(thm)],[f31,f8120]) ).
fof(f8169,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),c(X0)) = multiplication(X1,c(X0)),
inference(forward_demodulation,[status(thm)],[f65,f8121]) ).
fof(f8170,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,c(X0))) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f8122]) ).
fof(f8171,plain,
! [X0,X1] : multiplication(domain(X0),addition(c(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f8123]) ).
fof(f8172,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(c(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f8124]) ).
fof(f8175,plain,
! [X0] : domain_difference(c(X0),c(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f52,f8129]) ).
fof(f8176,plain,
! [X0] : domain_difference(domain(X0),c(antidomain(X0))) = zero,
inference(paramodulation,[status(thm)],[f47,f8129]) ).
fof(f8178,plain,
! [X0] : domain_difference(antidomain(antidomain(X0)),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f1096,f8129]) ).
fof(f8179,plain,
! [X0] : domain_difference(antidomain(domain(X0)),domain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f633,f8129]) ).
fof(f8180,plain,
! [X0,X1] : domain_difference(antidomain(backward_diamond(X0,c(X1))),backward_box(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f57,f8129]) ).
fof(f8181,plain,
! [X0,X1] : domain_difference(antidomain(forward_diamond(X0,c(X1))),forward_box(X0,X1)) = zero,
inference(paramodulation,[status(thm)],[f56,f8129]) ).
fof(f8189,plain,
! [X0] : domain_difference(c(X0),domain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f633,f8175]) ).
fof(f8190,plain,
! [X0] : domain_difference(domain(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f1096,f8176]) ).
fof(f8191,plain,
! [X0] : domain_difference(domain(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f47,f8178]) ).
fof(f8192,plain,
! [X0] : domain_difference(c(X0),domain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f52,f8179]) ).
fof(f8199,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)],[f703,f60]) ).
fof(f8203,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f88,f703]) ).
fof(f8204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f30,f703]) ).
fof(f8208,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f82,f703]) ).
fof(f8230,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(X2,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f186,f703]) ).
fof(f8231,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,X2),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f138,f703]) ).
fof(f8232,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(X2,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f37,f703]) ).
fof(f8233,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,X2),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f703]) ).
fof(f8234,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X2,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f88,f703]) ).
fof(f8235,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X2,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f30,f703]) ).
fof(f8255,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f82,f703]) ).
fof(f8256,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f82,f703]) ).
fof(f8258,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f703]) ).
fof(f8259,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f703]) ).
fof(f8264,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f703,f192]) ).
fof(f8268,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f703,f147]) ).
fof(f8269,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)],[f703,f60]) ).
fof(f8274,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)],[f703,f204]) ).
fof(f8275,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)],[f703,f155]) ).
fof(f8276,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f703,f88]) ).
fof(f8277,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f703,f30]) ).
fof(f8279,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f703,f228]) ).
fof(f8284,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f703,f82]) ).
fof(f8285,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != addition(X2,X1)
| leq(addition(X0,X1),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f703,f228]) ).
fof(f8286,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)],[f703,f227]) ).
fof(f8287,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)],[f703,f226]) ).
fof(f8288,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X0,X1))) = multiplication(X1,coantidomain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f703,f218]) ).
fof(f8290,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,X1)) = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f703,f171]) ).
fof(f8297,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f703,f88]) ).
fof(f8298,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f703,f82]) ).
fof(f8299,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f703,f82]) ).
fof(f8300,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f703,f231]) ).
fof(f8350,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f186,f8230]) ).
fof(f8351,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X0,X1),X0),X2),
inference(forward_demodulation,[status(thm)],[f186,f8350]) ).
fof(f8352,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,addition(X0,X0)),X2),
inference(forward_demodulation,[status(thm)],[f88,f8351]) ).
fof(f8353,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f32,f8352]) ).
fof(f8354,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f138,f8231]) ).
fof(f8355,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(addition(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f138,f8354]) ).
fof(f8356,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,addition(X1,X1))),
inference(forward_demodulation,[status(thm)],[f88,f8355]) ).
fof(f8357,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f32,f8356]) ).
fof(f8358,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f8232]) ).
fof(f8359,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(addition(X1,X0),X0),X2),
inference(forward_demodulation,[status(thm)],[f186,f8358]) ).
fof(f8360,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f88,f8359]) ).
fof(f8361,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f703,f8360]) ).
fof(f8362,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f8233]) ).
fof(f8363,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(addition(X2,X1),X1)),
inference(forward_demodulation,[status(thm)],[f138,f8362]) ).
fof(f8364,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f88,f8363]) ).
fof(f8365,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f703,f8364]) ).
fof(f8366,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f88,f8234]) ).
fof(f8367,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f88,f8235]) ).
fof(f8411,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X1,addition(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f88,f8255]) ).
fof(f8412,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f90,f8411]) ).
fof(f8413,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X2,addition(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f88,f8256]) ).
fof(f8415,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)],[f29,f8269]) ).
fof(f8416,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)],[f29,f8415]) ).
fof(f8417,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)],[f8416]) ).
fof(f8422,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)],[f82,f8274]) ).
fof(f8423,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)],[f204,f8422]) ).
fof(f8424,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)],[f703,f8423]) ).
fof(f8425,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)],[f82,f8275]) ).
fof(f8426,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)],[f155,f8425]) ).
fof(f8427,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)],[f703,f8426]) ).
fof(f8428,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(trivial_equality_resolution,[status(thm)],[f8286]) ).
fof(f8429,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(trivial_equality_resolution,[status(thm)],[f8287]) ).
fof(f8430,plain,
! [X0,X1] : zero = multiplication(X0,coantidomain(addition(X1,X0))),
inference(forward_demodulation,[status(thm)],[f48,f8288]) ).
fof(f8431,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f44,f8290]) ).
fof(f8432,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f8297]) ).
fof(f8433,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f8432]) ).
fof(f8434,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8298]) ).
fof(f8435,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f90,f8434]) ).
fof(f8436,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f88,f8299]) ).
fof(f8443,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f88,f724]) ).
fof(f8444,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f724]) ).
fof(f8467,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)],[f189,f724]) ).
fof(f8468,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)],[f204,f724]) ).
fof(f8469,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)],[f155,f724]) ).
fof(f8475,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f88,f724]) ).
fof(f8476,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f724]) ).
fof(f8490,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f217,f724]) ).
fof(f8491,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f192,f724]) ).
fof(f8492,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f177,f724]) ).
fof(f8493,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f147,f724]) ).
fof(f8497,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f82,f724]) ).
fof(f8498,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X2,X1),X0),
inference(paramodulation,[status(thm)],[f82,f724]) ).
fof(f8506,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f724,f192]) ).
fof(f8510,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f724,f147]) ).
fof(f8515,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)],[f724,f204]) ).
fof(f8516,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)],[f724,f155]) ).
fof(f8517,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f724,f88]) ).
fof(f8518,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f724,f30]) ).
fof(f8528,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != addition(X1,X2)
| leq(addition(X0,X1),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f724,f228]) ).
fof(f8529,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)],[f724,f227]) ).
fof(f8530,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)],[f724,f226]) ).
fof(f8531,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X1,X0))) = multiplication(X1,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f724,f218]) ).
fof(f8533,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X1,X0)) = multiplication(antidomain(addition(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f724,f171]) ).
fof(f8536,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f724,f1256]) ).
fof(f8537,plain,
! [X0,X1] : leq(addition(X0,X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f724,f1259]) ).
fof(f8540,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f724,f88]) ).
fof(f8541,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f724,f82]) ).
fof(f8542,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f724,f82]) ).
fof(f8543,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f724,f231]) ).
fof(f8545,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f724,f30]) ).
fof(f8549,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8443]) ).
fof(f8550,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f88,f8444]) ).
fof(f8551,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f724,f8550]) ).
fof(f8552,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f8551]) ).
fof(f8591,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)],[f189,f8467]) ).
fof(f8592,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)],[f204,f8591]) ).
fof(f8593,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)],[f32,f8592]) ).
fof(f8594,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)],[f204,f8468]) ).
fof(f8595,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)],[f724,f8594]) ).
fof(f8596,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)],[f88,f8595]) ).
fof(f8597,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f8596]) ).
fof(f8598,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)],[f155,f8469]) ).
fof(f8599,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)],[f724,f8598]) ).
fof(f8600,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)],[f88,f8599]) ).
fof(f8601,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f8600]) ).
fof(f8617,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8475]) ).
fof(f8618,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8476]) ).
fof(f8619,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f724,f8618]) ).
fof(f8620,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8619]) ).
fof(f8646,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f29,f8490]) ).
fof(f8647,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(forward_demodulation,[status(thm)],[f29,f8491]) ).
fof(f8648,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f8492]) ).
fof(f8649,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29,f8493]) ).
fof(f8656,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8497]) ).
fof(f8657,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8498]) ).
fof(f8663,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)],[f204,f8515]) ).
fof(f8664,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)],[f88,f8663]) ).
fof(f8665,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)],[f703,f8664]) ).
fof(f8666,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)],[f155,f8516]) ).
fof(f8667,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)],[f88,f8666]) ).
fof(f8668,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)],[f703,f8667]) ).
fof(f8669,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8517]) ).
fof(f8670,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f88,f8518]) ).
fof(f8671,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f724,f8670]) ).
fof(f8672,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f8671]) ).
fof(f8681,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f88,f8540]) ).
fof(f8682,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f724,f8681]) ).
fof(f8683,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f88,f8541]) ).
fof(f8684,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f88,f8542]) ).
fof(f8685,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f703,f8684]) ).
fof(f8686,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f8545]) ).
fof(f8687,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f8686]) ).
fof(f8706,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)],[f189,f8537]) ).
fof(f8709,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)],[f196,f8537]) ).
fof(f8710,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f186,f8537]) ).
fof(f8711,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f138,f8537]) ).
fof(f8714,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f88,f8537]) ).
fof(f8715,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f30,f8537]) ).
fof(f8729,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),X1),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f217,f8537]) ).
fof(f8730,plain,
! [X0,X1] : leq(multiplication(addition(one,X0),X1),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f192,f8537]) ).
fof(f8731,plain,
! [X0,X1] : leq(multiplication(X0,addition(X1,one)),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f177,f8537]) ).
fof(f8732,plain,
! [X0,X1] : leq(multiplication(X0,addition(one,X1)),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f147,f8537]) ).
fof(f8736,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f82,f8537]) ).
fof(f8737,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f82,f8537]) ).
fof(f8759,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)],[f189,f8537]) ).
fof(f8762,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)],[f196,f8537]) ).
fof(f8763,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f186,f8537]) ).
fof(f8764,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f138,f8537]) ).
fof(f8767,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f88,f8537]) ).
fof(f8768,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f30,f8537]) ).
fof(f8782,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f217,f8537]) ).
fof(f8783,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f192,f8537]) ).
fof(f8784,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f177,f8537]) ).
fof(f8785,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f147,f8537]) ).
fof(f8789,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f82,f8537]) ).
fof(f8790,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f82,f8537]) ).
fof(f8831,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)],[f196,f8706]) ).
fof(f8836,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)],[f189,f8709]) ).
fof(f8837,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f8710]) ).
fof(f8838,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f8711]) ).
fof(f8866,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),X1),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f29,f8729]) ).
fof(f8867,plain,
! [X0,X1] : leq(multiplication(addition(one,X0),X1),addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f29,f8730]) ).
fof(f8868,plain,
! [X0,X1] : leq(multiplication(X0,addition(X1,one)),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f29,f8731]) ).
fof(f8869,plain,
! [X0,X1] : leq(multiplication(X0,addition(one,X1)),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f29,f8732]) ).
fof(f8876,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f88,f8736]) ).
fof(f8877,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f88,f8737]) ).
fof(f8914,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)],[f196,f8759]) ).
fof(f8919,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)],[f189,f8762]) ).
fof(f8920,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f186,f8763]) ).
fof(f8921,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f138,f8764]) ).
fof(f8949,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(X1,one),X0)),
inference(forward_demodulation,[status(thm)],[f29,f8782]) ).
fof(f8950,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(one,X1),X0)),
inference(forward_demodulation,[status(thm)],[f29,f8783]) ).
fof(f8951,plain,
! [X0,X1] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f29,f8784]) ).
fof(f8952,plain,
! [X0,X1] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f29,f8785]) ).
fof(f8959,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f88,f8789]) ).
fof(f8960,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f88,f8790]) ).
fof(f8966,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f88,f1168]) ).
fof(f8967,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f30,f1168]) ).
fof(f8992,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)],[f204,f1168]) ).
fof(f8993,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)],[f155,f1168]) ).
fof(f8999,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f88,f1168]) ).
fof(f9000,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f30,f1168]) ).
fof(f9022,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f82,f1168]) ).
fof(f9023,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X2,X0))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f82,f1168]) ).
fof(f9031,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f1168,f192]) ).
fof(f9035,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f1168,f147]) ).
fof(f9036,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)],[f1168,f60]) ).
fof(f9041,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)],[f1168,f204]) ).
fof(f9042,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)],[f1168,f155]) ).
fof(f9043,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1168,f88]) ).
fof(f9044,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f1168,f30]) ).
fof(f9048,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f1168,f228]) ).
fof(f9058,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X2,X1)
| leq(addition(X0,X1),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f1168,f228]) ).
fof(f9059,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)],[f1168,f227]) ).
fof(f9060,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)],[f1168,f226]) ).
fof(f9061,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(addition(X1,X0))) = multiplication(X0,coantidomain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1168,f218]) ).
fof(f9063,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X1,X0)) = multiplication(antidomain(addition(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f1168,f171]) ).
fof(f9066,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f1168,f1256]) ).
fof(f9070,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1168,f88]) ).
fof(f9071,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1168,f82]) ).
fof(f9072,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1168,f82]) ).
fof(f9073,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f1168,f231]) ).
fof(f9075,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f1168,f30]) ).
fof(f9081,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f8966]) ).
fof(f9082,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f8967]) ).
fof(f9105,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)],[f88,f8992]) ).
fof(f9106,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)],[f204,f9105]) ).
fof(f9107,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)],[f1168,f9106]) ).
fof(f9108,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)],[f1168,f9107]) ).
fof(f9109,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)],[f88,f9108]) ).
fof(f9110,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(X0,multiplication(addition(X2,X1),X3)),
inference(forward_demodulation,[status(thm)],[f186,f9109]) ).
fof(f9111,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)],[f88,f8993]) ).
fof(f9112,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)],[f155,f9111]) ).
fof(f9113,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)],[f1168,f9112]) ).
fof(f9114,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)],[f1168,f9113]) ).
fof(f9115,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)],[f88,f9114]) ).
fof(f9116,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f138,f9115]) ).
fof(f9165,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f9022]) ).
fof(f9166,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f724,f9165]) ).
fof(f9167,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f88,f9166]) ).
fof(f9168,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f88,f9167]) ).
fof(f9169,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X2,X1)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f88,f9023]) ).
fof(f9170,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X2,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f9169]) ).
fof(f9171,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)],[f29,f9036]) ).
fof(f9172,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)],[f9171]) ).
fof(f9179,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)],[f204,f9041]) ).
fof(f9180,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)],[f82,f9179]) ).
fof(f9181,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)],[f204,f9180]) ).
fof(f9182,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X1,X0),X2),X3),
inference(forward_demodulation,[status(thm)],[f1168,f9181]) ).
fof(f9183,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)],[f155,f9042]) ).
fof(f9184,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)],[f82,f9183]) ).
fof(f9185,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)],[f155,f9184]) ).
fof(f9186,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f1168,f9185]) ).
fof(f9187,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f88,f9043]) ).
fof(f9188,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f9044]) ).
fof(f9203,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f88,f9070]) ).
fof(f9204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f88,f9203]) ).
fof(f9205,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f88,f9071]) ).
fof(f9206,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f724,f9205]) ).
fof(f9207,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f88,f9072]) ).
fof(f9208,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f88,f9075]) ).
fof(f9209,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f724,f9208]) ).
fof(f9210,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f30,f9209]) ).
fof(f9211,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(resolution,[status(thm)],[f252,f43]) ).
fof(f9215,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)],[f192,f252]) ).
fof(f9216,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)],[f209,f252]) ).
fof(f9217,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)],[f217,f252]) ).
fof(f9218,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)],[f215,f252]) ).
fof(f9219,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)],[f218,f252]) ).
fof(f9220,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)],[f211,f252]) ).
fof(f9221,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)],[f182,f252]) ).
fof(f9223,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)],[f180,f252]) ).
fof(f9224,plain,
! [X0,X1] : addition(antidomain(zero),addition(antidomain(multiplication(domain(X0),domain(c(X0)))),X1)) = addition(antidomain(multiplication(domain(X0),domain(c(X0)))),X1),
inference(paramodulation,[status(thm)],[f7771,f252]) ).
fof(f9225,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)],[f53,f252]) ).
fof(f9226,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)],[f3792,f252]) ).
fof(f9227,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)],[f33,f252]) ).
fof(f9228,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)],[f7329,f252]) ).
fof(f9229,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)],[f171,f252]) ).
fof(f9230,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)],[f162,f252]) ).
fof(f9231,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)],[f121,f252]) ).
fof(f9234,plain,
! [X0,X1] : addition(antidomain(X0),addition(antidomain(multiplication(one,domain(X0))),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(paramodulation,[status(thm)],[f35,f252]) ).
fof(f9235,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)],[f7625,f252]) ).
fof(f9236,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)],[f2026,f252]) ).
fof(f9237,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)],[f147,f252]) ).
fof(f9238,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)],[f166,f252]) ).
fof(f9239,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)],[f177,f252]) ).
fof(f9240,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)],[f175,f252]) ).
fof(f9241,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)],[f136,f252]) ).
fof(f9242,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)],[f129,f252]) ).
fof(f9246,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)],[f252,f252]) ).
fof(f9247,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)],[f237,f252]) ).
fof(f9248,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)],[f260,f252]) ).
fof(f9262,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)],[f217,f252]) ).
fof(f9263,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)],[f192,f252]) ).
fof(f9264,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)],[f177,f252]) ).
fof(f9265,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)],[f147,f252]) ).
fof(f9267,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)],[f724,f252]) ).
fof(f9268,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)],[f703,f252]) ).
fof(f9270,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)],[f82,f252]) ).
fof(f9271,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)],[f82,f252]) ).
fof(f9273,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)],[f29,f252]) ).
fof(f9274,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)],[f29,f252]) ).
fof(f9276,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)],[f209,f252]) ).
fof(f9277,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)],[f215,f252]) ).
fof(f9279,plain,
! [X0,X1] : addition(antidomain(multiplication(c(domain(X0)),X0)),addition(antidomain(zero),X1)) = addition(antidomain(multiplication(c(domain(X0)),domain(X0))),X1),
inference(paramodulation,[status(thm)],[f3923,f252]) ).
fof(f9280,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)],[f3792,f252]) ).
fof(f9281,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)],[f33,f252]) ).
fof(f9285,plain,
! [X0,X1] : addition(antidomain(multiplication(one,X0)),addition(antidomain(domain(X0)),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(paramodulation,[status(thm)],[f35,f252]) ).
fof(f9287,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)],[f181,f252]) ).
fof(f9288,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)],[f631,f252]) ).
fof(f9289,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)],[f54,f252]) ).
fof(f9304,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)],[f252,f228]) ).
fof(f9305,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)],[f252,f227]) ).
fof(f9306,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)],[f252,f226]) ).
fof(f9307,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)],[f252,f218]) ).
fof(f9309,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)],[f252,f171]) ).
fof(f9311,plain,
! [X0,X1,X2,X3] : leq(antidomain(multiplication(X0,X1)),addition(X2,addition(antidomain(multiplication(X0,domain(X1))),X3))),
inference(paramodulation,[status(thm)],[f252,f1257]) ).
fof(f9314,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(paramodulation,[status(thm)],[f252,f1163]) ).
fof(f9316,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)],[f252,f88]) ).
fof(f9317,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)],[f252,f82]) ).
fof(f9318,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)],[f252,f82]) ).
fof(f9319,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)],[f252,f231]) ).
fof(f9320,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)],[f252,f43]) ).
fof(f9321,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)],[f252,f30]) ).
fof(f9325,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)],[f293,f9221]) ).
fof(f9326,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)],[f181,f9325]) ).
fof(f9327,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)],[f181,f9326]) ).
fof(f9334,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)],[f293,f9223]) ).
fof(f9335,plain,
! [X0,X1] : addition(one,addition(antidomain(multiplication(domain(X0),domain(c(X0)))),X1)) = addition(antidomain(multiplication(domain(X0),domain(c(X0)))),X1),
inference(forward_demodulation,[status(thm)],[f293,f9224]) ).
fof(f9336,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)],[f631,f9225]) ).
fof(f9337,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)],[f631,f9336]) ).
fof(f9338,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)],[f33,f9227]) ).
fof(f9339,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)],[f33,f9338]) ).
fof(f9340,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)],[f293,f9228]) ).
fof(f9341,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)],[f181,f9340]) ).
fof(f9342,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)],[f181,f9341]) ).
fof(f9343,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)],[f293,f9231]) ).
fof(f9356,plain,
! [X0,X1] : addition(antidomain(X0),addition(antidomain(domain(X0)),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f35,f9234]) ).
fof(f9357,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f52,f9356]) ).
fof(f9358,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f35,f9357]) ).
fof(f9359,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f52,f9358]) ).
fof(f9360,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)],[f293,f9235]) ).
fof(f9361,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)],[f181,f9360]) ).
fof(f9362,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)],[f181,f9361]) ).
fof(f9363,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)],[f293,f9241]) ).
fof(f9364,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)],[f293,f9242]) ).
fof(f9384,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)],[f181,f9246]) ).
fof(f9385,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)],[f252,f9384]) ).
fof(f9386,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)],[f181,f9385]) ).
fof(f9387,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)],[f181,f9247]) ).
fof(f9388,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)],[f237,f9387]) ).
fof(f9389,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)],[f181,f9388]) ).
fof(f9390,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),c(multiplication(X0,domain(X1)))) = c(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f260,f9248]) ).
fof(f9405,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)],[f217,f9262]) ).
fof(f9406,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)],[f217,f9263]) ).
fof(f9407,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)],[f177,f9264]) ).
fof(f9408,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)],[f177,f9265]) ).
fof(f9410,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)],[f724,f9267]) ).
fof(f9411,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)],[f1168,f9268]) ).
fof(f9416,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)],[f82,f9276]) ).
fof(f9417,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)],[f52,f9416]) ).
fof(f9418,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)],[f209,f9417]) ).
fof(f9419,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)],[f82,f9277]) ).
fof(f9420,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)],[f52,f9419]) ).
fof(f9421,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)],[f215,f9420]) ).
fof(f9428,plain,
! [X0,X1] : addition(antidomain(zero),addition(X0,antidomain(multiplication(c(domain(X1)),X1)))) = addition(antidomain(multiplication(c(domain(X1)),domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f82,f9279]) ).
fof(f9429,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(multiplication(c(domain(X1)),X1)))) = addition(antidomain(multiplication(c(domain(X1)),domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f293,f9428]) ).
fof(f9430,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(multiplication(domain(c(X1)),X1)))) = addition(antidomain(multiplication(c(domain(X1)),domain(X1))),X0),
inference(forward_demodulation,[status(thm)],[f633,f9429]) ).
fof(f9431,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(multiplication(domain(c(X1)),X1)))) = addition(antidomain(zero),X0),
inference(forward_demodulation,[status(thm)],[f3923,f9430]) ).
fof(f9432,plain,
! [X0,X1] : addition(one,addition(X0,antidomain(multiplication(domain(c(X1)),X1)))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f293,f9431]) ).
fof(f9433,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)],[f82,f9280]) ).
fof(f9434,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)],[f52,f9433]) ).
fof(f9435,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)],[f181,f9434]) ).
fof(f9436,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(antidomain(c(X0)),X0)))) = addition(antidomain(domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f3792,f9435]) ).
fof(f9437,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(antidomain(c(X0)),X0)))) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f52,f9436]) ).
fof(f9438,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)],[f33,f9281]) ).
fof(f9439,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)],[f33,f9438]) ).
fof(f9459,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)],[f82,f9285]) ).
fof(f9460,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(multiplication(one,X0)))) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f52,f9459]) ).
fof(f9461,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(X0))) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f35,f9460]) ).
fof(f9462,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(multiplication(one,domain(X0))),X1),
inference(forward_demodulation,[status(thm)],[f82,f9461]) ).
fof(f9463,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(antidomain(domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f35,f9462]) ).
fof(f9464,plain,
! [X0,X1] : addition(antidomain(X0),addition(c(X0),X1)) = addition(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f52,f9463]) ).
fof(f9471,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)],[f181,f9287]) ).
fof(f9472,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)],[f631,f9288]) ).
fof(f9473,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)],[f82,f9289]) ).
fof(f9474,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)],[f54,f9473]) ).
fof(f9506,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)],[f9305]) ).
fof(f9507,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)],[f9306]) ).
fof(f9508,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(multiplication(X0,X1)),coantidomain(addition(antidomain(multiplication(X0,domain(X1))),X2))),
inference(forward_demodulation,[status(thm)],[f48,f9307]) ).
fof(f9509,plain,
! [X0,X1,X2] : zero = multiplication(antidomain(addition(antidomain(multiplication(X0,domain(X1))),X2)),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f44,f9309]) ).
fof(f9510,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)],[f88,f9316]) ).
fof(f9511,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)],[f82,f9510]) ).
fof(f9512,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)],[f88,f9511]) ).
fof(f9513,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)],[f88,f9317]) ).
fof(f9514,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)],[f88,f9318]) ).
fof(f9515,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)],[f82,f9514]) ).
fof(f9516,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)],[f252,f9515]) ).
fof(f9517,plain,
! [X0,X1,X2] : leq(antidomain(multiplication(X0,X1)),addition(antidomain(multiplication(X0,domain(X1))),X2)),
inference(trivial_equality_resolution,[status(thm)],[f9320]) ).
fof(f9518,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)],[f88,f9321]) ).
fof(f9519,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)],[f88,f9518]) ).
fof(f9521,plain,
! [X0,X1] : multiplication(antidomain(c(X0)),domain_difference(antidomain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f1096,f1349]) ).
fof(f9522,plain,
! [X0,X1] : multiplication(domain(c(X0)),domain_difference(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f633,f1349]) ).
fof(f9523,plain,
! [X0,X1,X2] : multiplication(backward_box(X0,X1),domain_difference(backward_diamond(X0,c(X1)),X2)) = zero,
inference(paramodulation,[status(thm)],[f57,f1349]) ).
fof(f9524,plain,
! [X0,X1,X2] : multiplication(forward_box(X0,X1),domain_difference(forward_diamond(X0,c(X1)),X2)) = zero,
inference(paramodulation,[status(thm)],[f56,f1349]) ).
fof(f9536,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)],[f1349,f252]) ).
fof(f9537,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)],[f1349,f254]) ).
fof(f9538,plain,
! [X0,X1] : leq(antidomain(zero),antidomain(multiplication(c(X0),domain(domain_difference(X0,X1))))),
inference(paramodulation,[status(thm)],[f1349,f238]) ).
fof(f9539,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)],[f1349,f204]) ).
fof(f9540,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)],[f1349,f204]) ).
fof(f9542,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)],[f1349,f196]) ).
fof(f9543,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)],[f1349,f196]) ).
fof(f9545,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)],[f1349,f189]) ).
fof(f9546,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)],[f1349,f189]) ).
fof(f9547,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)],[f1349,f186]) ).
fof(f9548,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)],[f1349,f186]) ).
fof(f9549,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)],[f1349,f155]) ).
fof(f9550,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)],[f1349,f155]) ).
fof(f9551,plain,
! [X0,X1] : multiplication(c(X0),addition(domain_difference(X0,X1),one)) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f1349,f177]) ).
fof(f9552,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = addition(c(X0),zero),
inference(paramodulation,[status(thm)],[f1349,f147]) ).
fof(f9553,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = addition(multiplication(c(X0),X2),zero),
inference(paramodulation,[status(thm)],[f1349,f138]) ).
fof(f9554,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = addition(zero,multiplication(c(X0),X1)),
inference(paramodulation,[status(thm)],[f1349,f138]) ).
fof(f9557,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)],[f1349,f309]) ).
fof(f9558,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)],[f1349,f237]) ).
fof(f9559,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)],[f1349,f37]) ).
fof(f9560,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)],[f1349,f37]) ).
fof(f9561,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = addition(multiplication(c(X0),X1),zero),
inference(paramodulation,[status(thm)],[f1349,f36]) ).
fof(f9562,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = addition(zero,multiplication(c(X0),X2)),
inference(paramodulation,[status(thm)],[f1349,f36]) ).
fof(f9563,plain,
! [X0,X1,X2] : multiplication(c(X0),multiplication(domain_difference(X0,X1),X2)) = multiplication(zero,X2),
inference(paramodulation,[status(thm)],[f1349,f33]) ).
fof(f9567,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)],[f293,f9536]) ).
fof(f9568,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)],[f38,f9537]) ).
fof(f9569,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)],[f293,f9568]) ).
fof(f9570,plain,
! [X0,X1,X2] : one = antidomain(multiplication(X0,multiplication(c(X1),domain(domain_difference(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f1215,f9569]) ).
fof(f9571,plain,
! [X0,X1] : leq(one,antidomain(multiplication(c(X0),domain(domain_difference(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f293,f9538]) ).
fof(f9572,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)],[f82,f9539]) ).
fof(f9573,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)],[f65,f9572]) ).
fof(f9574,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)],[f65,f9540]) ).
fof(f9578,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)],[f38,f9542]) ).
fof(f9579,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)],[f31,f9578]) ).
fof(f9580,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)],[f65,f9543]) ).
fof(f9583,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)],[f31,f9545]) ).
fof(f9584,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)],[f38,f9546]) ).
fof(f9585,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)],[f65,f9584]) ).
fof(f9586,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),X1),domain_difference(X0,X2)) = multiplication(X1,domain_difference(X0,X2)),
inference(forward_demodulation,[status(thm)],[f31,f9547]) ).
fof(f9587,plain,
! [X0,X1,X2] : multiplication(addition(X0,c(X1)),domain_difference(X1,X2)) = multiplication(X0,domain_difference(X1,X2)),
inference(forward_demodulation,[status(thm)],[f65,f9548]) ).
fof(f9588,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)],[f82,f9549]) ).
fof(f9589,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)],[f65,f9588]) ).
fof(f9590,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)],[f65,f9550]) ).
fof(f9591,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = addition(c(X0),zero),
inference(forward_demodulation,[status(thm)],[f29,f9551]) ).
fof(f9592,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = c(X0),
inference(forward_demodulation,[status(thm)],[f31,f9591]) ).
fof(f9593,plain,
! [X0,X1] : multiplication(c(X0),addition(one,domain_difference(X0,X1))) = c(X0),
inference(forward_demodulation,[status(thm)],[f31,f9552]) ).
fof(f9594,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = multiplication(c(X0),X2),
inference(forward_demodulation,[status(thm)],[f31,f9553]) ).
fof(f9595,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f65,f9554]) ).
fof(f9598,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)],[f363,f9557]) ).
fof(f9599,plain,
! [X0,X1] : one = coantidomain(multiplication(codomain(c(X0)),domain_difference(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1213,f9598]) ).
fof(f9600,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)],[f293,f9558]) ).
fof(f9601,plain,
! [X0,X1] : one = antidomain(multiplication(c(X0),domain(domain_difference(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1215,f9600]) ).
fof(f9602,plain,
! [X0,X1,X2] : multiplication(addition(X0,c(X1)),domain_difference(X1,X2)) = multiplication(X0,domain_difference(X1,X2)),
inference(forward_demodulation,[status(thm)],[f31,f9559]) ).
fof(f9603,plain,
! [X0,X1,X2] : multiplication(addition(c(X0),X1),domain_difference(X0,X2)) = multiplication(X1,domain_difference(X0,X2)),
inference(forward_demodulation,[status(thm)],[f65,f9560]) ).
fof(f9604,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(X1,domain_difference(X0,X2))) = multiplication(c(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f9561]) ).
fof(f9605,plain,
! [X0,X1,X2] : multiplication(c(X0),addition(domain_difference(X0,X1),X2)) = multiplication(c(X0),X2),
inference(forward_demodulation,[status(thm)],[f65,f9562]) ).
fof(f9606,plain,
! [X0,X1,X2] : multiplication(c(X0),multiplication(domain_difference(X0,X1),X2)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f9563]) ).
fof(f9607,plain,
! [X0] : addition(c(X0),antidomain(c(X0))) = one,
inference(forward_demodulation,[status(thm)],[f181,f284]) ).
fof(f9610,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(c(backward_diamond(X0,c(X1))))) = one,
inference(paramodulation,[status(thm)],[f57,f9607]) ).
fof(f9611,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(c(forward_diamond(X0,c(X1))))) = one,
inference(paramodulation,[status(thm)],[f56,f9607]) ).
fof(f9616,plain,
! [X0,X1] : addition(c(backward_diamond(X0,c(X1))),antidomain(backward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f57,f9607]) ).
fof(f9617,plain,
! [X0,X1] : addition(c(forward_diamond(X0,c(X1))),antidomain(forward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f56,f9607]) ).
fof(f9620,plain,
! [X0] : multiplication(one,c(X0)) = multiplication(c(X0),c(X0)),
inference(paramodulation,[status(thm)],[f9607,f215]) ).
fof(f9626,plain,
! [X0,X1] :
( addition(X0,one) != antidomain(c(X1))
| leq(addition(X0,c(X1)),antidomain(c(X1))) ),
inference(paramodulation,[status(thm)],[f9607,f228]) ).
fof(f9627,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)],[f9607,f227]) ).
fof(f9628,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)],[f9607,f226]) ).
fof(f9629,plain,
! [X0] : multiplication(one,coantidomain(antidomain(c(X0)))) = multiplication(c(X0),coantidomain(antidomain(c(X0)))),
inference(paramodulation,[status(thm)],[f9607,f218]) ).
fof(f9630,plain,
! [X0] : multiplication(one,coantidomain(c(X0))) = multiplication(antidomain(c(X0)),coantidomain(c(X0))),
inference(paramodulation,[status(thm)],[f9607,f211]) ).
fof(f9631,plain,
! [X0] : multiplication(antidomain(antidomain(c(X0))),one) = multiplication(antidomain(antidomain(c(X0))),c(X0)),
inference(paramodulation,[status(thm)],[f9607,f171]) ).
fof(f9632,plain,
! [X0] : multiplication(antidomain(c(X0)),one) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f9607,f162]) ).
fof(f9638,plain,
! [X0,X1] : addition(antidomain(c(X0)),addition(c(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f9607,f88]) ).
fof(f9639,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(c(X0)),X1)) = addition(X1,one),
inference(paramodulation,[status(thm)],[f9607,f82]) ).
fof(f9640,plain,
! [X0,X1] : addition(X0,one) = addition(antidomain(c(X1)),addition(X0,c(X1))),
inference(paramodulation,[status(thm)],[f9607,f82]) ).
fof(f9641,plain,
! [X0] :
( one != c(X0)
| leq(antidomain(c(X0)),c(X0)) ),
inference(paramodulation,[status(thm)],[f9607,f231]) ).
fof(f9642,plain,
! [X0] :
( one != antidomain(c(X0))
| leq(c(X0),antidomain(c(X0))) ),
inference(paramodulation,[status(thm)],[f9607,f43]) ).
fof(f9643,plain,
! [X0,X1] : addition(c(X0),addition(antidomain(c(X0)),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f9607,f30]) ).
fof(f9648,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f57,f9610]) ).
fof(f9649,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f56,f9611]) ).
fof(f9656,plain,
! [X0,X1] : addition(antidomain(backward_box(X0,X1)),c(backward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f29,f9616]) ).
fof(f9657,plain,
! [X0,X1] : addition(antidomain(backward_box(X0,X1)),backward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f57,f9656]) ).
fof(f9658,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f29,f9657]) ).
fof(f9659,plain,
! [X0,X1] : addition(antidomain(forward_box(X0,X1)),c(forward_diamond(X0,c(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f29,f9617]) ).
fof(f9660,plain,
! [X0,X1] : addition(antidomain(forward_box(X0,X1)),forward_box(X0,X1)) = one,
inference(forward_demodulation,[status(thm)],[f56,f9659]) ).
fof(f9661,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f29,f9660]) ).
fof(f9667,plain,
! [X0] : c(X0) = multiplication(c(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f35,f9620]) ).
fof(f9680,plain,
! [X0,X1] :
( X0 != multiplication(X0,antidomain(c(X1)))
| leq(multiplication(X0,c(X1)),multiplication(X0,antidomain(c(X1)))) ),
inference(forward_demodulation,[status(thm)],[f34,f9627]) ).
fof(f9681,plain,
! [X0,X1] :
( X1 != multiplication(antidomain(c(X0)),X1)
| leq(multiplication(c(X0),X1),multiplication(antidomain(c(X0)),X1)) ),
inference(forward_demodulation,[status(thm)],[f35,f9628]) ).
fof(f9682,plain,
! [X0] : coantidomain(antidomain(c(X0))) = multiplication(c(X0),coantidomain(antidomain(c(X0)))),
inference(forward_demodulation,[status(thm)],[f35,f9629]) ).
fof(f9683,plain,
! [X0] : coantidomain(c(X0)) = multiplication(antidomain(c(X0)),coantidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f35,f9630]) ).
fof(f9684,plain,
! [X0] : antidomain(antidomain(c(X0))) = multiplication(antidomain(antidomain(c(X0))),c(X0)),
inference(forward_demodulation,[status(thm)],[f34,f9631]) ).
fof(f9685,plain,
! [X0] : domain(c(X0)) = multiplication(antidomain(antidomain(c(X0))),c(X0)),
inference(forward_demodulation,[status(thm)],[f47,f9684]) ).
fof(f9686,plain,
! [X0] : domain(c(X0)) = multiplication(domain(c(X0)),c(X0)),
inference(forward_demodulation,[status(thm)],[f47,f9685]) ).
fof(f9687,plain,
! [X0] : domain(c(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f3792,f9686]) ).
fof(f9688,plain,
! [X0] : antidomain(c(X0)) = multiplication(antidomain(c(X0)),antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f34,f9632]) ).
fof(f9691,plain,
! [X0,X1] : addition(c(X0),addition(X1,antidomain(c(X0)))) = addition(one,X1),
inference(forward_demodulation,[status(thm)],[f82,f9638]) ).
fof(f9692,plain,
! [X0,X1] : addition(X0,one) = addition(c(X1),addition(antidomain(c(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f82,f9640]) ).
fof(f9695,plain,
! [X0] : forward_box(X0,zero) = c(X0),
inference(backward_demodulation,[status(thm)],[f9687,f1005]) ).
fof(f9696,plain,
! [X0] : c(X0) = c(domain(X0)),
inference(backward_demodulation,[status(thm)],[f9687,f633]) ).
fof(f9697,plain,
! [X0] : domain(antidomain(c(X0))) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f1096,f9687]) ).
fof(f9698,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f57,f9687]) ).
fof(f9699,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f56,f9687]) ).
fof(f9703,plain,
! [X0] : multiplication(c(X0),c(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f9687,f7771]) ).
fof(f9704,plain,
! [X0] : forward_diamond(c(X0),antidomain(c(X0))) = zero,
inference(paramodulation,[status(thm)],[f9687,f7336]) ).
fof(f9713,plain,
! [X0] : leq(c(X0),antidomain(c(c(X0)))),
inference(paramodulation,[status(thm)],[f9687,f3906]) ).
fof(f9715,plain,
! [X0] : c(X0) = multiplication(c(X0),c(X0)),
inference(paramodulation,[status(thm)],[f9687,f3792]) ).
fof(f9718,plain,
! [X0,X1] : leq(domain_difference(c(X0),X1),c(X0)),
inference(paramodulation,[status(thm)],[f9687,f3292]) ).
fof(f9722,plain,
! [X0] : addition(c(X0),c(c(X0))) = one,
inference(paramodulation,[status(thm)],[f9687,f657]) ).
fof(f9725,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)],[f9687,f60]) ).
fof(f9726,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)],[f9687,f60]) ).
fof(f9727,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)],[f9687,f60]) ).
fof(f9728,plain,
! [X0,X1] : forward_diamond(X0,c(X1)) = domain(multiplication(X0,c(X1))),
inference(paramodulation,[status(thm)],[f9687,f54]) ).
fof(f9729,plain,
! [X0,X1] : domain_difference(c(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f9687,f53]) ).
fof(f9733,plain,
! [X0] : c(c(X0)) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f631,f9697]) ).
fof(f9734,plain,
! [X0] : c(c(X0)) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f1096,f9733]) ).
fof(f9735,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f57,f9698]) ).
fof(f9736,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f56,f9699]) ).
fof(f9745,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)],[f9687,f9725]) ).
fof(f9746,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)],[f9687,f9745]) ).
fof(f9747,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)],[f9687,f9746]) ).
fof(f9748,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)],[f9687,f9726]) ).
fof(f9749,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)],[f9687,f9748]) ).
fof(f9750,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)],[f9687,f9749]) ).
fof(f9751,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)],[f9687,f9727]) ).
fof(f9752,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)],[f9687,f9751]) ).
fof(f9753,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)],[f9687,f9752]) ).
fof(f9777,plain,
! [X0] : c(domain(X0)) = c(antidomain(c(X0))),
inference(paramodulation,[status(thm)],[f181,f9696]) ).
fof(f9778,plain,
! [X0] : c(antidomain(X0)) = c(c(X0)),
inference(paramodulation,[status(thm)],[f631,f9696]) ).
fof(f9779,plain,
! [X0,X1] : c(multiplication(X0,domain(X1))) = c(forward_diamond(X0,X1)),
inference(paramodulation,[status(thm)],[f54,f9696]) ).
fof(f9785,plain,
! [X0,X1] : multiplication(c(X0),domain_difference(domain(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f9696,f1349]) ).
fof(f9788,plain,
! [X0] : forward_box(antidomain(c(X0)),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f9696,f7358]) ).
fof(f9789,plain,
! [X0] : forward_diamond(c(X0),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f9696,f7335]) ).
fof(f9805,plain,
! [X0] : forward_box(c(c(X0)),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f9696,f513]) ).
fof(f9806,plain,
! [X0] : multiplication(c(X0),domain(domain(X0))) = zero,
inference(paramodulation,[status(thm)],[f9696,f182]) ).
fof(f9807,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = c(backward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f9696,f57]) ).
fof(f9808,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = c(forward_diamond(X0,c(X1))),
inference(paramodulation,[status(thm)],[f9696,f56]) ).
fof(f9810,plain,
! [X0] : c(X0) = c(antidomain(c(X0))),
inference(forward_demodulation,[status(thm)],[f9696,f9777]) ).
fof(f9811,plain,
! [X0] : c(X0) = antidomain(c(c(X0))),
inference(forward_demodulation,[status(thm)],[f1096,f9810]) ).
fof(f9812,plain,
! [X0] : antidomain(c(X0)) = c(c(X0)),
inference(forward_demodulation,[status(thm)],[f1096,f9778]) ).
fof(f9820,plain,
! [X0] : forward_diamond(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f181,f9789]) ).
fof(f9830,plain,
! [X0] : multiplication(c(X0),antidomain(c(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f181,f9806]) ).
fof(f9831,plain,
! [X0,X1] : backward_box(X0,domain(X1)) = backward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f57,f9807]) ).
fof(f9832,plain,
! [X0,X1] : forward_box(X0,domain(X1)) = forward_box(X0,X1),
inference(forward_demodulation,[status(thm)],[f56,f9808]) ).
fof(f9837,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(c(backward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f57,f9734]) ).
fof(f9838,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(c(forward_diamond(X0,c(X1)))),
inference(paramodulation,[status(thm)],[f56,f9734]) ).
fof(f9844,plain,
! [X0,X1] : multiplication(antidomain(c(X0)),domain_difference(c(X0),X1)) = zero,
inference(paramodulation,[status(thm)],[f9734,f1349]) ).
fof(f9847,plain,
! [X0] : forward_box(antidomain(antidomain(c(X0))),c(X0)) = one,
inference(paramodulation,[status(thm)],[f9734,f7358]) ).
fof(f9865,plain,
! [X0,X1] : backward_box(X0,c(X1)) = c(backward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f9734,f57]) ).
fof(f9866,plain,
! [X0,X1] : forward_box(X0,c(X1)) = c(forward_diamond(X0,antidomain(c(X1)))),
inference(paramodulation,[status(thm)],[f9734,f56]) ).
fof(f9875,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(backward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f57,f9837]) ).
fof(f9876,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(forward_box(X0,X1)),
inference(forward_demodulation,[status(thm)],[f56,f9838]) ).
fof(f9886,plain,
! [X0] : forward_box(domain(c(X0)),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f47,f9847]) ).
fof(f9887,plain,
! [X0] : forward_box(c(X0),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f9687,f9886]) ).
fof(f9902,plain,
! [X0,X1] : multiplication(backward_box(X0,X1),c(backward_box(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f9735,f7771]) ).
fof(f9903,plain,
! [X0,X1] : forward_diamond(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f9735,f7336]) ).
fof(f9906,plain,
! [X0,X1] : leq(domain(backward_box(X0,X1)),codomain(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f9735,f6542]) ).
fof(f9907,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(domain(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f9735,f6542]) ).
fof(f9910,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(backward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f9735,f4169]) ).
fof(f9912,plain,
! [X0,X1] : leq(backward_box(X0,X1),antidomain(c(backward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f9735,f3906]) ).
fof(f9913,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f9735,f2278]) ).
fof(f9914,plain,
! [X0,X1] : backward_box(X0,X1) = multiplication(backward_box(X0,X1),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f9735,f3792]) ).
fof(f9915,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f9735,f2179]) ).
fof(f9917,plain,
! [X0,X1,X2] : leq(domain_difference(backward_box(X0,X1),X2),backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f9735,f3292]) ).
fof(f9918,plain,
! [X0,X1,X2] : leq(backward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f9735,f1740]) ).
fof(f9921,plain,
! [X0,X1] : addition(backward_box(X0,X1),c(backward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f9735,f657]) ).
fof(f9923,plain,
! [X0,X1] : domain(backward_box(X0,X1)) = antidomain(c(backward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f9735,f181]) ).
fof(f9924,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)],[f9735,f60]) ).
fof(f9925,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)],[f9735,f60]) ).
fof(f9926,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)],[f9735,f60]) ).
fof(f9927,plain,
! [X0,X1,X2] : forward_diamond(X0,backward_box(X1,X2)) = domain(multiplication(X0,backward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f9735,f54]) ).
fof(f9928,plain,
! [X0,X1,X2] : domain_difference(backward_box(X0,X1),X2) = multiplication(backward_box(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f9735,f53]) ).
fof(f9929,plain,
! [X0,X1] : addition(antidomain(backward_box(X0,X1)),backward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f9735,f283]) ).
fof(f9931,plain,
! [X0,X1] : c(backward_box(X0,X1)) = antidomain(backward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f9735,f52]) ).
fof(f9937,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f9735,f9906]) ).
fof(f9938,plain,
! [X0,X1] : leq(backward_box(X0,X1),codomain(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f9735,f9907]) ).
fof(f9940,plain,
! [X0,X1] : backward_box(X0,X1) = antidomain(c(backward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f9735,f9923]) ).
fof(f9941,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)],[f9735,f9924]) ).
fof(f9942,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)],[f9735,f9941]) ).
fof(f9943,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)],[f9735,f9942]) ).
fof(f9944,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)],[f9735,f9925]) ).
fof(f9945,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)],[f9735,f9944]) ).
fof(f9946,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)],[f9735,f9945]) ).
fof(f9947,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)],[f9735,f9926]) ).
fof(f9948,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)],[f9735,f9947]) ).
fof(f9949,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)],[f9735,f9948]) ).
fof(f9950,plain,
! [X0,X1] : addition(backward_box(X0,X1),antidomain(backward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f29,f9929]) ).
fof(f9958,plain,
! [X0,X1] : multiplication(forward_box(X0,X1),c(forward_box(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f9736,f7771]) ).
fof(f9959,plain,
! [X0,X1] : forward_diamond(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = zero,
inference(paramodulation,[status(thm)],[f9736,f7336]) ).
fof(f9962,plain,
! [X0,X1] : leq(domain(forward_box(X0,X1)),codomain(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f9736,f6542]) ).
fof(f9963,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(domain(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f9736,f6542]) ).
fof(f9966,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(forward_box(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f9736,f4169]) ).
fof(f9968,plain,
! [X0,X1] : leq(forward_box(X0,X1),antidomain(c(forward_box(X0,X1)))),
inference(paramodulation,[status(thm)],[f9736,f3906]) ).
fof(f9969,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f9736,f2278]) ).
fof(f9970,plain,
! [X0,X1] : forward_box(X0,X1) = multiplication(forward_box(X0,X1),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f9736,f3792]) ).
fof(f9971,plain,
! [X0,X1,X2] : X0 = addition(X0,multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f9736,f2179]) ).
fof(f9973,plain,
! [X0,X1,X2] : leq(domain_difference(forward_box(X0,X1),X2),forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f9736,f3292]) ).
fof(f9974,plain,
! [X0,X1,X2] : leq(forward_box(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f9736,f1740]) ).
fof(f9977,plain,
! [X0,X1] : addition(forward_box(X0,X1),c(forward_box(X0,X1))) = one,
inference(paramodulation,[status(thm)],[f9736,f657]) ).
fof(f9979,plain,
! [X0,X1] : domain(forward_box(X0,X1)) = antidomain(c(forward_box(X0,X1))),
inference(paramodulation,[status(thm)],[f9736,f181]) ).
fof(f9980,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)],[f9736,f60]) ).
fof(f9981,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)],[f9736,f60]) ).
fof(f9982,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)],[f9736,f60]) ).
fof(f9983,plain,
! [X0,X1,X2] : forward_diamond(X0,forward_box(X1,X2)) = domain(multiplication(X0,forward_box(X1,X2))),
inference(paramodulation,[status(thm)],[f9736,f54]) ).
fof(f9984,plain,
! [X0,X1,X2] : domain_difference(forward_box(X0,X1),X2) = multiplication(forward_box(X0,X1),antidomain(X2)),
inference(paramodulation,[status(thm)],[f9736,f53]) ).
fof(f9985,plain,
! [X0,X1] : addition(antidomain(forward_box(X0,X1)),forward_box(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f9736,f283]) ).
fof(f9987,plain,
! [X0,X1] : c(forward_box(X0,X1)) = antidomain(forward_box(X0,X1)),
inference(paramodulation,[status(thm)],[f9736,f52]) ).
fof(f9994,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f9736,f9962]) ).
fof(f9995,plain,
! [X0,X1] : leq(forward_box(X0,X1),codomain(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f9736,f9963]) ).
fof(f9997,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(c(forward_box(X0,X1))),
inference(forward_demodulation,[status(thm)],[f9736,f9979]) ).
fof(f9998,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)],[f9736,f9980]) ).
fof(f9999,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)],[f9736,f9998]) ).
fof(f10000,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)],[f9736,f9999]) ).
fof(f10001,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)],[f9736,f9981]) ).
fof(f10002,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)],[f9736,f10001]) ).
fof(f10003,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)],[f9736,f10002]) ).
fof(f10004,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)],[f9736,f9982]) ).
fof(f10005,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)],[f9736,f10004]) ).
fof(f10006,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)],[f9736,f10005]) ).
fof(f10007,plain,
! [X0,X1] : addition(forward_box(X0,X1),antidomain(forward_box(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f29,f9985]) ).
fof(f10012,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(antidomain(forward_box(X0,X1)),domain(forward_box(X0,X1))) ),
inference(paramodulation,[status(thm)],[f9736,f288]) ).
fof(f10013,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(antidomain(backward_box(X0,X1)),domain(backward_box(X0,X1))) ),
inference(paramodulation,[status(thm)],[f9735,f288]) ).
fof(f10014,plain,
! [X0] :
( one != c(X0)
| leq(antidomain(c(X0)),domain(c(X0))) ),
inference(paramodulation,[status(thm)],[f9687,f288]) ).
fof(f10015,plain,
! [X0] :
( one != antidomain(c(X0))
| leq(antidomain(domain(X0)),domain(domain(X0))) ),
inference(paramodulation,[status(thm)],[f181,f288]) ).
fof(f10016,plain,
! [X0] :
( one != c(X0)
| leq(antidomain(antidomain(X0)),domain(antidomain(X0))) ),
inference(paramodulation,[status(thm)],[f631,f288]) ).
fof(f10017,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(antidomain(multiplication(X0,domain(X1))),domain(multiplication(X0,domain(X1)))) ),
inference(paramodulation,[status(thm)],[f54,f288]) ).
fof(f10018,plain,
( one != zero
| leq(antidomain(zero),domain(zero)) ),
inference(paramodulation,[status(thm)],[f307,f288]) ).
fof(f10019,plain,
( one != one
| leq(antidomain(one),domain(one)) ),
inference(paramodulation,[status(thm)],[f290,f288]) ).
fof(f10022,plain,
! [X0,X1] :
( one != forward_box(X0,X1)
| leq(antidomain(forward_box(X0,X1)),forward_box(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f9736,f10012]) ).
fof(f10023,plain,
! [X0,X1] :
( one != backward_box(X0,X1)
| leq(antidomain(backward_box(X0,X1)),backward_box(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f9735,f10013]) ).
fof(f10024,plain,
! [X0] :
( one != c(X0)
| leq(antidomain(c(X0)),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f9687,f10014]) ).
fof(f10025,plain,
! [X0] :
( one != antidomain(c(X0))
| leq(c(X0),domain(domain(X0))) ),
inference(forward_demodulation,[status(thm)],[f52,f10015]) ).
fof(f10026,plain,
! [X0] :
( one != antidomain(c(X0))
| leq(c(X0),antidomain(c(X0))) ),
inference(forward_demodulation,[status(thm)],[f181,f10025]) ).
fof(f10027,plain,
! [X0] :
( one != c(X0)
| leq(domain(X0),domain(antidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f47,f10016]) ).
fof(f10028,plain,
! [X0] :
( one != c(X0)
| leq(domain(X0),c(X0)) ),
inference(forward_demodulation,[status(thm)],[f631,f10027]) ).
fof(f10029,plain,
! [X0,X1] :
( one != forward_diamond(X0,X1)
| leq(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f54,f10017]) ).
fof(f10030,definition,
( sQ11_spl
<=> leq(antidomain(zero),domain(zero)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f10031,plain,
( ~ sQ11_spl
| leq(antidomain(zero),domain(zero)) ),
inference(component_clause,[status(thm)],[f10030]) ).
fof(f10033,definition,
( sQ12_spl
<=> one = zero ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f10036,plain,
( ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f10018,f10030,f10033]) ).
fof(f10037,definition,
( sQ13_spl
<=> leq(antidomain(one),domain(one)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f10040,plain,
( ~ sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f10019,f10037,f1400]) ).
fof(f10043,plain,
( ~ sQ11_spl
| leq(one,domain(zero)) ),
inference(forward_demodulation,[status(thm)],[f293,f10031]) ).
fof(f10044,plain,
( ~ sQ11_spl
| leq(one,zero) ),
inference(forward_demodulation,[status(thm)],[f307,f10043]) ).
fof(f10045,plain,
( ~ sQ11_spl
| addition(one,zero) = zero ),
inference(resolution,[status(thm)],[f10044,f42]) ).
fof(f10046,plain,
( ~ sQ11_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f31,f10045]) ).
fof(f10108,plain,
! [X0] :
( ~ sQ11_spl
| multiplication(zero,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f10046,f35]) ).
fof(f10342,plain,
! [X0] :
( ~ sQ11_spl
| zero = X0 ),
inference(paramodulation,[status(thm)],[f39,f10108]) ).
fof(f10408,plain,
! [X0,X1] :
( ~ sQ11_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f10342,f10342]) ).
fof(f10410,plain,
! [X0,X1] :
( ~ sQ11_spl
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f10342,f225]) ).
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
| sQ13_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE174+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 22:49:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 7.33/1.50 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 7.33/1.50 % SZS output start Saturation for theBenchmark
% See solution above
% 2.66/1.63 % Elapsed time: 1.265052 seconds
% 2.66/1.63 % CPU time: 8.914042 seconds
% 2.66/1.63 % Total memory used: 105.425 MB
% 2.66/1.63 % Net memory used: 100.471 MB
%------------------------------------------------------------------------------