%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : CAT001-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:07:37 PM UTC 2026
% Result : Satisfiable 28.68s 4.28s
% Output : Saturation 8.97s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : codomain(domain(X)) = domain(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : domain(codomain(X)) = codomain(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : compose(domain(X),X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : compose(X,codomain(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : ifeq(codomain(X),domain(Y),domain(compose(X,Y)),domain(X)) = domain(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : ifeq(codomain(X),domain(Y),codomain(compose(X,Y)),codomain(Y)) = codomain(Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Y,Z,X] : ifeq(codomain(Y),domain(Z),ifeq(codomain(X),domain(Y),compose(X,compose(Y,Z)),compose(compose(X,Y),Z)),compose(compose(X,Y),Z)) = compose(compose(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
! [Z,X,Y] : ifeq(codomain(Z),domain(compose(a,b)),ifeq(codomain(X),domain(compose(a,b)),ifeq(compose(Z,compose(a,b)),Y,ifeq(compose(X,compose(a,b)),Y,X,Z),Z),Z),Z) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
codomain(a) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
codomain(a) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
compose(a,h) = compose(a,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : codomain(domain(X0)) = domain(X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0] : domain(codomain(X0)) = codomain(X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0] : compose(domain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0] : compose(X0,codomain(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(X0,X1)),domain(X0)) = domain(X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,X1)),codomain(X1)) = codomain(X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(X0,X1)),compose(compose(X2,X0),X1)),compose(compose(X2,X0),X1)) = compose(compose(X2,X0),X1),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,X0),X0),X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
codomain(a) = domain(b),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
codomain(a) = domain(h),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
codomain(a) = domain(g),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
compose(a,h) = compose(a,g),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
h != g,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f29,plain,
! [X0] : compose(domain(X0),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f30,plain,
! [X0] : domain(domain(X0)) = codomain(domain(X0)),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f31,plain,
! [X0] : codomain(codomain(X0)) = domain(codomain(X0)),
inference(paramodulation,[status(thm)],[f17,f16]) ).
fof(f32,plain,
! [X0] : compose(codomain(X0),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f33,plain,
! [X0] : domain(domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f16,f30]) ).
fof(f34,plain,
! [X0] : codomain(codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f17,f31]) ).
fof(f35,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),X1)),domain(domain(X0))) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f16,f20]) ).
fof(f36,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),domain(compose(X0,codomain(X1))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f17,f20]) ).
fof(f44,plain,
! [X0] : ifeq(domain(b),domain(X0),domain(compose(a,X0)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f24,f20]) ).
fof(f46,plain,
compose(a,domain(b)) = a,
inference(paramodulation,[status(thm)],[f24,f19]) ).
fof(f48,plain,
domain(b) = domain(h),
inference(forward_demodulation,[status(thm)],[f24,f25]) ).
fof(f49,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(h,X0)),domain(b)) = domain(h),
inference(paramodulation,[status(thm)],[f48,f20]) ).
fof(f50,plain,
! [X0] : ifeq(codomain(X0),domain(b),domain(compose(X0,h)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f48,f20]) ).
fof(f52,plain,
compose(domain(b),h) = h,
inference(paramodulation,[status(thm)],[f48,f18]) ).
fof(f53,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(h,X0)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f48,f49]) ).
fof(f55,plain,
domain(b) = domain(g),
inference(forward_demodulation,[status(thm)],[f24,f26]) ).
fof(f56,plain,
! [X0] : ifeq(codomain(g),domain(X0),domain(compose(g,X0)),domain(b)) = domain(g),
inference(paramodulation,[status(thm)],[f55,f20]) ).
fof(f57,plain,
! [X0] : ifeq(codomain(X0),domain(b),domain(compose(X0,g)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f55,f20]) ).
fof(f59,plain,
compose(domain(b),g) = g,
inference(paramodulation,[status(thm)],[f55,f18]) ).
fof(f60,plain,
! [X0] : ifeq(codomain(g),domain(X0),domain(compose(g,X0)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f55,f56]) ).
fof(f67,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(X0,domain(X1))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f33,f20]) ).
fof(f78,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),X1)),domain(codomain(X0))) = domain(codomain(X0)),
inference(paramodulation,[status(thm)],[f34,f20]) ).
fof(f82,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),X1)),codomain(X0)) = domain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f78]) ).
fof(f83,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),X1)),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f17,f82]) ).
fof(f85,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),X1)),codomain(X1)) = codomain(X1),
inference(paramodulation,[status(thm)],[f34,f21]) ).
fof(f86,plain,
! [X0] : ifeq(domain(b),domain(X0),codomain(compose(a,X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f24,f21]) ).
fof(f87,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),X1)),codomain(X1)) = codomain(X1),
inference(paramodulation,[status(thm)],[f16,f21]) ).
fof(f88,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,domain(X1))),codomain(domain(X1))) = codomain(domain(X1)),
inference(paramodulation,[status(thm)],[f33,f21]) ).
fof(f89,plain,
! [X0] : ifeq(codomain(X0),domain(b),codomain(compose(X0,g)),codomain(g)) = codomain(g),
inference(paramodulation,[status(thm)],[f55,f21]) ).
fof(f90,plain,
! [X0] : ifeq(codomain(X0),domain(b),codomain(compose(X0,h)),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f48,f21]) ).
fof(f91,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(X0,codomain(X1))),codomain(codomain(X1))) = codomain(codomain(X1)),
inference(paramodulation,[status(thm)],[f17,f21]) ).
fof(f95,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,a)),domain(b)) = codomain(a),
inference(paramodulation,[status(thm)],[f24,f21]) ).
fof(f97,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,domain(X1))),domain(X1)) = codomain(domain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f88]) ).
fof(f98,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,domain(X1))),domain(X1)) = domain(X1),
inference(forward_demodulation,[status(thm)],[f16,f97]) ).
fof(f99,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(X0,codomain(X1))),codomain(X1)) = codomain(codomain(X1)),
inference(forward_demodulation,[status(thm)],[f34,f91]) ).
fof(f100,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(X0,codomain(X1))),codomain(X1)) = codomain(X1),
inference(forward_demodulation,[status(thm)],[f34,f99]) ).
fof(f106,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,a)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f24,f95]) ).
fof(f184,plain,
! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(a,X0)),compose(compose(X1,a),X0)),compose(compose(X1,a),X0)) = compose(compose(X1,a),X0),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f185,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(domain(X0)),compose(X2,compose(domain(X0),X1)),compose(compose(X2,domain(X0)),X1)),compose(compose(X2,domain(X0)),X1)) = compose(compose(X2,domain(X0)),X1),
inference(paramodulation,[status(thm)],[f16,f22]) ).
fof(f186,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(X0,domain(X1))),compose(compose(X2,X0),domain(X1))),compose(compose(X2,X0),domain(X1))) = compose(compose(X2,X0),domain(X1)),
inference(paramodulation,[status(thm)],[f33,f22]) ).
fof(f187,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,g)),compose(compose(X1,X0),g)),compose(compose(X1,X0),g)) = compose(compose(X1,X0),g),
inference(paramodulation,[status(thm)],[f55,f22]) ).
fof(f188,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,h)),compose(compose(X1,X0),h)),compose(compose(X1,X0),h)) = compose(compose(X1,X0),h),
inference(paramodulation,[status(thm)],[f48,f22]) ).
fof(f189,plain,
! [X0,X1,X2] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(X0,codomain(X1))),compose(compose(X2,X0),codomain(X1))),compose(compose(X2,X0),codomain(X1))) = compose(compose(X2,X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f17,f22]) ).
fof(f190,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(X0,X1)),compose(compose(codomain(X2),X0),X1)),compose(compose(codomain(X2),X0),X1)) = compose(compose(codomain(X2),X0),X1),
inference(paramodulation,[status(thm)],[f34,f22]) ).
fof(f191,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(X0,X1)),compose(compose(a,X0),X1)),compose(compose(a,X0),X1)) = compose(compose(a,X0),X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f192,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(X0,X1)),compose(compose(domain(X2),X0),X1)),compose(compose(domain(X2),X0),X1)) = compose(compose(domain(X2),X0),X1),
inference(paramodulation,[status(thm)],[f16,f22]) ).
fof(f194,plain,
! [X0,X1] : ifeq(codomain(g),domain(X0),ifeq(codomain(X1),domain(b),compose(X1,compose(g,X0)),compose(compose(X1,g),X0)),compose(compose(X1,g),X0)) = compose(compose(X1,g),X0),
inference(paramodulation,[status(thm)],[f55,f22]) ).
fof(f195,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(b),compose(X1,compose(h,X0)),compose(compose(X1,h),X0)),compose(compose(X1,h),X0)) = compose(compose(X1,h),X0),
inference(paramodulation,[status(thm)],[f48,f22]) ).
fof(f196,plain,
! [X0,X1,X2] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),X1)),compose(compose(X2,codomain(X0)),X1)),compose(compose(X2,codomain(X0)),X1)) = compose(compose(X2,codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f17,f22]) ).
fof(f197,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(domain(compose(X0,X1))),domain(X0),compose(X0,X1),compose(compose(domain(compose(X0,X1)),X0),X1)),compose(compose(domain(compose(X0,X1)),X0),X1)) = compose(compose(domain(compose(X0,X1)),X0),X1),
inference(paramodulation,[status(thm)],[f18,f22]) ).
fof(f198,plain,
! [X0,X1] : ifeq(codomain(codomain(X0)),domain(codomain(X0)),ifeq(codomain(X1),domain(codomain(X0)),compose(X1,codomain(X0)),compose(compose(X1,codomain(X0)),codomain(X0))),compose(compose(X1,codomain(X0)),codomain(X0))) = compose(compose(X1,codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f32,f22]) ).
fof(f199,plain,
! [X0] : ifeq(codomain(a),domain(domain(b)),ifeq(codomain(X0),domain(a),compose(X0,a),compose(compose(X0,a),domain(b))),compose(compose(X0,a),domain(b))) = compose(compose(X0,a),domain(b)),
inference(paramodulation,[status(thm)],[f46,f22]) ).
fof(f200,plain,
! [X0] : ifeq(codomain(domain(b)),domain(g),ifeq(codomain(X0),domain(domain(b)),compose(X0,g),compose(compose(X0,domain(b)),g)),compose(compose(X0,domain(b)),g)) = compose(compose(X0,domain(b)),g),
inference(paramodulation,[status(thm)],[f59,f22]) ).
fof(f201,plain,
! [X0] : ifeq(codomain(domain(b)),domain(h),ifeq(codomain(X0),domain(domain(b)),compose(X0,h),compose(compose(X0,domain(b)),h)),compose(compose(X0,domain(b)),h)) = compose(compose(X0,domain(b)),h),
inference(paramodulation,[status(thm)],[f52,f22]) ).
fof(f202,plain,
! [X0,X1] : ifeq(codomain(domain(X0)),domain(domain(X0)),ifeq(codomain(X1),domain(domain(X0)),compose(X1,domain(X0)),compose(compose(X1,domain(X0)),domain(X0))),compose(compose(X1,domain(X0)),domain(X0))) = compose(compose(X1,domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f29,f22]) ).
fof(f203,plain,
! [X0,X1] : ifeq(codomain(domain(X0)),domain(X0),ifeq(codomain(X1),domain(domain(X0)),compose(X1,X0),compose(compose(X1,domain(X0)),X0)),compose(compose(X1,domain(X0)),X0)) = compose(compose(X1,domain(X0)),X0),
inference(paramodulation,[status(thm)],[f18,f22]) ).
fof(f204,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(X0)),ifeq(codomain(X1),domain(X0),compose(X1,X0),compose(compose(X1,X0),codomain(X0))),compose(compose(X1,X0),codomain(X0))) = compose(compose(X1,X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f205,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(compose(X1,X0))),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,codomain(compose(X1,X0)))),compose(X1,X0)),compose(compose(X1,X0),codomain(compose(X1,X0)))) = compose(compose(X1,X0),codomain(compose(X1,X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f206,plain,
! [X0,X1] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),X1)),compose(codomain(X0),X1)),compose(compose(codomain(X0),codomain(X0)),X1)) = compose(compose(codomain(X0),codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f32,f22]) ).
fof(f207,plain,
! [X0] : ifeq(codomain(domain(b)),domain(X0),ifeq(codomain(a),domain(domain(b)),compose(a,compose(domain(b),X0)),compose(a,X0)),compose(compose(a,domain(b)),X0)) = compose(compose(a,domain(b)),X0),
inference(paramodulation,[status(thm)],[f46,f22]) ).
fof(f208,plain,
! [X0] : ifeq(codomain(g),domain(X0),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,X0)),compose(g,X0)),compose(compose(domain(b),g),X0)) = compose(compose(domain(b),g),X0),
inference(paramodulation,[status(thm)],[f59,f22]) ).
fof(f209,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(b)),domain(h),compose(domain(b),compose(h,X0)),compose(h,X0)),compose(compose(domain(b),h),X0)) = compose(compose(domain(b),h),X0),
inference(paramodulation,[status(thm)],[f52,f22]) ).
fof(f210,plain,
! [X0,X1] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),X1)),compose(domain(X0),X1)),compose(compose(domain(X0),domain(X0)),X1)) = compose(compose(domain(X0),domain(X0)),X1),
inference(paramodulation,[status(thm)],[f29,f22]) ).
fof(f211,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(domain(X0)),domain(X0),compose(domain(X0),compose(X0,X1)),compose(X0,X1)),compose(compose(domain(X0),X0),X1)) = compose(compose(domain(X0),X0),X1),
inference(paramodulation,[status(thm)],[f18,f22]) ).
fof(f212,plain,
! [X0,X1] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),X1)),compose(X0,X1)),compose(compose(X0,codomain(X0)),X1)) = compose(compose(X0,codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f222,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),X1)),compose(compose(X2,domain(X0)),X1)),compose(compose(X2,domain(X0)),X1)) = compose(compose(X2,domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f33,f185]) ).
fof(f224,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),X1)),compose(compose(X2,codomain(X0)),X1)),compose(compose(X2,codomain(X0)),X1)) = compose(compose(X2,codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f34,f196]) ).
fof(f225,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(compose(X0,X1)),domain(X0),compose(X0,X1),compose(compose(domain(compose(X0,X1)),X0),X1)),compose(compose(domain(compose(X0,X1)),X0),X1)) = compose(compose(domain(compose(X0,X1)),X0),X1),
inference(forward_demodulation,[status(thm)],[f16,f197]) ).
fof(f226,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(X0)),ifeq(codomain(X1),domain(codomain(X0)),compose(X1,codomain(X0)),compose(compose(X1,codomain(X0)),codomain(X0))),compose(compose(X1,codomain(X0)),codomain(X0))) = compose(compose(X1,codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f198]) ).
fof(f227,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X0),ifeq(codomain(X1),domain(codomain(X0)),compose(X1,codomain(X0)),compose(compose(X1,codomain(X0)),codomain(X0))),compose(compose(X1,codomain(X0)),codomain(X0))) = compose(compose(X1,codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f226]) ).
fof(f228,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(X1)),compose(X0,codomain(X1)),compose(compose(X0,codomain(X1)),codomain(X1))) = compose(compose(X0,codomain(X1)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f227]) ).
fof(f229,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(X0,codomain(X1)),compose(compose(X0,codomain(X1)),codomain(X1))) = compose(compose(X0,codomain(X1)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f17,f228]) ).
fof(f230,plain,
! [X0] : ifeq(domain(b),domain(domain(b)),ifeq(codomain(X0),domain(a),compose(X0,a),compose(compose(X0,a),domain(b))),compose(compose(X0,a),domain(b))) = compose(compose(X0,a),domain(b)),
inference(forward_demodulation,[status(thm)],[f24,f199]) ).
fof(f231,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(a),compose(X0,a),compose(compose(X0,a),domain(b))),compose(compose(X0,a),domain(b))) = compose(compose(X0,a),domain(b)),
inference(forward_demodulation,[status(thm)],[f33,f230]) ).
fof(f232,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,a),compose(compose(X0,a),domain(b))) = compose(compose(X0,a),domain(b)),
inference(forward_demodulation,[status(thm)],[f15,f231]) ).
fof(f233,plain,
! [X0] : ifeq(domain(b),domain(g),ifeq(codomain(X0),domain(domain(b)),compose(X0,g),compose(compose(X0,domain(b)),g)),compose(compose(X0,domain(b)),g)) = compose(compose(X0,domain(b)),g),
inference(forward_demodulation,[status(thm)],[f16,f200]) ).
fof(f234,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(domain(b)),compose(X0,g),compose(compose(X0,domain(b)),g)),compose(compose(X0,domain(b)),g)) = compose(compose(X0,domain(b)),g),
inference(forward_demodulation,[status(thm)],[f55,f233]) ).
fof(f235,plain,
! [X0] : ifeq(codomain(X0),domain(domain(b)),compose(X0,g),compose(compose(X0,domain(b)),g)) = compose(compose(X0,domain(b)),g),
inference(forward_demodulation,[status(thm)],[f15,f234]) ).
fof(f236,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,g),compose(compose(X0,domain(b)),g)) = compose(compose(X0,domain(b)),g),
inference(forward_demodulation,[status(thm)],[f33,f235]) ).
fof(f237,plain,
! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(domain(b)),compose(X0,h),compose(compose(X0,domain(b)),h)),compose(compose(X0,domain(b)),h)) = compose(compose(X0,domain(b)),h),
inference(forward_demodulation,[status(thm)],[f16,f201]) ).
fof(f238,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(domain(b)),compose(X0,h),compose(compose(X0,domain(b)),h)),compose(compose(X0,domain(b)),h)) = compose(compose(X0,domain(b)),h),
inference(forward_demodulation,[status(thm)],[f48,f237]) ).
fof(f239,plain,
! [X0] : ifeq(codomain(X0),domain(domain(b)),compose(X0,h),compose(compose(X0,domain(b)),h)) = compose(compose(X0,domain(b)),h),
inference(forward_demodulation,[status(thm)],[f15,f238]) ).
fof(f240,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,h),compose(compose(X0,domain(b)),h)) = compose(compose(X0,domain(b)),h),
inference(forward_demodulation,[status(thm)],[f33,f239]) ).
fof(f241,plain,
! [X0,X1] : ifeq(domain(X0),domain(domain(X0)),ifeq(codomain(X1),domain(domain(X0)),compose(X1,domain(X0)),compose(compose(X1,domain(X0)),domain(X0))),compose(compose(X1,domain(X0)),domain(X0))) = compose(compose(X1,domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f202]) ).
fof(f242,plain,
! [X0,X1] : ifeq(domain(X0),domain(X0),ifeq(codomain(X1),domain(domain(X0)),compose(X1,domain(X0)),compose(compose(X1,domain(X0)),domain(X0))),compose(compose(X1,domain(X0)),domain(X0))) = compose(compose(X1,domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f241]) ).
fof(f243,plain,
! [X0,X1] : ifeq(codomain(X0),domain(domain(X1)),compose(X0,domain(X1)),compose(compose(X0,domain(X1)),domain(X1))) = compose(compose(X0,domain(X1)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f242]) ).
fof(f244,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(X0,domain(X1)),compose(compose(X0,domain(X1)),domain(X1))) = compose(compose(X0,domain(X1)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f33,f243]) ).
fof(f245,plain,
! [X0,X1] : ifeq(domain(X0),domain(X0),ifeq(codomain(X1),domain(domain(X0)),compose(X1,X0),compose(compose(X1,domain(X0)),X0)),compose(compose(X1,domain(X0)),X0)) = compose(compose(X1,domain(X0)),X0),
inference(forward_demodulation,[status(thm)],[f16,f203]) ).
fof(f246,plain,
! [X0,X1] : ifeq(codomain(X0),domain(domain(X1)),compose(X0,X1),compose(compose(X0,domain(X1)),X1)) = compose(compose(X0,domain(X1)),X1),
inference(forward_demodulation,[status(thm)],[f15,f245]) ).
fof(f247,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(X0,X1),compose(compose(X0,domain(X1)),X1)) = compose(compose(X0,domain(X1)),X1),
inference(forward_demodulation,[status(thm)],[f33,f246]) ).
fof(f248,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X0),ifeq(codomain(X1),domain(X0),compose(X1,X0),compose(compose(X1,X0),codomain(X0))),compose(compose(X1,X0),codomain(X0))) = compose(compose(X1,X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f204]) ).
fof(f249,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(X0,X1),compose(compose(X0,X1),codomain(X1))) = compose(compose(X0,X1),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f248]) ).
fof(f250,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(X1,X0)),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,codomain(compose(X1,X0)))),compose(X1,X0)),compose(compose(X1,X0),codomain(compose(X1,X0)))) = compose(compose(X1,X0),codomain(compose(X1,X0))),
inference(forward_demodulation,[status(thm)],[f17,f205]) ).
fof(f251,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(X1,X0)),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,codomain(compose(X1,X0)))),compose(X1,X0)),compose(X1,X0)) = compose(compose(X1,X0),codomain(compose(X1,X0))),
inference(forward_demodulation,[status(thm)],[f19,f250]) ).
fof(f252,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(X1,X0)),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,codomain(compose(X1,X0)))),compose(X1,X0)),compose(X1,X0)) = compose(X1,X0),
inference(forward_demodulation,[status(thm)],[f19,f251]) ).
fof(f253,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),X1)),compose(codomain(X0),X1)),compose(compose(codomain(X0),codomain(X0)),X1)) = compose(compose(codomain(X0),codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f34,f206]) ).
fof(f254,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X0),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),X1)),compose(codomain(X0),X1)),compose(compose(codomain(X0),codomain(X0)),X1)) = compose(compose(codomain(X0),codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f34,f253]) ).
fof(f255,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X0),codomain(X0),compose(codomain(X0),compose(codomain(X0),X1)),compose(codomain(X0),X1)),compose(compose(codomain(X0),codomain(X0)),X1)) = compose(compose(codomain(X0),codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f17,f254]) ).
fof(f256,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),compose(codomain(X0),X1)),compose(compose(codomain(X0),codomain(X0)),X1)) = compose(compose(codomain(X0),codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f15,f255]) ).
fof(f257,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),compose(codomain(X0),X1)),compose(codomain(X0),X1)) = compose(compose(codomain(X0),codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f32,f256]) ).
fof(f258,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),compose(codomain(X0),X1)),compose(codomain(X0),X1)) = compose(codomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f32,f257]) ).
fof(f259,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(a),domain(domain(b)),compose(a,compose(domain(b),X0)),compose(a,X0)),compose(compose(a,domain(b)),X0)) = compose(compose(a,domain(b)),X0),
inference(forward_demodulation,[status(thm)],[f16,f207]) ).
fof(f260,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(domain(b)),compose(a,compose(domain(b),X0)),compose(a,X0)),compose(compose(a,domain(b)),X0)) = compose(compose(a,domain(b)),X0),
inference(forward_demodulation,[status(thm)],[f24,f259]) ).
fof(f261,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(b),compose(a,compose(domain(b),X0)),compose(a,X0)),compose(compose(a,domain(b)),X0)) = compose(compose(a,domain(b)),X0),
inference(forward_demodulation,[status(thm)],[f33,f260]) ).
fof(f262,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),X0)),compose(compose(a,domain(b)),X0)) = compose(compose(a,domain(b)),X0),
inference(forward_demodulation,[status(thm)],[f15,f261]) ).
fof(f263,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),X0)),compose(a,X0)) = compose(compose(a,domain(b)),X0),
inference(forward_demodulation,[status(thm)],[f46,f262]) ).
fof(f264,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),X0)),compose(a,X0)) = compose(a,X0),
inference(forward_demodulation,[status(thm)],[f46,f263]) ).
fof(f265,plain,
! [X0] : ifeq(codomain(g),domain(X0),ifeq(domain(b),domain(g),compose(domain(b),compose(g,X0)),compose(g,X0)),compose(compose(domain(b),g),X0)) = compose(compose(domain(b),g),X0),
inference(forward_demodulation,[status(thm)],[f16,f208]) ).
fof(f266,plain,
! [X0] : ifeq(codomain(g),domain(X0),ifeq(domain(b),domain(b),compose(domain(b),compose(g,X0)),compose(g,X0)),compose(compose(domain(b),g),X0)) = compose(compose(domain(b),g),X0),
inference(forward_demodulation,[status(thm)],[f55,f265]) ).
fof(f267,plain,
! [X0] : ifeq(codomain(g),domain(X0),compose(domain(b),compose(g,X0)),compose(compose(domain(b),g),X0)) = compose(compose(domain(b),g),X0),
inference(forward_demodulation,[status(thm)],[f15,f266]) ).
fof(f268,plain,
! [X0] : ifeq(codomain(g),domain(X0),compose(domain(b),compose(g,X0)),compose(g,X0)) = compose(compose(domain(b),g),X0),
inference(forward_demodulation,[status(thm)],[f59,f267]) ).
fof(f269,plain,
! [X0] : ifeq(codomain(g),domain(X0),compose(domain(b),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(forward_demodulation,[status(thm)],[f59,f268]) ).
fof(f270,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(h),compose(domain(b),compose(h,X0)),compose(h,X0)),compose(compose(domain(b),h),X0)) = compose(compose(domain(b),h),X0),
inference(forward_demodulation,[status(thm)],[f16,f209]) ).
fof(f271,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(b),compose(domain(b),compose(h,X0)),compose(h,X0)),compose(compose(domain(b),h),X0)) = compose(compose(domain(b),h),X0),
inference(forward_demodulation,[status(thm)],[f48,f270]) ).
fof(f272,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(h,X0)),compose(compose(domain(b),h),X0)) = compose(compose(domain(b),h),X0),
inference(forward_demodulation,[status(thm)],[f15,f271]) ).
fof(f273,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(h,X0)),compose(h,X0)) = compose(compose(domain(b),h),X0),
inference(forward_demodulation,[status(thm)],[f52,f272]) ).
fof(f274,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(h,X0)),compose(h,X0)) = compose(h,X0),
inference(forward_demodulation,[status(thm)],[f52,f273]) ).
fof(f275,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),X1)),compose(domain(X0),X1)),compose(compose(domain(X0),domain(X0)),X1)) = compose(compose(domain(X0),domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f16,f210]) ).
fof(f276,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(X0),domain(domain(X0)),compose(domain(X0),compose(domain(X0),X1)),compose(domain(X0),X1)),compose(compose(domain(X0),domain(X0)),X1)) = compose(compose(domain(X0),domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f16,f275]) ).
fof(f277,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(domain(X0),X1)),compose(domain(X0),X1)),compose(compose(domain(X0),domain(X0)),X1)) = compose(compose(domain(X0),domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f33,f276]) ).
fof(f278,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),compose(domain(X0),X1)),compose(compose(domain(X0),domain(X0)),X1)) = compose(compose(domain(X0),domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f15,f277]) ).
fof(f279,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),compose(domain(X0),X1)),compose(domain(X0),X1)) = compose(compose(domain(X0),domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f29,f278]) ).
fof(f280,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),compose(domain(X0),X1)),compose(domain(X0),X1)) = compose(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f29,f279]) ).
fof(f281,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(X0,X1)),compose(X0,X1)),compose(compose(domain(X0),X0),X1)) = compose(compose(domain(X0),X0),X1),
inference(forward_demodulation,[status(thm)],[f16,f211]) ).
fof(f282,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(domain(X0),compose(X0,X1)),compose(compose(domain(X0),X0),X1)) = compose(compose(domain(X0),X0),X1),
inference(forward_demodulation,[status(thm)],[f15,f281]) ).
fof(f283,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(domain(X0),compose(X0,X1)),compose(X0,X1)) = compose(compose(domain(X0),X0),X1),
inference(forward_demodulation,[status(thm)],[f18,f282]) ).
fof(f284,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(domain(X0),compose(X0,X1)),compose(X0,X1)) = compose(X0,X1),
inference(forward_demodulation,[status(thm)],[f18,f283]) ).
fof(f285,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),X1)),compose(X0,X1)),compose(compose(X0,codomain(X0)),X1)) = compose(compose(X0,codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f34,f212]) ).
fof(f286,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X0),codomain(X0),compose(X0,compose(codomain(X0),X1)),compose(X0,X1)),compose(compose(X0,codomain(X0)),X1)) = compose(compose(X0,codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f17,f285]) ).
fof(f287,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(X0,compose(codomain(X0),X1)),compose(compose(X0,codomain(X0)),X1)) = compose(compose(X0,codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f15,f286]) ).
fof(f288,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(X0,compose(codomain(X0),X1)),compose(X0,X1)) = compose(compose(X0,codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f19,f287]) ).
fof(f289,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(X0,compose(codomain(X0),X1)),compose(X0,X1)) = compose(X0,X1),
inference(forward_demodulation,[status(thm)],[f19,f288]) ).
fof(f323,plain,
! [X0] : ifeq(codomain(g),domain(X0),ifeq(codomain(a),domain(g),compose(a,compose(g,X0)),compose(compose(a,g),X0)),compose(compose(a,h),X0)) = compose(compose(a,g),X0),
inference(paramodulation,[status(thm)],[f27,f22]) ).
fof(f325,plain,
! [X0] : ifeq(codomain(a),domain(g),ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,a),g)),compose(compose(X0,a),g)) = compose(compose(X0,a),g),
inference(paramodulation,[status(thm)],[f27,f22]) ).
fof(f326,plain,
ifeq(codomain(a),domain(g),codomain(compose(a,h)),codomain(g)) = codomain(g),
inference(paramodulation,[status(thm)],[f27,f21]) ).
fof(f327,plain,
ifeq(codomain(a),domain(g),domain(compose(a,h)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f27,f20]) ).
fof(f328,plain,
! [X0] : ifeq(codomain(g),domain(X0),ifeq(domain(b),domain(g),compose(a,compose(g,X0)),compose(compose(a,g),X0)),compose(compose(a,h),X0)) = compose(compose(a,g),X0),
inference(forward_demodulation,[status(thm)],[f24,f323]) ).
fof(f329,plain,
! [X0] : ifeq(codomain(g),domain(X0),ifeq(domain(b),domain(b),compose(a,compose(g,X0)),compose(compose(a,g),X0)),compose(compose(a,h),X0)) = compose(compose(a,g),X0),
inference(forward_demodulation,[status(thm)],[f55,f328]) ).
fof(f330,plain,
! [X0] : ifeq(codomain(g),domain(X0),compose(a,compose(g,X0)),compose(compose(a,h),X0)) = compose(compose(a,g),X0),
inference(forward_demodulation,[status(thm)],[f15,f329]) ).
fof(f331,plain,
! [X0] : ifeq(codomain(g),domain(X0),compose(a,compose(g,X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(forward_demodulation,[status(thm)],[f27,f330]) ).
fof(f337,plain,
! [X0] : ifeq(domain(b),domain(g),ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,a),g)),compose(compose(X0,a),g)) = compose(compose(X0,a),g),
inference(forward_demodulation,[status(thm)],[f24,f325]) ).
fof(f338,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,a),g)),compose(compose(X0,a),g)) = compose(compose(X0,a),g),
inference(forward_demodulation,[status(thm)],[f55,f337]) ).
fof(f339,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,a),g)) = compose(compose(X0,a),g),
inference(forward_demodulation,[status(thm)],[f15,f338]) ).
fof(f340,plain,
ifeq(domain(b),domain(g),codomain(compose(a,h)),codomain(g)) = codomain(g),
inference(forward_demodulation,[status(thm)],[f24,f326]) ).
fof(f341,plain,
ifeq(domain(b),domain(b),codomain(compose(a,h)),codomain(g)) = codomain(g),
inference(forward_demodulation,[status(thm)],[f55,f340]) ).
fof(f342,plain,
codomain(compose(a,h)) = codomain(g),
inference(forward_demodulation,[status(thm)],[f15,f341]) ).
fof(f343,plain,
ifeq(domain(b),domain(g),domain(compose(a,h)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f24,f327]) ).
fof(f344,plain,
ifeq(domain(b),domain(b),domain(compose(a,h)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f55,f343]) ).
fof(f345,plain,
domain(compose(a,h)) = domain(a),
inference(forward_demodulation,[status(thm)],[f15,f344]) ).
fof(f346,plain,
ifeq(codomain(a),domain(h),codomain(g),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f342,f21]) ).
fof(f347,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(g),domain(X0),compose(compose(a,h),compose(X0,X1)),compose(compose(compose(a,h),X0),X1)),compose(compose(compose(a,h),X0),X1)) = compose(compose(compose(a,h),X0),X1),
inference(paramodulation,[status(thm)],[f342,f22]) ).
fof(f348,plain,
! [X0,X1] : ifeq(codomain(g),domain(X0),ifeq(codomain(X1),domain(compose(a,h)),compose(X1,compose(compose(a,h),X0)),compose(compose(X1,compose(a,h)),X0)),compose(compose(X1,compose(a,h)),X0)) = compose(compose(X1,compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f342,f22]) ).
fof(f352,plain,
! [X0] : ifeq(codomain(g),domain(X0),codomain(compose(compose(a,h),X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f342,f21]) ).
fof(f356,plain,
compose(compose(a,h),codomain(g)) = compose(a,h),
inference(paramodulation,[status(thm)],[f342,f19]) ).
fof(f357,plain,
ifeq(domain(b),domain(h),codomain(g),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f24,f346]) ).
fof(f358,plain,
ifeq(domain(b),domain(b),codomain(g),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f48,f357]) ).
fof(f359,plain,
codomain(g) = codomain(h),
inference(forward_demodulation,[status(thm)],[f15,f358]) ).
fof(f367,plain,
codomain(compose(a,h)) = codomain(h),
inference(backward_demodulation,[status(thm)],[f359,f342]) ).
fof(f368,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(X0,X1)),compose(compose(g,X0),X1)),compose(compose(g,X0),X1)) = compose(compose(g,X0),X1),
inference(paramodulation,[status(thm)],[f359,f22]) ).
fof(f373,plain,
! [X0] : ifeq(codomain(h),domain(X0),codomain(compose(g,X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f359,f21]) ).
fof(f377,plain,
compose(g,codomain(h)) = g,
inference(paramodulation,[status(thm)],[f359,f19]) ).
fof(f389,plain,
! [X0,X1] : ifeq(codomain(h),domain(compose(a,b)),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(g,compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,g),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f23]) ).
fof(f390,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(codomain(X0),compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f23]) ).
fof(f391,plain,
! [X0,X1] : ifeq(domain(b),domain(compose(a,b)),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(a,compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,a),a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f392,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(domain(X0),compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f23]) ).
fof(f394,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(codomain(X1),compose(a,b)),X2,codomain(X1),X0),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f34,f23]) ).
fof(f395,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(domain(b),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,compose(a,b)),X1,a,X0),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f396,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(domain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(domain(X1),compose(a,b)),X2,domain(X1),X0),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f16,f23]) ).
fof(f397,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X1,compose(a,b)),compose(X0,compose(a,b)),X1,X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f15,f23]) ).
fof(f398,plain,
! [X0,X1] : ifeq(codomain(domain(compose(a,b))),domain(compose(a,b)),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(compose(a,b))),domain(compose(a,b))),domain(compose(a,b))),domain(compose(a,b))) = domain(compose(a,b)),
inference(paramodulation,[status(thm)],[f18,f23]) ).
fof(f399,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),compose(X1,compose(a,b)),X1,X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f15,f23]) ).
fof(f400,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(domain(compose(a,b))),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,b),X1,domain(compose(a,b)),X0),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f18,f23]) ).
fof(f401,plain,
! [X0,X1] : ifeq(domain(compose(a,b)),domain(compose(a,b)),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(compose(a,b))),domain(compose(a,b))),domain(compose(a,b))),domain(compose(a,b))) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f16,f398]) ).
fof(f402,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(compose(a,b))),domain(compose(a,b))),domain(compose(a,b))) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f15,f401]) ).
fof(f403,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(domain(compose(a,b)),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,b),X1,domain(compose(a,b)),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f16,f400]) ).
fof(f404,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,b),X1,domain(compose(a,b)),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f15,f403]) ).
fof(f405,plain,
! [X0] : ifeq(codomain(codomain(h)),domain(X0),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),X0)),compose(compose(g,codomain(h)),X0)),compose(g,X0)) = compose(compose(g,codomain(h)),X0),
inference(paramodulation,[status(thm)],[f377,f22]) ).
fof(f407,plain,
! [X0] : ifeq(codomain(g),domain(codomain(h)),ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),codomain(h))),compose(compose(X0,g),codomain(h))) = compose(compose(X0,g),codomain(h)),
inference(paramodulation,[status(thm)],[f377,f22]) ).
fof(f410,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),X0)),compose(compose(g,codomain(h)),X0)),compose(g,X0)) = compose(compose(g,codomain(h)),X0),
inference(forward_demodulation,[status(thm)],[f34,f405]) ).
fof(f411,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(codomain(h)),compose(g,compose(codomain(h),X0)),compose(compose(g,codomain(h)),X0)),compose(g,X0)) = compose(compose(g,codomain(h)),X0),
inference(forward_demodulation,[status(thm)],[f359,f410]) ).
fof(f412,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(h),compose(g,compose(codomain(h),X0)),compose(compose(g,codomain(h)),X0)),compose(g,X0)) = compose(compose(g,codomain(h)),X0),
inference(forward_demodulation,[status(thm)],[f17,f411]) ).
fof(f413,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(g,compose(codomain(h),X0)),compose(g,X0)) = compose(compose(g,codomain(h)),X0),
inference(forward_demodulation,[status(thm)],[f15,f412]) ).
fof(f414,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(g,compose(codomain(h),X0)),compose(g,X0)) = compose(g,X0),
inference(forward_demodulation,[status(thm)],[f377,f413]) ).
fof(f421,plain,
! [X0] : ifeq(codomain(h),domain(codomain(h)),ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),codomain(h))),compose(compose(X0,g),codomain(h))) = compose(compose(X0,g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f359,f407]) ).
fof(f422,plain,
! [X0] : ifeq(codomain(h),codomain(h),ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),codomain(h))),compose(compose(X0,g),codomain(h))) = compose(compose(X0,g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f421]) ).
fof(f423,plain,
! [X0] : ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),codomain(h))) = compose(compose(X0,g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f422]) ).
fof(f424,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,g),compose(compose(X0,g),codomain(h))) = compose(compose(X0,g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f55,f423]) ).
fof(f433,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(a,h))),compose(compose(X1,X0),compose(a,h))),compose(compose(X1,X0),compose(a,h))) = compose(compose(X1,X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f22]) ).
fof(f439,plain,
! [X0] : ifeq(codomain(X0),domain(a),domain(compose(X0,compose(a,h))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f345,f20]) ).
fof(f441,plain,
compose(domain(a),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f345,f18]) ).
fof(f452,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(h),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(compose(a,h),compose(a,b)),X1,compose(a,h),X0),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f367,f23]) ).
fof(f453,plain,
! [X0,X1] : ifeq(codomain(h),domain(compose(a,b)),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(compose(a,h),compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f23]) ).
fof(f458,plain,
! [X0] : ifeq(codomain(X0),domain(compose(a,h)),codomain(compose(X0,compose(a,h))),codomain(h)) = codomain(compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f21]) ).
fof(f461,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),X0)),domain(compose(a,h))) = domain(compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f20]) ).
fof(f471,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,h))),codomain(h)) = codomain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f458]) ).
fof(f472,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,h))),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f367,f471]) ).
fof(f474,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),X0)),domain(a)) = domain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f461]) ).
fof(f475,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),X0)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f345,f474]) ).
fof(f477,plain,
compose(compose(a,h),codomain(h)) = compose(a,h),
inference(forward_demodulation,[status(thm)],[f359,f356]) ).
fof(f480,plain,
! [X0] : ifeq(codomain(codomain(h)),domain(X0),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),X0)),compose(compose(compose(a,h),codomain(h)),X0)),compose(compose(a,h),X0)) = compose(compose(compose(a,h),codomain(h)),X0),
inference(paramodulation,[status(thm)],[f477,f22]) ).
fof(f482,plain,
! [X0] : ifeq(codomain(compose(a,h)),domain(codomain(h)),ifeq(codomain(X0),domain(compose(a,h)),compose(X0,compose(a,h)),compose(compose(X0,compose(a,h)),codomain(h))),compose(compose(X0,compose(a,h)),codomain(h))) = compose(compose(X0,compose(a,h)),codomain(h)),
inference(paramodulation,[status(thm)],[f477,f22]) ).
fof(f497,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),X0)),compose(compose(compose(a,h),codomain(h)),X0)),compose(compose(a,h),X0)) = compose(compose(compose(a,h),codomain(h)),X0),
inference(forward_demodulation,[status(thm)],[f34,f480]) ).
fof(f498,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),X0)),compose(compose(compose(a,h),codomain(h)),X0)),compose(compose(a,h),X0)) = compose(compose(compose(a,h),codomain(h)),X0),
inference(forward_demodulation,[status(thm)],[f367,f497]) ).
fof(f499,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(h),compose(compose(a,h),compose(codomain(h),X0)),compose(compose(compose(a,h),codomain(h)),X0)),compose(compose(a,h),X0)) = compose(compose(compose(a,h),codomain(h)),X0),
inference(forward_demodulation,[status(thm)],[f17,f498]) ).
fof(f500,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(codomain(h),X0)),compose(compose(a,h),X0)) = compose(compose(compose(a,h),codomain(h)),X0),
inference(forward_demodulation,[status(thm)],[f15,f499]) ).
fof(f501,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(codomain(h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(forward_demodulation,[status(thm)],[f477,f500]) ).
fof(f508,plain,
! [X0] : ifeq(codomain(h),domain(codomain(h)),ifeq(codomain(X0),domain(compose(a,h)),compose(X0,compose(a,h)),compose(compose(X0,compose(a,h)),codomain(h))),compose(compose(X0,compose(a,h)),codomain(h))) = compose(compose(X0,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f367,f482]) ).
fof(f509,plain,
! [X0] : ifeq(codomain(h),codomain(h),ifeq(codomain(X0),domain(compose(a,h)),compose(X0,compose(a,h)),compose(compose(X0,compose(a,h)),codomain(h))),compose(compose(X0,compose(a,h)),codomain(h))) = compose(compose(X0,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f508]) ).
fof(f510,plain,
! [X0] : ifeq(codomain(X0),domain(compose(a,h)),compose(X0,compose(a,h)),compose(compose(X0,compose(a,h)),codomain(h))) = compose(compose(X0,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f509]) ).
fof(f511,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,compose(a,h)),codomain(h))) = compose(compose(X0,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f345,f510]) ).
fof(f519,plain,
! [X0] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),X0)),compose(compose(domain(a),compose(a,h)),X0)),compose(compose(a,h),X0)) = compose(compose(domain(a),compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f441,f22]) ).
fof(f521,plain,
! [X0] : ifeq(codomain(domain(a)),domain(compose(a,h)),ifeq(codomain(X0),domain(domain(a)),compose(X0,compose(a,h)),compose(compose(X0,domain(a)),compose(a,h))),compose(compose(X0,domain(a)),compose(a,h))) = compose(compose(X0,domain(a)),compose(a,h)),
inference(paramodulation,[status(thm)],[f441,f22]) ).
fof(f529,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),X0)),compose(compose(domain(a),compose(a,h)),X0)),compose(compose(a,h),X0)) = compose(compose(domain(a),compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f367,f519]) ).
fof(f530,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(a),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),X0)),compose(compose(domain(a),compose(a,h)),X0)),compose(compose(a,h),X0)) = compose(compose(domain(a),compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f16,f529]) ).
fof(f531,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,h),X0)),compose(compose(domain(a),compose(a,h)),X0)),compose(compose(a,h),X0)) = compose(compose(domain(a),compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f345,f530]) ).
fof(f532,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(a),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(domain(a),compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f15,f531]) ).
fof(f533,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(a),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(forward_demodulation,[status(thm)],[f441,f532]) ).
fof(f540,plain,
! [X0] : ifeq(domain(a),domain(compose(a,h)),ifeq(codomain(X0),domain(domain(a)),compose(X0,compose(a,h)),compose(compose(X0,domain(a)),compose(a,h))),compose(compose(X0,domain(a)),compose(a,h))) = compose(compose(X0,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f521]) ).
fof(f541,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(domain(a)),compose(X0,compose(a,h)),compose(compose(X0,domain(a)),compose(a,h))),compose(compose(X0,domain(a)),compose(a,h))) = compose(compose(X0,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f540]) ).
fof(f542,plain,
! [X0] : ifeq(codomain(X0),domain(domain(a)),compose(X0,compose(a,h)),compose(compose(X0,domain(a)),compose(a,h))) = compose(compose(X0,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f541]) ).
fof(f543,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,domain(a)),compose(a,h))) = compose(compose(X0,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f33,f542]) ).
fof(f550,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),X1)),domain(X0)) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f35]) ).
fof(f551,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),X1)),domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f33,f550]) ).
fof(f558,plain,
! [X0] : ifeq(domain(X0),domain(a),domain(compose(domain(X0),compose(a,h))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f345,f551]) ).
fof(f559,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),domain(X1))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f33,f551]) ).
fof(f560,plain,
! [X0] : ifeq(domain(X0),domain(b),domain(compose(domain(X0),g)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f55,f551]) ).
fof(f561,plain,
! [X0] : ifeq(domain(X0),domain(b),domain(compose(domain(X0),h)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f48,f551]) ).
fof(f562,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),domain(compose(domain(X0),codomain(X1))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f17,f551]) ).
fof(f637,plain,
! [X0] : ifeq(codomain(h),codomain(X0),domain(compose(compose(a,h),codomain(X0))),domain(compose(a,h))) = domain(compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f36]) ).
fof(f638,plain,
! [X0] : ifeq(codomain(h),codomain(X0),domain(compose(g,codomain(X0))),domain(g)) = domain(g),
inference(paramodulation,[status(thm)],[f359,f36]) ).
fof(f639,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),domain(compose(codomain(X0),codomain(X1))),domain(codomain(X0))) = domain(codomain(X0)),
inference(paramodulation,[status(thm)],[f34,f36]) ).
fof(f640,plain,
! [X0] : ifeq(domain(b),codomain(X0),domain(compose(a,codomain(X0))),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f24,f36]) ).
fof(f660,plain,
! [X0] : ifeq(codomain(h),codomain(X0),domain(compose(h,codomain(X0))),domain(b)) = domain(h),
inference(paramodulation,[status(thm)],[f48,f36]) ).
fof(f663,plain,
! [X0] : ifeq(codomain(h),codomain(X0),domain(compose(compose(a,h),codomain(X0))),domain(a)) = domain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f637]) ).
fof(f664,plain,
! [X0] : ifeq(codomain(h),codomain(X0),domain(compose(compose(a,h),codomain(X0))),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f345,f663]) ).
fof(f665,plain,
! [X0] : ifeq(codomain(h),codomain(X0),domain(compose(g,codomain(X0))),domain(b)) = domain(g),
inference(forward_demodulation,[status(thm)],[f55,f638]) ).
fof(f666,plain,
! [X0] : ifeq(codomain(h),codomain(X0),domain(compose(g,codomain(X0))),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f55,f665]) ).
fof(f667,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),domain(compose(codomain(X0),codomain(X1))),codomain(X0)) = domain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f639]) ).
fof(f668,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),domain(compose(codomain(X0),codomain(X1))),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f17,f667]) ).
fof(f695,plain,
! [X0] : ifeq(codomain(h),codomain(X0),domain(compose(h,codomain(X0))),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f48,f660]) ).
fof(f698,plain,
ifeq(codomain(h),domain(b),domain(compose(compose(a,h),h)),domain(compose(a,h))) = domain(compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f50]) ).
fof(f699,plain,
ifeq(codomain(h),domain(b),domain(compose(g,h)),domain(g)) = domain(g),
inference(paramodulation,[status(thm)],[f359,f50]) ).
fof(f700,plain,
! [X0] : ifeq(codomain(X0),domain(b),domain(compose(codomain(X0),h)),domain(codomain(X0))) = domain(codomain(X0)),
inference(paramodulation,[status(thm)],[f34,f50]) ).
fof(f709,plain,
ifeq(codomain(h),domain(b),domain(compose(h,h)),domain(b)) = domain(h),
inference(paramodulation,[status(thm)],[f48,f50]) ).
fof(f711,plain,
ifeq(codomain(h),domain(b),domain(compose(compose(a,h),h)),domain(a)) = domain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f698]) ).
fof(f712,plain,
ifeq(codomain(h),domain(b),domain(compose(compose(a,h),h)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f345,f711]) ).
fof(f713,plain,
ifeq(codomain(h),domain(b),domain(compose(g,h)),domain(b)) = domain(g),
inference(forward_demodulation,[status(thm)],[f55,f699]) ).
fof(f714,plain,
ifeq(codomain(h),domain(b),domain(compose(g,h)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f55,f713]) ).
fof(f715,plain,
! [X0] : ifeq(codomain(X0),domain(b),domain(compose(codomain(X0),h)),codomain(X0)) = domain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f700]) ).
fof(f716,plain,
! [X0] : ifeq(codomain(X0),domain(b),domain(compose(codomain(X0),h)),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f17,f715]) ).
fof(f735,plain,
ifeq(codomain(h),domain(b),domain(compose(h,h)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f48,f709]) ).
fof(f738,plain,
ifeq(codomain(h),domain(b),domain(compose(compose(a,h),g)),domain(compose(a,h))) = domain(compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f57]) ).
fof(f739,plain,
ifeq(codomain(h),domain(b),domain(compose(g,g)),domain(g)) = domain(g),
inference(paramodulation,[status(thm)],[f359,f57]) ).
fof(f740,plain,
! [X0] : ifeq(codomain(X0),domain(b),domain(compose(codomain(X0),g)),domain(codomain(X0))) = domain(codomain(X0)),
inference(paramodulation,[status(thm)],[f34,f57]) ).
fof(f749,plain,
ifeq(codomain(h),domain(b),domain(compose(h,g)),domain(b)) = domain(h),
inference(paramodulation,[status(thm)],[f48,f57]) ).
fof(f751,plain,
ifeq(codomain(h),domain(b),domain(compose(compose(a,h),g)),domain(a)) = domain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f738]) ).
fof(f752,plain,
ifeq(codomain(h),domain(b),domain(compose(compose(a,h),g)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f345,f751]) ).
fof(f753,plain,
ifeq(codomain(h),domain(b),domain(compose(g,g)),domain(b)) = domain(g),
inference(forward_demodulation,[status(thm)],[f55,f739]) ).
fof(f754,plain,
ifeq(codomain(h),domain(b),domain(compose(g,g)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f55,f753]) ).
fof(f755,plain,
! [X0] : ifeq(codomain(X0),domain(b),domain(compose(codomain(X0),g)),codomain(X0)) = domain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f740]) ).
fof(f756,plain,
! [X0] : ifeq(codomain(X0),domain(b),domain(compose(codomain(X0),g)),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f17,f755]) ).
fof(f775,plain,
ifeq(codomain(h),domain(b),domain(compose(h,g)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f48,f749]) ).
fof(f778,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),domain(X0))),domain(compose(a,h))) = domain(compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f67]) ).
fof(f779,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(g,domain(X0))),domain(g)) = domain(g),
inference(paramodulation,[status(thm)],[f359,f67]) ).
fof(f780,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),domain(X1))),domain(codomain(X0))) = domain(codomain(X0)),
inference(paramodulation,[status(thm)],[f34,f67]) ).
fof(f781,plain,
! [X0] : ifeq(domain(b),domain(X0),domain(compose(a,domain(X0))),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f24,f67]) ).
fof(f799,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(h,domain(X0))),domain(b)) = domain(h),
inference(paramodulation,[status(thm)],[f48,f67]) ).
fof(f801,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),domain(X0))),domain(a)) = domain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f778]) ).
fof(f802,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(compose(a,h),domain(X0))),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f345,f801]) ).
fof(f803,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(g,domain(X0))),domain(b)) = domain(g),
inference(forward_demodulation,[status(thm)],[f55,f779]) ).
fof(f804,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(g,domain(X0))),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f55,f803]) ).
fof(f805,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),domain(X1))),codomain(X0)) = domain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f780]) ).
fof(f806,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),domain(X1))),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f17,f805]) ).
fof(f830,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(h,domain(X0))),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f48,f799]) ).
fof(f838,plain,
! [X0] : ifeq(codomain(X0),domain(a),domain(compose(codomain(X0),compose(a,h))),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f345,f83]) ).
fof(f911,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,h))),codomain(compose(a,h))) = codomain(compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f85]) ).
fof(f912,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),domain(X1))),codomain(domain(X1))) = codomain(domain(X1)),
inference(paramodulation,[status(thm)],[f33,f85]) ).
fof(f913,plain,
! [X0] : ifeq(codomain(X0),domain(b),codomain(compose(codomain(X0),g)),codomain(g)) = codomain(g),
inference(paramodulation,[status(thm)],[f55,f85]) ).
fof(f914,plain,
! [X0] : ifeq(codomain(X0),domain(b),codomain(compose(codomain(X0),h)),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f48,f85]) ).
fof(f915,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(codomain(X0),codomain(X1))),codomain(codomain(X1))) = codomain(codomain(X1)),
inference(paramodulation,[status(thm)],[f17,f85]) ).
fof(f926,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),a)),domain(b)) = codomain(a),
inference(paramodulation,[status(thm)],[f24,f85]) ).
fof(f933,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,h))),codomain(h)) = codomain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f367,f911]) ).
fof(f934,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,h))),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f367,f933]) ).
fof(f935,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),domain(X1))),domain(X1)) = codomain(domain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f912]) ).
fof(f936,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),domain(X1))),domain(X1)) = domain(X1),
inference(forward_demodulation,[status(thm)],[f16,f935]) ).
fof(f937,plain,
! [X0] : ifeq(codomain(X0),domain(b),codomain(compose(codomain(X0),g)),codomain(h)) = codomain(g),
inference(forward_demodulation,[status(thm)],[f359,f913]) ).
fof(f938,plain,
! [X0] : ifeq(codomain(X0),domain(b),codomain(compose(codomain(X0),g)),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f359,f937]) ).
fof(f939,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(codomain(X0),codomain(X1))),codomain(X1)) = codomain(codomain(X1)),
inference(forward_demodulation,[status(thm)],[f34,f915]) ).
fof(f940,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(codomain(X0),codomain(X1))),codomain(X1)) = codomain(X1),
inference(forward_demodulation,[status(thm)],[f34,f939]) ).
fof(f956,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),a)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f24,f926]) ).
fof(f959,plain,
codomain(compose(a,b)) = codomain(b),
inference(paramodulation,[status(thm)],[f15,f86]) ).
fof(f960,plain,
ifeq(domain(b),domain(a),codomain(compose(a,compose(a,h))),codomain(compose(a,h))) = codomain(compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f86]) ).
fof(f961,plain,
! [X0] : ifeq(domain(b),domain(X0),codomain(compose(a,domain(X0))),codomain(domain(X0))) = codomain(domain(X0)),
inference(paramodulation,[status(thm)],[f33,f86]) ).
fof(f964,plain,
! [X0] : ifeq(domain(b),codomain(X0),codomain(compose(a,codomain(X0))),codomain(codomain(X0))) = codomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f17,f86]) ).
fof(f972,plain,
ifeq(domain(b),domain(a),codomain(compose(a,a)),domain(b)) = codomain(a),
inference(paramodulation,[status(thm)],[f24,f86]) ).
fof(f975,plain,
ifeq(domain(b),domain(a),codomain(compose(a,compose(a,h))),codomain(h)) = codomain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f367,f960]) ).
fof(f976,plain,
ifeq(domain(b),domain(a),codomain(compose(a,compose(a,h))),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f367,f975]) ).
fof(f977,plain,
! [X0] : ifeq(domain(b),domain(X0),codomain(compose(a,domain(X0))),domain(X0)) = codomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f961]) ).
fof(f978,plain,
! [X0] : ifeq(domain(b),domain(X0),codomain(compose(a,domain(X0))),domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f16,f977]) ).
fof(f983,plain,
! [X0] : ifeq(domain(b),codomain(X0),codomain(compose(a,codomain(X0))),codomain(X0)) = codomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f964]) ).
fof(f984,plain,
! [X0] : ifeq(domain(b),codomain(X0),codomain(compose(a,codomain(X0))),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f34,f983]) ).
fof(f1005,plain,
ifeq(domain(b),domain(a),codomain(compose(a,a)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f24,f972]) ).
fof(f1023,plain,
! [X0,X1] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(b),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(compose(a,b),compose(a,b)),X1,compose(a,b),X0),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f959,f23]) ).
fof(f1024,plain,
! [X0,X1] : ifeq(codomain(b),domain(compose(a,b)),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(compose(a,b),compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f23]) ).
fof(f1025,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,X1)),compose(compose(compose(a,b),X0),X1)),compose(compose(compose(a,b),X0),X1)) = compose(compose(compose(a,b),X0),X1),
inference(paramodulation,[status(thm)],[f959,f22]) ).
fof(f1026,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(compose(a,b)),compose(X1,compose(compose(a,b),X0)),compose(compose(X1,compose(a,b)),X0)),compose(compose(X1,compose(a,b)),X0)) = compose(compose(X1,compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f959,f22]) ).
fof(f1030,plain,
! [X0] : ifeq(codomain(b),domain(X0),codomain(compose(compose(a,b),X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f959,f21]) ).
fof(f1034,plain,
compose(compose(a,b),codomain(b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f19]) ).
fof(f1061,plain,
! [X0] : ifeq(codomain(codomain(b)),domain(X0),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),X0)),compose(compose(compose(a,b),codomain(b)),X0)),compose(compose(a,b),X0)) = compose(compose(compose(a,b),codomain(b)),X0),
inference(paramodulation,[status(thm)],[f1034,f22]) ).
fof(f1077,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),X0)),compose(compose(compose(a,b),codomain(b)),X0)),compose(compose(a,b),X0)) = compose(compose(compose(a,b),codomain(b)),X0),
inference(forward_demodulation,[status(thm)],[f34,f1061]) ).
fof(f1078,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),X0)),compose(compose(compose(a,b),codomain(b)),X0)),compose(compose(a,b),X0)) = compose(compose(compose(a,b),codomain(b)),X0),
inference(forward_demodulation,[status(thm)],[f959,f1077]) ).
fof(f1079,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),codomain(b),compose(compose(a,b),compose(codomain(b),X0)),compose(compose(compose(a,b),codomain(b)),X0)),compose(compose(a,b),X0)) = compose(compose(compose(a,b),codomain(b)),X0),
inference(forward_demodulation,[status(thm)],[f17,f1078]) ).
fof(f1080,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(codomain(b),X0)),compose(compose(a,b),X0)) = compose(compose(compose(a,b),codomain(b)),X0),
inference(forward_demodulation,[status(thm)],[f15,f1079]) ).
fof(f1081,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(codomain(b),X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(forward_demodulation,[status(thm)],[f1034,f1080]) ).
fof(f1103,plain,
! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,h))),codomain(compose(a,h))) = codomain(compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f87]) ).
fof(f1104,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),domain(X1))),codomain(domain(X1))) = codomain(domain(X1)),
inference(paramodulation,[status(thm)],[f33,f87]) ).
fof(f1105,plain,
! [X0] : ifeq(domain(X0),domain(b),codomain(compose(domain(X0),g)),codomain(g)) = codomain(g),
inference(paramodulation,[status(thm)],[f55,f87]) ).
fof(f1106,plain,
! [X0] : ifeq(domain(X0),domain(b),codomain(compose(domain(X0),h)),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f48,f87]) ).
fof(f1107,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),codomain(compose(domain(X0),codomain(X1))),codomain(codomain(X1))) = codomain(codomain(X1)),
inference(paramodulation,[status(thm)],[f17,f87]) ).
fof(f1123,plain,
! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),a)),domain(b)) = codomain(a),
inference(paramodulation,[status(thm)],[f24,f87]) ).
fof(f1131,plain,
! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,h))),codomain(h)) = codomain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f367,f1103]) ).
fof(f1132,plain,
! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,h))),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f367,f1131]) ).
fof(f1133,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),domain(X1))),domain(X1)) = codomain(domain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f1104]) ).
fof(f1134,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),domain(X1))),domain(X1)) = domain(X1),
inference(forward_demodulation,[status(thm)],[f16,f1133]) ).
fof(f1135,plain,
! [X0] : ifeq(domain(X0),domain(b),codomain(compose(domain(X0),g)),codomain(h)) = codomain(g),
inference(forward_demodulation,[status(thm)],[f359,f1105]) ).
fof(f1136,plain,
! [X0] : ifeq(domain(X0),domain(b),codomain(compose(domain(X0),g)),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f359,f1135]) ).
fof(f1137,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),codomain(compose(domain(X0),codomain(X1))),codomain(X1)) = codomain(codomain(X1)),
inference(forward_demodulation,[status(thm)],[f34,f1107]) ).
fof(f1138,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),codomain(compose(domain(X0),codomain(X1))),codomain(X1)) = codomain(X1),
inference(forward_demodulation,[status(thm)],[f34,f1137]) ).
fof(f1160,plain,
! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),a)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f24,f1123]) ).
fof(f1163,plain,
domain(compose(a,b)) = domain(a),
inference(paramodulation,[status(thm)],[f15,f44]) ).
fof(f1164,plain,
ifeq(domain(b),domain(a),domain(compose(a,compose(a,h))),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f345,f44]) ).
fof(f1183,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(compose(a,b)),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,X0),X0),X0),X0) = X0,
inference(backward_demodulation,[status(thm)],[f1163,f23]) ).
fof(f1186,plain,
ifeq(domain(b),domain(a),domain(compose(a,compose(a,b))),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f1163,f44]) ).
fof(f1188,plain,
! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f87]) ).
fof(f1190,plain,
ifeq(domain(b),domain(a),codomain(compose(a,compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f86]) ).
fof(f1191,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f85]) ).
fof(f1192,plain,
! [X0] : ifeq(codomain(X0),domain(a),domain(compose(codomain(X0),compose(a,b))),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f1163,f83]) ).
fof(f1193,plain,
! [X0] : ifeq(codomain(compose(a,b)),domain(X0),domain(compose(compose(a,b),domain(X0))),domain(a)) = domain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f67]) ).
fof(f1196,plain,
ifeq(codomain(compose(a,b)),domain(b),domain(compose(compose(a,b),g)),domain(a)) = domain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f57]) ).
fof(f1197,plain,
ifeq(codomain(compose(a,b)),domain(b),domain(compose(compose(a,b),h)),domain(a)) = domain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f50]) ).
fof(f1198,plain,
! [X0] : ifeq(codomain(compose(a,b)),codomain(X0),domain(compose(compose(a,b),codomain(X0))),domain(a)) = domain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f36]) ).
fof(f1201,plain,
! [X0] : ifeq(domain(X0),domain(a),domain(compose(domain(X0),compose(a,b))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f1163,f551]) ).
fof(f1204,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(a,b))),compose(compose(X1,X0),compose(a,b))),compose(compose(X1,X0),compose(a,b))) = compose(compose(X1,X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f22]) ).
fof(f1207,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f21]) ).
fof(f1209,plain,
! [X0] : ifeq(codomain(compose(a,b)),domain(X0),domain(compose(compose(a,b),X0)),domain(a)) = domain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f20]) ).
fof(f1210,plain,
! [X0] : ifeq(codomain(X0),domain(a),domain(compose(X0,compose(a,b))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f1163,f20]) ).
fof(f1212,plain,
compose(domain(a),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f1163,f18]) ).
fof(f1213,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f1183]) ).
fof(f1216,plain,
! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,b))),codomain(b)) = codomain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1188]) ).
fof(f1217,plain,
! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,b))),codomain(b)) = codomain(b),
inference(forward_demodulation,[status(thm)],[f959,f1216]) ).
fof(f1219,plain,
ifeq(domain(b),domain(a),codomain(compose(a,compose(a,b))),codomain(b)) = codomain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1190]) ).
fof(f1220,plain,
ifeq(domain(b),domain(a),codomain(compose(a,compose(a,b))),codomain(b)) = codomain(b),
inference(forward_demodulation,[status(thm)],[f959,f1219]) ).
fof(f1221,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,b))),codomain(b)) = codomain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1191]) ).
fof(f1222,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,b))),codomain(b)) = codomain(b),
inference(forward_demodulation,[status(thm)],[f959,f1221]) ).
fof(f1223,plain,
! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),domain(X0))),domain(a)) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1193]) ).
fof(f1224,plain,
! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),domain(X0))),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f1163,f1223]) ).
fof(f1227,plain,
ifeq(codomain(b),domain(b),domain(compose(compose(a,b),g)),domain(a)) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1196]) ).
fof(f1228,plain,
ifeq(codomain(b),domain(b),domain(compose(compose(a,b),g)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f1163,f1227]) ).
fof(f1229,plain,
ifeq(codomain(b),domain(b),domain(compose(compose(a,b),h)),domain(a)) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1197]) ).
fof(f1230,plain,
ifeq(codomain(b),domain(b),domain(compose(compose(a,b),h)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f1163,f1229]) ).
fof(f1231,plain,
! [X0] : ifeq(codomain(b),codomain(X0),domain(compose(compose(a,b),codomain(X0))),domain(a)) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1198]) ).
fof(f1232,plain,
! [X0] : ifeq(codomain(b),codomain(X0),domain(compose(compose(a,b),codomain(X0))),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f1163,f1231]) ).
fof(f1247,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,b))),codomain(b)) = codomain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1207]) ).
fof(f1248,plain,
! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,b))),codomain(b)) = codomain(b),
inference(forward_demodulation,[status(thm)],[f959,f1247]) ).
fof(f1250,plain,
! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),X0)),domain(a)) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1209]) ).
fof(f1251,plain,
! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),X0)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f1163,f1250]) ).
fof(f1256,plain,
! [X0] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),X0)),compose(compose(domain(a),compose(a,b)),X0)),compose(compose(a,b),X0)) = compose(compose(domain(a),compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f1212,f22]) ).
fof(f1258,plain,
! [X0] : ifeq(codomain(domain(a)),domain(compose(a,b)),ifeq(codomain(X0),domain(domain(a)),compose(X0,compose(a,b)),compose(compose(X0,domain(a)),compose(a,b))),compose(compose(X0,domain(a)),compose(a,b))) = compose(compose(X0,domain(a)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1212,f22]) ).
fof(f1268,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),X0)),compose(compose(domain(a),compose(a,b)),X0)),compose(compose(a,b),X0)) = compose(compose(domain(a),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f959,f1256]) ).
fof(f1269,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),X0)),compose(compose(domain(a),compose(a,b)),X0)),compose(compose(a,b),X0)) = compose(compose(domain(a),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f16,f1268]) ).
fof(f1270,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,b),X0)),compose(compose(domain(a),compose(a,b)),X0)),compose(compose(a,b),X0)) = compose(compose(domain(a),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f1269]) ).
fof(f1271,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(domain(a),compose(compose(a,b),X0)),compose(compose(a,b),X0)) = compose(compose(domain(a),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f15,f1270]) ).
fof(f1272,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(domain(a),compose(compose(a,b),X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(forward_demodulation,[status(thm)],[f1212,f1271]) ).
fof(f1279,plain,
! [X0] : ifeq(domain(a),domain(compose(a,b)),ifeq(codomain(X0),domain(domain(a)),compose(X0,compose(a,b)),compose(compose(X0,domain(a)),compose(a,b))),compose(compose(X0,domain(a)),compose(a,b))) = compose(compose(X0,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f16,f1258]) ).
fof(f1280,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(domain(a)),compose(X0,compose(a,b)),compose(compose(X0,domain(a)),compose(a,b))),compose(compose(X0,domain(a)),compose(a,b))) = compose(compose(X0,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f1279]) ).
fof(f1281,plain,
! [X0] : ifeq(codomain(X0),domain(domain(a)),compose(X0,compose(a,b)),compose(compose(X0,domain(a)),compose(a,b))) = compose(compose(X0,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f15,f1280]) ).
fof(f1282,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,domain(a)),compose(a,b))) = compose(compose(X0,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f33,f1281]) ).
fof(f1289,plain,
! [X0] : ifeq(codomain(b),domain(X0),codomain(compose(compose(a,b),domain(X0))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f959,f98]) ).
fof(f1290,plain,
! [X0] : ifeq(codomain(h),domain(X0),codomain(compose(compose(a,h),domain(X0))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f367,f98]) ).
fof(f1291,plain,
! [X0] : ifeq(codomain(h),domain(X0),codomain(compose(g,domain(X0))),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f359,f98]) ).
fof(f1378,plain,
! [X0] : ifeq(codomain(b),codomain(X0),codomain(compose(compose(a,b),codomain(X0))),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f959,f100]) ).
fof(f1379,plain,
! [X0] : ifeq(codomain(h),codomain(X0),codomain(compose(compose(a,h),codomain(X0))),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f367,f100]) ).
fof(f1380,plain,
! [X0] : ifeq(codomain(h),codomain(X0),codomain(compose(g,codomain(X0))),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f359,f100]) ).
fof(f1482,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(g,compose(a,b)),X1,g,X0),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f359,f1213]) ).
fof(f1507,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f373]) ).
fof(f1508,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,compose(a,h))),codomain(compose(a,h))) = codomain(compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f373]) ).
fof(f1510,plain,
ifeq(codomain(h),domain(b),codomain(compose(g,g)),codomain(g)) = codomain(g),
inference(paramodulation,[status(thm)],[f55,f373]) ).
fof(f1511,plain,
ifeq(codomain(h),domain(b),codomain(compose(g,h)),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f48,f373]) ).
fof(f1519,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,a)),domain(b)) = codomain(a),
inference(paramodulation,[status(thm)],[f24,f373]) ).
fof(f1521,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,compose(a,b))),codomain(b)) = codomain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f1507]) ).
fof(f1522,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,compose(a,b))),codomain(b)) = codomain(b),
inference(forward_demodulation,[status(thm)],[f959,f1521]) ).
fof(f1523,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,compose(a,h))),codomain(h)) = codomain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f367,f1508]) ).
fof(f1524,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,compose(a,h))),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f367,f1523]) ).
fof(f1527,plain,
ifeq(codomain(h),domain(b),codomain(compose(g,g)),codomain(h)) = codomain(g),
inference(forward_demodulation,[status(thm)],[f359,f1510]) ).
fof(f1528,plain,
ifeq(codomain(h),domain(b),codomain(compose(g,g)),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f359,f1527]) ).
fof(f1547,plain,
ifeq(codomain(h),domain(a),codomain(compose(g,a)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f24,f1519]) ).
fof(f1550,plain,
ifeq(codomain(h),domain(a),domain(compose(h,compose(a,b))),domain(b)) = domain(b),
inference(paramodulation,[status(thm)],[f1163,f53]) ).
fof(f1551,plain,
ifeq(codomain(h),domain(a),domain(compose(h,compose(a,h))),domain(b)) = domain(b),
inference(paramodulation,[status(thm)],[f345,f53]) ).
fof(f1559,plain,
! [X0] : ifeq(codomain(h),domain(X0),domain(compose(g,X0)),domain(b)) = domain(b),
inference(forward_demodulation,[status(thm)],[f359,f60]) ).
fof(f1560,plain,
ifeq(codomain(h),domain(a),domain(compose(g,compose(a,b))),domain(b)) = domain(b),
inference(paramodulation,[status(thm)],[f1163,f1559]) ).
fof(f1561,plain,
ifeq(codomain(h),domain(a),domain(compose(g,compose(a,h))),domain(b)) = domain(b),
inference(paramodulation,[status(thm)],[f345,f1559]) ).
fof(f1573,plain,
! [X0] : ifeq(codomain(X0),domain(b),codomain(compose(X0,g)),codomain(h)) = codomain(g),
inference(forward_demodulation,[status(thm)],[f359,f89]) ).
fof(f1574,plain,
! [X0] : ifeq(codomain(X0),domain(b),codomain(compose(X0,g)),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f359,f1573]) ).
fof(f1575,plain,
ifeq(codomain(b),domain(b),codomain(compose(compose(a,b),g)),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f959,f1574]) ).
fof(f1576,plain,
ifeq(codomain(h),domain(b),codomain(compose(compose(a,h),g)),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f367,f1574]) ).
fof(f1593,plain,
ifeq(codomain(b),domain(b),codomain(compose(compose(a,b),h)),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f959,f90]) ).
fof(f1594,plain,
ifeq(codomain(h),domain(b),codomain(compose(compose(a,h),h)),codomain(h)) = codomain(h),
inference(paramodulation,[status(thm)],[f367,f90]) ).
fof(f1607,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),a)),domain(b)) = domain(b),
inference(paramodulation,[status(thm)],[f959,f106]) ).
fof(f1608,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),a)),domain(b)) = domain(b),
inference(paramodulation,[status(thm)],[f367,f106]) ).
fof(f1798,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,a),b)) = compose(compose(X0,a),b),
inference(paramodulation,[status(thm)],[f15,f184]) ).
fof(f1799,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(a,b))),compose(compose(X0,a),compose(a,b))),compose(compose(X0,a),compose(a,b))) = compose(compose(X0,a),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f184]) ).
fof(f1800,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(a,h))),compose(compose(X0,a),compose(a,h))),compose(compose(X0,a),compose(a,h))) = compose(compose(X0,a),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f184]) ).
fof(f1801,plain,
! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(a,domain(X0))),compose(compose(X1,a),domain(X0))),compose(compose(X1,a),domain(X0))) = compose(compose(X1,a),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f184]) ).
fof(f1803,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,a),h)),compose(compose(X0,a),h)) = compose(compose(X0,a),h),
inference(paramodulation,[status(thm)],[f48,f184]) ).
fof(f1804,plain,
! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(a,codomain(X0))),compose(compose(X1,a),codomain(X0))),compose(compose(X1,a),codomain(X0))) = compose(compose(X1,a),codomain(X0)),
inference(paramodulation,[status(thm)],[f17,f184]) ).
fof(f1805,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,X0)),compose(compose(compose(a,b),a),X0)),compose(compose(compose(a,b),a),X0)) = compose(compose(compose(a,b),a),X0),
inference(paramodulation,[status(thm)],[f959,f184]) ).
fof(f1806,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,X0)),compose(compose(compose(a,h),a),X0)),compose(compose(compose(a,h),a),X0)) = compose(compose(compose(a,h),a),X0),
inference(paramodulation,[status(thm)],[f367,f184]) ).
fof(f1807,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(a,X0)),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
inference(paramodulation,[status(thm)],[f359,f184]) ).
fof(f1808,plain,
! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(a,X0)),compose(compose(codomain(X1),a),X0)),compose(compose(codomain(X1),a),X0)) = compose(compose(codomain(X1),a),X0),
inference(paramodulation,[status(thm)],[f34,f184]) ).
fof(f1809,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(a,X0)),compose(compose(a,a),X0)),compose(compose(a,a),X0)) = compose(compose(a,a),X0),
inference(paramodulation,[status(thm)],[f24,f184]) ).
fof(f1810,plain,
! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(a,X0)),compose(compose(domain(X1),a),X0)),compose(compose(domain(X1),a),X0)) = compose(compose(domain(X1),a),X0),
inference(paramodulation,[status(thm)],[f16,f184]) ).
fof(f1813,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(domain(compose(a,X0))),domain(a),compose(a,X0),compose(compose(domain(compose(a,X0)),a),X0)),compose(compose(domain(compose(a,X0)),a),X0)) = compose(compose(domain(compose(a,X0)),a),X0),
inference(paramodulation,[status(thm)],[f18,f184]) ).
fof(f1817,plain,
! [X0] : ifeq(domain(b),domain(codomain(compose(X0,a))),ifeq(codomain(X0),domain(a),compose(X0,compose(a,codomain(compose(X0,a)))),compose(X0,a)),compose(compose(X0,a),codomain(compose(X0,a)))) = compose(compose(X0,a),codomain(compose(X0,a))),
inference(paramodulation,[status(thm)],[f19,f184]) ).
fof(f1818,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(domain(a)),domain(a),compose(domain(a),compose(a,X0)),compose(a,X0)),compose(compose(domain(a),a),X0)) = compose(compose(domain(a),a),X0),
inference(paramodulation,[status(thm)],[f18,f184]) ).
fof(f1824,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,h)),compose(compose(X0,a),h)) = compose(compose(X0,a),h),
inference(forward_demodulation,[status(thm)],[f15,f1803]) ).
fof(f1832,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(a,X0)),domain(a),compose(a,X0),compose(compose(domain(compose(a,X0)),a),X0)),compose(compose(domain(compose(a,X0)),a),X0)) = compose(compose(domain(compose(a,X0)),a),X0),
inference(forward_demodulation,[status(thm)],[f16,f1813]) ).
fof(f1842,plain,
! [X0] : ifeq(domain(b),codomain(compose(X0,a)),ifeq(codomain(X0),domain(a),compose(X0,compose(a,codomain(compose(X0,a)))),compose(X0,a)),compose(compose(X0,a),codomain(compose(X0,a)))) = compose(compose(X0,a),codomain(compose(X0,a))),
inference(forward_demodulation,[status(thm)],[f17,f1817]) ).
fof(f1843,plain,
! [X0] : ifeq(domain(b),codomain(compose(X0,a)),ifeq(codomain(X0),domain(a),compose(X0,compose(a,codomain(compose(X0,a)))),compose(X0,a)),compose(X0,a)) = compose(compose(X0,a),codomain(compose(X0,a))),
inference(forward_demodulation,[status(thm)],[f19,f1842]) ).
fof(f1844,plain,
! [X0] : ifeq(domain(b),codomain(compose(X0,a)),ifeq(codomain(X0),domain(a),compose(X0,compose(a,codomain(compose(X0,a)))),compose(X0,a)),compose(X0,a)) = compose(X0,a),
inference(forward_demodulation,[status(thm)],[f19,f1843]) ).
fof(f1845,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(a),compose(domain(a),compose(a,X0)),compose(a,X0)),compose(compose(domain(a),a),X0)) = compose(compose(domain(a),a),X0),
inference(forward_demodulation,[status(thm)],[f16,f1818]) ).
fof(f1846,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(domain(a),compose(a,X0)),compose(compose(domain(a),a),X0)) = compose(compose(domain(a),a),X0),
inference(forward_demodulation,[status(thm)],[f15,f1845]) ).
fof(f1847,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(domain(a),compose(a,X0)),compose(a,X0)) = compose(compose(domain(a),a),X0),
inference(forward_demodulation,[status(thm)],[f18,f1846]) ).
fof(f1848,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(domain(a),compose(a,X0)),compose(a,X0)) = compose(a,X0),
inference(forward_demodulation,[status(thm)],[f18,f1847]) ).
fof(f2148,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(a,b))),compose(compose(X1,domain(X0)),compose(a,b))),compose(compose(X1,domain(X0)),compose(a,b))) = compose(compose(X1,domain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f222]) ).
fof(f2149,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(a,h))),compose(compose(X1,domain(X0)),compose(a,h))),compose(compose(X1,domain(X0)),compose(a,h))) = compose(compose(X1,domain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f222]) ).
fof(f2150,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),domain(X1))),compose(compose(X2,domain(X0)),domain(X1))),compose(compose(X2,domain(X0)),domain(X1))) = compose(compose(X2,domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f33,f222]) ).
fof(f2151,plain,
! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),g)),compose(compose(X1,domain(X0)),g)),compose(compose(X1,domain(X0)),g)) = compose(compose(X1,domain(X0)),g),
inference(paramodulation,[status(thm)],[f55,f222]) ).
fof(f2152,plain,
! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),h)),compose(compose(X1,domain(X0)),h)),compose(compose(X1,domain(X0)),h)) = compose(compose(X1,domain(X0)),h),
inference(paramodulation,[status(thm)],[f48,f222]) ).
fof(f2153,plain,
! [X0,X1,X2] : ifeq(domain(X0),codomain(X1),ifeq(codomain(X2),domain(X0),compose(X2,compose(domain(X0),codomain(X1))),compose(compose(X2,domain(X0)),codomain(X1))),compose(compose(X2,domain(X0)),codomain(X1))) = compose(compose(X2,domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f17,f222]) ).
fof(f2154,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),X1)),compose(compose(compose(a,b),domain(X0)),X1)),compose(compose(compose(a,b),domain(X0)),X1)) = compose(compose(compose(a,b),domain(X0)),X1),
inference(paramodulation,[status(thm)],[f959,f222]) ).
fof(f2155,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),X1)),compose(compose(compose(a,h),domain(X0)),X1)),compose(compose(compose(a,h),domain(X0)),X1)) = compose(compose(compose(a,h),domain(X0)),X1),
inference(paramodulation,[status(thm)],[f367,f222]) ).
fof(f2156,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),X1)),compose(compose(g,domain(X0)),X1)),compose(compose(g,domain(X0)),X1)) = compose(compose(g,domain(X0)),X1),
inference(paramodulation,[status(thm)],[f359,f222]) ).
fof(f2157,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),X1)),compose(compose(codomain(X2),domain(X0)),X1)),compose(compose(codomain(X2),domain(X0)),X1)) = compose(compose(codomain(X2),domain(X0)),X1),
inference(paramodulation,[status(thm)],[f34,f222]) ).
fof(f2158,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),X1)),compose(compose(a,domain(X0)),X1)),compose(compose(a,domain(X0)),X1)) = compose(compose(a,domain(X0)),X1),
inference(paramodulation,[status(thm)],[f24,f222]) ).
fof(f2159,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),X1)),compose(compose(domain(X2),domain(X0)),X1)),compose(compose(domain(X2),domain(X0)),X1)) = compose(compose(domain(X2),domain(X0)),X1),
inference(paramodulation,[status(thm)],[f16,f222]) ).
fof(f2166,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(domain(compose(domain(X0),X1))),domain(X0),compose(domain(X0),X1),compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1)),compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1)) = compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1),
inference(paramodulation,[status(thm)],[f18,f222]) ).
fof(f2180,plain,
! [X0,X1] : ifeq(domain(X0),domain(codomain(compose(X1,domain(X0)))),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),codomain(compose(X1,domain(X0))))),compose(X1,domain(X0))),compose(compose(X1,domain(X0)),codomain(compose(X1,domain(X0))))) = compose(compose(X1,domain(X0)),codomain(compose(X1,domain(X0)))),
inference(paramodulation,[status(thm)],[f19,f222]) ).
fof(f2262,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(compose(domain(X0),X1)),domain(X0),compose(domain(X0),X1),compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1)),compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1)) = compose(compose(domain(compose(domain(X0),X1)),domain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f16,f2166]) ).
fof(f2309,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(X1,domain(X0))),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),codomain(compose(X1,domain(X0))))),compose(X1,domain(X0))),compose(compose(X1,domain(X0)),codomain(compose(X1,domain(X0))))) = compose(compose(X1,domain(X0)),codomain(compose(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f2180]) ).
fof(f2310,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(X1,domain(X0))),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),codomain(compose(X1,domain(X0))))),compose(X1,domain(X0))),compose(X1,domain(X0))) = compose(compose(X1,domain(X0)),codomain(compose(X1,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f2309]) ).
fof(f2311,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(X1,domain(X0))),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),codomain(compose(X1,domain(X0))))),compose(X1,domain(X0))),compose(X1,domain(X0))) = compose(X1,domain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f2310]) ).
fof(f2477,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(codomain(X0),domain(compose(a,b)),compose(X0,compose(compose(a,b),g)),compose(compose(X0,compose(a,b)),g)),compose(compose(X0,compose(a,b)),g)) = compose(compose(X0,compose(a,b)),g),
inference(paramodulation,[status(thm)],[f959,f187]) ).
fof(f2478,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(compose(a,h)),compose(X0,compose(compose(a,h),g)),compose(compose(X0,compose(a,h)),g)),compose(compose(X0,compose(a,h)),g)) = compose(compose(X0,compose(a,h)),g),
inference(paramodulation,[status(thm)],[f367,f187]) ).
fof(f2480,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),domain(codomain(X0)),compose(X1,compose(codomain(X0),g)),compose(compose(X1,codomain(X0)),g)),compose(compose(X1,codomain(X0)),g)) = compose(compose(X1,codomain(X0)),g),
inference(paramodulation,[status(thm)],[f34,f187]) ).
fof(f2483,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,g)),compose(compose(compose(a,b),X0),g)),compose(compose(compose(a,b),X0),g)) = compose(compose(compose(a,b),X0),g),
inference(paramodulation,[status(thm)],[f959,f187]) ).
fof(f2484,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,g)),compose(compose(compose(a,h),X0),g)),compose(compose(compose(a,h),X0),g)) = compose(compose(compose(a,h),X0),g),
inference(paramodulation,[status(thm)],[f367,f187]) ).
fof(f2485,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(h),domain(X0),compose(g,compose(X0,g)),compose(compose(g,X0),g)),compose(compose(g,X0),g)) = compose(compose(g,X0),g),
inference(paramodulation,[status(thm)],[f359,f187]) ).
fof(f2486,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,g)),compose(compose(codomain(X1),X0),g)),compose(compose(codomain(X1),X0),g)) = compose(compose(codomain(X1),X0),g),
inference(paramodulation,[status(thm)],[f34,f187]) ).
fof(f2487,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(b),domain(X0),compose(a,compose(X0,g)),compose(compose(a,X0),g)),compose(compose(a,X0),g)) = compose(compose(a,X0),g),
inference(paramodulation,[status(thm)],[f24,f187]) ).
fof(f2488,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,g)),compose(compose(domain(X1),X0),g)),compose(compose(domain(X1),X0),g)) = compose(compose(domain(X1),X0),g),
inference(paramodulation,[status(thm)],[f16,f187]) ).
fof(f2492,plain,
! [X0] : ifeq(codomain(g),domain(b),ifeq(codomain(X0),domain(b),compose(X0,compose(g,g)),compose(compose(X0,g),g)),compose(compose(X0,g),g)) = compose(compose(X0,g),g),
inference(paramodulation,[status(thm)],[f55,f187]) ).
fof(f2493,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(b),compose(X0,compose(h,g)),compose(compose(X0,h),g)),compose(compose(X0,h),g)) = compose(compose(X0,h),g),
inference(paramodulation,[status(thm)],[f48,f187]) ).
fof(f2495,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(domain(compose(X0,g))),domain(X0),compose(X0,g),compose(compose(domain(compose(X0,g)),X0),g)),compose(compose(domain(compose(X0,g)),X0),g)) = compose(compose(domain(compose(X0,g)),X0),g),
inference(paramodulation,[status(thm)],[f18,f187]) ).
fof(f2499,plain,
ifeq(codomain(codomain(b)),domain(b),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)),compose(compose(compose(a,b),codomain(b)),g)) = compose(compose(compose(a,b),codomain(b)),g),
inference(paramodulation,[status(thm)],[f1034,f187]) ).
fof(f2500,plain,
ifeq(codomain(codomain(h)),domain(b),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),g)),compose(compose(a,h),g)),compose(compose(compose(a,h),codomain(h)),g)) = compose(compose(compose(a,h),codomain(h)),g),
inference(paramodulation,[status(thm)],[f477,f187]) ).
fof(f2501,plain,
ifeq(codomain(codomain(h)),domain(b),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),g)),compose(g,g)),compose(compose(g,codomain(h)),g)) = compose(compose(g,codomain(h)),g),
inference(paramodulation,[status(thm)],[f377,f187]) ).
fof(f2502,plain,
! [X0] : ifeq(codomain(codomain(X0)),domain(b),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)),compose(compose(codomain(X0),codomain(X0)),g)) = compose(compose(codomain(X0),codomain(X0)),g),
inference(paramodulation,[status(thm)],[f32,f187]) ).
fof(f2503,plain,
ifeq(codomain(g),domain(b),ifeq(codomain(a),domain(g),compose(a,compose(g,g)),compose(compose(a,h),g)),compose(compose(a,g),g)) = compose(compose(a,g),g),
inference(paramodulation,[status(thm)],[f27,f187]) ).
fof(f2505,plain,
ifeq(codomain(compose(a,b)),domain(b),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)),compose(compose(domain(a),compose(a,b)),g)) = compose(compose(domain(a),compose(a,b)),g),
inference(paramodulation,[status(thm)],[f1212,f187]) ).
fof(f2506,plain,
ifeq(codomain(compose(a,h)),domain(b),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),g)),compose(compose(a,h),g)),compose(compose(domain(a),compose(a,h)),g)) = compose(compose(domain(a),compose(a,h)),g),
inference(paramodulation,[status(thm)],[f441,f187]) ).
fof(f2507,plain,
ifeq(codomain(g),domain(b),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,g)),compose(g,g)),compose(compose(domain(b),g),g)) = compose(compose(domain(b),g),g),
inference(paramodulation,[status(thm)],[f59,f187]) ).
fof(f2508,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(b)),domain(h),compose(domain(b),compose(h,g)),compose(h,g)),compose(compose(domain(b),h),g)) = compose(compose(domain(b),h),g),
inference(paramodulation,[status(thm)],[f52,f187]) ).
fof(f2509,plain,
! [X0] : ifeq(codomain(domain(X0)),domain(b),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)),compose(compose(domain(X0),domain(X0)),g)) = compose(compose(domain(X0),domain(X0)),g),
inference(paramodulation,[status(thm)],[f29,f187]) ).
fof(f2510,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(domain(X0)),domain(X0),compose(domain(X0),compose(X0,g)),compose(X0,g)),compose(compose(domain(X0),X0),g)) = compose(compose(domain(X0),X0),g),
inference(paramodulation,[status(thm)],[f18,f187]) ).
fof(f2511,plain,
! [X0] : ifeq(codomain(codomain(X0)),domain(b),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),g)),compose(X0,g)),compose(compose(X0,codomain(X0)),g)) = compose(compose(X0,codomain(X0)),g),
inference(paramodulation,[status(thm)],[f19,f187]) ).
fof(f2525,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),g)),compose(compose(X0,compose(a,b)),g)),compose(compose(X0,compose(a,b)),g)) = compose(compose(X0,compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1163,f2477]) ).
fof(f2526,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),g)),compose(compose(X0,compose(a,h)),g)),compose(compose(X0,compose(a,h)),g)) = compose(compose(X0,compose(a,h)),g),
inference(forward_demodulation,[status(thm)],[f345,f2478]) ).
fof(f2528,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),g)),compose(compose(X1,codomain(X0)),g)),compose(compose(X1,codomain(X0)),g)) = compose(compose(X1,codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f17,f2480]) ).
fof(f2535,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(b),compose(X0,compose(g,g)),compose(compose(X0,g),g)),compose(compose(X0,g),g)) = compose(compose(X0,g),g),
inference(forward_demodulation,[status(thm)],[f359,f2492]) ).
fof(f2537,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(compose(X0,g)),domain(X0),compose(X0,g),compose(compose(domain(compose(X0,g)),X0),g)),compose(compose(domain(compose(X0,g)),X0),g)) = compose(compose(domain(compose(X0,g)),X0),g),
inference(forward_demodulation,[status(thm)],[f16,f2495]) ).
fof(f2550,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)),compose(compose(compose(a,b),codomain(b)),g)) = compose(compose(compose(a,b),codomain(b)),g),
inference(forward_demodulation,[status(thm)],[f34,f2499]) ).
fof(f2551,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(b),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)),compose(compose(compose(a,b),codomain(b)),g)) = compose(compose(compose(a,b),codomain(b)),g),
inference(forward_demodulation,[status(thm)],[f959,f2550]) ).
fof(f2552,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(b),codomain(b),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)),compose(compose(compose(a,b),codomain(b)),g)) = compose(compose(compose(a,b),codomain(b)),g),
inference(forward_demodulation,[status(thm)],[f17,f2551]) ).
fof(f2553,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),compose(codomain(b),g)),compose(compose(compose(a,b),codomain(b)),g)) = compose(compose(compose(a,b),codomain(b)),g),
inference(forward_demodulation,[status(thm)],[f15,f2552]) ).
fof(f2554,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)) = compose(compose(compose(a,b),codomain(b)),g),
inference(forward_demodulation,[status(thm)],[f1034,f2553]) ).
fof(f2555,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(forward_demodulation,[status(thm)],[f1034,f2554]) ).
fof(f2556,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),g)),compose(compose(a,h),g)),compose(compose(compose(a,h),codomain(h)),g)) = compose(compose(compose(a,h),codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f34,f2500]) ).
fof(f2557,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),g)),compose(compose(a,h),g)),compose(compose(compose(a,h),codomain(h)),g)) = compose(compose(compose(a,h),codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f367,f2556]) ).
fof(f2558,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),codomain(h),compose(compose(a,h),compose(codomain(h),g)),compose(compose(a,h),g)),compose(compose(compose(a,h),codomain(h)),g)) = compose(compose(compose(a,h),codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f17,f2557]) ).
fof(f2559,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),compose(codomain(h),g)),compose(compose(compose(a,h),codomain(h)),g)) = compose(compose(compose(a,h),codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f15,f2558]) ).
fof(f2560,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),compose(codomain(h),g)),compose(compose(a,h),g)) = compose(compose(compose(a,h),codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f477,f2559]) ).
fof(f2561,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),compose(codomain(h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(forward_demodulation,[status(thm)],[f477,f2560]) ).
fof(f2562,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),g)),compose(g,g)),compose(compose(g,codomain(h)),g)) = compose(compose(g,codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f34,f2501]) ).
fof(f2563,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(codomain(h)),compose(g,compose(codomain(h),g)),compose(g,g)),compose(compose(g,codomain(h)),g)) = compose(compose(g,codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f359,f2562]) ).
fof(f2564,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),codomain(h),compose(g,compose(codomain(h),g)),compose(g,g)),compose(compose(g,codomain(h)),g)) = compose(compose(g,codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f17,f2563]) ).
fof(f2565,plain,
ifeq(codomain(h),domain(b),compose(g,compose(codomain(h),g)),compose(compose(g,codomain(h)),g)) = compose(compose(g,codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f15,f2564]) ).
fof(f2566,plain,
ifeq(codomain(h),domain(b),compose(g,compose(codomain(h),g)),compose(g,g)) = compose(compose(g,codomain(h)),g),
inference(forward_demodulation,[status(thm)],[f377,f2565]) ).
fof(f2567,plain,
ifeq(codomain(h),domain(b),compose(g,compose(codomain(h),g)),compose(g,g)) = compose(g,g),
inference(forward_demodulation,[status(thm)],[f377,f2566]) ).
fof(f2568,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)),compose(compose(codomain(X0),codomain(X0)),g)) = compose(compose(codomain(X0),codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f34,f2502]) ).
fof(f2569,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(X0),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)),compose(compose(codomain(X0),codomain(X0)),g)) = compose(compose(codomain(X0),codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f34,f2568]) ).
fof(f2570,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(X0),codomain(X0),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)),compose(compose(codomain(X0),codomain(X0)),g)) = compose(compose(codomain(X0),codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f17,f2569]) ).
fof(f2571,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(codomain(X0),g)),compose(compose(codomain(X0),codomain(X0)),g)) = compose(compose(codomain(X0),codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f15,f2570]) ).
fof(f2572,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(compose(codomain(X0),codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f32,f2571]) ).
fof(f2573,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(codomain(X0),g),
inference(forward_demodulation,[status(thm)],[f32,f2572]) ).
fof(f2574,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(a),domain(g),compose(a,compose(g,g)),compose(compose(a,h),g)),compose(compose(a,g),g)) = compose(compose(a,g),g),
inference(forward_demodulation,[status(thm)],[f359,f2503]) ).
fof(f2575,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(g),compose(a,compose(g,g)),compose(compose(a,h),g)),compose(compose(a,g),g)) = compose(compose(a,g),g),
inference(forward_demodulation,[status(thm)],[f24,f2574]) ).
fof(f2576,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(b),compose(a,compose(g,g)),compose(compose(a,h),g)),compose(compose(a,g),g)) = compose(compose(a,g),g),
inference(forward_demodulation,[status(thm)],[f55,f2575]) ).
fof(f2577,plain,
ifeq(codomain(h),domain(b),compose(a,compose(g,g)),compose(compose(a,g),g)) = compose(compose(a,g),g),
inference(forward_demodulation,[status(thm)],[f15,f2576]) ).
fof(f2578,plain,
ifeq(codomain(h),domain(b),compose(a,compose(g,g)),compose(compose(a,h),g)) = compose(compose(a,g),g),
inference(forward_demodulation,[status(thm)],[f27,f2577]) ).
fof(f2579,plain,
ifeq(codomain(h),domain(b),compose(a,compose(g,g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(forward_demodulation,[status(thm)],[f27,f2578]) ).
fof(f2588,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)),compose(compose(domain(a),compose(a,b)),g)) = compose(compose(domain(a),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f959,f2505]) ).
fof(f2589,plain,
ifeq(codomain(b),domain(b),ifeq(domain(a),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)),compose(compose(domain(a),compose(a,b)),g)) = compose(compose(domain(a),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f16,f2588]) ).
fof(f2590,plain,
ifeq(codomain(b),domain(b),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)),compose(compose(domain(a),compose(a,b)),g)) = compose(compose(domain(a),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1163,f2589]) ).
fof(f2591,plain,
ifeq(codomain(b),domain(b),compose(domain(a),compose(compose(a,b),g)),compose(compose(domain(a),compose(a,b)),g)) = compose(compose(domain(a),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f15,f2590]) ).
fof(f2592,plain,
ifeq(codomain(b),domain(b),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(domain(a),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1212,f2591]) ).
fof(f2593,plain,
ifeq(codomain(b),domain(b),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(forward_demodulation,[status(thm)],[f1212,f2592]) ).
fof(f2594,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),g)),compose(compose(a,h),g)),compose(compose(domain(a),compose(a,h)),g)) = compose(compose(domain(a),compose(a,h)),g),
inference(forward_demodulation,[status(thm)],[f367,f2506]) ).
fof(f2595,plain,
ifeq(codomain(h),domain(b),ifeq(domain(a),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),g)),compose(compose(a,h),g)),compose(compose(domain(a),compose(a,h)),g)) = compose(compose(domain(a),compose(a,h)),g),
inference(forward_demodulation,[status(thm)],[f16,f2594]) ).
fof(f2596,plain,
ifeq(codomain(h),domain(b),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,h),g)),compose(compose(a,h),g)),compose(compose(domain(a),compose(a,h)),g)) = compose(compose(domain(a),compose(a,h)),g),
inference(forward_demodulation,[status(thm)],[f345,f2595]) ).
fof(f2597,plain,
ifeq(codomain(h),domain(b),compose(domain(a),compose(compose(a,h),g)),compose(compose(domain(a),compose(a,h)),g)) = compose(compose(domain(a),compose(a,h)),g),
inference(forward_demodulation,[status(thm)],[f15,f2596]) ).
fof(f2598,plain,
ifeq(codomain(h),domain(b),compose(domain(a),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(domain(a),compose(a,h)),g),
inference(forward_demodulation,[status(thm)],[f441,f2597]) ).
fof(f2599,plain,
ifeq(codomain(h),domain(b),compose(domain(a),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(forward_demodulation,[status(thm)],[f441,f2598]) ).
fof(f2600,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,g)),compose(g,g)),compose(compose(domain(b),g),g)) = compose(compose(domain(b),g),g),
inference(forward_demodulation,[status(thm)],[f359,f2507]) ).
fof(f2601,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(g),compose(domain(b),compose(g,g)),compose(g,g)),compose(compose(domain(b),g),g)) = compose(compose(domain(b),g),g),
inference(forward_demodulation,[status(thm)],[f16,f2600]) ).
fof(f2602,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(b),compose(domain(b),compose(g,g)),compose(g,g)),compose(compose(domain(b),g),g)) = compose(compose(domain(b),g),g),
inference(forward_demodulation,[status(thm)],[f55,f2601]) ).
fof(f2603,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(g,g)),compose(compose(domain(b),g),g)) = compose(compose(domain(b),g),g),
inference(forward_demodulation,[status(thm)],[f15,f2602]) ).
fof(f2604,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(g,g)),compose(g,g)) = compose(compose(domain(b),g),g),
inference(forward_demodulation,[status(thm)],[f59,f2603]) ).
fof(f2605,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(g,g)),compose(g,g)) = compose(g,g),
inference(forward_demodulation,[status(thm)],[f59,f2604]) ).
fof(f2606,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(h),compose(domain(b),compose(h,g)),compose(h,g)),compose(compose(domain(b),h),g)) = compose(compose(domain(b),h),g),
inference(forward_demodulation,[status(thm)],[f16,f2508]) ).
fof(f2607,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(b),compose(domain(b),compose(h,g)),compose(h,g)),compose(compose(domain(b),h),g)) = compose(compose(domain(b),h),g),
inference(forward_demodulation,[status(thm)],[f48,f2606]) ).
fof(f2608,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(h,g)),compose(compose(domain(b),h),g)) = compose(compose(domain(b),h),g),
inference(forward_demodulation,[status(thm)],[f15,f2607]) ).
fof(f2609,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(h,g)),compose(h,g)) = compose(compose(domain(b),h),g),
inference(forward_demodulation,[status(thm)],[f52,f2608]) ).
fof(f2610,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(h,g)),compose(h,g)) = compose(h,g),
inference(forward_demodulation,[status(thm)],[f52,f2609]) ).
fof(f2611,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)),compose(compose(domain(X0),domain(X0)),g)) = compose(compose(domain(X0),domain(X0)),g),
inference(forward_demodulation,[status(thm)],[f16,f2509]) ).
fof(f2612,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(domain(X0),domain(domain(X0)),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)),compose(compose(domain(X0),domain(X0)),g)) = compose(compose(domain(X0),domain(X0)),g),
inference(forward_demodulation,[status(thm)],[f16,f2611]) ).
fof(f2613,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)),compose(compose(domain(X0),domain(X0)),g)) = compose(compose(domain(X0),domain(X0)),g),
inference(forward_demodulation,[status(thm)],[f33,f2612]) ).
fof(f2614,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),compose(domain(X0),g)),compose(compose(domain(X0),domain(X0)),g)) = compose(compose(domain(X0),domain(X0)),g),
inference(forward_demodulation,[status(thm)],[f15,f2613]) ).
fof(f2615,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)) = compose(compose(domain(X0),domain(X0)),g),
inference(forward_demodulation,[status(thm)],[f29,f2614]) ).
fof(f2616,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)) = compose(domain(X0),g),
inference(forward_demodulation,[status(thm)],[f29,f2615]) ).
fof(f2617,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(X0,g)),compose(X0,g)),compose(compose(domain(X0),X0),g)) = compose(compose(domain(X0),X0),g),
inference(forward_demodulation,[status(thm)],[f16,f2510]) ).
fof(f2618,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(domain(X0),compose(X0,g)),compose(compose(domain(X0),X0),g)) = compose(compose(domain(X0),X0),g),
inference(forward_demodulation,[status(thm)],[f15,f2617]) ).
fof(f2619,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(domain(X0),compose(X0,g)),compose(X0,g)) = compose(compose(domain(X0),X0),g),
inference(forward_demodulation,[status(thm)],[f18,f2618]) ).
fof(f2620,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(domain(X0),compose(X0,g)),compose(X0,g)) = compose(X0,g),
inference(forward_demodulation,[status(thm)],[f18,f2619]) ).
fof(f2621,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),g)),compose(X0,g)),compose(compose(X0,codomain(X0)),g)) = compose(compose(X0,codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f34,f2511]) ).
fof(f2622,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(X0),codomain(X0),compose(X0,compose(codomain(X0),g)),compose(X0,g)),compose(compose(X0,codomain(X0)),g)) = compose(compose(X0,codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f17,f2621]) ).
fof(f2623,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,compose(codomain(X0),g)),compose(compose(X0,codomain(X0)),g)) = compose(compose(X0,codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f15,f2622]) ).
fof(f2624,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,compose(codomain(X0),g)),compose(X0,g)) = compose(compose(X0,codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f19,f2623]) ).
fof(f2625,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,compose(codomain(X0),g)),compose(X0,g)) = compose(X0,g),
inference(forward_demodulation,[status(thm)],[f19,f2624]) ).
fof(f2860,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(codomain(X0),domain(compose(a,b)),compose(X0,compose(compose(a,b),h)),compose(compose(X0,compose(a,b)),h)),compose(compose(X0,compose(a,b)),h)) = compose(compose(X0,compose(a,b)),h),
inference(paramodulation,[status(thm)],[f959,f188]) ).
fof(f2861,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(compose(a,h)),compose(X0,compose(compose(a,h),h)),compose(compose(X0,compose(a,h)),h)),compose(compose(X0,compose(a,h)),h)) = compose(compose(X0,compose(a,h)),h),
inference(paramodulation,[status(thm)],[f367,f188]) ).
fof(f2863,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),domain(codomain(X0)),compose(X1,compose(codomain(X0),h)),compose(compose(X1,codomain(X0)),h)),compose(compose(X1,codomain(X0)),h)) = compose(compose(X1,codomain(X0)),h),
inference(paramodulation,[status(thm)],[f34,f188]) ).
fof(f2866,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,h)),compose(compose(compose(a,b),X0),h)),compose(compose(compose(a,b),X0),h)) = compose(compose(compose(a,b),X0),h),
inference(paramodulation,[status(thm)],[f959,f188]) ).
fof(f2867,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,h)),compose(compose(compose(a,h),X0),h)),compose(compose(compose(a,h),X0),h)) = compose(compose(compose(a,h),X0),h),
inference(paramodulation,[status(thm)],[f367,f188]) ).
fof(f2868,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(h),domain(X0),compose(g,compose(X0,h)),compose(compose(g,X0),h)),compose(compose(g,X0),h)) = compose(compose(g,X0),h),
inference(paramodulation,[status(thm)],[f359,f188]) ).
fof(f2869,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,h)),compose(compose(codomain(X1),X0),h)),compose(compose(codomain(X1),X0),h)) = compose(compose(codomain(X1),X0),h),
inference(paramodulation,[status(thm)],[f34,f188]) ).
fof(f2870,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(b),domain(X0),compose(a,compose(X0,h)),compose(compose(a,X0),h)),compose(compose(a,X0),h)) = compose(compose(a,X0),h),
inference(paramodulation,[status(thm)],[f24,f188]) ).
fof(f2871,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,h)),compose(compose(domain(X1),X0),h)),compose(compose(domain(X1),X0),h)) = compose(compose(domain(X1),X0),h),
inference(paramodulation,[status(thm)],[f16,f188]) ).
fof(f2875,plain,
! [X0] : ifeq(codomain(g),domain(b),ifeq(codomain(X0),domain(b),compose(X0,compose(g,h)),compose(compose(X0,g),h)),compose(compose(X0,g),h)) = compose(compose(X0,g),h),
inference(paramodulation,[status(thm)],[f55,f188]) ).
fof(f2876,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(b),compose(X0,compose(h,h)),compose(compose(X0,h),h)),compose(compose(X0,h),h)) = compose(compose(X0,h),h),
inference(paramodulation,[status(thm)],[f48,f188]) ).
fof(f2879,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(domain(compose(X0,h))),domain(X0),compose(X0,h),compose(compose(domain(compose(X0,h)),X0),h)),compose(compose(domain(compose(X0,h)),X0),h)) = compose(compose(domain(compose(X0,h)),X0),h),
inference(paramodulation,[status(thm)],[f18,f188]) ).
fof(f2882,plain,
ifeq(codomain(codomain(b)),domain(b),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),h)),compose(compose(a,b),h)),compose(compose(compose(a,b),codomain(b)),h)) = compose(compose(compose(a,b),codomain(b)),h),
inference(paramodulation,[status(thm)],[f1034,f188]) ).
fof(f2883,plain,
ifeq(codomain(codomain(h)),domain(b),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),h)),compose(compose(a,h),h)),compose(compose(compose(a,h),codomain(h)),h)) = compose(compose(compose(a,h),codomain(h)),h),
inference(paramodulation,[status(thm)],[f477,f188]) ).
fof(f2884,plain,
ifeq(codomain(codomain(h)),domain(b),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),h)),compose(g,h)),compose(compose(g,codomain(h)),h)) = compose(compose(g,codomain(h)),h),
inference(paramodulation,[status(thm)],[f377,f188]) ).
fof(f2885,plain,
! [X0] : ifeq(codomain(codomain(X0)),domain(b),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),h)),compose(codomain(X0),h)),compose(compose(codomain(X0),codomain(X0)),h)) = compose(compose(codomain(X0),codomain(X0)),h),
inference(paramodulation,[status(thm)],[f32,f188]) ).
fof(f2886,plain,
ifeq(codomain(g),domain(b),ifeq(codomain(a),domain(g),compose(a,compose(g,h)),compose(compose(a,h),h)),compose(compose(a,g),h)) = compose(compose(a,g),h),
inference(paramodulation,[status(thm)],[f27,f188]) ).
fof(f2888,plain,
ifeq(codomain(compose(a,b)),domain(b),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),h)),compose(compose(a,b),h)),compose(compose(domain(a),compose(a,b)),h)) = compose(compose(domain(a),compose(a,b)),h),
inference(paramodulation,[status(thm)],[f1212,f188]) ).
fof(f2889,plain,
ifeq(codomain(compose(a,h)),domain(b),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),h)),compose(compose(a,h),h)),compose(compose(domain(a),compose(a,h)),h)) = compose(compose(domain(a),compose(a,h)),h),
inference(paramodulation,[status(thm)],[f441,f188]) ).
fof(f2890,plain,
ifeq(codomain(g),domain(b),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,h)),compose(g,h)),compose(compose(domain(b),g),h)) = compose(compose(domain(b),g),h),
inference(paramodulation,[status(thm)],[f59,f188]) ).
fof(f2891,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(b)),domain(h),compose(domain(b),compose(h,h)),compose(h,h)),compose(compose(domain(b),h),h)) = compose(compose(domain(b),h),h),
inference(paramodulation,[status(thm)],[f52,f188]) ).
fof(f2892,plain,
! [X0] : ifeq(codomain(domain(X0)),domain(b),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),h)),compose(domain(X0),h)),compose(compose(domain(X0),domain(X0)),h)) = compose(compose(domain(X0),domain(X0)),h),
inference(paramodulation,[status(thm)],[f29,f188]) ).
fof(f2893,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(domain(X0)),domain(X0),compose(domain(X0),compose(X0,h)),compose(X0,h)),compose(compose(domain(X0),X0),h)) = compose(compose(domain(X0),X0),h),
inference(paramodulation,[status(thm)],[f18,f188]) ).
fof(f2894,plain,
! [X0] : ifeq(codomain(codomain(X0)),domain(b),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),h)),compose(X0,h)),compose(compose(X0,codomain(X0)),h)) = compose(compose(X0,codomain(X0)),h),
inference(paramodulation,[status(thm)],[f19,f188]) ).
fof(f2908,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),h)),compose(compose(X0,compose(a,b)),h)),compose(compose(X0,compose(a,b)),h)) = compose(compose(X0,compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1163,f2860]) ).
fof(f2909,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),h)),compose(compose(X0,compose(a,h)),h)),compose(compose(X0,compose(a,h)),h)) = compose(compose(X0,compose(a,h)),h),
inference(forward_demodulation,[status(thm)],[f345,f2861]) ).
fof(f2911,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),h)),compose(compose(X1,codomain(X0)),h)),compose(compose(X1,codomain(X0)),h)) = compose(compose(X1,codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f17,f2863]) ).
fof(f2917,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(b),compose(X0,compose(g,h)),compose(compose(X0,g),h)),compose(compose(X0,g),h)) = compose(compose(X0,g),h),
inference(forward_demodulation,[status(thm)],[f359,f2875]) ).
fof(f2923,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(compose(X0,h)),domain(X0),compose(X0,h),compose(compose(domain(compose(X0,h)),X0),h)),compose(compose(domain(compose(X0,h)),X0),h)) = compose(compose(domain(compose(X0,h)),X0),h),
inference(forward_demodulation,[status(thm)],[f16,f2879]) ).
fof(f2934,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),h)),compose(compose(a,b),h)),compose(compose(compose(a,b),codomain(b)),h)) = compose(compose(compose(a,b),codomain(b)),h),
inference(forward_demodulation,[status(thm)],[f34,f2882]) ).
fof(f2935,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(b),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),h)),compose(compose(a,b),h)),compose(compose(compose(a,b),codomain(b)),h)) = compose(compose(compose(a,b),codomain(b)),h),
inference(forward_demodulation,[status(thm)],[f959,f2934]) ).
fof(f2936,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(b),codomain(b),compose(compose(a,b),compose(codomain(b),h)),compose(compose(a,b),h)),compose(compose(compose(a,b),codomain(b)),h)) = compose(compose(compose(a,b),codomain(b)),h),
inference(forward_demodulation,[status(thm)],[f17,f2935]) ).
fof(f2937,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),compose(codomain(b),h)),compose(compose(compose(a,b),codomain(b)),h)) = compose(compose(compose(a,b),codomain(b)),h),
inference(forward_demodulation,[status(thm)],[f15,f2936]) ).
fof(f2938,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),compose(codomain(b),h)),compose(compose(a,b),h)) = compose(compose(compose(a,b),codomain(b)),h),
inference(forward_demodulation,[status(thm)],[f1034,f2937]) ).
fof(f2939,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),compose(codomain(b),h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(forward_demodulation,[status(thm)],[f1034,f2938]) ).
fof(f2940,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),h)),compose(compose(a,h),h)),compose(compose(compose(a,h),codomain(h)),h)) = compose(compose(compose(a,h),codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f34,f2883]) ).
fof(f2941,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),h)),compose(compose(a,h),h)),compose(compose(compose(a,h),codomain(h)),h)) = compose(compose(compose(a,h),codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f367,f2940]) ).
fof(f2942,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),codomain(h),compose(compose(a,h),compose(codomain(h),h)),compose(compose(a,h),h)),compose(compose(compose(a,h),codomain(h)),h)) = compose(compose(compose(a,h),codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f17,f2941]) ).
fof(f2943,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),compose(codomain(h),h)),compose(compose(compose(a,h),codomain(h)),h)) = compose(compose(compose(a,h),codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f15,f2942]) ).
fof(f2944,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),compose(codomain(h),h)),compose(compose(a,h),h)) = compose(compose(compose(a,h),codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f477,f2943]) ).
fof(f2945,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),compose(codomain(h),h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(forward_demodulation,[status(thm)],[f477,f2944]) ).
fof(f2946,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),h)),compose(g,h)),compose(compose(g,codomain(h)),h)) = compose(compose(g,codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f34,f2884]) ).
fof(f2947,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(codomain(h)),compose(g,compose(codomain(h),h)),compose(g,h)),compose(compose(g,codomain(h)),h)) = compose(compose(g,codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f359,f2946]) ).
fof(f2948,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),codomain(h),compose(g,compose(codomain(h),h)),compose(g,h)),compose(compose(g,codomain(h)),h)) = compose(compose(g,codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f17,f2947]) ).
fof(f2949,plain,
ifeq(codomain(h),domain(b),compose(g,compose(codomain(h),h)),compose(compose(g,codomain(h)),h)) = compose(compose(g,codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f15,f2948]) ).
fof(f2950,plain,
ifeq(codomain(h),domain(b),compose(g,compose(codomain(h),h)),compose(g,h)) = compose(compose(g,codomain(h)),h),
inference(forward_demodulation,[status(thm)],[f377,f2949]) ).
fof(f2951,plain,
ifeq(codomain(h),domain(b),compose(g,compose(codomain(h),h)),compose(g,h)) = compose(g,h),
inference(forward_demodulation,[status(thm)],[f377,f2950]) ).
fof(f2952,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),h)),compose(codomain(X0),h)),compose(compose(codomain(X0),codomain(X0)),h)) = compose(compose(codomain(X0),codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f34,f2885]) ).
fof(f2953,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(X0),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),h)),compose(codomain(X0),h)),compose(compose(codomain(X0),codomain(X0)),h)) = compose(compose(codomain(X0),codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f34,f2952]) ).
fof(f2954,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(X0),codomain(X0),compose(codomain(X0),compose(codomain(X0),h)),compose(codomain(X0),h)),compose(compose(codomain(X0),codomain(X0)),h)) = compose(compose(codomain(X0),codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f17,f2953]) ).
fof(f2955,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(codomain(X0),h)),compose(compose(codomain(X0),codomain(X0)),h)) = compose(compose(codomain(X0),codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f15,f2954]) ).
fof(f2956,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(codomain(X0),h)),compose(codomain(X0),h)) = compose(compose(codomain(X0),codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f32,f2955]) ).
fof(f2957,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(codomain(X0),h)),compose(codomain(X0),h)) = compose(codomain(X0),h),
inference(forward_demodulation,[status(thm)],[f32,f2956]) ).
fof(f2958,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(a),domain(g),compose(a,compose(g,h)),compose(compose(a,h),h)),compose(compose(a,g),h)) = compose(compose(a,g),h),
inference(forward_demodulation,[status(thm)],[f359,f2886]) ).
fof(f2959,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(g),compose(a,compose(g,h)),compose(compose(a,h),h)),compose(compose(a,g),h)) = compose(compose(a,g),h),
inference(forward_demodulation,[status(thm)],[f24,f2958]) ).
fof(f2960,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(b),compose(a,compose(g,h)),compose(compose(a,h),h)),compose(compose(a,g),h)) = compose(compose(a,g),h),
inference(forward_demodulation,[status(thm)],[f55,f2959]) ).
fof(f2961,plain,
ifeq(codomain(h),domain(b),compose(a,compose(g,h)),compose(compose(a,g),h)) = compose(compose(a,g),h),
inference(forward_demodulation,[status(thm)],[f15,f2960]) ).
fof(f2962,plain,
ifeq(codomain(h),domain(b),compose(a,compose(g,h)),compose(compose(a,h),h)) = compose(compose(a,g),h),
inference(forward_demodulation,[status(thm)],[f27,f2961]) ).
fof(f2963,plain,
ifeq(codomain(h),domain(b),compose(a,compose(g,h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(forward_demodulation,[status(thm)],[f27,f2962]) ).
fof(f2970,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),h)),compose(compose(a,b),h)),compose(compose(domain(a),compose(a,b)),h)) = compose(compose(domain(a),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f959,f2888]) ).
fof(f2971,plain,
ifeq(codomain(b),domain(b),ifeq(domain(a),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),h)),compose(compose(a,b),h)),compose(compose(domain(a),compose(a,b)),h)) = compose(compose(domain(a),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f16,f2970]) ).
fof(f2972,plain,
ifeq(codomain(b),domain(b),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,b),h)),compose(compose(a,b),h)),compose(compose(domain(a),compose(a,b)),h)) = compose(compose(domain(a),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1163,f2971]) ).
fof(f2973,plain,
ifeq(codomain(b),domain(b),compose(domain(a),compose(compose(a,b),h)),compose(compose(domain(a),compose(a,b)),h)) = compose(compose(domain(a),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f15,f2972]) ).
fof(f2974,plain,
ifeq(codomain(b),domain(b),compose(domain(a),compose(compose(a,b),h)),compose(compose(a,b),h)) = compose(compose(domain(a),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1212,f2973]) ).
fof(f2975,plain,
ifeq(codomain(b),domain(b),compose(domain(a),compose(compose(a,b),h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(forward_demodulation,[status(thm)],[f1212,f2974]) ).
fof(f2976,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),h)),compose(compose(a,h),h)),compose(compose(domain(a),compose(a,h)),h)) = compose(compose(domain(a),compose(a,h)),h),
inference(forward_demodulation,[status(thm)],[f367,f2889]) ).
fof(f2977,plain,
ifeq(codomain(h),domain(b),ifeq(domain(a),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),h)),compose(compose(a,h),h)),compose(compose(domain(a),compose(a,h)),h)) = compose(compose(domain(a),compose(a,h)),h),
inference(forward_demodulation,[status(thm)],[f16,f2976]) ).
fof(f2978,plain,
ifeq(codomain(h),domain(b),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,h),h)),compose(compose(a,h),h)),compose(compose(domain(a),compose(a,h)),h)) = compose(compose(domain(a),compose(a,h)),h),
inference(forward_demodulation,[status(thm)],[f345,f2977]) ).
fof(f2979,plain,
ifeq(codomain(h),domain(b),compose(domain(a),compose(compose(a,h),h)),compose(compose(domain(a),compose(a,h)),h)) = compose(compose(domain(a),compose(a,h)),h),
inference(forward_demodulation,[status(thm)],[f15,f2978]) ).
fof(f2980,plain,
ifeq(codomain(h),domain(b),compose(domain(a),compose(compose(a,h),h)),compose(compose(a,h),h)) = compose(compose(domain(a),compose(a,h)),h),
inference(forward_demodulation,[status(thm)],[f441,f2979]) ).
fof(f2981,plain,
ifeq(codomain(h),domain(b),compose(domain(a),compose(compose(a,h),h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(forward_demodulation,[status(thm)],[f441,f2980]) ).
fof(f2982,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,h)),compose(g,h)),compose(compose(domain(b),g),h)) = compose(compose(domain(b),g),h),
inference(forward_demodulation,[status(thm)],[f359,f2890]) ).
fof(f2983,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(g),compose(domain(b),compose(g,h)),compose(g,h)),compose(compose(domain(b),g),h)) = compose(compose(domain(b),g),h),
inference(forward_demodulation,[status(thm)],[f16,f2982]) ).
fof(f2984,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(b),compose(domain(b),compose(g,h)),compose(g,h)),compose(compose(domain(b),g),h)) = compose(compose(domain(b),g),h),
inference(forward_demodulation,[status(thm)],[f55,f2983]) ).
fof(f2985,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(g,h)),compose(compose(domain(b),g),h)) = compose(compose(domain(b),g),h),
inference(forward_demodulation,[status(thm)],[f15,f2984]) ).
fof(f2986,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(g,h)),compose(g,h)) = compose(compose(domain(b),g),h),
inference(forward_demodulation,[status(thm)],[f59,f2985]) ).
fof(f2987,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(g,h)),compose(g,h)) = compose(g,h),
inference(forward_demodulation,[status(thm)],[f59,f2986]) ).
fof(f2988,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(h),compose(domain(b),compose(h,h)),compose(h,h)),compose(compose(domain(b),h),h)) = compose(compose(domain(b),h),h),
inference(forward_demodulation,[status(thm)],[f16,f2891]) ).
fof(f2989,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(b),compose(domain(b),compose(h,h)),compose(h,h)),compose(compose(domain(b),h),h)) = compose(compose(domain(b),h),h),
inference(forward_demodulation,[status(thm)],[f48,f2988]) ).
fof(f2990,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(h,h)),compose(compose(domain(b),h),h)) = compose(compose(domain(b),h),h),
inference(forward_demodulation,[status(thm)],[f15,f2989]) ).
fof(f2991,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(h,h)),compose(h,h)) = compose(compose(domain(b),h),h),
inference(forward_demodulation,[status(thm)],[f52,f2990]) ).
fof(f2992,plain,
ifeq(codomain(h),domain(b),compose(domain(b),compose(h,h)),compose(h,h)) = compose(h,h),
inference(forward_demodulation,[status(thm)],[f52,f2991]) ).
fof(f2993,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),h)),compose(domain(X0),h)),compose(compose(domain(X0),domain(X0)),h)) = compose(compose(domain(X0),domain(X0)),h),
inference(forward_demodulation,[status(thm)],[f16,f2892]) ).
fof(f2994,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(domain(X0),domain(domain(X0)),compose(domain(X0),compose(domain(X0),h)),compose(domain(X0),h)),compose(compose(domain(X0),domain(X0)),h)) = compose(compose(domain(X0),domain(X0)),h),
inference(forward_demodulation,[status(thm)],[f16,f2993]) ).
fof(f2995,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(domain(X0),h)),compose(domain(X0),h)),compose(compose(domain(X0),domain(X0)),h)) = compose(compose(domain(X0),domain(X0)),h),
inference(forward_demodulation,[status(thm)],[f33,f2994]) ).
fof(f2996,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),compose(domain(X0),h)),compose(compose(domain(X0),domain(X0)),h)) = compose(compose(domain(X0),domain(X0)),h),
inference(forward_demodulation,[status(thm)],[f15,f2995]) ).
fof(f2997,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),compose(domain(X0),h)),compose(domain(X0),h)) = compose(compose(domain(X0),domain(X0)),h),
inference(forward_demodulation,[status(thm)],[f29,f2996]) ).
fof(f2998,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),compose(domain(X0),h)),compose(domain(X0),h)) = compose(domain(X0),h),
inference(forward_demodulation,[status(thm)],[f29,f2997]) ).
fof(f2999,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(X0,h)),compose(X0,h)),compose(compose(domain(X0),X0),h)) = compose(compose(domain(X0),X0),h),
inference(forward_demodulation,[status(thm)],[f16,f2893]) ).
fof(f3000,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(domain(X0),compose(X0,h)),compose(compose(domain(X0),X0),h)) = compose(compose(domain(X0),X0),h),
inference(forward_demodulation,[status(thm)],[f15,f2999]) ).
fof(f3001,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(domain(X0),compose(X0,h)),compose(X0,h)) = compose(compose(domain(X0),X0),h),
inference(forward_demodulation,[status(thm)],[f18,f3000]) ).
fof(f3002,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(domain(X0),compose(X0,h)),compose(X0,h)) = compose(X0,h),
inference(forward_demodulation,[status(thm)],[f18,f3001]) ).
fof(f3003,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),h)),compose(X0,h)),compose(compose(X0,codomain(X0)),h)) = compose(compose(X0,codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f34,f2894]) ).
fof(f3004,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(X0),codomain(X0),compose(X0,compose(codomain(X0),h)),compose(X0,h)),compose(compose(X0,codomain(X0)),h)) = compose(compose(X0,codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f17,f3003]) ).
fof(f3005,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,compose(codomain(X0),h)),compose(compose(X0,codomain(X0)),h)) = compose(compose(X0,codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f15,f3004]) ).
fof(f3006,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,compose(codomain(X0),h)),compose(X0,h)) = compose(compose(X0,codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f19,f3005]) ).
fof(f3007,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,compose(codomain(X0),h)),compose(X0,h)) = compose(X0,h),
inference(forward_demodulation,[status(thm)],[f19,f3006]) ).
fof(f3071,plain,
! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(compose(a,b)),compose(X1,compose(compose(a,b),codomain(X0))),compose(compose(X1,compose(a,b)),codomain(X0))),compose(compose(X1,compose(a,b)),codomain(X0))) = compose(compose(X1,compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f189]) ).
fof(f3072,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(compose(a,h)),compose(X1,compose(compose(a,h),codomain(X0))),compose(compose(X1,compose(a,h)),codomain(X0))),compose(compose(X1,compose(a,h)),codomain(X0))) = compose(compose(X1,compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f367,f189]) ).
fof(f3074,plain,
! [X0,X1,X2] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),domain(codomain(X0)),compose(X2,compose(codomain(X0),codomain(X1))),compose(compose(X2,codomain(X0)),codomain(X1))),compose(compose(X2,codomain(X0)),codomain(X1))) = compose(compose(X2,codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f34,f189]) ).
fof(f3083,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,codomain(X1))),compose(compose(compose(a,b),X0),codomain(X1))),compose(compose(compose(a,b),X0),codomain(X1))) = compose(compose(compose(a,b),X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f959,f189]) ).
fof(f3084,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,codomain(X1))),compose(compose(compose(a,h),X0),codomain(X1))),compose(compose(compose(a,h),X0),codomain(X1))) = compose(compose(compose(a,h),X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f367,f189]) ).
fof(f3085,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(X0,codomain(X1))),compose(compose(g,X0),codomain(X1))),compose(compose(g,X0),codomain(X1))) = compose(compose(g,X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f359,f189]) ).
fof(f3086,plain,
! [X0,X1,X2] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(X0,codomain(X1))),compose(compose(codomain(X2),X0),codomain(X1))),compose(compose(codomain(X2),X0),codomain(X1))) = compose(compose(codomain(X2),X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f34,f189]) ).
fof(f3087,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(a,compose(X0,codomain(X1))),compose(compose(a,X0),codomain(X1))),compose(compose(a,X0),codomain(X1))) = compose(compose(a,X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f24,f189]) ).
fof(f3088,plain,
! [X0,X1,X2] : ifeq(codomain(X0),codomain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(X0,codomain(X1))),compose(compose(domain(X2),X0),codomain(X1))),compose(compose(domain(X2),X0),codomain(X1))) = compose(compose(domain(X2),X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f16,f189]) ).
fof(f3092,plain,
! [X0,X1] : ifeq(codomain(g),codomain(X0),ifeq(codomain(X1),domain(b),compose(X1,compose(g,codomain(X0))),compose(compose(X1,g),codomain(X0))),compose(compose(X1,g),codomain(X0))) = compose(compose(X1,g),codomain(X0)),
inference(paramodulation,[status(thm)],[f55,f189]) ).
fof(f3093,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(b),compose(X1,compose(h,codomain(X0))),compose(compose(X1,h),codomain(X0))),compose(compose(X1,h),codomain(X0))) = compose(compose(X1,h),codomain(X0)),
inference(paramodulation,[status(thm)],[f48,f189]) ).
fof(f3095,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(domain(compose(X0,codomain(X1)))),domain(X0),compose(X0,codomain(X1)),compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1))),compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1))) = compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f18,f189]) ).
fof(f3096,plain,
! [X0] : ifeq(codomain(compose(a,b)),codomain(b),ifeq(codomain(X0),domain(compose(a,b)),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(b))),compose(compose(X0,compose(a,b)),codomain(b))) = compose(compose(X0,compose(a,b)),codomain(b)),
inference(paramodulation,[status(thm)],[f1034,f189]) ).
fof(f3111,plain,
! [X0] : ifeq(codomain(codomain(b)),codomain(X0),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),codomain(X0))),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,b),codomain(b)),codomain(X0))) = compose(compose(compose(a,b),codomain(b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f1034,f189]) ).
fof(f3112,plain,
! [X0] : ifeq(codomain(codomain(h)),codomain(X0),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),codomain(h)),codomain(X0))) = compose(compose(compose(a,h),codomain(h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f477,f189]) ).
fof(f3113,plain,
! [X0] : ifeq(codomain(codomain(h)),codomain(X0),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),codomain(X0))),compose(g,codomain(X0))),compose(compose(g,codomain(h)),codomain(X0))) = compose(compose(g,codomain(h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f377,f189]) ).
fof(f3114,plain,
! [X0,X1] : ifeq(codomain(codomain(X0)),codomain(X1),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(codomain(X0),codomain(X1))),compose(compose(codomain(X0),codomain(X0)),codomain(X1))) = compose(compose(codomain(X0),codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f32,f189]) ).
fof(f3115,plain,
! [X0] : ifeq(codomain(g),codomain(X0),ifeq(codomain(a),domain(g),compose(a,compose(g,codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(a,g),codomain(X0))) = compose(compose(a,g),codomain(X0)),
inference(paramodulation,[status(thm)],[f27,f189]) ).
fof(f3116,plain,
! [X0] : ifeq(codomain(domain(b)),codomain(X0),ifeq(codomain(a),domain(domain(b)),compose(a,compose(domain(b),codomain(X0))),compose(a,codomain(X0))),compose(compose(a,domain(b)),codomain(X0))) = compose(compose(a,domain(b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f46,f189]) ).
fof(f3117,plain,
! [X0] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))),compose(compose(domain(a),compose(a,b)),codomain(X0))) = compose(compose(domain(a),compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f1212,f189]) ).
fof(f3118,plain,
! [X0] : ifeq(codomain(compose(a,h)),codomain(X0),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(domain(a),compose(a,h)),codomain(X0))) = compose(compose(domain(a),compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f441,f189]) ).
fof(f3119,plain,
! [X0] : ifeq(codomain(g),codomain(X0),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,codomain(X0))),compose(g,codomain(X0))),compose(compose(domain(b),g),codomain(X0))) = compose(compose(domain(b),g),codomain(X0)),
inference(paramodulation,[status(thm)],[f59,f189]) ).
fof(f3120,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(domain(b)),domain(h),compose(domain(b),compose(h,codomain(X0))),compose(h,codomain(X0))),compose(compose(domain(b),h),codomain(X0))) = compose(compose(domain(b),h),codomain(X0)),
inference(paramodulation,[status(thm)],[f52,f189]) ).
fof(f3121,plain,
! [X0,X1] : ifeq(codomain(domain(X0)),codomain(X1),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(domain(X0),codomain(X1))),compose(compose(domain(X0),domain(X0)),codomain(X1))) = compose(compose(domain(X0),domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f29,f189]) ).
fof(f3122,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(domain(X0)),domain(X0),compose(domain(X0),compose(X0,codomain(X1))),compose(X0,codomain(X1))),compose(compose(domain(X0),X0),codomain(X1))) = compose(compose(domain(X0),X0),codomain(X1)),
inference(paramodulation,[status(thm)],[f18,f189]) ).
fof(f3123,plain,
! [X0,X1] : ifeq(codomain(codomain(X0)),codomain(X1),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),codomain(X1))),compose(X0,codomain(X1))),compose(compose(X0,codomain(X0)),codomain(X1))) = compose(compose(X0,codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f19,f189]) ).
fof(f3154,plain,
! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,b),codomain(X0))),compose(compose(X1,compose(a,b)),codomain(X0))),compose(compose(X1,compose(a,b)),codomain(X0))) = compose(compose(X1,compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f3071]) ).
fof(f3155,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,h),codomain(X0))),compose(compose(X1,compose(a,h)),codomain(X0))),compose(compose(X1,compose(a,h)),codomain(X0))) = compose(compose(X1,compose(a,h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f345,f3072]) ).
fof(f3157,plain,
! [X0,X1,X2] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),codomain(X1))),compose(compose(X2,codomain(X0)),codomain(X1))),compose(compose(X2,codomain(X0)),codomain(X1))) = compose(compose(X2,codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f17,f3074]) ).
fof(f3186,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(b),compose(X1,compose(g,codomain(X0))),compose(compose(X1,g),codomain(X0))),compose(compose(X1,g),codomain(X0))) = compose(compose(X1,g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f359,f3092]) ).
fof(f3188,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(compose(X0,codomain(X1))),domain(X0),compose(X0,codomain(X1)),compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1))),compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1))) = compose(compose(domain(compose(X0,codomain(X1))),X0),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f3095]) ).
fof(f3189,plain,
! [X0] : ifeq(codomain(b),codomain(b),ifeq(codomain(X0),domain(compose(a,b)),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(b))),compose(compose(X0,compose(a,b)),codomain(b))) = compose(compose(X0,compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f959,f3096]) ).
fof(f3190,plain,
! [X0] : ifeq(codomain(X0),domain(compose(a,b)),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(b))) = compose(compose(X0,compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f15,f3189]) ).
fof(f3191,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(b))) = compose(compose(X0,compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f1163,f3190]) ).
fof(f3244,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),codomain(X0))),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,b),codomain(b)),codomain(X0))) = compose(compose(compose(a,b),codomain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f3111]) ).
fof(f3245,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),codomain(X0))),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,b),codomain(b)),codomain(X0))) = compose(compose(compose(a,b),codomain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f959,f3244]) ).
fof(f3246,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),codomain(b),compose(compose(a,b),compose(codomain(b),codomain(X0))),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,b),codomain(b)),codomain(X0))) = compose(compose(compose(a,b),codomain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f3245]) ).
fof(f3247,plain,
! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(b),codomain(X0))),compose(compose(compose(a,b),codomain(b)),codomain(X0))) = compose(compose(compose(a,b),codomain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3246]) ).
fof(f3248,plain,
! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(compose(a,b),codomain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1034,f3247]) ).
fof(f3249,plain,
! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1034,f3248]) ).
fof(f3250,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),codomain(h)),codomain(X0))) = compose(compose(compose(a,h),codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f3112]) ).
fof(f3251,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),codomain(h)),codomain(X0))) = compose(compose(compose(a,h),codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f367,f3250]) ).
fof(f3252,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),codomain(h),compose(compose(a,h),compose(codomain(h),codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),codomain(h)),codomain(X0))) = compose(compose(compose(a,h),codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f3251]) ).
fof(f3253,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(h),codomain(X0))),compose(compose(compose(a,h),codomain(h)),codomain(X0))) = compose(compose(compose(a,h),codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3252]) ).
fof(f3254,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(compose(a,h),codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f477,f3253]) ).
fof(f3255,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f477,f3254]) ).
fof(f3256,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),codomain(X0))),compose(g,codomain(X0))),compose(compose(g,codomain(h)),codomain(X0))) = compose(compose(g,codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f3113]) ).
fof(f3257,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(codomain(h)),compose(g,compose(codomain(h),codomain(X0))),compose(g,codomain(X0))),compose(compose(g,codomain(h)),codomain(X0))) = compose(compose(g,codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f359,f3256]) ).
fof(f3258,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),codomain(h),compose(g,compose(codomain(h),codomain(X0))),compose(g,codomain(X0))),compose(compose(g,codomain(h)),codomain(X0))) = compose(compose(g,codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f3257]) ).
fof(f3259,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(h),codomain(X0))),compose(compose(g,codomain(h)),codomain(X0))) = compose(compose(g,codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3258]) ).
fof(f3260,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(h),codomain(X0))),compose(g,codomain(X0))) = compose(compose(g,codomain(h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f377,f3259]) ).
fof(f3261,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(h),codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f377,f3260]) ).
fof(f3262,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(codomain(X0),codomain(X1))),compose(compose(codomain(X0),codomain(X0)),codomain(X1))) = compose(compose(codomain(X0),codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f34,f3114]) ).
fof(f3263,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X0),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(codomain(X0),codomain(X1))),compose(compose(codomain(X0),codomain(X0)),codomain(X1))) = compose(compose(codomain(X0),codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f34,f3262]) ).
fof(f3264,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X0),codomain(X0),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(codomain(X0),codomain(X1))),compose(compose(codomain(X0),codomain(X0)),codomain(X1))) = compose(compose(codomain(X0),codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f17,f3263]) ).
fof(f3265,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(compose(codomain(X0),codomain(X0)),codomain(X1))) = compose(compose(codomain(X0),codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f3264]) ).
fof(f3266,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(codomain(X0),codomain(X1))) = compose(compose(codomain(X0),codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f32,f3265]) ).
fof(f3267,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(codomain(X0),compose(codomain(X0),codomain(X1))),compose(codomain(X0),codomain(X1))) = compose(codomain(X0),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f32,f3266]) ).
fof(f3268,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(a),domain(g),compose(a,compose(g,codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(a,g),codomain(X0))) = compose(compose(a,g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f359,f3115]) ).
fof(f3269,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(b),domain(g),compose(a,compose(g,codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(a,g),codomain(X0))) = compose(compose(a,g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f24,f3268]) ).
fof(f3270,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(b),domain(b),compose(a,compose(g,codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(a,g),codomain(X0))) = compose(compose(a,g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f55,f3269]) ).
fof(f3271,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(a,compose(g,codomain(X0))),compose(compose(a,g),codomain(X0))) = compose(compose(a,g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3270]) ).
fof(f3272,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(a,compose(g,codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f27,f3271]) ).
fof(f3273,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(a,compose(g,codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f27,f3272]) ).
fof(f3274,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(a),domain(domain(b)),compose(a,compose(domain(b),codomain(X0))),compose(a,codomain(X0))),compose(compose(a,domain(b)),codomain(X0))) = compose(compose(a,domain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f3116]) ).
fof(f3275,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(domain(b)),compose(a,compose(domain(b),codomain(X0))),compose(a,codomain(X0))),compose(compose(a,domain(b)),codomain(X0))) = compose(compose(a,domain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f24,f3274]) ).
fof(f3276,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(b),compose(a,compose(domain(b),codomain(X0))),compose(a,codomain(X0))),compose(compose(a,domain(b)),codomain(X0))) = compose(compose(a,domain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f3275]) ).
fof(f3277,plain,
! [X0] : ifeq(domain(b),codomain(X0),compose(a,compose(domain(b),codomain(X0))),compose(compose(a,domain(b)),codomain(X0))) = compose(compose(a,domain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3276]) ).
fof(f3278,plain,
! [X0] : ifeq(domain(b),codomain(X0),compose(a,compose(domain(b),codomain(X0))),compose(a,codomain(X0))) = compose(compose(a,domain(b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f46,f3277]) ).
fof(f3279,plain,
! [X0] : ifeq(domain(b),codomain(X0),compose(a,compose(domain(b),codomain(X0))),compose(a,codomain(X0))) = compose(a,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f46,f3278]) ).
fof(f3280,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))),compose(compose(domain(a),compose(a,b)),codomain(X0))) = compose(compose(domain(a),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f959,f3117]) ).
fof(f3281,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))),compose(compose(domain(a),compose(a,b)),codomain(X0))) = compose(compose(domain(a),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f3280]) ).
fof(f3282,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))),compose(compose(domain(a),compose(a,b)),codomain(X0))) = compose(compose(domain(a),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f3281]) ).
fof(f3283,plain,
! [X0] : ifeq(codomain(b),codomain(X0),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(domain(a),compose(a,b)),codomain(X0))) = compose(compose(domain(a),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3282]) ).
fof(f3284,plain,
! [X0] : ifeq(codomain(b),codomain(X0),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(domain(a),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1212,f3283]) ).
fof(f3285,plain,
! [X0] : ifeq(codomain(b),codomain(X0),compose(domain(a),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1212,f3284]) ).
fof(f3286,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(domain(a),compose(a,h)),codomain(X0))) = compose(compose(domain(a),compose(a,h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f367,f3118]) ).
fof(f3287,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(a),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(domain(a),compose(a,h)),codomain(X0))) = compose(compose(domain(a),compose(a,h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f3286]) ).
fof(f3288,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(domain(a),compose(a,h)),codomain(X0))) = compose(compose(domain(a),compose(a,h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f345,f3287]) ).
fof(f3289,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(domain(a),compose(a,h)),codomain(X0))) = compose(compose(domain(a),compose(a,h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3288]) ).
fof(f3290,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(domain(a),compose(a,h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f441,f3289]) ).
fof(f3291,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(a),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f441,f3290]) ).
fof(f3292,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,codomain(X0))),compose(g,codomain(X0))),compose(compose(domain(b),g),codomain(X0))) = compose(compose(domain(b),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f359,f3119]) ).
fof(f3293,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(b),domain(g),compose(domain(b),compose(g,codomain(X0))),compose(g,codomain(X0))),compose(compose(domain(b),g),codomain(X0))) = compose(compose(domain(b),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f3292]) ).
fof(f3294,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(b),domain(b),compose(domain(b),compose(g,codomain(X0))),compose(g,codomain(X0))),compose(compose(domain(b),g),codomain(X0))) = compose(compose(domain(b),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f55,f3293]) ).
fof(f3295,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(b),compose(g,codomain(X0))),compose(compose(domain(b),g),codomain(X0))) = compose(compose(domain(b),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3294]) ).
fof(f3296,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(b),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(compose(domain(b),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f59,f3295]) ).
fof(f3297,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(b),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f59,f3296]) ).
fof(f3298,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(b),domain(h),compose(domain(b),compose(h,codomain(X0))),compose(h,codomain(X0))),compose(compose(domain(b),h),codomain(X0))) = compose(compose(domain(b),h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f3120]) ).
fof(f3299,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(b),domain(b),compose(domain(b),compose(h,codomain(X0))),compose(h,codomain(X0))),compose(compose(domain(b),h),codomain(X0))) = compose(compose(domain(b),h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f3298]) ).
fof(f3300,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(b),compose(h,codomain(X0))),compose(compose(domain(b),h),codomain(X0))) = compose(compose(domain(b),h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3299]) ).
fof(f3301,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(b),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(compose(domain(b),h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f3300]) ).
fof(f3302,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(domain(b),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f3301]) ).
fof(f3303,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(domain(X0),codomain(X1))),compose(compose(domain(X0),domain(X0)),codomain(X1))) = compose(compose(domain(X0),domain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f3121]) ).
fof(f3304,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(domain(X0),domain(domain(X0)),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(domain(X0),codomain(X1))),compose(compose(domain(X0),domain(X0)),codomain(X1))) = compose(compose(domain(X0),domain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f3303]) ).
fof(f3305,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(domain(X0),codomain(X1))),compose(compose(domain(X0),domain(X0)),codomain(X1))) = compose(compose(domain(X0),domain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f33,f3304]) ).
fof(f3306,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(compose(domain(X0),domain(X0)),codomain(X1))) = compose(compose(domain(X0),domain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f3305]) ).
fof(f3307,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(domain(X0),codomain(X1))) = compose(compose(domain(X0),domain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f29,f3306]) ).
fof(f3308,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),compose(domain(X0),compose(domain(X0),codomain(X1))),compose(domain(X0),codomain(X1))) = compose(domain(X0),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f29,f3307]) ).
fof(f3309,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(X0,codomain(X1))),compose(X0,codomain(X1))),compose(compose(domain(X0),X0),codomain(X1))) = compose(compose(domain(X0),X0),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f3122]) ).
fof(f3310,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(domain(X0),compose(X0,codomain(X1))),compose(compose(domain(X0),X0),codomain(X1))) = compose(compose(domain(X0),X0),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f3309]) ).
fof(f3311,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(domain(X0),compose(X0,codomain(X1))),compose(X0,codomain(X1))) = compose(compose(domain(X0),X0),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f18,f3310]) ).
fof(f3312,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(domain(X0),compose(X0,codomain(X1))),compose(X0,codomain(X1))) = compose(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f18,f3311]) ).
fof(f3313,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),codomain(X1))),compose(X0,codomain(X1))),compose(compose(X0,codomain(X0)),codomain(X1))) = compose(compose(X0,codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f34,f3123]) ).
fof(f3314,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X0),codomain(X0),compose(X0,compose(codomain(X0),codomain(X1))),compose(X0,codomain(X1))),compose(compose(X0,codomain(X0)),codomain(X1))) = compose(compose(X0,codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f17,f3313]) ).
fof(f3315,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(X0,compose(codomain(X0),codomain(X1))),compose(compose(X0,codomain(X0)),codomain(X1))) = compose(compose(X0,codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f3314]) ).
fof(f3316,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(X0,compose(codomain(X0),codomain(X1))),compose(X0,codomain(X1))) = compose(compose(X0,codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f19,f3315]) ).
fof(f3317,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(X0,compose(codomain(X0),codomain(X1))),compose(X0,codomain(X1))) = compose(X0,codomain(X1)),
inference(forward_demodulation,[status(thm)],[f19,f3316]) ).
fof(f3635,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(compose(a,b),X0)),compose(compose(a,compose(a,b)),X0)),compose(compose(a,compose(a,b)),X0)) = compose(compose(a,compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f959,f191]) ).
fof(f3636,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(compose(a,h)),compose(a,compose(compose(a,h),X0)),compose(compose(a,compose(a,h)),X0)),compose(compose(a,compose(a,h)),X0)) = compose(compose(a,compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f367,f191]) ).
fof(f3638,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(codomain(X0)),compose(a,compose(codomain(X0),X1)),compose(compose(a,codomain(X0)),X1)),compose(compose(a,codomain(X0)),X1)) = compose(compose(a,codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f34,f191]) ).
fof(f3641,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(a,b))),compose(compose(a,X0),compose(a,b))),compose(compose(a,X0),compose(a,b))) = compose(compose(a,X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f191]) ).
fof(f3642,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(a,h))),compose(compose(a,X0),compose(a,h))),compose(compose(a,X0),compose(a,h))) = compose(compose(a,X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f191]) ).
fof(f3643,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(X0,domain(X1))),compose(compose(a,X0),domain(X1))),compose(compose(a,X0),domain(X1))) = compose(compose(a,X0),domain(X1)),
inference(paramodulation,[status(thm)],[f33,f191]) ).
fof(f3647,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(a,compose(b,X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(paramodulation,[status(thm)],[f15,f191]) ).
fof(f3652,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(b),compose(a,compose(h,X0)),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(paramodulation,[status(thm)],[f48,f191]) ).
fof(f3654,plain,
ifeq(codomain(compose(a,b)),domain(codomain(b)),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(a,b)),compose(compose(a,compose(a,b)),codomain(b))),compose(compose(a,compose(a,b)),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)),
inference(paramodulation,[status(thm)],[f1034,f191]) ).
fof(f3655,plain,
ifeq(codomain(compose(a,h)),domain(codomain(h)),ifeq(domain(b),domain(compose(a,h)),compose(a,compose(a,h)),compose(compose(a,compose(a,h)),codomain(h))),compose(compose(a,compose(a,h)),codomain(h))) = compose(compose(a,compose(a,h)),codomain(h)),
inference(paramodulation,[status(thm)],[f477,f191]) ).
fof(f3657,plain,
! [X0] : ifeq(codomain(codomain(X0)),domain(codomain(X0)),ifeq(domain(b),domain(codomain(X0)),compose(a,codomain(X0)),compose(compose(a,codomain(X0)),codomain(X0))),compose(compose(a,codomain(X0)),codomain(X0))) = compose(compose(a,codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f32,f191]) ).
fof(f3658,plain,
ifeq(codomain(a),domain(g),ifeq(domain(b),domain(a),compose(a,compose(a,h)),compose(compose(a,a),g)),compose(compose(a,a),g)) = compose(compose(a,a),g),
inference(paramodulation,[status(thm)],[f27,f191]) ).
fof(f3659,plain,
ifeq(codomain(a),domain(domain(b)),ifeq(domain(b),domain(a),compose(a,a),compose(compose(a,a),domain(b))),compose(compose(a,a),domain(b))) = compose(compose(a,a),domain(b)),
inference(paramodulation,[status(thm)],[f46,f191]) ).
fof(f3660,plain,
ifeq(codomain(domain(a)),domain(compose(a,b)),ifeq(domain(b),domain(domain(a)),compose(a,compose(a,b)),compose(compose(a,domain(a)),compose(a,b))),compose(compose(a,domain(a)),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1212,f191]) ).
fof(f3661,plain,
ifeq(codomain(domain(a)),domain(compose(a,h)),ifeq(domain(b),domain(domain(a)),compose(a,compose(a,h)),compose(compose(a,domain(a)),compose(a,h))),compose(compose(a,domain(a)),compose(a,h))) = compose(compose(a,domain(a)),compose(a,h)),
inference(paramodulation,[status(thm)],[f441,f191]) ).
fof(f3664,plain,
! [X0] : ifeq(codomain(domain(X0)),domain(domain(X0)),ifeq(domain(b),domain(domain(X0)),compose(a,domain(X0)),compose(compose(a,domain(X0)),domain(X0))),compose(compose(a,domain(X0)),domain(X0))) = compose(compose(a,domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f29,f191]) ).
fof(f3665,plain,
! [X0] : ifeq(codomain(domain(X0)),domain(X0),ifeq(domain(b),domain(domain(X0)),compose(a,X0),compose(compose(a,domain(X0)),X0)),compose(compose(a,domain(X0)),X0)) = compose(compose(a,domain(X0)),X0),
inference(paramodulation,[status(thm)],[f18,f191]) ).
fof(f3666,plain,
! [X0] : ifeq(codomain(X0),domain(codomain(X0)),ifeq(domain(b),domain(X0),compose(a,X0),compose(compose(a,X0),codomain(X0))),compose(compose(a,X0),codomain(X0))) = compose(compose(a,X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f19,f191]) ).
fof(f3669,plain,
! [X0] : ifeq(codomain(X0),domain(codomain(compose(a,X0))),ifeq(domain(b),domain(X0),compose(a,compose(X0,codomain(compose(a,X0)))),compose(a,X0)),compose(compose(a,X0),codomain(compose(a,X0)))) = compose(compose(a,X0),codomain(compose(a,X0))),
inference(paramodulation,[status(thm)],[f19,f191]) ).
fof(f3679,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),X0)),compose(compose(a,compose(a,b)),X0)),compose(compose(a,compose(a,b)),X0)) = compose(compose(a,compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f3635]) ).
fof(f3680,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),X0)),compose(compose(a,compose(a,h)),X0)),compose(compose(a,compose(a,h)),X0)) = compose(compose(a,compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f345,f3636]) ).
fof(f3685,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),X1)),compose(compose(a,codomain(X0)),X1)),compose(compose(a,codomain(X0)),X1)) = compose(compose(a,codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f17,f3638]) ).
fof(f3694,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(a,compose(h,X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(forward_demodulation,[status(thm)],[f15,f3652]) ).
fof(f3696,plain,
ifeq(codomain(b),domain(codomain(b)),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(a,b)),compose(compose(a,compose(a,b)),codomain(b))),compose(compose(a,compose(a,b)),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f959,f3654]) ).
fof(f3697,plain,
ifeq(codomain(b),codomain(b),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(a,b)),compose(compose(a,compose(a,b)),codomain(b))),compose(compose(a,compose(a,b)),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f17,f3696]) ).
fof(f3698,plain,
ifeq(domain(b),domain(compose(a,b)),compose(a,compose(a,b)),compose(compose(a,compose(a,b)),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f15,f3697]) ).
fof(f3699,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,b)),compose(compose(a,compose(a,b)),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f1163,f3698]) ).
fof(f3700,plain,
ifeq(codomain(h),domain(codomain(h)),ifeq(domain(b),domain(compose(a,h)),compose(a,compose(a,h)),compose(compose(a,compose(a,h)),codomain(h))),compose(compose(a,compose(a,h)),codomain(h))) = compose(compose(a,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f367,f3655]) ).
fof(f3701,plain,
ifeq(codomain(h),codomain(h),ifeq(domain(b),domain(compose(a,h)),compose(a,compose(a,h)),compose(compose(a,compose(a,h)),codomain(h))),compose(compose(a,compose(a,h)),codomain(h))) = compose(compose(a,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f3700]) ).
fof(f3702,plain,
ifeq(domain(b),domain(compose(a,h)),compose(a,compose(a,h)),compose(compose(a,compose(a,h)),codomain(h))) = compose(compose(a,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f3701]) ).
fof(f3703,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,h)),compose(compose(a,compose(a,h)),codomain(h))) = compose(compose(a,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f345,f3702]) ).
fof(f3711,plain,
! [X0] : ifeq(codomain(X0),domain(codomain(X0)),ifeq(domain(b),domain(codomain(X0)),compose(a,codomain(X0)),compose(compose(a,codomain(X0)),codomain(X0))),compose(compose(a,codomain(X0)),codomain(X0))) = compose(compose(a,codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f3657]) ).
fof(f3712,plain,
! [X0] : ifeq(codomain(X0),codomain(X0),ifeq(domain(b),domain(codomain(X0)),compose(a,codomain(X0)),compose(compose(a,codomain(X0)),codomain(X0))),compose(compose(a,codomain(X0)),codomain(X0))) = compose(compose(a,codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f3711]) ).
fof(f3713,plain,
! [X0] : ifeq(domain(b),domain(codomain(X0)),compose(a,codomain(X0)),compose(compose(a,codomain(X0)),codomain(X0))) = compose(compose(a,codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3712]) ).
fof(f3714,plain,
! [X0] : ifeq(domain(b),codomain(X0),compose(a,codomain(X0)),compose(compose(a,codomain(X0)),codomain(X0))) = compose(compose(a,codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f3713]) ).
fof(f3715,plain,
ifeq(domain(b),domain(g),ifeq(domain(b),domain(a),compose(a,compose(a,h)),compose(compose(a,a),g)),compose(compose(a,a),g)) = compose(compose(a,a),g),
inference(forward_demodulation,[status(thm)],[f24,f3658]) ).
fof(f3716,plain,
ifeq(domain(b),domain(b),ifeq(domain(b),domain(a),compose(a,compose(a,h)),compose(compose(a,a),g)),compose(compose(a,a),g)) = compose(compose(a,a),g),
inference(forward_demodulation,[status(thm)],[f55,f3715]) ).
fof(f3717,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,h)),compose(compose(a,a),g)) = compose(compose(a,a),g),
inference(forward_demodulation,[status(thm)],[f15,f3716]) ).
fof(f3718,plain,
ifeq(domain(b),domain(domain(b)),ifeq(domain(b),domain(a),compose(a,a),compose(compose(a,a),domain(b))),compose(compose(a,a),domain(b))) = compose(compose(a,a),domain(b)),
inference(forward_demodulation,[status(thm)],[f24,f3659]) ).
fof(f3719,plain,
ifeq(domain(b),domain(b),ifeq(domain(b),domain(a),compose(a,a),compose(compose(a,a),domain(b))),compose(compose(a,a),domain(b))) = compose(compose(a,a),domain(b)),
inference(forward_demodulation,[status(thm)],[f33,f3718]) ).
fof(f3720,plain,
ifeq(domain(b),domain(a),compose(a,a),compose(compose(a,a),domain(b))) = compose(compose(a,a),domain(b)),
inference(forward_demodulation,[status(thm)],[f15,f3719]) ).
fof(f3721,plain,
ifeq(domain(a),domain(compose(a,b)),ifeq(domain(b),domain(domain(a)),compose(a,compose(a,b)),compose(compose(a,domain(a)),compose(a,b))),compose(compose(a,domain(a)),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f16,f3660]) ).
fof(f3722,plain,
ifeq(domain(a),domain(a),ifeq(domain(b),domain(domain(a)),compose(a,compose(a,b)),compose(compose(a,domain(a)),compose(a,b))),compose(compose(a,domain(a)),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f3721]) ).
fof(f3723,plain,
ifeq(domain(b),domain(domain(a)),compose(a,compose(a,b)),compose(compose(a,domain(a)),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f15,f3722]) ).
fof(f3724,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,b)),compose(compose(a,domain(a)),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f33,f3723]) ).
fof(f3725,plain,
ifeq(domain(a),domain(compose(a,h)),ifeq(domain(b),domain(domain(a)),compose(a,compose(a,h)),compose(compose(a,domain(a)),compose(a,h))),compose(compose(a,domain(a)),compose(a,h))) = compose(compose(a,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f3661]) ).
fof(f3726,plain,
ifeq(domain(a),domain(a),ifeq(domain(b),domain(domain(a)),compose(a,compose(a,h)),compose(compose(a,domain(a)),compose(a,h))),compose(compose(a,domain(a)),compose(a,h))) = compose(compose(a,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f3725]) ).
fof(f3727,plain,
ifeq(domain(b),domain(domain(a)),compose(a,compose(a,h)),compose(compose(a,domain(a)),compose(a,h))) = compose(compose(a,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f3726]) ).
fof(f3728,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,h)),compose(compose(a,domain(a)),compose(a,h))) = compose(compose(a,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f33,f3727]) ).
fof(f3741,plain,
! [X0] : ifeq(domain(X0),domain(domain(X0)),ifeq(domain(b),domain(domain(X0)),compose(a,domain(X0)),compose(compose(a,domain(X0)),domain(X0))),compose(compose(a,domain(X0)),domain(X0))) = compose(compose(a,domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f3664]) ).
fof(f3742,plain,
! [X0] : ifeq(domain(X0),domain(X0),ifeq(domain(b),domain(domain(X0)),compose(a,domain(X0)),compose(compose(a,domain(X0)),domain(X0))),compose(compose(a,domain(X0)),domain(X0))) = compose(compose(a,domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f3741]) ).
fof(f3743,plain,
! [X0] : ifeq(domain(b),domain(domain(X0)),compose(a,domain(X0)),compose(compose(a,domain(X0)),domain(X0))) = compose(compose(a,domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3742]) ).
fof(f3744,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,domain(X0)),compose(compose(a,domain(X0)),domain(X0))) = compose(compose(a,domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f3743]) ).
fof(f3745,plain,
! [X0] : ifeq(domain(X0),domain(X0),ifeq(domain(b),domain(domain(X0)),compose(a,X0),compose(compose(a,domain(X0)),X0)),compose(compose(a,domain(X0)),X0)) = compose(compose(a,domain(X0)),X0),
inference(forward_demodulation,[status(thm)],[f16,f3665]) ).
fof(f3746,plain,
! [X0] : ifeq(domain(b),domain(domain(X0)),compose(a,X0),compose(compose(a,domain(X0)),X0)) = compose(compose(a,domain(X0)),X0),
inference(forward_demodulation,[status(thm)],[f15,f3745]) ).
fof(f3747,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,X0),compose(compose(a,domain(X0)),X0)) = compose(compose(a,domain(X0)),X0),
inference(forward_demodulation,[status(thm)],[f33,f3746]) ).
fof(f3748,plain,
! [X0] : ifeq(codomain(X0),codomain(X0),ifeq(domain(b),domain(X0),compose(a,X0),compose(compose(a,X0),codomain(X0))),compose(compose(a,X0),codomain(X0))) = compose(compose(a,X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f3666]) ).
fof(f3749,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,X0),compose(compose(a,X0),codomain(X0))) = compose(compose(a,X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f3748]) ).
fof(f3759,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(a,X0)),ifeq(domain(b),domain(X0),compose(a,compose(X0,codomain(compose(a,X0)))),compose(a,X0)),compose(compose(a,X0),codomain(compose(a,X0)))) = compose(compose(a,X0),codomain(compose(a,X0))),
inference(forward_demodulation,[status(thm)],[f17,f3669]) ).
fof(f3760,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(a,X0)),ifeq(domain(b),domain(X0),compose(a,compose(X0,codomain(compose(a,X0)))),compose(a,X0)),compose(a,X0)) = compose(compose(a,X0),codomain(compose(a,X0))),
inference(forward_demodulation,[status(thm)],[f19,f3759]) ).
fof(f3761,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(a,X0)),ifeq(domain(b),domain(X0),compose(a,compose(X0,codomain(compose(a,X0)))),compose(a,X0)),compose(a,X0)) = compose(a,X0),
inference(forward_demodulation,[status(thm)],[f19,f3760]) ).
fof(f4169,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(compose(a,b)),compose(domain(X1),compose(compose(a,b),X0)),compose(compose(domain(X1),compose(a,b)),X0)),compose(compose(domain(X1),compose(a,b)),X0)) = compose(compose(domain(X1),compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f959,f192]) ).
fof(f4170,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(compose(a,h)),compose(domain(X1),compose(compose(a,h),X0)),compose(compose(domain(X1),compose(a,h)),X0)),compose(compose(domain(X1),compose(a,h)),X0)) = compose(compose(domain(X1),compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f367,f192]) ).
fof(f4172,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),domain(codomain(X0)),compose(domain(X2),compose(codomain(X0),X1)),compose(compose(domain(X2),codomain(X0)),X1)),compose(compose(domain(X2),codomain(X0)),X1)) = compose(compose(domain(X2),codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f34,f192]) ).
fof(f4175,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(a,b))),compose(compose(domain(X1),X0),compose(a,b))),compose(compose(domain(X1),X0),compose(a,b))) = compose(compose(domain(X1),X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f192]) ).
fof(f4176,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(a,h))),compose(compose(domain(X1),X0),compose(a,h))),compose(compose(domain(X1),X0),compose(a,h))) = compose(compose(domain(X1),X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f192]) ).
fof(f4177,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(X0,domain(X1))),compose(compose(domain(X2),X0),domain(X1))),compose(compose(domain(X2),X0),domain(X1))) = compose(compose(domain(X2),X0),domain(X1)),
inference(paramodulation,[status(thm)],[f33,f192]) ).
fof(f4191,plain,
! [X0,X1] : ifeq(codomain(g),domain(X0),ifeq(domain(X1),domain(b),compose(domain(X1),compose(g,X0)),compose(compose(domain(X1),g),X0)),compose(compose(domain(X1),g),X0)) = compose(compose(domain(X1),g),X0),
inference(paramodulation,[status(thm)],[f55,f192]) ).
fof(f4192,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(b),compose(domain(X1),compose(h,X0)),compose(compose(domain(X1),h),X0)),compose(compose(domain(X1),h),X0)) = compose(compose(domain(X1),h),X0),
inference(paramodulation,[status(thm)],[f48,f192]) ).
fof(f4203,plain,
! [X0] : ifeq(codomain(compose(a,b)),domain(codomain(b)),ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),compose(a,b)),codomain(b))),compose(compose(domain(X0),compose(a,b)),codomain(b))) = compose(compose(domain(X0),compose(a,b)),codomain(b)),
inference(paramodulation,[status(thm)],[f1034,f192]) ).
fof(f4204,plain,
! [X0] : ifeq(codomain(compose(a,h)),domain(codomain(h)),ifeq(domain(X0),domain(compose(a,h)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),compose(a,h)),codomain(h))),compose(compose(domain(X0),compose(a,h)),codomain(h))) = compose(compose(domain(X0),compose(a,h)),codomain(h)),
inference(paramodulation,[status(thm)],[f477,f192]) ).
fof(f4205,plain,
! [X0] : ifeq(codomain(g),domain(codomain(h)),ifeq(domain(X0),domain(g),compose(domain(X0),g),compose(compose(domain(X0),g),codomain(h))),compose(compose(domain(X0),g),codomain(h))) = compose(compose(domain(X0),g),codomain(h)),
inference(paramodulation,[status(thm)],[f377,f192]) ).
fof(f4206,plain,
! [X0,X1] : ifeq(codomain(codomain(X0)),domain(codomain(X0)),ifeq(domain(X1),domain(codomain(X0)),compose(domain(X1),codomain(X0)),compose(compose(domain(X1),codomain(X0)),codomain(X0))),compose(compose(domain(X1),codomain(X0)),codomain(X0))) = compose(compose(domain(X1),codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f32,f192]) ).
fof(f4207,plain,
! [X0] : ifeq(codomain(a),domain(g),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),a),g)),compose(compose(domain(X0),a),g)) = compose(compose(domain(X0),a),g),
inference(paramodulation,[status(thm)],[f27,f192]) ).
fof(f4208,plain,
! [X0] : ifeq(codomain(a),domain(domain(b)),ifeq(domain(X0),domain(a),compose(domain(X0),a),compose(compose(domain(X0),a),domain(b))),compose(compose(domain(X0),a),domain(b))) = compose(compose(domain(X0),a),domain(b)),
inference(paramodulation,[status(thm)],[f46,f192]) ).
fof(f4209,plain,
! [X0] : ifeq(codomain(domain(a)),domain(compose(a,b)),ifeq(domain(X0),domain(domain(a)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),domain(a)),compose(a,b))),compose(compose(domain(X0),domain(a)),compose(a,b))) = compose(compose(domain(X0),domain(a)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1212,f192]) ).
fof(f4210,plain,
! [X0] : ifeq(codomain(domain(a)),domain(compose(a,h)),ifeq(domain(X0),domain(domain(a)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),domain(a)),compose(a,h))),compose(compose(domain(X0),domain(a)),compose(a,h))) = compose(compose(domain(X0),domain(a)),compose(a,h)),
inference(paramodulation,[status(thm)],[f441,f192]) ).
fof(f4211,plain,
! [X0] : ifeq(codomain(domain(b)),domain(g),ifeq(domain(X0),domain(domain(b)),compose(domain(X0),g),compose(compose(domain(X0),domain(b)),g)),compose(compose(domain(X0),domain(b)),g)) = compose(compose(domain(X0),domain(b)),g),
inference(paramodulation,[status(thm)],[f59,f192]) ).
fof(f4212,plain,
! [X0] : ifeq(codomain(domain(b)),domain(h),ifeq(domain(X0),domain(domain(b)),compose(domain(X0),h),compose(compose(domain(X0),domain(b)),h)),compose(compose(domain(X0),domain(b)),h)) = compose(compose(domain(X0),domain(b)),h),
inference(paramodulation,[status(thm)],[f52,f192]) ).
fof(f4213,plain,
! [X0,X1] : ifeq(codomain(domain(X0)),domain(domain(X0)),ifeq(domain(X1),domain(domain(X0)),compose(domain(X1),domain(X0)),compose(compose(domain(X1),domain(X0)),domain(X0))),compose(compose(domain(X1),domain(X0)),domain(X0))) = compose(compose(domain(X1),domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f29,f192]) ).
fof(f4214,plain,
! [X0,X1] : ifeq(codomain(domain(X0)),domain(X0),ifeq(domain(X1),domain(domain(X0)),compose(domain(X1),X0),compose(compose(domain(X1),domain(X0)),X0)),compose(compose(domain(X1),domain(X0)),X0)) = compose(compose(domain(X1),domain(X0)),X0),
inference(paramodulation,[status(thm)],[f18,f192]) ).
fof(f4215,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(X0)),ifeq(domain(X1),domain(X0),compose(domain(X1),X0),compose(compose(domain(X1),X0),codomain(X0))),compose(compose(domain(X1),X0),codomain(X0))) = compose(compose(domain(X1),X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f19,f192]) ).
fof(f4216,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(compose(domain(X1),X0))),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,codomain(compose(domain(X1),X0)))),compose(domain(X1),X0)),compose(compose(domain(X1),X0),codomain(compose(domain(X1),X0)))) = compose(compose(domain(X1),X0),codomain(compose(domain(X1),X0))),
inference(paramodulation,[status(thm)],[f19,f192]) ).
fof(f4244,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),X0)),compose(compose(domain(X1),compose(a,b)),X0)),compose(compose(domain(X1),compose(a,b)),X0)) = compose(compose(domain(X1),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f4169]) ).
fof(f4245,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),X0)),compose(compose(domain(X1),compose(a,h)),X0)),compose(compose(domain(X1),compose(a,h)),X0)) = compose(compose(domain(X1),compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f345,f4170]) ).
fof(f4247,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),X1)),compose(compose(domain(X2),codomain(X0)),X1)),compose(compose(domain(X2),codomain(X0)),X1)) = compose(compose(domain(X2),codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f17,f4172]) ).
fof(f4278,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(b),compose(domain(X1),compose(g,X0)),compose(compose(domain(X1),g),X0)),compose(compose(domain(X1),g),X0)) = compose(compose(domain(X1),g),X0),
inference(forward_demodulation,[status(thm)],[f359,f4191]) ).
fof(f4311,plain,
! [X0] : ifeq(codomain(b),domain(codomain(b)),ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),compose(a,b)),codomain(b))),compose(compose(domain(X0),compose(a,b)),codomain(b))) = compose(compose(domain(X0),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f959,f4203]) ).
fof(f4312,plain,
! [X0] : ifeq(codomain(b),codomain(b),ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),compose(a,b)),codomain(b))),compose(compose(domain(X0),compose(a,b)),codomain(b))) = compose(compose(domain(X0),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f17,f4311]) ).
fof(f4313,plain,
! [X0] : ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),compose(a,b)),codomain(b))) = compose(compose(domain(X0),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f15,f4312]) ).
fof(f4314,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),compose(a,b)),codomain(b))) = compose(compose(domain(X0),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f1163,f4313]) ).
fof(f4315,plain,
! [X0] : ifeq(codomain(h),domain(codomain(h)),ifeq(domain(X0),domain(compose(a,h)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),compose(a,h)),codomain(h))),compose(compose(domain(X0),compose(a,h)),codomain(h))) = compose(compose(domain(X0),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f367,f4204]) ).
fof(f4316,plain,
! [X0] : ifeq(codomain(h),codomain(h),ifeq(domain(X0),domain(compose(a,h)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),compose(a,h)),codomain(h))),compose(compose(domain(X0),compose(a,h)),codomain(h))) = compose(compose(domain(X0),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f4315]) ).
fof(f4317,plain,
! [X0] : ifeq(domain(X0),domain(compose(a,h)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),compose(a,h)),codomain(h))) = compose(compose(domain(X0),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f4316]) ).
fof(f4318,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),compose(a,h)),codomain(h))) = compose(compose(domain(X0),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f345,f4317]) ).
fof(f4319,plain,
! [X0] : ifeq(codomain(h),domain(codomain(h)),ifeq(domain(X0),domain(g),compose(domain(X0),g),compose(compose(domain(X0),g),codomain(h))),compose(compose(domain(X0),g),codomain(h))) = compose(compose(domain(X0),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f359,f4205]) ).
fof(f4320,plain,
! [X0] : ifeq(codomain(h),codomain(h),ifeq(domain(X0),domain(g),compose(domain(X0),g),compose(compose(domain(X0),g),codomain(h))),compose(compose(domain(X0),g),codomain(h))) = compose(compose(domain(X0),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f4319]) ).
fof(f4321,plain,
! [X0] : ifeq(domain(X0),domain(g),compose(domain(X0),g),compose(compose(domain(X0),g),codomain(h))) = compose(compose(domain(X0),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f4320]) ).
fof(f4322,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),g),compose(compose(domain(X0),g),codomain(h))) = compose(compose(domain(X0),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f55,f4321]) ).
fof(f4323,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(X0)),ifeq(domain(X1),domain(codomain(X0)),compose(domain(X1),codomain(X0)),compose(compose(domain(X1),codomain(X0)),codomain(X0))),compose(compose(domain(X1),codomain(X0)),codomain(X0))) = compose(compose(domain(X1),codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f4206]) ).
fof(f4324,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X0),ifeq(domain(X1),domain(codomain(X0)),compose(domain(X1),codomain(X0)),compose(compose(domain(X1),codomain(X0)),codomain(X0))),compose(compose(domain(X1),codomain(X0)),codomain(X0))) = compose(compose(domain(X1),codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f4323]) ).
fof(f4325,plain,
! [X0,X1] : ifeq(domain(X0),domain(codomain(X1)),compose(domain(X0),codomain(X1)),compose(compose(domain(X0),codomain(X1)),codomain(X1))) = compose(compose(domain(X0),codomain(X1)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f4324]) ).
fof(f4326,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),compose(domain(X0),codomain(X1)),compose(compose(domain(X0),codomain(X1)),codomain(X1))) = compose(compose(domain(X0),codomain(X1)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f17,f4325]) ).
fof(f4327,plain,
! [X0] : ifeq(domain(b),domain(g),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),a),g)),compose(compose(domain(X0),a),g)) = compose(compose(domain(X0),a),g),
inference(forward_demodulation,[status(thm)],[f24,f4207]) ).
fof(f4328,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),a),g)),compose(compose(domain(X0),a),g)) = compose(compose(domain(X0),a),g),
inference(forward_demodulation,[status(thm)],[f55,f4327]) ).
fof(f4329,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),a),g)) = compose(compose(domain(X0),a),g),
inference(forward_demodulation,[status(thm)],[f15,f4328]) ).
fof(f4330,plain,
! [X0] : ifeq(domain(b),domain(domain(b)),ifeq(domain(X0),domain(a),compose(domain(X0),a),compose(compose(domain(X0),a),domain(b))),compose(compose(domain(X0),a),domain(b))) = compose(compose(domain(X0),a),domain(b)),
inference(forward_demodulation,[status(thm)],[f24,f4208]) ).
fof(f4331,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(domain(X0),domain(a),compose(domain(X0),a),compose(compose(domain(X0),a),domain(b))),compose(compose(domain(X0),a),domain(b))) = compose(compose(domain(X0),a),domain(b)),
inference(forward_demodulation,[status(thm)],[f33,f4330]) ).
fof(f4332,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),a),compose(compose(domain(X0),a),domain(b))) = compose(compose(domain(X0),a),domain(b)),
inference(forward_demodulation,[status(thm)],[f15,f4331]) ).
fof(f4333,plain,
! [X0] : ifeq(domain(a),domain(compose(a,b)),ifeq(domain(X0),domain(domain(a)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),domain(a)),compose(a,b))),compose(compose(domain(X0),domain(a)),compose(a,b))) = compose(compose(domain(X0),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f16,f4209]) ).
fof(f4334,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(domain(a)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),domain(a)),compose(a,b))),compose(compose(domain(X0),domain(a)),compose(a,b))) = compose(compose(domain(X0),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f4333]) ).
fof(f4335,plain,
! [X0] : ifeq(domain(X0),domain(domain(a)),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),domain(a)),compose(a,b))) = compose(compose(domain(X0),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f15,f4334]) ).
fof(f4336,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),domain(a)),compose(a,b))) = compose(compose(domain(X0),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f33,f4335]) ).
fof(f4337,plain,
! [X0] : ifeq(domain(a),domain(compose(a,h)),ifeq(domain(X0),domain(domain(a)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),domain(a)),compose(a,h))),compose(compose(domain(X0),domain(a)),compose(a,h))) = compose(compose(domain(X0),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f4210]) ).
fof(f4338,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(domain(a)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),domain(a)),compose(a,h))),compose(compose(domain(X0),domain(a)),compose(a,h))) = compose(compose(domain(X0),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f4337]) ).
fof(f4339,plain,
! [X0] : ifeq(domain(X0),domain(domain(a)),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),domain(a)),compose(a,h))) = compose(compose(domain(X0),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f4338]) ).
fof(f4340,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),domain(a)),compose(a,h))) = compose(compose(domain(X0),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f33,f4339]) ).
fof(f4341,plain,
! [X0] : ifeq(domain(b),domain(g),ifeq(domain(X0),domain(domain(b)),compose(domain(X0),g),compose(compose(domain(X0),domain(b)),g)),compose(compose(domain(X0),domain(b)),g)) = compose(compose(domain(X0),domain(b)),g),
inference(forward_demodulation,[status(thm)],[f16,f4211]) ).
fof(f4342,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(domain(X0),domain(domain(b)),compose(domain(X0),g),compose(compose(domain(X0),domain(b)),g)),compose(compose(domain(X0),domain(b)),g)) = compose(compose(domain(X0),domain(b)),g),
inference(forward_demodulation,[status(thm)],[f55,f4341]) ).
fof(f4343,plain,
! [X0] : ifeq(domain(X0),domain(domain(b)),compose(domain(X0),g),compose(compose(domain(X0),domain(b)),g)) = compose(compose(domain(X0),domain(b)),g),
inference(forward_demodulation,[status(thm)],[f15,f4342]) ).
fof(f4344,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),g),compose(compose(domain(X0),domain(b)),g)) = compose(compose(domain(X0),domain(b)),g),
inference(forward_demodulation,[status(thm)],[f33,f4343]) ).
fof(f4345,plain,
! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(domain(b)),compose(domain(X0),h),compose(compose(domain(X0),domain(b)),h)),compose(compose(domain(X0),domain(b)),h)) = compose(compose(domain(X0),domain(b)),h),
inference(forward_demodulation,[status(thm)],[f16,f4212]) ).
fof(f4346,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(domain(X0),domain(domain(b)),compose(domain(X0),h),compose(compose(domain(X0),domain(b)),h)),compose(compose(domain(X0),domain(b)),h)) = compose(compose(domain(X0),domain(b)),h),
inference(forward_demodulation,[status(thm)],[f48,f4345]) ).
fof(f4347,plain,
! [X0] : ifeq(domain(X0),domain(domain(b)),compose(domain(X0),h),compose(compose(domain(X0),domain(b)),h)) = compose(compose(domain(X0),domain(b)),h),
inference(forward_demodulation,[status(thm)],[f15,f4346]) ).
fof(f4348,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),h),compose(compose(domain(X0),domain(b)),h)) = compose(compose(domain(X0),domain(b)),h),
inference(forward_demodulation,[status(thm)],[f33,f4347]) ).
fof(f4349,plain,
! [X0,X1] : ifeq(domain(X0),domain(domain(X0)),ifeq(domain(X1),domain(domain(X0)),compose(domain(X1),domain(X0)),compose(compose(domain(X1),domain(X0)),domain(X0))),compose(compose(domain(X1),domain(X0)),domain(X0))) = compose(compose(domain(X1),domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f4213]) ).
fof(f4350,plain,
! [X0,X1] : ifeq(domain(X0),domain(X0),ifeq(domain(X1),domain(domain(X0)),compose(domain(X1),domain(X0)),compose(compose(domain(X1),domain(X0)),domain(X0))),compose(compose(domain(X1),domain(X0)),domain(X0))) = compose(compose(domain(X1),domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f4349]) ).
fof(f4351,plain,
! [X0,X1] : ifeq(domain(X0),domain(domain(X1)),compose(domain(X0),domain(X1)),compose(compose(domain(X0),domain(X1)),domain(X1))) = compose(compose(domain(X0),domain(X1)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f4350]) ).
fof(f4352,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),domain(X1)),compose(compose(domain(X0),domain(X1)),domain(X1))) = compose(compose(domain(X0),domain(X1)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f33,f4351]) ).
fof(f4353,plain,
! [X0,X1] : ifeq(domain(X0),domain(X0),ifeq(domain(X1),domain(domain(X0)),compose(domain(X1),X0),compose(compose(domain(X1),domain(X0)),X0)),compose(compose(domain(X1),domain(X0)),X0)) = compose(compose(domain(X1),domain(X0)),X0),
inference(forward_demodulation,[status(thm)],[f16,f4214]) ).
fof(f4354,plain,
! [X0,X1] : ifeq(domain(X0),domain(domain(X1)),compose(domain(X0),X1),compose(compose(domain(X0),domain(X1)),X1)) = compose(compose(domain(X0),domain(X1)),X1),
inference(forward_demodulation,[status(thm)],[f15,f4353]) ).
fof(f4355,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),X1),compose(compose(domain(X0),domain(X1)),X1)) = compose(compose(domain(X0),domain(X1)),X1),
inference(forward_demodulation,[status(thm)],[f33,f4354]) ).
fof(f4356,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X0),ifeq(domain(X1),domain(X0),compose(domain(X1),X0),compose(compose(domain(X1),X0),codomain(X0))),compose(compose(domain(X1),X0),codomain(X0))) = compose(compose(domain(X1),X0),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f4215]) ).
fof(f4357,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),X1),compose(compose(domain(X0),X1),codomain(X1))) = compose(compose(domain(X0),X1),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f4356]) ).
fof(f4358,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(domain(X1),X0)),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,codomain(compose(domain(X1),X0)))),compose(domain(X1),X0)),compose(compose(domain(X1),X0),codomain(compose(domain(X1),X0)))) = compose(compose(domain(X1),X0),codomain(compose(domain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f17,f4216]) ).
fof(f4359,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(domain(X1),X0)),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,codomain(compose(domain(X1),X0)))),compose(domain(X1),X0)),compose(domain(X1),X0)) = compose(compose(domain(X1),X0),codomain(compose(domain(X1),X0))),
inference(forward_demodulation,[status(thm)],[f19,f4358]) ).
fof(f4360,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(domain(X1),X0)),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,codomain(compose(domain(X1),X0)))),compose(domain(X1),X0)),compose(domain(X1),X0)) = compose(domain(X1),X0),
inference(forward_demodulation,[status(thm)],[f19,f4359]) ).
fof(f4547,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(b),compose(X1,compose(g,X0)),compose(compose(X1,g),X0)),compose(compose(X1,g),X0)) = compose(compose(X1,g),X0),
inference(forward_demodulation,[status(thm)],[f359,f194]) ).
fof(f4548,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(b),compose(X0,compose(g,compose(a,b))),compose(compose(X0,g),compose(a,b))),compose(compose(X0,g),compose(a,b))) = compose(compose(X0,g),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4547]) ).
fof(f4549,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(b),compose(X0,compose(g,compose(a,h))),compose(compose(X0,g),compose(a,h))),compose(compose(X0,g),compose(a,h))) = compose(compose(X0,g),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f4547]) ).
fof(f4550,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(b),compose(X1,compose(g,domain(X0))),compose(compose(X1,g),domain(X0))),compose(compose(X1,g),domain(X0))) = compose(compose(X1,g),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f4547]) ).
fof(f4554,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(g,X0)),compose(compose(compose(a,b),g),X0)),compose(compose(compose(a,b),g),X0)) = compose(compose(compose(a,b),g),X0),
inference(paramodulation,[status(thm)],[f959,f4547]) ).
fof(f4555,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,X0)),compose(compose(compose(a,h),g),X0)),compose(compose(compose(a,h),g),X0)) = compose(compose(compose(a,h),g),X0),
inference(paramodulation,[status(thm)],[f367,f4547]) ).
fof(f4556,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(b),compose(g,compose(g,X0)),compose(compose(g,g),X0)),compose(compose(g,g),X0)) = compose(compose(g,g),X0),
inference(paramodulation,[status(thm)],[f359,f4547]) ).
fof(f4557,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(b),compose(codomain(X1),compose(g,X0)),compose(compose(codomain(X1),g),X0)),compose(compose(codomain(X1),g),X0)) = compose(compose(codomain(X1),g),X0),
inference(paramodulation,[status(thm)],[f34,f4547]) ).
fof(f4560,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(compose(g,X0))),domain(b),compose(g,X0),compose(compose(domain(compose(g,X0)),g),X0)),compose(compose(domain(compose(g,X0)),g),X0)) = compose(compose(domain(compose(g,X0)),g),X0),
inference(paramodulation,[status(thm)],[f18,f4547]) ).
fof(f4563,plain,
! [X0] : ifeq(codomain(h),domain(codomain(compose(X0,g))),ifeq(codomain(X0),domain(b),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(compose(X0,g),codomain(compose(X0,g)))) = compose(compose(X0,g),codomain(compose(X0,g))),
inference(paramodulation,[status(thm)],[f19,f4547]) ).
fof(f4574,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(g,X0)),domain(b),compose(g,X0),compose(compose(domain(compose(g,X0)),g),X0)),compose(compose(domain(compose(g,X0)),g),X0)) = compose(compose(domain(compose(g,X0)),g),X0),
inference(forward_demodulation,[status(thm)],[f16,f4560]) ).
fof(f4582,plain,
! [X0] : ifeq(codomain(h),codomain(compose(X0,g)),ifeq(codomain(X0),domain(b),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(compose(X0,g),codomain(compose(X0,g)))) = compose(compose(X0,g),codomain(compose(X0,g))),
inference(forward_demodulation,[status(thm)],[f17,f4563]) ).
fof(f4583,plain,
! [X0] : ifeq(codomain(h),codomain(compose(X0,g)),ifeq(codomain(X0),domain(b),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(X0,g)) = compose(compose(X0,g),codomain(compose(X0,g))),
inference(forward_demodulation,[status(thm)],[f19,f4582]) ).
fof(f4584,plain,
! [X0] : ifeq(codomain(h),codomain(compose(X0,g)),ifeq(codomain(X0),domain(b),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(X0,g)) = compose(X0,g),
inference(forward_demodulation,[status(thm)],[f19,f4583]) ).
fof(f4693,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(b),compose(X0,compose(h,compose(a,b))),compose(compose(X0,h),compose(a,b))),compose(compose(X0,h),compose(a,b))) = compose(compose(X0,h),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f195]) ).
fof(f4694,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(b),compose(X0,compose(h,compose(a,h))),compose(compose(X0,h),compose(a,h))),compose(compose(X0,h),compose(a,h))) = compose(compose(X0,h),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f195]) ).
fof(f4695,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(b),compose(X1,compose(h,domain(X0))),compose(compose(X1,h),domain(X0))),compose(compose(X1,h),domain(X0))) = compose(compose(X1,h),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f195]) ).
fof(f4699,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(h,X0)),compose(compose(compose(a,b),h),X0)),compose(compose(compose(a,b),h),X0)) = compose(compose(compose(a,b),h),X0),
inference(paramodulation,[status(thm)],[f959,f195]) ).
fof(f4700,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,X0)),compose(compose(compose(a,h),h),X0)),compose(compose(compose(a,h),h),X0)) = compose(compose(compose(a,h),h),X0),
inference(paramodulation,[status(thm)],[f367,f195]) ).
fof(f4701,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(b),compose(g,compose(h,X0)),compose(compose(g,h),X0)),compose(compose(g,h),X0)) = compose(compose(g,h),X0),
inference(paramodulation,[status(thm)],[f359,f195]) ).
fof(f4702,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(b),compose(codomain(X1),compose(h,X0)),compose(compose(codomain(X1),h),X0)),compose(compose(codomain(X1),h),X0)) = compose(compose(codomain(X1),h),X0),
inference(paramodulation,[status(thm)],[f34,f195]) ).
fof(f4705,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(compose(h,X0))),domain(b),compose(h,X0),compose(compose(domain(compose(h,X0)),h),X0)),compose(compose(domain(compose(h,X0)),h),X0)) = compose(compose(domain(compose(h,X0)),h),X0),
inference(paramodulation,[status(thm)],[f18,f195]) ).
fof(f4706,plain,
! [X0] : ifeq(codomain(h),domain(codomain(h)),ifeq(codomain(X0),domain(b),compose(X0,h),compose(compose(X0,h),codomain(h))),compose(compose(X0,h),codomain(h))) = compose(compose(X0,h),codomain(h)),
inference(paramodulation,[status(thm)],[f19,f195]) ).
fof(f4708,plain,
! [X0] : ifeq(codomain(h),domain(codomain(compose(X0,h))),ifeq(codomain(X0),domain(b),compose(X0,compose(h,codomain(compose(X0,h)))),compose(X0,h)),compose(compose(X0,h),codomain(compose(X0,h)))) = compose(compose(X0,h),codomain(compose(X0,h))),
inference(paramodulation,[status(thm)],[f19,f195]) ).
fof(f4716,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(h,X0)),domain(b),compose(h,X0),compose(compose(domain(compose(h,X0)),h),X0)),compose(compose(domain(compose(h,X0)),h),X0)) = compose(compose(domain(compose(h,X0)),h),X0),
inference(forward_demodulation,[status(thm)],[f16,f4705]) ).
fof(f4717,plain,
! [X0] : ifeq(codomain(h),codomain(h),ifeq(codomain(X0),domain(b),compose(X0,h),compose(compose(X0,h),codomain(h))),compose(compose(X0,h),codomain(h))) = compose(compose(X0,h),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f4706]) ).
fof(f4718,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(X0,h),compose(compose(X0,h),codomain(h))) = compose(compose(X0,h),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f4717]) ).
fof(f4724,plain,
! [X0] : ifeq(codomain(h),codomain(compose(X0,h)),ifeq(codomain(X0),domain(b),compose(X0,compose(h,codomain(compose(X0,h)))),compose(X0,h)),compose(compose(X0,h),codomain(compose(X0,h)))) = compose(compose(X0,h),codomain(compose(X0,h))),
inference(forward_demodulation,[status(thm)],[f17,f4708]) ).
fof(f4725,plain,
! [X0] : ifeq(codomain(h),codomain(compose(X0,h)),ifeq(codomain(X0),domain(b),compose(X0,compose(h,codomain(compose(X0,h)))),compose(X0,h)),compose(X0,h)) = compose(compose(X0,h),codomain(compose(X0,h))),
inference(forward_demodulation,[status(thm)],[f19,f4724]) ).
fof(f4726,plain,
! [X0] : ifeq(codomain(h),codomain(compose(X0,h)),ifeq(codomain(X0),domain(b),compose(X0,compose(h,codomain(compose(X0,h)))),compose(X0,h)),compose(X0,h)) = compose(X0,h),
inference(forward_demodulation,[status(thm)],[f19,f4725]) ).
fof(f4759,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(a,b))),compose(compose(X1,codomain(X0)),compose(a,b))),compose(compose(X1,codomain(X0)),compose(a,b))) = compose(compose(X1,codomain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f224]) ).
fof(f4760,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(a,h))),compose(compose(X1,codomain(X0)),compose(a,h))),compose(compose(X1,codomain(X0)),compose(a,h))) = compose(compose(X1,codomain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f224]) ).
fof(f4761,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),codomain(X0),compose(X2,compose(codomain(X0),domain(X1))),compose(compose(X2,codomain(X0)),domain(X1))),compose(compose(X2,codomain(X0)),domain(X1))) = compose(compose(X2,codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f33,f224]) ).
fof(f4766,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),X1)),compose(compose(compose(a,b),codomain(X0)),X1)),compose(compose(compose(a,b),codomain(X0)),X1)) = compose(compose(compose(a,b),codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f959,f224]) ).
fof(f4767,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),X1)),compose(compose(compose(a,h),codomain(X0)),X1)),compose(compose(compose(a,h),codomain(X0)),X1)) = compose(compose(compose(a,h),codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f367,f224]) ).
fof(f4768,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),X1)),compose(compose(g,codomain(X0)),X1)),compose(compose(g,codomain(X0)),X1)) = compose(compose(g,codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f359,f224]) ).
fof(f4769,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),codomain(X0),compose(codomain(X2),compose(codomain(X0),X1)),compose(compose(codomain(X2),codomain(X0)),X1)),compose(compose(codomain(X2),codomain(X0)),X1)) = compose(compose(codomain(X2),codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f34,f224]) ).
fof(f4778,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(domain(compose(codomain(X0),X1))),codomain(X0),compose(codomain(X0),X1),compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1)),compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1)) = compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1),
inference(paramodulation,[status(thm)],[f18,f224]) ).
fof(f4787,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(compose(X1,codomain(X0)))),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),codomain(compose(X1,codomain(X0))))),compose(X1,codomain(X0))),compose(compose(X1,codomain(X0)),codomain(compose(X1,codomain(X0))))) = compose(compose(X1,codomain(X0)),codomain(compose(X1,codomain(X0)))),
inference(paramodulation,[status(thm)],[f19,f224]) ).
fof(f4875,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(compose(codomain(X0),X1)),codomain(X0),compose(codomain(X0),X1),compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1)),compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1)) = compose(compose(domain(compose(codomain(X0),X1)),codomain(X0)),X1),
inference(forward_demodulation,[status(thm)],[f16,f4778]) ).
fof(f4913,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(X1,codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),codomain(compose(X1,codomain(X0))))),compose(X1,codomain(X0))),compose(compose(X1,codomain(X0)),codomain(compose(X1,codomain(X0))))) = compose(compose(X1,codomain(X0)),codomain(compose(X1,codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f4787]) ).
fof(f4914,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(X1,codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),codomain(compose(X1,codomain(X0))))),compose(X1,codomain(X0))),compose(X1,codomain(X0))) = compose(compose(X1,codomain(X0)),codomain(compose(X1,codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f4913]) ).
fof(f4915,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(X1,codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),codomain(compose(X1,codomain(X0))))),compose(X1,codomain(X0))),compose(X1,codomain(X0))) = compose(X1,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f4914]) ).
fof(f5023,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(a,b),X0)),domain(compose(a,b)),compose(compose(a,b),X0),compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0)),compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0)) = compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f959,f225]) ).
fof(f5024,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(compose(a,h),X0)),domain(compose(a,h)),compose(compose(a,h),X0),compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0)),compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0)) = compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f367,f225]) ).
fof(f5029,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(compose(X0,compose(a,b))),domain(X0),compose(X0,compose(a,b)),compose(compose(domain(compose(X0,compose(a,b))),X0),compose(a,b))),compose(compose(domain(compose(X0,compose(a,b))),X0),compose(a,b))) = compose(compose(domain(compose(X0,compose(a,b))),X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f225]) ).
fof(f5030,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(compose(X0,compose(a,h))),domain(X0),compose(X0,compose(a,h)),compose(compose(domain(compose(X0,compose(a,h))),X0),compose(a,h))),compose(compose(domain(compose(X0,compose(a,h))),X0),compose(a,h))) = compose(compose(domain(compose(X0,compose(a,h))),X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f225]) ).
fof(f5031,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(compose(X0,domain(X1))),domain(X0),compose(X0,domain(X1)),compose(compose(domain(compose(X0,domain(X1))),X0),domain(X1))),compose(compose(domain(compose(X0,domain(X1))),X0),domain(X1))) = compose(compose(domain(compose(X0,domain(X1))),X0),domain(X1)),
inference(paramodulation,[status(thm)],[f33,f225]) ).
fof(f5099,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(a,b),X0)),domain(a),compose(compose(a,b),X0),compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0)),compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0)) = compose(compose(domain(compose(compose(a,b),X0)),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f5023]) ).
fof(f5100,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(compose(a,h),X0)),domain(a),compose(compose(a,h),X0),compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0)),compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0)) = compose(compose(domain(compose(compose(a,h),X0)),compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f345,f5024]) ).
fof(f5582,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(compose(a,b),X0),compose(compose(compose(a,b),domain(X0)),X0)) = compose(compose(compose(a,b),domain(X0)),X0),
inference(paramodulation,[status(thm)],[f959,f247]) ).
fof(f5583,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(compose(a,h),X0),compose(compose(compose(a,h),domain(X0)),X0)) = compose(compose(compose(a,h),domain(X0)),X0),
inference(paramodulation,[status(thm)],[f367,f247]) ).
fof(f5584,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(g,X0),compose(compose(g,domain(X0)),X0)) = compose(compose(g,domain(X0)),X0),
inference(paramodulation,[status(thm)],[f359,f247]) ).
fof(f5585,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),X1),compose(compose(codomain(X0),domain(X1)),X1)) = compose(compose(codomain(X0),domain(X1)),X1),
inference(paramodulation,[status(thm)],[f34,f247]) ).
fof(f5714,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(compose(a,b),X0),compose(compose(compose(a,b),X0),codomain(X0))) = compose(compose(compose(a,b),X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f249]) ).
fof(f5715,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(compose(a,h),X0),compose(compose(compose(a,h),X0),codomain(X0))) = compose(compose(compose(a,h),X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f367,f249]) ).
fof(f5716,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(g,X0),compose(compose(g,X0),codomain(X0))) = compose(compose(g,X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f249]) ).
fof(f5717,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),X1),compose(compose(codomain(X0),X1),codomain(X1))) = compose(compose(codomain(X0),X1),codomain(X1)),
inference(paramodulation,[status(thm)],[f34,f249]) ).
fof(f5911,plain,
! [X0] : ifeq(codomain(b),codomain(compose(X0,compose(a,b))),ifeq(codomain(X0),domain(compose(a,b)),compose(X0,compose(compose(a,b),codomain(compose(X0,compose(a,b))))),compose(X0,compose(a,b))),compose(X0,compose(a,b))) = compose(X0,compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f252]) ).
fof(f5912,plain,
! [X0] : ifeq(codomain(h),codomain(compose(X0,compose(a,h))),ifeq(codomain(X0),domain(compose(a,h)),compose(X0,compose(compose(a,h),codomain(compose(X0,compose(a,h))))),compose(X0,compose(a,h))),compose(X0,compose(a,h))) = compose(X0,compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f252]) ).
fof(f5932,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(compose(a,b),X0)),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,codomain(compose(compose(a,b),X0)))),compose(compose(a,b),X0)),compose(compose(a,b),X0)) = compose(compose(a,b),X0),
inference(paramodulation,[status(thm)],[f959,f252]) ).
fof(f5933,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(compose(a,h),X0)),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,codomain(compose(compose(a,h),X0)))),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(paramodulation,[status(thm)],[f367,f252]) ).
fof(f5934,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(g,X0)),ifeq(codomain(h),domain(X0),compose(g,compose(X0,codomain(compose(g,X0)))),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(paramodulation,[status(thm)],[f359,f252]) ).
fof(f5935,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(codomain(X1),X0)),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,codomain(compose(codomain(X1),X0)))),compose(codomain(X1),X0)),compose(codomain(X1),X0)) = compose(codomain(X1),X0),
inference(paramodulation,[status(thm)],[f34,f252]) ).
fof(f5985,plain,
! [X0] : ifeq(codomain(b),codomain(compose(X0,compose(a,b))),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),codomain(compose(X0,compose(a,b))))),compose(X0,compose(a,b))),compose(X0,compose(a,b))) = compose(X0,compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f5911]) ).
fof(f5986,plain,
! [X0] : ifeq(codomain(h),codomain(compose(X0,compose(a,h))),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),codomain(compose(X0,compose(a,h))))),compose(X0,compose(a,h))),compose(X0,compose(a,h))) = compose(X0,compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f5912]) ).
fof(f6391,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(domain(X0),compose(X0,compose(a,b))),compose(X0,compose(a,b))) = compose(X0,compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f284]) ).
fof(f6392,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(domain(X0),compose(X0,compose(a,h))),compose(X0,compose(a,h))) = compose(X0,compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f284]) ).
fof(f6393,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(domain(X0),compose(X0,domain(X1))),compose(X0,domain(X1))) = compose(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f33,f284]) ).
fof(f6554,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(codomain(X0),compose(a,b))),compose(X0,compose(a,b))) = compose(X0,compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f289]) ).
fof(f6555,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(codomain(X0),compose(a,h))),compose(X0,compose(a,h))) = compose(X0,compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f289]) ).
fof(f6556,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(X0,compose(codomain(X0),domain(X1))),compose(X0,domain(X1))) = compose(X0,domain(X1)),
inference(paramodulation,[status(thm)],[f33,f289]) ).
fof(f6648,plain,
! [X0] : ifeq(codomain(h),domain(X0),codomain(compose(compose(a,h),X0)),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f359,f352]) ).
fof(f6649,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f6648]) ).
fof(f6650,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),compose(a,h))),codomain(compose(a,h))) = codomain(compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f6648]) ).
fof(f6663,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),compose(a,b))),codomain(b)) = codomain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f6649]) ).
fof(f6664,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),compose(a,b))),codomain(b)) = codomain(b),
inference(forward_demodulation,[status(thm)],[f959,f6663]) ).
fof(f6665,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),compose(a,h))),codomain(h)) = codomain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f367,f6650]) ).
fof(f6666,plain,
ifeq(codomain(h),domain(a),codomain(compose(compose(a,h),compose(a,h))),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f367,f6665]) ).
fof(f6692,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(a,compose(g,X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
inference(forward_demodulation,[status(thm)],[f359,f331]) ).
fof(f6693,plain,
ifeq(codomain(h),domain(a),compose(a,compose(g,compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f6692]) ).
fof(f6694,plain,
ifeq(codomain(h),domain(a),compose(a,compose(g,compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f6692]) ).
fof(f6695,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(a,compose(g,domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f6692]) ).
fof(f6721,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,h))),domain(compose(a,b))) = domain(compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f439]) ).
fof(f6722,plain,
ifeq(codomain(h),domain(a),domain(compose(compose(a,h),compose(a,h))),domain(compose(a,h))) = domain(compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f439]) ).
fof(f6735,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,h))),domain(a)) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f6721]) ).
fof(f6736,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,h))),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f1163,f6735]) ).
fof(f6737,plain,
ifeq(codomain(h),domain(a),domain(compose(compose(a,h),compose(a,h))),domain(a)) = domain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f6722]) ).
fof(f6738,plain,
ifeq(codomain(h),domain(a),domain(compose(compose(a,h),compose(a,h))),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f345,f6737]) ).
fof(f6862,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),a),g)) = compose(compose(compose(a,b),a),g),
inference(paramodulation,[status(thm)],[f959,f339]) ).
fof(f6863,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),a),g)) = compose(compose(compose(a,h),a),g),
inference(paramodulation,[status(thm)],[f367,f339]) ).
fof(f6864,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,a),g)) = compose(compose(g,a),g),
inference(paramodulation,[status(thm)],[f359,f339]) ).
fof(f6865,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),a),g)) = compose(compose(codomain(X0),a),g),
inference(paramodulation,[status(thm)],[f34,f339]) ).
fof(f7004,plain,
! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(a,compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,a),a),a),a) = a,
inference(forward_demodulation,[status(thm)],[f1163,f391]) ).
fof(f7005,plain,
! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(a,compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,a),a),a),a) = a,
inference(forward_demodulation,[status(thm)],[f1163,f7004]) ).
fof(f7006,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(a,compose(a,b)),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),a),a),a),a) = a,
inference(paramodulation,[status(thm)],[f959,f7005]) ).
fof(f7007,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(a,compose(a,b)),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),a),a),a),a) = a,
inference(paramodulation,[status(thm)],[f367,f7005]) ).
fof(f7008,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(a,compose(a,b)),X0,ifeq(compose(g,compose(a,b)),X0,g,a),a),a),a) = a,
inference(paramodulation,[status(thm)],[f359,f7005]) ).
fof(f7009,plain,
! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(a,compose(a,b)),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),a),a),a),a) = a,
inference(paramodulation,[status(thm)],[f34,f7005]) ).
fof(f7010,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),X0,ifeq(compose(a,compose(a,b)),X0,a,a),a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7005]) ).
fof(f7011,plain,
! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(a,compose(a,b)),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),a),a),a),a) = a,
inference(paramodulation,[status(thm)],[f16,f7005]) ).
fof(f7012,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,compose(a,b)),X0,a),a),a) = a,
inference(paramodulation,[status(thm)],[f15,f7005]) ).
fof(f7013,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(a,compose(a,b)),compose(X0,compose(a,b)),X0,a),a),a) = a,
inference(paramodulation,[status(thm)],[f15,f7005]) ).
fof(f7014,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(domain(a)),domain(a),ifeq(compose(a,compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),a),a),a),a) = a,
inference(paramodulation,[status(thm)],[f1212,f7005]) ).
fof(f7016,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(a),ifeq(compose(a,compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),a),a),a),a) = a,
inference(forward_demodulation,[status(thm)],[f16,f7014]) ).
fof(f7017,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),a),a),a) = a,
inference(forward_demodulation,[status(thm)],[f15,f7016]) ).
fof(f7044,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f1030]) ).
fof(f7045,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,h))),codomain(compose(a,h))) = codomain(compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f1030]) ).
fof(f7058,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,b))),codomain(b)) = codomain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f7044]) ).
fof(f7059,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,b))),codomain(b)) = codomain(b),
inference(forward_demodulation,[status(thm)],[f959,f7058]) ).
fof(f7060,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,h))),codomain(h)) = codomain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f367,f7045]) ).
fof(f7061,plain,
ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,h))),codomain(h)) = codomain(h),
inference(forward_demodulation,[status(thm)],[f367,f7060]) ).
fof(f7153,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(domain(X0),compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f1163,f392]) ).
fof(f7154,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f1163,f7153]) ).
fof(f7162,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(compose(a,b),compose(a,b)),X1,compose(a,b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f959,f7154]) ).
fof(f7163,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(compose(a,h),compose(a,b)),X1,compose(a,h),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f367,f7154]) ).
fof(f7164,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(g,compose(a,b)),X1,g,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f359,f7154]) ).
fof(f7165,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),X2,ifeq(compose(codomain(X1),compose(a,b)),X2,codomain(X1),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f34,f7154]) ).
fof(f7166,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(a,compose(a,b)),X1,a,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f24,f7154]) ).
fof(f7167,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),X2,ifeq(compose(domain(X1),compose(a,b)),X2,domain(X1),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7154]) ).
fof(f7168,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X1,compose(a,b)),compose(domain(X0),compose(a,b)),X1,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f15,f7154]) ).
fof(f7177,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(X1,compose(a,b)),X1,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f15,f7154]) ).
fof(f7178,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(a)),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f1212,f7154]) ).
fof(f7288,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f16,f7178]) ).
fof(f7289,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f15,f7288]) ).
fof(f7479,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,b))),domain(compose(a,b))) = domain(compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f1210]) ).
fof(f7480,plain,
ifeq(codomain(h),domain(a),domain(compose(compose(a,h),compose(a,b))),domain(compose(a,h))) = domain(compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f1210]) ).
fof(f7493,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,b))),domain(a)) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f7479]) ).
fof(f7494,plain,
ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,b))),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f1163,f7493]) ).
fof(f7495,plain,
ifeq(codomain(h),domain(a),domain(compose(compose(a,h),compose(a,b))),domain(a)) = domain(compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f7480]) ).
fof(f7496,plain,
ifeq(codomain(h),domain(a),domain(compose(compose(a,h),compose(a,b))),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f345,f7495]) ).
fof(f7522,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,compose(a,b)),X1,a,X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f395]) ).
fof(f7523,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,compose(a,b)),X1,a,X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f7522]) ).
fof(f7524,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(a,compose(a,b)),X0,a,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7523]) ).
fof(f7525,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(b),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(a,compose(a,b)),X0,a,compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7523]) ).
fof(f7526,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(b),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(a,compose(a,b)),X0,a,g),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7523]) ).
fof(f7527,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(a,compose(a,b)),X1,a,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7523]) ).
fof(f7530,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(X0,compose(a,b)),a,X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f15,f7523]) ).
fof(f7531,plain,
! [X0] : ifeq(codomain(domain(a)),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(a,compose(a,b)),X0,a,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f1212,f7523]) ).
fof(f7533,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,compose(a,b)),a,X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f15,f7523]) ).
fof(f7534,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(a,compose(a,b)),X0,a,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f16,f7531]) ).
fof(f7535,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(a,compose(a,b)),X0,a,domain(a)),domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f15,f7534]) ).
fof(f7543,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(domain(X1),compose(a,b)),X2,domain(X1),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f396]) ).
fof(f7544,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(domain(X1),compose(a,b)),X2,domain(X1),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f7543]) ).
fof(f7545,plain,
! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7544]) ).
fof(f7546,plain,
! [X0,X1] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7544]) ).
fof(f7547,plain,
! [X0,X1] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(g,compose(a,b)),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),g),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7544]) ).
fof(f7548,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X2,ifeq(compose(domain(X1),compose(a,b)),X2,domain(X1),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7544]) ).
fof(f7558,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X1),compose(a,b)),compose(X0,compose(a,b)),domain(X1),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f15,f7544]) ).
fof(f7559,plain,
! [X0,X1] : ifeq(codomain(domain(a)),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f1212,f7544]) ).
fof(f7561,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(X0,compose(a,b)),compose(domain(X1),compose(a,b)),domain(X1),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f15,f7544]) ).
fof(f7592,plain,
! [X0,X1] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f16,f7559]) ).
fof(f7593,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(domain(X0),compose(a,b)),X1,domain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f15,f7592]) ).
fof(f7636,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X1,compose(a,b)),compose(X0,compose(a,b)),X1,X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f397]) ).
fof(f7637,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X1,compose(a,b)),compose(X0,compose(a,b)),X1,X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f7636]) ).
fof(f7638,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(compose(a,b),compose(a,b)),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7637]) ).
fof(f7639,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(compose(a,h),compose(a,b)),X0,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7637]) ).
fof(f7640,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(g,compose(a,b)),X0,g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7637]) ).
fof(f7641,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X1,compose(a,b)),compose(codomain(X0),compose(a,b)),X1,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7637]) ).
fof(f7644,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(X0,compose(a,b)),compose(a,b),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f959,f7637]) ).
fof(f7645,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(X0,compose(a,b)),compose(a,h),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f367,f7637]) ).
fof(f7646,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(X0,compose(a,b)),g,X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f359,f7637]) ).
fof(f7647,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X1),compose(a,b)),compose(X0,compose(a,b)),codomain(X1),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f34,f7637]) ).
fof(f7650,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(a),X0,X0),X0) = X0,
inference(paramodulation,[status(thm)],[f15,f7637]) ).
fof(f7651,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(a),ifeq(compose(a,b),compose(X0,compose(a,b)),domain(a),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f1212,f7637]) ).
fof(f7653,plain,
! [X0] : ifeq(codomain(domain(a)),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,b),X0,domain(a)),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f1212,f7637]) ).
fof(f7655,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(a),ifeq(compose(a,b),compose(X0,compose(a,b)),domain(a),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f16,f7651]) ).
fof(f7656,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(X0,compose(a,b)),domain(a),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f15,f7655]) ).
fof(f7661,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,b),X0,domain(a)),domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f16,f7653]) ).
fof(f7662,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,b),X0,domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f15,f7661]) ).
fof(f7669,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(compose(a,b)),domain(a),compose(a,b),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7650]) ).
fof(f7670,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(compose(a,h)),domain(a),compose(a,h),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7650]) ).
fof(f7671,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(g),domain(a),g,g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7650]) ).
fof(f7672,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(codomain(X0)),domain(a),codomain(X0),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7650]) ).
fof(f7673,plain,
ifeq(domain(b),domain(a),ifeq(codomain(a),domain(a),a,a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7650]) ).
fof(f7674,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(X0)),domain(a),domain(X0),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7650]) ).
fof(f7681,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),compose(a,b),compose(a,b)),compose(a,b)) = compose(a,b),
inference(forward_demodulation,[status(thm)],[f959,f7669]) ).
fof(f7682,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(a,h),compose(a,h)),compose(a,h)) = compose(a,h),
inference(forward_demodulation,[status(thm)],[f367,f7670]) ).
fof(f7683,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),g,g),g) = g,
inference(forward_demodulation,[status(thm)],[f359,f7671]) ).
fof(f7684,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(a),codomain(X0),codomain(X0)),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f34,f7672]) ).
fof(f7685,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),a,a),a) = a,
inference(forward_demodulation,[status(thm)],[f24,f7673]) ).
fof(f7686,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(X0),domain(a),domain(X0),domain(X0)),domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f16,f7674]) ).
fof(f7693,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(compose(a,b))),domain(compose(a,b))),domain(compose(a,b))) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f402]) ).
fof(f7694,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(a)),domain(compose(a,b))),domain(compose(a,b))) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f7693]) ).
fof(f7695,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(a)),domain(a)),domain(compose(a,b))) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f7694]) ).
fof(f7696,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(a)),domain(a)),domain(a)) = domain(compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f7695]) ).
fof(f7697,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,compose(a,b)),X1,X0,domain(a)),domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f1163,f7696]) ).
fof(f7698,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),domain(a)),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f959,f7697]) ).
fof(f7699,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),domain(a)),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f367,f7697]) ).
fof(f7700,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(compose(a,b),X0,ifeq(compose(g,compose(a,b)),X0,g,domain(a)),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f359,f7697]) ).
fof(f7701,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f34,f7697]) ).
fof(f7705,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(X0,compose(a,b)),X0,domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f15,f7697]) ).
fof(f7706,plain,
! [X0] : ifeq(codomain(domain(a)),domain(a),ifeq(compose(a,b),X0,ifeq(compose(a,b),X0,domain(a),domain(a)),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f1212,f7697]) ).
fof(f7708,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(compose(a,b),X0,ifeq(compose(a,b),X0,domain(a),domain(a)),domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f16,f7706]) ).
fof(f7709,plain,
! [X0] : ifeq(compose(a,b),X0,ifeq(compose(a,b),X0,domain(a),domain(a)),domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f15,f7708]) ).
fof(f7714,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),compose(X1,compose(a,b)),X1,X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f399]) ).
fof(f7715,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),compose(X1,compose(a,b)),X1,X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f7714]) ).
fof(f7717,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(X0,compose(a,b)),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7715]) ).
fof(f7718,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(X0,compose(a,b)),X0,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7715]) ).
fof(f7719,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(g,compose(a,b)),compose(X0,compose(a,b)),X0,g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7715]) ).
fof(f7720,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(X1,compose(a,b)),X1,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7715]) ).
fof(f7723,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(X0,compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f959,f7715]) ).
fof(f7724,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(X0,compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f367,f7715]) ).
fof(f7725,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(X0,compose(a,b)),compose(g,compose(a,b)),g,X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f359,f7715]) ).
fof(f7726,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),compose(codomain(X1),compose(a,b)),codomain(X1),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f34,f7715]) ).
fof(f7732,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,b),domain(a),X0),X0),X0) = X0,
inference(paramodulation,[status(thm)],[f1212,f7715]) ).
fof(f7743,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,b),domain(a),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f16,f7732]) ).
fof(f7744,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),compose(a,b),domain(a),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f15,f7743]) ).
fof(f7749,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,b),X1,domain(compose(a,b)),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f404]) ).
fof(f7750,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f7749]) ).
fof(f7751,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7750]) ).
fof(f7752,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7750]) ).
fof(f7753,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(a,b),X0,domain(a),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7750]) ).
fof(f7754,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(a,b),X1,domain(a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7750]) ).
fof(f8520,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(compose(a,b)),compose(X1,compose(compose(a,b),domain(X0))),compose(compose(X1,compose(a,b)),domain(X0))),compose(compose(X1,compose(a,b)),domain(X0))) = compose(compose(X1,compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f186]) ).
fof(f8521,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(compose(a,h)),compose(X1,compose(compose(a,h),domain(X0))),compose(compose(X1,compose(a,h)),domain(X0))),compose(compose(X1,compose(a,h)),domain(X0))) = compose(compose(X1,compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f367,f186]) ).
fof(f8532,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,domain(X1))),compose(compose(compose(a,b),X0),domain(X1))),compose(compose(compose(a,b),X0),domain(X1))) = compose(compose(compose(a,b),X0),domain(X1)),
inference(paramodulation,[status(thm)],[f959,f186]) ).
fof(f8533,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,domain(X1))),compose(compose(compose(a,h),X0),domain(X1))),compose(compose(compose(a,h),X0),domain(X1))) = compose(compose(compose(a,h),X0),domain(X1)),
inference(paramodulation,[status(thm)],[f367,f186]) ).
fof(f8534,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(X0,domain(X1))),compose(compose(g,X0),domain(X1))),compose(compose(g,X0),domain(X1))) = compose(compose(g,X0),domain(X1)),
inference(paramodulation,[status(thm)],[f359,f186]) ).
fof(f8535,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(X0,domain(X1))),compose(compose(codomain(X2),X0),domain(X1))),compose(compose(codomain(X2),X0),domain(X1))) = compose(compose(codomain(X2),X0),domain(X1)),
inference(paramodulation,[status(thm)],[f34,f186]) ).
fof(f8554,plain,
! [X0] : ifeq(codomain(codomain(b)),domain(X0),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),domain(X0))),compose(compose(a,b),domain(X0))),compose(compose(compose(a,b),codomain(b)),domain(X0))) = compose(compose(compose(a,b),codomain(b)),domain(X0)),
inference(paramodulation,[status(thm)],[f1034,f186]) ).
fof(f8555,plain,
! [X0] : ifeq(codomain(codomain(h)),domain(X0),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),codomain(h)),domain(X0))) = compose(compose(compose(a,h),codomain(h)),domain(X0)),
inference(paramodulation,[status(thm)],[f477,f186]) ).
fof(f8556,plain,
! [X0] : ifeq(codomain(codomain(h)),domain(X0),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),domain(X0))),compose(g,domain(X0))),compose(compose(g,codomain(h)),domain(X0))) = compose(compose(g,codomain(h)),domain(X0)),
inference(paramodulation,[status(thm)],[f377,f186]) ).
fof(f8557,plain,
! [X0,X1] : ifeq(codomain(codomain(X0)),domain(X1),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),domain(X1))),compose(codomain(X0),domain(X1))),compose(compose(codomain(X0),codomain(X0)),domain(X1))) = compose(compose(codomain(X0),codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f32,f186]) ).
fof(f8559,plain,
! [X0] : ifeq(codomain(domain(b)),domain(X0),ifeq(codomain(a),domain(domain(b)),compose(a,compose(domain(b),domain(X0))),compose(a,domain(X0))),compose(compose(a,domain(b)),domain(X0))) = compose(compose(a,domain(b)),domain(X0)),
inference(paramodulation,[status(thm)],[f46,f186]) ).
fof(f8560,plain,
! [X0] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))),compose(compose(domain(a),compose(a,b)),domain(X0))) = compose(compose(domain(a),compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f1212,f186]) ).
fof(f8561,plain,
! [X0] : ifeq(codomain(compose(a,h)),domain(X0),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(domain(a),compose(a,h)),domain(X0))) = compose(compose(domain(a),compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f441,f186]) ).
fof(f8562,plain,
! [X0] : ifeq(codomain(g),domain(X0),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,domain(X0))),compose(g,domain(X0))),compose(compose(domain(b),g),domain(X0))) = compose(compose(domain(b),g),domain(X0)),
inference(paramodulation,[status(thm)],[f59,f186]) ).
fof(f8563,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(b)),domain(h),compose(domain(b),compose(h,domain(X0))),compose(h,domain(X0))),compose(compose(domain(b),h),domain(X0))) = compose(compose(domain(b),h),domain(X0)),
inference(paramodulation,[status(thm)],[f52,f186]) ).
fof(f8564,plain,
! [X0,X1] : ifeq(codomain(domain(X0)),domain(X1),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),domain(X1))),compose(domain(X0),domain(X1))),compose(compose(domain(X0),domain(X0)),domain(X1))) = compose(compose(domain(X0),domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f29,f186]) ).
fof(f8592,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,b),domain(X0))),compose(compose(X1,compose(a,b)),domain(X0))),compose(compose(X1,compose(a,b)),domain(X0))) = compose(compose(X1,compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f8520]) ).
fof(f8593,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,h),domain(X0))),compose(compose(X1,compose(a,h)),domain(X0))),compose(compose(X1,compose(a,h)),domain(X0))) = compose(compose(X1,compose(a,h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f345,f8521]) ).
fof(f8660,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),domain(X0))),compose(compose(a,b),domain(X0))),compose(compose(compose(a,b),codomain(b)),domain(X0))) = compose(compose(compose(a,b),codomain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f8554]) ).
fof(f8661,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),domain(X0))),compose(compose(a,b),domain(X0))),compose(compose(compose(a,b),codomain(b)),domain(X0))) = compose(compose(compose(a,b),codomain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f959,f8660]) ).
fof(f8662,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),codomain(b),compose(compose(a,b),compose(codomain(b),domain(X0))),compose(compose(a,b),domain(X0))),compose(compose(compose(a,b),codomain(b)),domain(X0))) = compose(compose(compose(a,b),codomain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f8661]) ).
fof(f8663,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(codomain(b),domain(X0))),compose(compose(compose(a,b),codomain(b)),domain(X0))) = compose(compose(compose(a,b),codomain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f8662]) ).
fof(f8664,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(codomain(b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(compose(a,b),codomain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1034,f8663]) ).
fof(f8665,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(codomain(b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1034,f8664]) ).
fof(f8666,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),codomain(h)),domain(X0))) = compose(compose(compose(a,h),codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f8555]) ).
fof(f8667,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),codomain(h)),domain(X0))) = compose(compose(compose(a,h),codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f367,f8666]) ).
fof(f8668,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(h),compose(compose(a,h),compose(codomain(h),domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),codomain(h)),domain(X0))) = compose(compose(compose(a,h),codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f8667]) ).
fof(f8669,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(codomain(h),domain(X0))),compose(compose(compose(a,h),codomain(h)),domain(X0))) = compose(compose(compose(a,h),codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f8668]) ).
fof(f8670,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(codomain(h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(compose(a,h),codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f477,f8669]) ).
fof(f8671,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(codomain(h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(forward_demodulation,[status(thm)],[f477,f8670]) ).
fof(f8672,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(g),domain(codomain(h)),compose(g,compose(codomain(h),domain(X0))),compose(g,domain(X0))),compose(compose(g,codomain(h)),domain(X0))) = compose(compose(g,codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f8556]) ).
fof(f8673,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(codomain(h)),compose(g,compose(codomain(h),domain(X0))),compose(g,domain(X0))),compose(compose(g,codomain(h)),domain(X0))) = compose(compose(g,codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f359,f8672]) ).
fof(f8674,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),codomain(h),compose(g,compose(codomain(h),domain(X0))),compose(g,domain(X0))),compose(compose(g,codomain(h)),domain(X0))) = compose(compose(g,codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f8673]) ).
fof(f8675,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(g,compose(codomain(h),domain(X0))),compose(compose(g,codomain(h)),domain(X0))) = compose(compose(g,codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f8674]) ).
fof(f8676,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(g,compose(codomain(h),domain(X0))),compose(g,domain(X0))) = compose(compose(g,codomain(h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f377,f8675]) ).
fof(f8677,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(g,compose(codomain(h),domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(forward_demodulation,[status(thm)],[f377,f8676]) ).
fof(f8678,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),domain(X1))),compose(codomain(X0),domain(X1))),compose(compose(codomain(X0),codomain(X0)),domain(X1))) = compose(compose(codomain(X0),codomain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f34,f8557]) ).
fof(f8679,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X0),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),domain(X1))),compose(codomain(X0),domain(X1))),compose(compose(codomain(X0),codomain(X0)),domain(X1))) = compose(compose(codomain(X0),codomain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f34,f8678]) ).
fof(f8680,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X0),codomain(X0),compose(codomain(X0),compose(codomain(X0),domain(X1))),compose(codomain(X0),domain(X1))),compose(compose(codomain(X0),codomain(X0)),domain(X1))) = compose(compose(codomain(X0),codomain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f17,f8679]) ).
fof(f8681,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),compose(codomain(X0),domain(X1))),compose(compose(codomain(X0),codomain(X0)),domain(X1))) = compose(compose(codomain(X0),codomain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f8680]) ).
fof(f8682,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),compose(codomain(X0),domain(X1))),compose(codomain(X0),domain(X1))) = compose(compose(codomain(X0),codomain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f32,f8681]) ).
fof(f8683,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),compose(codomain(X0),domain(X1))),compose(codomain(X0),domain(X1))) = compose(codomain(X0),domain(X1)),
inference(forward_demodulation,[status(thm)],[f32,f8682]) ).
fof(f8690,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(a),domain(domain(b)),compose(a,compose(domain(b),domain(X0))),compose(a,domain(X0))),compose(compose(a,domain(b)),domain(X0))) = compose(compose(a,domain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f8559]) ).
fof(f8691,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(domain(b)),compose(a,compose(domain(b),domain(X0))),compose(a,domain(X0))),compose(compose(a,domain(b)),domain(X0))) = compose(compose(a,domain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f24,f8690]) ).
fof(f8692,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(b),compose(a,compose(domain(b),domain(X0))),compose(a,domain(X0))),compose(compose(a,domain(b)),domain(X0))) = compose(compose(a,domain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f8691]) ).
fof(f8693,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),domain(X0))),compose(compose(a,domain(b)),domain(X0))) = compose(compose(a,domain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f8692]) ).
fof(f8694,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),domain(X0))),compose(a,domain(X0))) = compose(compose(a,domain(b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f46,f8693]) ).
fof(f8695,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),domain(X0))),compose(a,domain(X0))) = compose(a,domain(X0)),
inference(forward_demodulation,[status(thm)],[f46,f8694]) ).
fof(f8696,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))),compose(compose(domain(a),compose(a,b)),domain(X0))) = compose(compose(domain(a),compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f959,f8560]) ).
fof(f8697,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))),compose(compose(domain(a),compose(a,b)),domain(X0))) = compose(compose(domain(a),compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f8696]) ).
fof(f8698,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))),compose(compose(domain(a),compose(a,b)),domain(X0))) = compose(compose(domain(a),compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f8697]) ).
fof(f8699,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(domain(a),compose(a,b)),domain(X0))) = compose(compose(domain(a),compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f8698]) ).
fof(f8700,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(domain(a),compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1212,f8699]) ).
fof(f8701,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(domain(a),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1212,f8700]) ).
fof(f8702,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(domain(a),compose(a,h)),domain(X0))) = compose(compose(domain(a),compose(a,h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f367,f8561]) ).
fof(f8703,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(a),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(domain(a),compose(a,h)),domain(X0))) = compose(compose(domain(a),compose(a,h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f8702]) ).
fof(f8704,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(domain(a),compose(a,h)),domain(X0))) = compose(compose(domain(a),compose(a,h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f345,f8703]) ).
fof(f8705,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(domain(a),compose(a,h)),domain(X0))) = compose(compose(domain(a),compose(a,h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f8704]) ).
fof(f8706,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(domain(a),compose(a,h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f441,f8705]) ).
fof(f8707,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(a),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(forward_demodulation,[status(thm)],[f441,f8706]) ).
fof(f8708,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(b)),domain(g),compose(domain(b),compose(g,domain(X0))),compose(g,domain(X0))),compose(compose(domain(b),g),domain(X0))) = compose(compose(domain(b),g),domain(X0)),
inference(forward_demodulation,[status(thm)],[f359,f8562]) ).
fof(f8709,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(g),compose(domain(b),compose(g,domain(X0))),compose(g,domain(X0))),compose(compose(domain(b),g),domain(X0))) = compose(compose(domain(b),g),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f8708]) ).
fof(f8710,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(b),compose(domain(b),compose(g,domain(X0))),compose(g,domain(X0))),compose(compose(domain(b),g),domain(X0))) = compose(compose(domain(b),g),domain(X0)),
inference(forward_demodulation,[status(thm)],[f55,f8709]) ).
fof(f8711,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(g,domain(X0))),compose(compose(domain(b),g),domain(X0))) = compose(compose(domain(b),g),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f8710]) ).
fof(f8712,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(g,domain(X0))),compose(g,domain(X0))) = compose(compose(domain(b),g),domain(X0)),
inference(forward_demodulation,[status(thm)],[f59,f8711]) ).
fof(f8713,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(forward_demodulation,[status(thm)],[f59,f8712]) ).
fof(f8714,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(h),compose(domain(b),compose(h,domain(X0))),compose(h,domain(X0))),compose(compose(domain(b),h),domain(X0))) = compose(compose(domain(b),h),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f8563]) ).
fof(f8715,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(b),compose(domain(b),compose(h,domain(X0))),compose(h,domain(X0))),compose(compose(domain(b),h),domain(X0))) = compose(compose(domain(b),h),domain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f8714]) ).
fof(f8716,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(h,domain(X0))),compose(compose(domain(b),h),domain(X0))) = compose(compose(domain(b),h),domain(X0)),
inference(forward_demodulation,[status(thm)],[f15,f8715]) ).
fof(f8717,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(h,domain(X0))),compose(h,domain(X0))) = compose(compose(domain(b),h),domain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f8716]) ).
fof(f8718,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(h,domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f8717]) ).
fof(f8719,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),domain(X1))),compose(domain(X0),domain(X1))),compose(compose(domain(X0),domain(X0)),domain(X1))) = compose(compose(domain(X0),domain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f8564]) ).
fof(f8720,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(X0),domain(domain(X0)),compose(domain(X0),compose(domain(X0),domain(X1))),compose(domain(X0),domain(X1))),compose(compose(domain(X0),domain(X0)),domain(X1))) = compose(compose(domain(X0),domain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f8719]) ).
fof(f8721,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(domain(X0),domain(X1))),compose(domain(X0),domain(X1))),compose(compose(domain(X0),domain(X0)),domain(X1))) = compose(compose(domain(X0),domain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f33,f8720]) ).
fof(f8722,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),compose(domain(X0),domain(X1))),compose(compose(domain(X0),domain(X0)),domain(X1))) = compose(compose(domain(X0),domain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f8721]) ).
fof(f8723,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),compose(domain(X0),domain(X1))),compose(domain(X0),domain(X1))) = compose(compose(domain(X0),domain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f29,f8722]) ).
fof(f8724,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),compose(domain(X0),compose(domain(X0),domain(X1))),compose(domain(X0),domain(X1))) = compose(domain(X0),domain(X1)),
inference(forward_demodulation,[status(thm)],[f29,f8723]) ).
fof(f8925,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(compose(a,b)),compose(codomain(X1),compose(compose(a,b),X0)),compose(compose(codomain(X1),compose(a,b)),X0)),compose(compose(codomain(X1),compose(a,b)),X0)) = compose(compose(codomain(X1),compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f959,f190]) ).
fof(f8926,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(compose(a,h)),compose(codomain(X1),compose(compose(a,h),X0)),compose(compose(codomain(X1),compose(a,h)),X0)),compose(compose(codomain(X1),compose(a,h)),X0)) = compose(compose(codomain(X1),compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f367,f190]) ).
fof(f8931,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(a,b))),compose(compose(codomain(X1),X0),compose(a,b))),compose(compose(codomain(X1),X0),compose(a,b))) = compose(compose(codomain(X1),X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f190]) ).
fof(f8932,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(a,h))),compose(compose(codomain(X1),X0),compose(a,h))),compose(compose(codomain(X1),X0),compose(a,h))) = compose(compose(codomain(X1),X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f190]) ).
fof(f8955,plain,
! [X0] : ifeq(codomain(compose(a,b)),domain(codomain(b)),ifeq(codomain(X0),domain(compose(a,b)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),compose(a,b)),codomain(b))),compose(compose(codomain(X0),compose(a,b)),codomain(b))) = compose(compose(codomain(X0),compose(a,b)),codomain(b)),
inference(paramodulation,[status(thm)],[f1034,f190]) ).
fof(f8956,plain,
! [X0] : ifeq(codomain(compose(a,h)),domain(codomain(h)),ifeq(codomain(X0),domain(compose(a,h)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),compose(a,h)),codomain(h))),compose(compose(codomain(X0),compose(a,h)),codomain(h))) = compose(compose(codomain(X0),compose(a,h)),codomain(h)),
inference(paramodulation,[status(thm)],[f477,f190]) ).
fof(f8957,plain,
! [X0] : ifeq(codomain(g),domain(codomain(h)),ifeq(codomain(X0),domain(g),compose(codomain(X0),g),compose(compose(codomain(X0),g),codomain(h))),compose(compose(codomain(X0),g),codomain(h))) = compose(compose(codomain(X0),g),codomain(h)),
inference(paramodulation,[status(thm)],[f377,f190]) ).
fof(f8958,plain,
! [X0,X1] : ifeq(codomain(codomain(X0)),domain(codomain(X0)),ifeq(codomain(X1),domain(codomain(X0)),compose(codomain(X1),codomain(X0)),compose(compose(codomain(X1),codomain(X0)),codomain(X0))),compose(compose(codomain(X1),codomain(X0)),codomain(X0))) = compose(compose(codomain(X1),codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f32,f190]) ).
fof(f8960,plain,
! [X0] : ifeq(codomain(a),domain(domain(b)),ifeq(codomain(X0),domain(a),compose(codomain(X0),a),compose(compose(codomain(X0),a),domain(b))),compose(compose(codomain(X0),a),domain(b))) = compose(compose(codomain(X0),a),domain(b)),
inference(paramodulation,[status(thm)],[f46,f190]) ).
fof(f8961,plain,
! [X0] : ifeq(codomain(domain(a)),domain(compose(a,b)),ifeq(codomain(X0),domain(domain(a)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),domain(a)),compose(a,b))),compose(compose(codomain(X0),domain(a)),compose(a,b))) = compose(compose(codomain(X0),domain(a)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1212,f190]) ).
fof(f8962,plain,
! [X0] : ifeq(codomain(domain(a)),domain(compose(a,h)),ifeq(codomain(X0),domain(domain(a)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),domain(a)),compose(a,h))),compose(compose(codomain(X0),domain(a)),compose(a,h))) = compose(compose(codomain(X0),domain(a)),compose(a,h)),
inference(paramodulation,[status(thm)],[f441,f190]) ).
fof(f8963,plain,
! [X0] : ifeq(codomain(domain(b)),domain(g),ifeq(codomain(X0),domain(domain(b)),compose(codomain(X0),g),compose(compose(codomain(X0),domain(b)),g)),compose(compose(codomain(X0),domain(b)),g)) = compose(compose(codomain(X0),domain(b)),g),
inference(paramodulation,[status(thm)],[f59,f190]) ).
fof(f8964,plain,
! [X0] : ifeq(codomain(domain(b)),domain(h),ifeq(codomain(X0),domain(domain(b)),compose(codomain(X0),h),compose(compose(codomain(X0),domain(b)),h)),compose(compose(codomain(X0),domain(b)),h)) = compose(compose(codomain(X0),domain(b)),h),
inference(paramodulation,[status(thm)],[f52,f190]) ).
fof(f8965,plain,
! [X0,X1] : ifeq(codomain(domain(X0)),domain(domain(X0)),ifeq(codomain(X1),domain(domain(X0)),compose(codomain(X1),domain(X0)),compose(compose(codomain(X1),domain(X0)),domain(X0))),compose(compose(codomain(X1),domain(X0)),domain(X0))) = compose(compose(codomain(X1),domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f29,f190]) ).
fof(f8986,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),X0)),compose(compose(codomain(X1),compose(a,b)),X0)),compose(compose(codomain(X1),compose(a,b)),X0)) = compose(compose(codomain(X1),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f8925]) ).
fof(f8987,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),X0)),compose(compose(codomain(X1),compose(a,h)),X0)),compose(compose(codomain(X1),compose(a,h)),X0)) = compose(compose(codomain(X1),compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f345,f8926]) ).
fof(f9044,plain,
! [X0] : ifeq(codomain(b),domain(codomain(b)),ifeq(codomain(X0),domain(compose(a,b)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),compose(a,b)),codomain(b))),compose(compose(codomain(X0),compose(a,b)),codomain(b))) = compose(compose(codomain(X0),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f959,f8955]) ).
fof(f9045,plain,
! [X0] : ifeq(codomain(b),codomain(b),ifeq(codomain(X0),domain(compose(a,b)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),compose(a,b)),codomain(b))),compose(compose(codomain(X0),compose(a,b)),codomain(b))) = compose(compose(codomain(X0),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f17,f9044]) ).
fof(f9046,plain,
! [X0] : ifeq(codomain(X0),domain(compose(a,b)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),compose(a,b)),codomain(b))) = compose(compose(codomain(X0),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f15,f9045]) ).
fof(f9047,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),compose(a,b)),codomain(b))) = compose(compose(codomain(X0),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f1163,f9046]) ).
fof(f9048,plain,
! [X0] : ifeq(codomain(h),domain(codomain(h)),ifeq(codomain(X0),domain(compose(a,h)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),compose(a,h)),codomain(h))),compose(compose(codomain(X0),compose(a,h)),codomain(h))) = compose(compose(codomain(X0),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f367,f8956]) ).
fof(f9049,plain,
! [X0] : ifeq(codomain(h),codomain(h),ifeq(codomain(X0),domain(compose(a,h)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),compose(a,h)),codomain(h))),compose(compose(codomain(X0),compose(a,h)),codomain(h))) = compose(compose(codomain(X0),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f9048]) ).
fof(f9050,plain,
! [X0] : ifeq(codomain(X0),domain(compose(a,h)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),compose(a,h)),codomain(h))) = compose(compose(codomain(X0),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f9049]) ).
fof(f9051,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),compose(a,h)),codomain(h))) = compose(compose(codomain(X0),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f345,f9050]) ).
fof(f9052,plain,
! [X0] : ifeq(codomain(h),domain(codomain(h)),ifeq(codomain(X0),domain(g),compose(codomain(X0),g),compose(compose(codomain(X0),g),codomain(h))),compose(compose(codomain(X0),g),codomain(h))) = compose(compose(codomain(X0),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f359,f8957]) ).
fof(f9053,plain,
! [X0] : ifeq(codomain(h),codomain(h),ifeq(codomain(X0),domain(g),compose(codomain(X0),g),compose(compose(codomain(X0),g),codomain(h))),compose(compose(codomain(X0),g),codomain(h))) = compose(compose(codomain(X0),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f9052]) ).
fof(f9054,plain,
! [X0] : ifeq(codomain(X0),domain(g),compose(codomain(X0),g),compose(compose(codomain(X0),g),codomain(h))) = compose(compose(codomain(X0),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f9053]) ).
fof(f9055,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),g),compose(compose(codomain(X0),g),codomain(h))) = compose(compose(codomain(X0),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f55,f9054]) ).
fof(f9056,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(X0)),ifeq(codomain(X1),domain(codomain(X0)),compose(codomain(X1),codomain(X0)),compose(compose(codomain(X1),codomain(X0)),codomain(X0))),compose(compose(codomain(X1),codomain(X0)),codomain(X0))) = compose(compose(codomain(X1),codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f8958]) ).
fof(f9057,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X0),ifeq(codomain(X1),domain(codomain(X0)),compose(codomain(X1),codomain(X0)),compose(compose(codomain(X1),codomain(X0)),codomain(X0))),compose(compose(codomain(X1),codomain(X0)),codomain(X0))) = compose(compose(codomain(X1),codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f17,f9056]) ).
fof(f9058,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(X1)),compose(codomain(X0),codomain(X1)),compose(compose(codomain(X0),codomain(X1)),codomain(X1))) = compose(compose(codomain(X0),codomain(X1)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f9057]) ).
fof(f9059,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),compose(codomain(X0),codomain(X1)),compose(compose(codomain(X0),codomain(X1)),codomain(X1))) = compose(compose(codomain(X0),codomain(X1)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f17,f9058]) ).
fof(f9063,plain,
! [X0] : ifeq(domain(b),domain(domain(b)),ifeq(codomain(X0),domain(a),compose(codomain(X0),a),compose(compose(codomain(X0),a),domain(b))),compose(compose(codomain(X0),a),domain(b))) = compose(compose(codomain(X0),a),domain(b)),
inference(forward_demodulation,[status(thm)],[f24,f8960]) ).
fof(f9064,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(a),compose(codomain(X0),a),compose(compose(codomain(X0),a),domain(b))),compose(compose(codomain(X0),a),domain(b))) = compose(compose(codomain(X0),a),domain(b)),
inference(forward_demodulation,[status(thm)],[f33,f9063]) ).
fof(f9065,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),a),compose(compose(codomain(X0),a),domain(b))) = compose(compose(codomain(X0),a),domain(b)),
inference(forward_demodulation,[status(thm)],[f15,f9064]) ).
fof(f9066,plain,
! [X0] : ifeq(domain(a),domain(compose(a,b)),ifeq(codomain(X0),domain(domain(a)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),domain(a)),compose(a,b))),compose(compose(codomain(X0),domain(a)),compose(a,b))) = compose(compose(codomain(X0),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f16,f8961]) ).
fof(f9067,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(domain(a)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),domain(a)),compose(a,b))),compose(compose(codomain(X0),domain(a)),compose(a,b))) = compose(compose(codomain(X0),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f9066]) ).
fof(f9068,plain,
! [X0] : ifeq(codomain(X0),domain(domain(a)),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),domain(a)),compose(a,b))) = compose(compose(codomain(X0),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f15,f9067]) ).
fof(f9069,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),domain(a)),compose(a,b))) = compose(compose(codomain(X0),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f33,f9068]) ).
fof(f9070,plain,
! [X0] : ifeq(domain(a),domain(compose(a,h)),ifeq(codomain(X0),domain(domain(a)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),domain(a)),compose(a,h))),compose(compose(codomain(X0),domain(a)),compose(a,h))) = compose(compose(codomain(X0),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f8962]) ).
fof(f9071,plain,
! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(domain(a)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),domain(a)),compose(a,h))),compose(compose(codomain(X0),domain(a)),compose(a,h))) = compose(compose(codomain(X0),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f9070]) ).
fof(f9072,plain,
! [X0] : ifeq(codomain(X0),domain(domain(a)),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),domain(a)),compose(a,h))) = compose(compose(codomain(X0),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f9071]) ).
fof(f9073,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),domain(a)),compose(a,h))) = compose(compose(codomain(X0),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f33,f9072]) ).
fof(f9074,plain,
! [X0] : ifeq(domain(b),domain(g),ifeq(codomain(X0),domain(domain(b)),compose(codomain(X0),g),compose(compose(codomain(X0),domain(b)),g)),compose(compose(codomain(X0),domain(b)),g)) = compose(compose(codomain(X0),domain(b)),g),
inference(forward_demodulation,[status(thm)],[f16,f8963]) ).
fof(f9075,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(domain(b)),compose(codomain(X0),g),compose(compose(codomain(X0),domain(b)),g)),compose(compose(codomain(X0),domain(b)),g)) = compose(compose(codomain(X0),domain(b)),g),
inference(forward_demodulation,[status(thm)],[f55,f9074]) ).
fof(f9076,plain,
! [X0] : ifeq(codomain(X0),domain(domain(b)),compose(codomain(X0),g),compose(compose(codomain(X0),domain(b)),g)) = compose(compose(codomain(X0),domain(b)),g),
inference(forward_demodulation,[status(thm)],[f15,f9075]) ).
fof(f9077,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),g),compose(compose(codomain(X0),domain(b)),g)) = compose(compose(codomain(X0),domain(b)),g),
inference(forward_demodulation,[status(thm)],[f33,f9076]) ).
fof(f9078,plain,
! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(domain(b)),compose(codomain(X0),h),compose(compose(codomain(X0),domain(b)),h)),compose(compose(codomain(X0),domain(b)),h)) = compose(compose(codomain(X0),domain(b)),h),
inference(forward_demodulation,[status(thm)],[f16,f8964]) ).
fof(f9079,plain,
! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(domain(b)),compose(codomain(X0),h),compose(compose(codomain(X0),domain(b)),h)),compose(compose(codomain(X0),domain(b)),h)) = compose(compose(codomain(X0),domain(b)),h),
inference(forward_demodulation,[status(thm)],[f48,f9078]) ).
fof(f9080,plain,
! [X0] : ifeq(codomain(X0),domain(domain(b)),compose(codomain(X0),h),compose(compose(codomain(X0),domain(b)),h)) = compose(compose(codomain(X0),domain(b)),h),
inference(forward_demodulation,[status(thm)],[f15,f9079]) ).
fof(f9081,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),h),compose(compose(codomain(X0),domain(b)),h)) = compose(compose(codomain(X0),domain(b)),h),
inference(forward_demodulation,[status(thm)],[f33,f9080]) ).
fof(f9082,plain,
! [X0,X1] : ifeq(domain(X0),domain(domain(X0)),ifeq(codomain(X1),domain(domain(X0)),compose(codomain(X1),domain(X0)),compose(compose(codomain(X1),domain(X0)),domain(X0))),compose(compose(codomain(X1),domain(X0)),domain(X0))) = compose(compose(codomain(X1),domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f8965]) ).
fof(f9083,plain,
! [X0,X1] : ifeq(domain(X0),domain(X0),ifeq(codomain(X1),domain(domain(X0)),compose(codomain(X1),domain(X0)),compose(compose(codomain(X1),domain(X0)),domain(X0))),compose(compose(codomain(X1),domain(X0)),domain(X0))) = compose(compose(codomain(X1),domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f33,f9082]) ).
fof(f9084,plain,
! [X0,X1] : ifeq(codomain(X0),domain(domain(X1)),compose(codomain(X0),domain(X1)),compose(compose(codomain(X0),domain(X1)),domain(X1))) = compose(compose(codomain(X0),domain(X1)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f15,f9083]) ).
fof(f9085,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),compose(codomain(X0),domain(X1)),compose(compose(codomain(X0),domain(X1)),domain(X1))) = compose(compose(codomain(X0),domain(X1)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f33,f9084]) ).
fof(f9170,plain,
ifeq(domain(b),domain(a),compose(a,compose(domain(b),compose(a,b))),compose(a,compose(a,b))) = compose(a,compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f264]) ).
fof(f9171,plain,
ifeq(domain(b),domain(a),compose(a,compose(domain(b),compose(a,h))),compose(a,compose(a,h))) = compose(a,compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f264]) ).
fof(f9205,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(domain(b),compose(g,X0)),compose(g,X0)) = compose(g,X0),
inference(forward_demodulation,[status(thm)],[f359,f269]) ).
fof(f9206,plain,
ifeq(codomain(h),domain(a),compose(domain(b),compose(g,compose(a,b))),compose(g,compose(a,b))) = compose(g,compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f9205]) ).
fof(f9207,plain,
ifeq(codomain(h),domain(a),compose(domain(b),compose(g,compose(a,h))),compose(g,compose(a,h))) = compose(g,compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f9205]) ).
fof(f9232,plain,
ifeq(codomain(h),domain(a),compose(domain(b),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f274]) ).
fof(f9233,plain,
ifeq(codomain(h),domain(a),compose(domain(b),compose(h,compose(a,h))),compose(h,compose(a,h))) = compose(h,compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f274]) ).
fof(f9248,plain,
ifeq(codomain(h),domain(a),compose(g,compose(codomain(h),compose(a,b))),compose(g,compose(a,b))) = compose(g,compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f414]) ).
fof(f9249,plain,
ifeq(codomain(h),domain(a),compose(g,compose(codomain(h),compose(a,h))),compose(g,compose(a,h))) = compose(g,compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f414]) ).
fof(f9309,plain,
! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(a,b),codomain(X0)),compose(compose(compose(a,b),codomain(X0)),codomain(X0))) = compose(compose(compose(a,b),codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f229]) ).
fof(f9310,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(compose(a,h),codomain(X0)),compose(compose(compose(a,h),codomain(X0)),codomain(X0))) = compose(compose(compose(a,h),codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f367,f229]) ).
fof(f9311,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(g,codomain(X0)),compose(compose(g,codomain(X0)),codomain(X0))) = compose(compose(g,codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f229]) ).
fof(f9538,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),a),compose(compose(compose(a,b),a),domain(b))) = compose(compose(compose(a,b),a),domain(b)),
inference(paramodulation,[status(thm)],[f959,f232]) ).
fof(f9539,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),a),compose(compose(compose(a,h),a),domain(b))) = compose(compose(compose(a,h),a),domain(b)),
inference(paramodulation,[status(thm)],[f367,f232]) ).
fof(f9540,plain,
ifeq(codomain(h),domain(a),compose(g,a),compose(compose(g,a),domain(b))) = compose(compose(g,a),domain(b)),
inference(paramodulation,[status(thm)],[f359,f232]) ).
fof(f9611,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),g),compose(compose(compose(a,b),domain(b)),g)) = compose(compose(compose(a,b),domain(b)),g),
inference(paramodulation,[status(thm)],[f959,f236]) ).
fof(f9612,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),g),compose(compose(compose(a,h),domain(b)),g)) = compose(compose(compose(a,h),domain(b)),g),
inference(paramodulation,[status(thm)],[f367,f236]) ).
fof(f9613,plain,
ifeq(codomain(h),domain(b),compose(g,g),compose(compose(g,domain(b)),g)) = compose(compose(g,domain(b)),g),
inference(paramodulation,[status(thm)],[f359,f236]) ).
fof(f9709,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),h),compose(compose(compose(a,b),domain(b)),h)) = compose(compose(compose(a,b),domain(b)),h),
inference(paramodulation,[status(thm)],[f959,f240]) ).
fof(f9710,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),h),compose(compose(compose(a,h),domain(b)),h)) = compose(compose(compose(a,h),domain(b)),h),
inference(paramodulation,[status(thm)],[f367,f240]) ).
fof(f9711,plain,
ifeq(codomain(h),domain(b),compose(g,h),compose(compose(g,domain(b)),h)) = compose(compose(g,domain(b)),h),
inference(paramodulation,[status(thm)],[f359,f240]) ).
fof(f9797,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(compose(a,b),domain(X0)),compose(compose(compose(a,b),domain(X0)),domain(X0))) = compose(compose(compose(a,b),domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f244]) ).
fof(f9798,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(compose(a,h),domain(X0)),compose(compose(compose(a,h),domain(X0)),domain(X0))) = compose(compose(compose(a,h),domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f367,f244]) ).
fof(f9799,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(g,domain(X0)),compose(compose(g,domain(X0)),domain(X0))) = compose(compose(g,domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f359,f244]) ).
fof(f9982,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))) = compose(codomain(X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f258]) ).
fof(f9983,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(codomain(X0),compose(a,h))),compose(codomain(X0),compose(a,h))) = compose(codomain(X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f258]) ).
fof(f10125,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))) = compose(domain(X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f280]) ).
fof(f10126,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(domain(X0),compose(a,h))),compose(domain(X0),compose(a,h))) = compose(domain(X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f280]) ).
fof(f10288,plain,
ifeq(domain(b),domain(a),compose(domain(a),compose(a,compose(a,b))),compose(a,compose(a,b))) = compose(a,compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f1848]) ).
fof(f10289,plain,
ifeq(domain(b),domain(a),compose(domain(a),compose(a,compose(a,h))),compose(a,compose(a,h))) = compose(a,compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f1848]) ).
fof(f10290,plain,
! [X0] : ifeq(domain(b),domain(X0),compose(domain(a),compose(a,domain(X0))),compose(a,domain(X0))) = compose(a,domain(X0)),
inference(paramodulation,[status(thm)],[f33,f1848]) ).
fof(f10293,plain,
! [X0] : ifeq(domain(b),codomain(X0),compose(domain(a),compose(a,codomain(X0))),compose(a,codomain(X0))) = compose(a,codomain(X0)),
inference(paramodulation,[status(thm)],[f17,f1848]) ).
fof(f10331,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,X1)),compose(compose(compose(a,h),X0),X1)),compose(compose(compose(a,h),X0),X1)) = compose(compose(compose(a,h),X0),X1),
inference(forward_demodulation,[status(thm)],[f359,f347]) ).
fof(f10332,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(compose(a,b),X0)),compose(compose(compose(a,h),compose(a,b)),X0)),compose(compose(compose(a,h),compose(a,b)),X0)) = compose(compose(compose(a,h),compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f959,f10331]) ).
fof(f10333,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(compose(a,h)),compose(compose(a,h),compose(compose(a,h),X0)),compose(compose(compose(a,h),compose(a,h)),X0)),compose(compose(compose(a,h),compose(a,h)),X0)) = compose(compose(compose(a,h),compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f367,f10331]) ).
fof(f10338,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,compose(a,b))),compose(compose(compose(a,h),X0),compose(a,b))),compose(compose(compose(a,h),X0),compose(a,b))) = compose(compose(compose(a,h),X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f10331]) ).
fof(f10339,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(X0,compose(a,h))),compose(compose(compose(a,h),X0),compose(a,h))),compose(compose(compose(a,h),X0),compose(a,h))) = compose(compose(compose(a,h),X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f10331]) ).
fof(f10350,plain,
ifeq(codomain(compose(a,b)),domain(codomain(b)),ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),compose(a,b)),codomain(b))),compose(compose(compose(a,h),compose(a,b)),codomain(b))) = compose(compose(compose(a,h),compose(a,b)),codomain(b)),
inference(paramodulation,[status(thm)],[f1034,f10331]) ).
fof(f10351,plain,
ifeq(codomain(compose(a,h)),domain(codomain(h)),ifeq(codomain(h),domain(compose(a,h)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),compose(a,h)),codomain(h))),compose(compose(compose(a,h),compose(a,h)),codomain(h))) = compose(compose(compose(a,h),compose(a,h)),codomain(h)),
inference(paramodulation,[status(thm)],[f477,f10331]) ).
fof(f10352,plain,
ifeq(codomain(g),domain(codomain(h)),ifeq(codomain(h),domain(g),compose(compose(a,h),g),compose(compose(compose(a,h),g),codomain(h))),compose(compose(compose(a,h),g),codomain(h))) = compose(compose(compose(a,h),g),codomain(h)),
inference(paramodulation,[status(thm)],[f377,f10331]) ).
fof(f10356,plain,
ifeq(codomain(domain(a)),domain(compose(a,b)),ifeq(codomain(h),domain(domain(a)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),domain(a)),compose(a,b))),compose(compose(compose(a,h),domain(a)),compose(a,b))) = compose(compose(compose(a,h),domain(a)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1212,f10331]) ).
fof(f10357,plain,
ifeq(codomain(domain(a)),domain(compose(a,h)),ifeq(codomain(h),domain(domain(a)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),domain(a)),compose(a,h))),compose(compose(compose(a,h),domain(a)),compose(a,h))) = compose(compose(compose(a,h),domain(a)),compose(a,h)),
inference(paramodulation,[status(thm)],[f441,f10331]) ).
fof(f10369,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),X0)),compose(compose(compose(a,h),compose(a,b)),X0)),compose(compose(compose(a,h),compose(a,b)),X0)) = compose(compose(compose(a,h),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f10332]) ).
fof(f10370,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),X0)),compose(compose(compose(a,h),compose(a,h)),X0)),compose(compose(compose(a,h),compose(a,h)),X0)) = compose(compose(compose(a,h),compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f345,f10333]) ).
fof(f10379,plain,
ifeq(codomain(b),domain(codomain(b)),ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),compose(a,b)),codomain(b))),compose(compose(compose(a,h),compose(a,b)),codomain(b))) = compose(compose(compose(a,h),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f959,f10350]) ).
fof(f10380,plain,
ifeq(codomain(b),codomain(b),ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),compose(a,b)),codomain(b))),compose(compose(compose(a,h),compose(a,b)),codomain(b))) = compose(compose(compose(a,h),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f17,f10379]) ).
fof(f10381,plain,
ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),compose(a,b)),codomain(b))) = compose(compose(compose(a,h),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f15,f10380]) ).
fof(f10382,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),compose(a,b)),codomain(b))) = compose(compose(compose(a,h),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f1163,f10381]) ).
fof(f10383,plain,
ifeq(codomain(h),domain(codomain(h)),ifeq(codomain(h),domain(compose(a,h)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),compose(a,h)),codomain(h))),compose(compose(compose(a,h),compose(a,h)),codomain(h))) = compose(compose(compose(a,h),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f367,f10351]) ).
fof(f10384,plain,
ifeq(codomain(h),codomain(h),ifeq(codomain(h),domain(compose(a,h)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),compose(a,h)),codomain(h))),compose(compose(compose(a,h),compose(a,h)),codomain(h))) = compose(compose(compose(a,h),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f10383]) ).
fof(f10385,plain,
ifeq(codomain(h),domain(compose(a,h)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),compose(a,h)),codomain(h))) = compose(compose(compose(a,h),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f10384]) ).
fof(f10386,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),compose(a,h)),codomain(h))) = compose(compose(compose(a,h),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f345,f10385]) ).
fof(f10387,plain,
ifeq(codomain(h),domain(codomain(h)),ifeq(codomain(h),domain(g),compose(compose(a,h),g),compose(compose(compose(a,h),g),codomain(h))),compose(compose(compose(a,h),g),codomain(h))) = compose(compose(compose(a,h),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f359,f10352]) ).
fof(f10388,plain,
ifeq(codomain(h),codomain(h),ifeq(codomain(h),domain(g),compose(compose(a,h),g),compose(compose(compose(a,h),g),codomain(h))),compose(compose(compose(a,h),g),codomain(h))) = compose(compose(compose(a,h),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f17,f10387]) ).
fof(f10389,plain,
ifeq(codomain(h),domain(g),compose(compose(a,h),g),compose(compose(compose(a,h),g),codomain(h))) = compose(compose(compose(a,h),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f15,f10388]) ).
fof(f10390,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),g),compose(compose(compose(a,h),g),codomain(h))) = compose(compose(compose(a,h),g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f55,f10389]) ).
fof(f10401,plain,
ifeq(domain(a),domain(compose(a,b)),ifeq(codomain(h),domain(domain(a)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),domain(a)),compose(a,b))),compose(compose(compose(a,h),domain(a)),compose(a,b))) = compose(compose(compose(a,h),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f16,f10356]) ).
fof(f10402,plain,
ifeq(domain(a),domain(a),ifeq(codomain(h),domain(domain(a)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),domain(a)),compose(a,b))),compose(compose(compose(a,h),domain(a)),compose(a,b))) = compose(compose(compose(a,h),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f10401]) ).
fof(f10403,plain,
ifeq(codomain(h),domain(domain(a)),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),domain(a)),compose(a,b))) = compose(compose(compose(a,h),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f15,f10402]) ).
fof(f10404,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),domain(a)),compose(a,b))) = compose(compose(compose(a,h),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f33,f10403]) ).
fof(f10405,plain,
ifeq(domain(a),domain(compose(a,h)),ifeq(codomain(h),domain(domain(a)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),domain(a)),compose(a,h))),compose(compose(compose(a,h),domain(a)),compose(a,h))) = compose(compose(compose(a,h),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f10357]) ).
fof(f10406,plain,
ifeq(domain(a),domain(a),ifeq(codomain(h),domain(domain(a)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),domain(a)),compose(a,h))),compose(compose(compose(a,h),domain(a)),compose(a,h))) = compose(compose(compose(a,h),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f10405]) ).
fof(f10407,plain,
ifeq(codomain(h),domain(domain(a)),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),domain(a)),compose(a,h))) = compose(compose(compose(a,h),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f10406]) ).
fof(f10408,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),domain(a)),compose(a,h))) = compose(compose(compose(a,h),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f33,f10407]) ).
fof(f10456,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(compose(a,h)),compose(X1,compose(compose(a,h),X0)),compose(compose(X1,compose(a,h)),X0)),compose(compose(X1,compose(a,h)),X0)) = compose(compose(X1,compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f359,f348]) ).
fof(f10457,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,h),X0)),compose(compose(X1,compose(a,h)),X0)),compose(compose(X1,compose(a,h)),X0)) = compose(compose(X1,compose(a,h)),X0),
inference(forward_demodulation,[status(thm)],[f345,f10456]) ).
fof(f10458,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),compose(a,b))),compose(compose(X0,compose(a,h)),compose(a,b))),compose(compose(X0,compose(a,h)),compose(a,b))) = compose(compose(X0,compose(a,h)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f10457]) ).
fof(f10459,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,h),compose(a,h))),compose(compose(X0,compose(a,h)),compose(a,h))),compose(compose(X0,compose(a,h)),compose(a,h))) = compose(compose(X0,compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f10457]) ).
fof(f10464,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),X0)),compose(compose(compose(a,b),compose(a,h)),X0)),compose(compose(compose(a,b),compose(a,h)),X0)) = compose(compose(compose(a,b),compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f959,f10457]) ).
fof(f10466,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),X0)),compose(compose(g,compose(a,h)),X0)),compose(compose(g,compose(a,h)),X0)) = compose(compose(g,compose(a,h)),X0),
inference(paramodulation,[status(thm)],[f359,f10457]) ).
fof(f10517,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(codomain(X0),compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f1163,f390]) ).
fof(f10518,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X2,ifeq(compose(X1,compose(a,b)),X2,X1,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f1163,f10517]) ).
fof(f10525,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(compose(a,b),compose(a,b)),X1,compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f959,f10518]) ).
fof(f10526,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(compose(a,h),compose(a,b)),X1,compose(a,h),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f367,f10518]) ).
fof(f10527,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X1,ifeq(compose(g,compose(a,b)),X1,g,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f359,f10518]) ).
fof(f10528,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),X2,ifeq(compose(codomain(X1),compose(a,b)),X2,codomain(X1),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f10518]) ).
fof(f10787,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(codomain(X1),compose(a,b)),X2,codomain(X1),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f394]) ).
fof(f10788,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(X0,compose(a,b)),X2,ifeq(compose(codomain(X1),compose(a,b)),X2,codomain(X1),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f10787]) ).
fof(f10789,plain,
! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f10788]) ).
fof(f10790,plain,
! [X0,X1] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f10788]) ).
fof(f10791,plain,
! [X0,X1] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(g,compose(a,b)),X1,ifeq(compose(codomain(X0),compose(a,b)),X1,codomain(X0),g),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f10788]) ).
fof(f11204,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(compose(a,b)),compose(X0,compose(compose(a,b),compose(a,h))),compose(compose(X0,compose(a,b)),compose(a,h))),compose(compose(X0,compose(a,b)),compose(a,h))) = compose(compose(X0,compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f433]) ).
fof(f11210,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(a,h))),compose(compose(compose(a,b),X0),compose(a,h))),compose(compose(compose(a,b),X0),compose(a,h))) = compose(compose(compose(a,b),X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f433]) ).
fof(f11212,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(g,compose(X0,compose(a,h))),compose(compose(g,X0),compose(a,h))),compose(compose(g,X0),compose(a,h))) = compose(compose(g,X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f433]) ).
fof(f11225,plain,
ifeq(codomain(codomain(b)),domain(a),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(a,h))),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,b),codomain(b)),compose(a,h))) = compose(compose(compose(a,b),codomain(b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f1034,f433]) ).
fof(f11226,plain,
ifeq(codomain(codomain(h)),domain(a),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),compose(a,h))),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,h),codomain(h)),compose(a,h))) = compose(compose(compose(a,h),codomain(h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f477,f433]) ).
fof(f11231,plain,
ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))),compose(compose(domain(a),compose(a,b)),compose(a,h))) = compose(compose(domain(a),compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f1212,f433]) ).
fof(f11232,plain,
ifeq(codomain(compose(a,h)),domain(a),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))),compose(compose(domain(a),compose(a,h)),compose(a,h))) = compose(compose(domain(a),compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f441,f433]) ).
fof(f11251,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(a,h))),compose(compose(X0,compose(a,b)),compose(a,h))),compose(compose(X0,compose(a,b)),compose(a,h))) = compose(compose(X0,compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1163,f11204]) ).
fof(f11269,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(a,h))),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,b),codomain(b)),compose(a,h))) = compose(compose(compose(a,b),codomain(b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f34,f11225]) ).
fof(f11270,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(a,h))),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,b),codomain(b)),compose(a,h))) = compose(compose(compose(a,b),codomain(b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f959,f11269]) ).
fof(f11271,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),codomain(b),compose(compose(a,b),compose(codomain(b),compose(a,h))),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,b),codomain(b)),compose(a,h))) = compose(compose(compose(a,b),codomain(b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f17,f11270]) ).
fof(f11272,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(codomain(b),compose(a,h))),compose(compose(compose(a,b),codomain(b)),compose(a,h))) = compose(compose(compose(a,b),codomain(b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f11271]) ).
fof(f11273,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(codomain(b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(compose(a,b),codomain(b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1034,f11272]) ).
fof(f11274,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(codomain(b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1034,f11273]) ).
fof(f11275,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(compose(a,h)),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),compose(a,h))),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,h),codomain(h)),compose(a,h))) = compose(compose(compose(a,h),codomain(h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f34,f11226]) ).
fof(f11276,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(codomain(h)),compose(compose(a,h),compose(codomain(h),compose(a,h))),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,h),codomain(h)),compose(a,h))) = compose(compose(compose(a,h),codomain(h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f367,f11275]) ).
fof(f11277,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),codomain(h),compose(compose(a,h),compose(codomain(h),compose(a,h))),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,h),codomain(h)),compose(a,h))) = compose(compose(compose(a,h),codomain(h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f17,f11276]) ).
fof(f11278,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(codomain(h),compose(a,h))),compose(compose(compose(a,h),codomain(h)),compose(a,h))) = compose(compose(compose(a,h),codomain(h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f11277]) ).
fof(f11279,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(codomain(h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(compose(a,h),codomain(h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f477,f11278]) ).
fof(f11280,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(codomain(h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f477,f11279]) ).
fof(f11305,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))),compose(compose(domain(a),compose(a,b)),compose(a,h))) = compose(compose(domain(a),compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f959,f11231]) ).
fof(f11306,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))),compose(compose(domain(a),compose(a,b)),compose(a,h))) = compose(compose(domain(a),compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f11305]) ).
fof(f11307,plain,
ifeq(codomain(b),domain(a),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))),compose(compose(domain(a),compose(a,b)),compose(a,h))) = compose(compose(domain(a),compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1163,f11306]) ).
fof(f11308,plain,
ifeq(codomain(b),domain(a),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(domain(a),compose(a,b)),compose(a,h))) = compose(compose(domain(a),compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f11307]) ).
fof(f11309,plain,
ifeq(codomain(b),domain(a),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(domain(a),compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1212,f11308]) ).
fof(f11310,plain,
ifeq(codomain(b),domain(a),compose(domain(a),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1212,f11309]) ).
fof(f11311,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(domain(a)),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))),compose(compose(domain(a),compose(a,h)),compose(a,h))) = compose(compose(domain(a),compose(a,h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f367,f11232]) ).
fof(f11312,plain,
ifeq(codomain(h),domain(a),ifeq(domain(a),domain(compose(a,h)),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))),compose(compose(domain(a),compose(a,h)),compose(a,h))) = compose(compose(domain(a),compose(a,h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f11311]) ).
fof(f11313,plain,
ifeq(codomain(h),domain(a),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))),compose(compose(domain(a),compose(a,h)),compose(a,h))) = compose(compose(domain(a),compose(a,h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f11312]) ).
fof(f11314,plain,
ifeq(codomain(h),domain(a),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(domain(a),compose(a,h)),compose(a,h))) = compose(compose(domain(a),compose(a,h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f15,f11313]) ).
fof(f11315,plain,
ifeq(codomain(h),domain(a),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(domain(a),compose(a,h)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f441,f11314]) ).
fof(f11316,plain,
ifeq(codomain(h),domain(a),compose(domain(a),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f441,f11315]) ).
fof(f11407,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(compose(a,h),compose(a,b)),X1,compose(a,h),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f452]) ).
fof(f11408,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(compose(a,h),compose(a,b)),X1,compose(a,h),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f11407]) ).
fof(f11409,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f11408]) ).
fof(f11410,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f11408]) ).
fof(f11411,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(compose(a,h),compose(a,b)),X0,compose(a,h),g),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f11408]) ).
fof(f11428,plain,
! [X0,X1] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(compose(a,h),compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(forward_demodulation,[status(thm)],[f1163,f453]) ).
fof(f11429,plain,
! [X0,X1] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(forward_demodulation,[status(thm)],[f1163,f11428]) ).
fof(f11430,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f959,f11429]) ).
fof(f11432,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),X0,ifeq(compose(g,compose(a,b)),X0,g,compose(a,h)),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f359,f11429]) ).
fof(f11970,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),a),b)) = compose(compose(compose(a,b),a),b),
inference(paramodulation,[status(thm)],[f959,f1798]) ).
fof(f11971,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(compose(a,h),a),b)) = compose(compose(compose(a,h),a),b),
inference(paramodulation,[status(thm)],[f367,f1798]) ).
fof(f11972,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,a),b)) = compose(compose(g,a),b),
inference(paramodulation,[status(thm)],[f359,f1798]) ).
fof(f11973,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,b)),compose(compose(codomain(X0),a),b)) = compose(compose(codomain(X0),a),b),
inference(paramodulation,[status(thm)],[f34,f1798]) ).
fof(f11974,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,b)),compose(compose(a,a),b)) = compose(compose(a,a),b),
inference(paramodulation,[status(thm)],[f24,f1798]) ).
fof(f11975,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,b)),compose(compose(domain(X0),a),b)) = compose(compose(domain(X0),a),b),
inference(paramodulation,[status(thm)],[f16,f1798]) ).
fof(f11992,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(a,h))),compose(compose(compose(a,b),a),compose(a,h))),compose(compose(compose(a,b),a),compose(a,h))) = compose(compose(compose(a,b),a),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f1800]) ).
fof(f11993,plain,
ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,compose(a,h))),compose(compose(compose(a,h),a),compose(a,h))),compose(compose(compose(a,h),a),compose(a,h))) = compose(compose(compose(a,h),a),compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f1800]) ).
fof(f11994,plain,
ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(a,compose(a,h))),compose(compose(g,a),compose(a,h))),compose(compose(g,a),compose(a,h))) = compose(compose(g,a),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f1800]) ).
fof(f11995,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(a,h))),compose(compose(codomain(X0),a),compose(a,h))),compose(compose(codomain(X0),a),compose(a,h))) = compose(compose(codomain(X0),a),compose(a,h)),
inference(paramodulation,[status(thm)],[f34,f1800]) ).
fof(f11996,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),compose(a,compose(a,compose(a,h))),compose(compose(a,a),compose(a,h))),compose(compose(a,a),compose(a,h))) = compose(compose(a,a),compose(a,h)),
inference(paramodulation,[status(thm)],[f24,f1800]) ).
fof(f11997,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(a,h))),compose(compose(domain(X0),a),compose(a,h))),compose(compose(domain(X0),a),compose(a,h))) = compose(compose(domain(X0),a),compose(a,h)),
inference(paramodulation,[status(thm)],[f16,f1800]) ).
fof(f11998,plain,
ifeq(domain(b),domain(a),ifeq(codomain(domain(compose(a,compose(a,h)))),domain(a),compose(a,compose(a,h)),compose(compose(domain(compose(a,compose(a,h))),a),compose(a,h))),compose(compose(domain(compose(a,compose(a,h))),a),compose(a,h))) = compose(compose(domain(compose(a,compose(a,h))),a),compose(a,h)),
inference(paramodulation,[status(thm)],[f18,f1800]) ).
fof(f12001,plain,
ifeq(domain(b),domain(a),ifeq(domain(compose(a,compose(a,h))),domain(a),compose(a,compose(a,h)),compose(compose(domain(compose(a,compose(a,h))),a),compose(a,h))),compose(compose(domain(compose(a,compose(a,h))),a),compose(a,h))) = compose(compose(domain(compose(a,compose(a,h))),a),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f11998]) ).
fof(f12009,plain,
ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(a,b),compose(a,b)),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7656]) ).
fof(f12010,plain,
ifeq(codomain(h),domain(a),ifeq(compose(a,b),compose(compose(a,h),compose(a,b)),domain(a),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7656]) ).
fof(f12011,plain,
ifeq(codomain(h),domain(a),ifeq(compose(a,b),compose(g,compose(a,b)),domain(a),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7656]) ).
fof(f12012,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(codomain(X0),compose(a,b)),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7656]) ).
fof(f12013,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(a,compose(a,b)),domain(a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7656]) ).
fof(f12014,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),compose(domain(X0),compose(a,b)),domain(a),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7656]) ).
fof(f12030,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,domain(X0))),compose(compose(compose(a,b),a),domain(X0))),compose(compose(compose(a,b),a),domain(X0))) = compose(compose(compose(a,b),a),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f1801]) ).
fof(f12031,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,domain(X0))),compose(compose(compose(a,h),a),domain(X0))),compose(compose(compose(a,h),a),domain(X0))) = compose(compose(compose(a,h),a),domain(X0)),
inference(paramodulation,[status(thm)],[f367,f1801]) ).
fof(f12032,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(a,domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
inference(paramodulation,[status(thm)],[f359,f1801]) ).
fof(f12033,plain,
! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(a,domain(X0))),compose(compose(codomain(X1),a),domain(X0))),compose(compose(codomain(X1),a),domain(X0))) = compose(compose(codomain(X1),a),domain(X0)),
inference(paramodulation,[status(thm)],[f34,f1801]) ).
fof(f12034,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(a,domain(X0))),compose(compose(a,a),domain(X0))),compose(compose(a,a),domain(X0))) = compose(compose(a,a),domain(X0)),
inference(paramodulation,[status(thm)],[f24,f1801]) ).
fof(f12035,plain,
! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(a,domain(X0))),compose(compose(domain(X1),a),domain(X0))),compose(compose(domain(X1),a),domain(X0))) = compose(compose(domain(X1),a),domain(X0)),
inference(paramodulation,[status(thm)],[f16,f1801]) ).
fof(f12036,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(domain(compose(a,domain(X0)))),domain(a),compose(a,domain(X0)),compose(compose(domain(compose(a,domain(X0))),a),domain(X0))),compose(compose(domain(compose(a,domain(X0))),a),domain(X0))) = compose(compose(domain(compose(a,domain(X0))),a),domain(X0)),
inference(paramodulation,[status(thm)],[f18,f1801]) ).
fof(f12086,plain,
! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(a,domain(X0))),domain(a),compose(a,domain(X0)),compose(compose(domain(compose(a,domain(X0))),a),domain(X0))),compose(compose(domain(compose(a,domain(X0))),a),domain(X0))) = compose(compose(domain(compose(a,domain(X0))),a),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f12036]) ).
fof(f12176,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(a,b),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7744]) ).
fof(f12177,plain,
ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(a,b),domain(a),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7744]) ).
fof(f12178,plain,
ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(a,b),domain(a),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7744]) ).
fof(f12179,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(a,b),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7744]) ).
fof(f12180,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(a,b),domain(a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7744]) ).
fof(f12181,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(a,b),domain(a),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7744]) ).
fof(f12193,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),a),h)) = compose(compose(compose(a,b),a),h),
inference(paramodulation,[status(thm)],[f959,f1824]) ).
fof(f12194,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(compose(a,h),a),h)) = compose(compose(compose(a,h),a),h),
inference(paramodulation,[status(thm)],[f367,f1824]) ).
fof(f12195,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,a),h)) = compose(compose(g,a),h),
inference(paramodulation,[status(thm)],[f359,f1824]) ).
fof(f12196,plain,
! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,h)),compose(compose(codomain(X0),a),h)) = compose(compose(codomain(X0),a),h),
inference(paramodulation,[status(thm)],[f34,f1824]) ).
fof(f12197,plain,
ifeq(domain(b),domain(a),compose(a,compose(a,h)),compose(compose(a,a),h)) = compose(compose(a,a),h),
inference(paramodulation,[status(thm)],[f24,f1824]) ).
fof(f12198,plain,
! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,h)),compose(compose(domain(X0),a),h)) = compose(compose(domain(X0),a),h),
inference(paramodulation,[status(thm)],[f16,f1824]) ).
fof(f12224,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,codomain(X0))),compose(compose(compose(a,b),a),codomain(X0))),compose(compose(compose(a,b),a),codomain(X0))) = compose(compose(compose(a,b),a),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f1804]) ).
fof(f12225,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,codomain(X0))),compose(compose(compose(a,h),a),codomain(X0))),compose(compose(compose(a,h),a),codomain(X0))) = compose(compose(compose(a,h),a),codomain(X0)),
inference(paramodulation,[status(thm)],[f367,f1804]) ).
fof(f12226,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(h),domain(a),compose(g,compose(a,codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f1804]) ).
fof(f12227,plain,
! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(a,codomain(X0))),compose(compose(codomain(X1),a),codomain(X0))),compose(compose(codomain(X1),a),codomain(X0))) = compose(compose(codomain(X1),a),codomain(X0)),
inference(paramodulation,[status(thm)],[f34,f1804]) ).
fof(f12228,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(a),compose(a,compose(a,codomain(X0))),compose(compose(a,a),codomain(X0))),compose(compose(a,a),codomain(X0))) = compose(compose(a,a),codomain(X0)),
inference(paramodulation,[status(thm)],[f24,f1804]) ).
fof(f12229,plain,
! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(a,codomain(X0))),compose(compose(domain(X1),a),codomain(X0))),compose(compose(domain(X1),a),codomain(X0))) = compose(compose(domain(X1),a),codomain(X0)),
inference(paramodulation,[status(thm)],[f16,f1804]) ).
fof(f12230,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(domain(compose(a,codomain(X0)))),domain(a),compose(a,codomain(X0)),compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0))),compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0))) = compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0)),
inference(paramodulation,[status(thm)],[f18,f1804]) ).
fof(f12276,plain,
! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(compose(a,codomain(X0))),domain(a),compose(a,codomain(X0)),compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0))),compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0))) = compose(compose(domain(compose(a,codomain(X0))),a),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f12230]) ).
fof(f12503,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,domain(compose(a,b))),compose(a,b))) = compose(compose(g,domain(compose(a,b))),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f5584]) ).
fof(f12504,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,domain(compose(a,h))),compose(a,h))) = compose(compose(g,domain(compose(a,h))),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f5584]) ).
fof(f12517,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,domain(a)),compose(a,b))) = compose(compose(g,domain(compose(a,b))),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f12503]) ).
fof(f12518,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,domain(a)),compose(a,b))) = compose(compose(g,domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f12517]) ).
fof(f12519,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,domain(a)),compose(a,h))) = compose(compose(g,domain(compose(a,h))),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f12504]) ).
fof(f12520,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,domain(a)),compose(a,h))) = compose(compose(g,domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f12519]) ).
fof(f12551,plain,
ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,compose(a,b))),compose(compose(compose(a,h),a),compose(a,b))),compose(compose(compose(a,h),a),compose(a,b))) = compose(compose(compose(a,h),a),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f1806]) ).
fof(f12560,plain,
ifeq(domain(b),domain(codomain(compose(compose(a,h),a))),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,codomain(compose(compose(a,h),a)))),compose(compose(a,h),a)),compose(compose(compose(a,h),a),codomain(compose(compose(a,h),a)))) = compose(compose(compose(a,h),a),codomain(compose(compose(a,h),a))),
inference(paramodulation,[status(thm)],[f19,f1806]) ).
fof(f12575,plain,
ifeq(domain(b),codomain(compose(compose(a,h),a)),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,codomain(compose(compose(a,h),a)))),compose(compose(a,h),a)),compose(compose(compose(a,h),a),codomain(compose(compose(a,h),a)))) = compose(compose(compose(a,h),a),codomain(compose(compose(a,h),a))),
inference(forward_demodulation,[status(thm)],[f17,f12560]) ).
fof(f12576,plain,
ifeq(domain(b),codomain(compose(compose(a,h),a)),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,codomain(compose(compose(a,h),a)))),compose(compose(a,h),a)),compose(compose(a,h),a)) = compose(compose(compose(a,h),a),codomain(compose(compose(a,h),a))),
inference(forward_demodulation,[status(thm)],[f19,f12575]) ).
fof(f12577,plain,
ifeq(domain(b),codomain(compose(compose(a,h),a)),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(a,codomain(compose(compose(a,h),a)))),compose(compose(a,h),a)),compose(compose(a,h),a)) = compose(compose(a,h),a),
inference(forward_demodulation,[status(thm)],[f19,f12576]) ).
fof(f12581,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,compose(a,b)),codomain(compose(a,b)))) = compose(compose(g,compose(a,b)),codomain(compose(a,b))),
inference(paramodulation,[status(thm)],[f1163,f5716]) ).
fof(f12582,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,compose(a,h)),codomain(compose(a,h)))) = compose(compose(g,compose(a,h)),codomain(compose(a,h))),
inference(paramodulation,[status(thm)],[f345,f5716]) ).
fof(f12584,plain,
ifeq(codomain(h),domain(b),compose(g,g),compose(compose(g,g),codomain(g))) = compose(compose(g,g),codomain(g)),
inference(paramodulation,[status(thm)],[f55,f5716]) ).
fof(f12585,plain,
ifeq(codomain(h),domain(b),compose(g,h),compose(compose(g,h),codomain(h))) = compose(compose(g,h),codomain(h)),
inference(paramodulation,[status(thm)],[f48,f5716]) ).
fof(f12597,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,compose(a,b)),codomain(b))) = compose(compose(g,compose(a,b)),codomain(compose(a,b))),
inference(forward_demodulation,[status(thm)],[f959,f12581]) ).
fof(f12598,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,b)),compose(compose(g,compose(a,b)),codomain(b))) = compose(compose(g,compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f959,f12597]) ).
fof(f12599,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,compose(a,h)),codomain(h))) = compose(compose(g,compose(a,h)),codomain(compose(a,h))),
inference(forward_demodulation,[status(thm)],[f367,f12582]) ).
fof(f12600,plain,
ifeq(codomain(h),domain(a),compose(g,compose(a,h)),compose(compose(g,compose(a,h)),codomain(h))) = compose(compose(g,compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f367,f12599]) ).
fof(f12603,plain,
ifeq(codomain(h),domain(b),compose(g,g),compose(compose(g,g),codomain(h))) = compose(compose(g,g),codomain(g)),
inference(forward_demodulation,[status(thm)],[f359,f12584]) ).
fof(f12604,plain,
ifeq(codomain(h),domain(b),compose(g,g),compose(compose(g,g),codomain(h))) = compose(compose(g,g),codomain(h)),
inference(forward_demodulation,[status(thm)],[f359,f12603]) ).
fof(f12639,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(a,b))),compose(compose(codomain(X0),a),compose(a,b))),compose(compose(codomain(X0),a),compose(a,b))) = compose(compose(codomain(X0),a),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f1808]) ).
fof(f12660,plain,
! [X0] : ifeq(domain(b),domain(codomain(compose(codomain(X0),a))),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,codomain(compose(codomain(X0),a)))),compose(codomain(X0),a)),compose(compose(codomain(X0),a),codomain(compose(codomain(X0),a)))) = compose(compose(codomain(X0),a),codomain(compose(codomain(X0),a))),
inference(paramodulation,[status(thm)],[f19,f1808]) ).
fof(f12735,plain,
! [X0] : ifeq(domain(b),codomain(compose(codomain(X0),a)),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,codomain(compose(codomain(X0),a)))),compose(codomain(X0),a)),compose(compose(codomain(X0),a),codomain(compose(codomain(X0),a)))) = compose(compose(codomain(X0),a),codomain(compose(codomain(X0),a))),
inference(forward_demodulation,[status(thm)],[f17,f12660]) ).
fof(f12736,plain,
! [X0] : ifeq(domain(b),codomain(compose(codomain(X0),a)),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,codomain(compose(codomain(X0),a)))),compose(codomain(X0),a)),compose(codomain(X0),a)) = compose(compose(codomain(X0),a),codomain(compose(codomain(X0),a))),
inference(forward_demodulation,[status(thm)],[f19,f12735]) ).
fof(f12737,plain,
! [X0] : ifeq(domain(b),codomain(compose(codomain(X0),a)),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,codomain(compose(codomain(X0),a)))),compose(codomain(X0),a)),compose(codomain(X0),a)) = compose(codomain(X0),a),
inference(forward_demodulation,[status(thm)],[f19,f12736]) ).
fof(f12790,plain,
ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),compose(a,compose(a,compose(a,b))),compose(compose(a,a),compose(a,b))),compose(compose(a,a),compose(a,b))) = compose(compose(a,a),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f1809]) ).
fof(f12799,plain,
ifeq(domain(b),domain(codomain(compose(a,a))),ifeq(domain(b),domain(a),compose(a,compose(a,codomain(compose(a,a)))),compose(a,a)),compose(compose(a,a),codomain(compose(a,a)))) = compose(compose(a,a),codomain(compose(a,a))),
inference(paramodulation,[status(thm)],[f19,f1809]) ).
fof(f12812,plain,
ifeq(domain(b),codomain(compose(a,a)),ifeq(domain(b),domain(a),compose(a,compose(a,codomain(compose(a,a)))),compose(a,a)),compose(compose(a,a),codomain(compose(a,a)))) = compose(compose(a,a),codomain(compose(a,a))),
inference(forward_demodulation,[status(thm)],[f17,f12799]) ).
fof(f12813,plain,
ifeq(domain(b),codomain(compose(a,a)),ifeq(domain(b),domain(a),compose(a,compose(a,codomain(compose(a,a)))),compose(a,a)),compose(a,a)) = compose(compose(a,a),codomain(compose(a,a))),
inference(forward_demodulation,[status(thm)],[f19,f12812]) ).
fof(f12814,plain,
ifeq(domain(b),codomain(compose(a,a)),ifeq(domain(b),domain(a),compose(a,compose(a,codomain(compose(a,a)))),compose(a,a)),compose(a,a)) = compose(a,a),
inference(forward_demodulation,[status(thm)],[f19,f12813]) ).
fof(f12819,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(a,b))),compose(compose(domain(X0),a),compose(a,b))),compose(compose(domain(X0),a),compose(a,b))) = compose(compose(domain(X0),a),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f1810]) ).
fof(f12844,plain,
! [X0] : ifeq(domain(b),domain(codomain(compose(domain(X0),a))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,codomain(compose(domain(X0),a)))),compose(domain(X0),a)),compose(compose(domain(X0),a),codomain(compose(domain(X0),a)))) = compose(compose(domain(X0),a),codomain(compose(domain(X0),a))),
inference(paramodulation,[status(thm)],[f19,f1810]) ).
fof(f12936,plain,
! [X0] : ifeq(domain(b),codomain(compose(domain(X0),a)),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,codomain(compose(domain(X0),a)))),compose(domain(X0),a)),compose(compose(domain(X0),a),codomain(compose(domain(X0),a)))) = compose(compose(domain(X0),a),codomain(compose(domain(X0),a))),
inference(forward_demodulation,[status(thm)],[f17,f12844]) ).
fof(f12937,plain,
! [X0] : ifeq(domain(b),codomain(compose(domain(X0),a)),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,codomain(compose(domain(X0),a)))),compose(domain(X0),a)),compose(domain(X0),a)) = compose(compose(domain(X0),a),codomain(compose(domain(X0),a))),
inference(forward_demodulation,[status(thm)],[f19,f12936]) ).
fof(f12938,plain,
! [X0] : ifeq(domain(b),codomain(compose(domain(X0),a)),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,codomain(compose(domain(X0),a)))),compose(domain(X0),a)),compose(domain(X0),a)) = compose(domain(X0),a),
inference(forward_demodulation,[status(thm)],[f19,f12937]) ).
fof(f13009,plain,
ifeq(domain(b),domain(a),ifeq(domain(compose(a,compose(a,b))),domain(a),compose(a,compose(a,b)),compose(compose(domain(compose(a,compose(a,b))),a),compose(a,b))),compose(compose(domain(compose(a,compose(a,b))),a),compose(a,b))) = compose(compose(domain(compose(a,compose(a,b))),a),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f1832]) ).
fof(f13443,plain,
ifeq(domain(b),codomain(compose(compose(a,b),a)),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,codomain(compose(compose(a,b),a)))),compose(compose(a,b),a)),compose(compose(a,b),a)) = compose(compose(a,b),a),
inference(paramodulation,[status(thm)],[f959,f1844]) ).
fof(f13445,plain,
ifeq(domain(b),codomain(compose(g,a)),ifeq(codomain(h),domain(a),compose(g,compose(a,codomain(compose(g,a)))),compose(g,a)),compose(g,a)) = compose(g,a),
inference(paramodulation,[status(thm)],[f359,f1844]) ).
fof(f13756,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(a,h))),compose(compose(compose(a,b),domain(X0)),compose(a,h))),compose(compose(compose(a,b),domain(X0)),compose(a,h))) = compose(compose(compose(a,b),domain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f2149]) ).
fof(f13757,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),compose(a,h))),compose(compose(compose(a,h),domain(X0)),compose(a,h))),compose(compose(compose(a,h),domain(X0)),compose(a,h))) = compose(compose(compose(a,h),domain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f2149]) ).
fof(f13758,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),compose(a,h))),compose(compose(g,domain(X0)),compose(a,h))),compose(compose(g,domain(X0)),compose(a,h))) = compose(compose(g,domain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f2149]) ).
fof(f13759,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(a,h))),compose(compose(codomain(X1),domain(X0)),compose(a,h))),compose(compose(codomain(X1),domain(X0)),compose(a,h))) = compose(compose(codomain(X1),domain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f34,f2149]) ).
fof(f13760,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(a,h))),compose(compose(a,domain(X0)),compose(a,h))),compose(compose(a,domain(X0)),compose(a,h))) = compose(compose(a,domain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f24,f2149]) ).
fof(f13761,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(a,h))),compose(compose(domain(X1),domain(X0)),compose(a,h))),compose(compose(domain(X1),domain(X0)),compose(a,h))) = compose(compose(domain(X1),domain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f16,f2149]) ).
fof(f13768,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(compose(domain(X0),compose(a,h)))),domain(X0),compose(domain(X0),compose(a,h)),compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h))),compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h))) = compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f18,f2149]) ).
fof(f13859,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(compose(domain(X0),compose(a,h))),domain(X0),compose(domain(X0),compose(a,h)),compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h))),compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h))) = compose(compose(domain(compose(domain(X0),compose(a,h))),domain(X0)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f13768]) ).
fof(f13998,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),domain(X1))),compose(compose(compose(a,b),domain(X0)),domain(X1))),compose(compose(compose(a,b),domain(X0)),domain(X1))) = compose(compose(compose(a,b),domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f959,f2150]) ).
fof(f13999,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),domain(X1))),compose(compose(compose(a,h),domain(X0)),domain(X1))),compose(compose(compose(a,h),domain(X0)),domain(X1))) = compose(compose(compose(a,h),domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f367,f2150]) ).
fof(f14000,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),domain(X1))),compose(compose(g,domain(X0)),domain(X1))),compose(compose(g,domain(X0)),domain(X1))) = compose(compose(g,domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f359,f2150]) ).
fof(f14001,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),domain(X1))),compose(compose(codomain(X2),domain(X0)),domain(X1))),compose(compose(codomain(X2),domain(X0)),domain(X1))) = compose(compose(codomain(X2),domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f34,f2150]) ).
fof(f14002,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),domain(X1))),compose(compose(a,domain(X0)),domain(X1))),compose(compose(a,domain(X0)),domain(X1))) = compose(compose(a,domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f24,f2150]) ).
fof(f14003,plain,
! [X0,X1,X2] : ifeq(domain(X0),domain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),domain(X1))),compose(compose(domain(X2),domain(X0)),domain(X1))),compose(compose(domain(X2),domain(X0)),domain(X1))) = compose(compose(domain(X2),domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f16,f2150]) ).
fof(f14010,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(domain(compose(domain(X0),domain(X1)))),domain(X0),compose(domain(X0),domain(X1)),compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1))),compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1))) = compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f18,f2150]) ).
fof(f14141,plain,
! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(compose(domain(X0),domain(X1))),domain(X0),compose(domain(X0),domain(X1)),compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1))),compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1))) = compose(compose(domain(compose(domain(X0),domain(X1))),domain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f14010]) ).
fof(f14340,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),g)),compose(compose(compose(a,b),domain(X0)),g)),compose(compose(compose(a,b),domain(X0)),g)) = compose(compose(compose(a,b),domain(X0)),g),
inference(paramodulation,[status(thm)],[f959,f2151]) ).
fof(f14341,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),g)),compose(compose(compose(a,h),domain(X0)),g)),compose(compose(compose(a,h),domain(X0)),g)) = compose(compose(compose(a,h),domain(X0)),g),
inference(paramodulation,[status(thm)],[f367,f2151]) ).
fof(f14342,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),g)),compose(compose(g,domain(X0)),g)),compose(compose(g,domain(X0)),g)) = compose(compose(g,domain(X0)),g),
inference(paramodulation,[status(thm)],[f359,f2151]) ).
fof(f14343,plain,
! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),g)),compose(compose(codomain(X1),domain(X0)),g)),compose(compose(codomain(X1),domain(X0)),g)) = compose(compose(codomain(X1),domain(X0)),g),
inference(paramodulation,[status(thm)],[f34,f2151]) ).
fof(f14344,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),g)),compose(compose(a,domain(X0)),g)),compose(compose(a,domain(X0)),g)) = compose(compose(a,domain(X0)),g),
inference(paramodulation,[status(thm)],[f24,f2151]) ).
fof(f14345,plain,
! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),g)),compose(compose(domain(X1),domain(X0)),g)),compose(compose(domain(X1),domain(X0)),g)) = compose(compose(domain(X1),domain(X0)),g),
inference(paramodulation,[status(thm)],[f16,f2151]) ).
fof(f14352,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(domain(compose(domain(X0),g))),domain(X0),compose(domain(X0),g),compose(compose(domain(compose(domain(X0),g)),domain(X0)),g)),compose(compose(domain(compose(domain(X0),g)),domain(X0)),g)) = compose(compose(domain(compose(domain(X0),g)),domain(X0)),g),
inference(paramodulation,[status(thm)],[f18,f2151]) ).
fof(f14443,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(domain(compose(domain(X0),g)),domain(X0),compose(domain(X0),g),compose(compose(domain(compose(domain(X0),g)),domain(X0)),g)),compose(compose(domain(compose(domain(X0),g)),domain(X0)),g)) = compose(compose(domain(compose(domain(X0),g)),domain(X0)),g),
inference(forward_demodulation,[status(thm)],[f16,f14352]) ).
fof(f14574,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),g),compose(compose(compose(a,b),g),codomain(h))) = compose(compose(compose(a,b),g),codomain(h)),
inference(paramodulation,[status(thm)],[f959,f424]) ).
fof(f14621,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),h)),compose(compose(compose(a,b),domain(X0)),h)),compose(compose(compose(a,b),domain(X0)),h)) = compose(compose(compose(a,b),domain(X0)),h),
inference(paramodulation,[status(thm)],[f959,f2152]) ).
fof(f14622,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),h)),compose(compose(compose(a,h),domain(X0)),h)),compose(compose(compose(a,h),domain(X0)),h)) = compose(compose(compose(a,h),domain(X0)),h),
inference(paramodulation,[status(thm)],[f367,f2152]) ).
fof(f14623,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),h)),compose(compose(g,domain(X0)),h)),compose(compose(g,domain(X0)),h)) = compose(compose(g,domain(X0)),h),
inference(paramodulation,[status(thm)],[f359,f2152]) ).
fof(f14624,plain,
! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),h)),compose(compose(codomain(X1),domain(X0)),h)),compose(compose(codomain(X1),domain(X0)),h)) = compose(compose(codomain(X1),domain(X0)),h),
inference(paramodulation,[status(thm)],[f34,f2152]) ).
fof(f14625,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),h)),compose(compose(a,domain(X0)),h)),compose(compose(a,domain(X0)),h)) = compose(compose(a,domain(X0)),h),
inference(paramodulation,[status(thm)],[f24,f2152]) ).
fof(f14626,plain,
! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),h)),compose(compose(domain(X1),domain(X0)),h)),compose(compose(domain(X1),domain(X0)),h)) = compose(compose(domain(X1),domain(X0)),h),
inference(paramodulation,[status(thm)],[f16,f2152]) ).
fof(f14633,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(codomain(domain(compose(domain(X0),h))),domain(X0),compose(domain(X0),h),compose(compose(domain(compose(domain(X0),h)),domain(X0)),h)),compose(compose(domain(compose(domain(X0),h)),domain(X0)),h)) = compose(compose(domain(compose(domain(X0),h)),domain(X0)),h),
inference(paramodulation,[status(thm)],[f18,f2152]) ).
fof(f14724,plain,
! [X0] : ifeq(domain(X0),domain(b),ifeq(domain(compose(domain(X0),h)),domain(X0),compose(domain(X0),h),compose(compose(domain(compose(domain(X0),h)),domain(X0)),h)),compose(compose(domain(compose(domain(X0),h)),domain(X0)),h)) = compose(compose(domain(compose(domain(X0),h)),domain(X0)),h),
inference(forward_demodulation,[status(thm)],[f16,f14633]) ).
fof(f14863,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),codomain(X1))),compose(compose(compose(a,b),domain(X0)),codomain(X1))),compose(compose(compose(a,b),domain(X0)),codomain(X1))) = compose(compose(compose(a,b),domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f959,f2153]) ).
fof(f14864,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),codomain(X1))),compose(compose(compose(a,h),domain(X0)),codomain(X1))),compose(compose(compose(a,h),domain(X0)),codomain(X1))) = compose(compose(compose(a,h),domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f367,f2153]) ).
fof(f14865,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))),compose(compose(g,domain(X0)),codomain(X1))) = compose(compose(g,domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f359,f2153]) ).
fof(f14866,plain,
! [X0,X1,X2] : ifeq(domain(X0),codomain(X1),ifeq(codomain(X2),domain(X0),compose(codomain(X2),compose(domain(X0),codomain(X1))),compose(compose(codomain(X2),domain(X0)),codomain(X1))),compose(compose(codomain(X2),domain(X0)),codomain(X1))) = compose(compose(codomain(X2),domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f34,f2153]) ).
fof(f14867,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(X1))),compose(compose(a,domain(X0)),codomain(X1))),compose(compose(a,domain(X0)),codomain(X1))) = compose(compose(a,domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f24,f2153]) ).
fof(f14868,plain,
! [X0,X1,X2] : ifeq(domain(X0),codomain(X1),ifeq(domain(X2),domain(X0),compose(domain(X2),compose(domain(X0),codomain(X1))),compose(compose(domain(X2),domain(X0)),codomain(X1))),compose(compose(domain(X2),domain(X0)),codomain(X1))) = compose(compose(domain(X2),domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f16,f2153]) ).
fof(f14875,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(codomain(domain(compose(domain(X0),codomain(X1)))),domain(X0),compose(domain(X0),codomain(X1)),compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1))),compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1))) = compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f18,f2153]) ).
fof(f15006,plain,
! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(domain(compose(domain(X0),codomain(X1))),domain(X0),compose(domain(X0),codomain(X1)),compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1))),compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1))) = compose(compose(domain(compose(domain(X0),codomain(X1))),domain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f14875]) ).
fof(f15211,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),compose(a,b))),compose(compose(compose(a,h),domain(X0)),compose(a,b))),compose(compose(compose(a,h),domain(X0)),compose(a,b))) = compose(compose(compose(a,h),domain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f2155]) ).
fof(f15236,plain,
! [X0] : ifeq(domain(X0),domain(codomain(compose(compose(a,h),domain(X0)))),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),codomain(compose(compose(a,h),domain(X0))))),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),domain(X0)),codomain(compose(compose(a,h),domain(X0))))) = compose(compose(compose(a,h),domain(X0)),codomain(compose(compose(a,h),domain(X0)))),
inference(paramodulation,[status(thm)],[f19,f2155]) ).
fof(f15358,plain,
! [X0] : ifeq(domain(X0),codomain(compose(compose(a,h),domain(X0))),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),codomain(compose(compose(a,h),domain(X0))))),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),domain(X0)),codomain(compose(compose(a,h),domain(X0))))) = compose(compose(compose(a,h),domain(X0)),codomain(compose(compose(a,h),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f15236]) ).
fof(f15359,plain,
! [X0] : ifeq(domain(X0),codomain(compose(compose(a,h),domain(X0))),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),codomain(compose(compose(a,h),domain(X0))))),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(compose(a,h),domain(X0)),codomain(compose(compose(a,h),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f15358]) ).
fof(f15360,plain,
! [X0] : ifeq(domain(X0),codomain(compose(compose(a,h),domain(X0))),ifeq(codomain(h),domain(X0),compose(compose(a,h),compose(domain(X0),codomain(compose(compose(a,h),domain(X0))))),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f15359]) ).
fof(f15822,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(a,b))),compose(compose(codomain(X1),domain(X0)),compose(a,b))),compose(compose(codomain(X1),domain(X0)),compose(a,b))) = compose(compose(codomain(X1),domain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f2157]) ).
fof(f15859,plain,
! [X0,X1] : ifeq(domain(X0),domain(codomain(compose(codomain(X1),domain(X0)))),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),codomain(compose(codomain(X1),domain(X0))))),compose(codomain(X1),domain(X0))),compose(compose(codomain(X1),domain(X0)),codomain(compose(codomain(X1),domain(X0))))) = compose(compose(codomain(X1),domain(X0)),codomain(compose(codomain(X1),domain(X0)))),
inference(paramodulation,[status(thm)],[f19,f2157]) ).
fof(f16041,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(codomain(X1),domain(X0))),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),codomain(compose(codomain(X1),domain(X0))))),compose(codomain(X1),domain(X0))),compose(compose(codomain(X1),domain(X0)),codomain(compose(codomain(X1),domain(X0))))) = compose(compose(codomain(X1),domain(X0)),codomain(compose(codomain(X1),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f15859]) ).
fof(f16042,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(codomain(X1),domain(X0))),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),codomain(compose(codomain(X1),domain(X0))))),compose(codomain(X1),domain(X0))),compose(codomain(X1),domain(X0))) = compose(compose(codomain(X1),domain(X0)),codomain(compose(codomain(X1),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f16041]) ).
fof(f16043,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(codomain(X1),domain(X0))),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),codomain(compose(codomain(X1),domain(X0))))),compose(codomain(X1),domain(X0))),compose(codomain(X1),domain(X0))) = compose(codomain(X1),domain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f16042]) ).
fof(f16156,plain,
ifeq(codomain(b),domain(a),compose(a,compose(b,compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f3647]) ).
fof(f16157,plain,
ifeq(codomain(b),domain(a),compose(a,compose(b,compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f3647]) ).
fof(f16158,plain,
! [X0] : ifeq(codomain(b),domain(X0),compose(a,compose(b,domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f3647]) ).
fof(f16159,plain,
ifeq(codomain(b),domain(b),compose(a,compose(b,g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(paramodulation,[status(thm)],[f55,f3647]) ).
fof(f16160,plain,
ifeq(codomain(b),domain(b),compose(a,compose(b,h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(paramodulation,[status(thm)],[f48,f3647]) ).
fof(f16161,plain,
! [X0] : ifeq(codomain(b),codomain(X0),compose(a,compose(b,codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(paramodulation,[status(thm)],[f17,f3647]) ).
fof(f16182,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(a,b))),compose(compose(a,domain(X0)),compose(a,b))),compose(compose(a,domain(X0)),compose(a,b))) = compose(compose(a,domain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f2158]) ).
fof(f16208,plain,
! [X0] : ifeq(domain(X0),domain(codomain(compose(a,domain(X0)))),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(compose(a,domain(X0))))),compose(a,domain(X0))),compose(compose(a,domain(X0)),codomain(compose(a,domain(X0))))) = compose(compose(a,domain(X0)),codomain(compose(a,domain(X0)))),
inference(paramodulation,[status(thm)],[f19,f2158]) ).
fof(f16350,plain,
! [X0] : ifeq(domain(X0),codomain(compose(a,domain(X0))),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(compose(a,domain(X0))))),compose(a,domain(X0))),compose(compose(a,domain(X0)),codomain(compose(a,domain(X0))))) = compose(compose(a,domain(X0)),codomain(compose(a,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f16208]) ).
fof(f16351,plain,
! [X0] : ifeq(domain(X0),codomain(compose(a,domain(X0))),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(compose(a,domain(X0))))),compose(a,domain(X0))),compose(a,domain(X0))) = compose(compose(a,domain(X0)),codomain(compose(a,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f16350]) ).
fof(f16352,plain,
! [X0] : ifeq(domain(X0),codomain(compose(a,domain(X0))),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),codomain(compose(a,domain(X0))))),compose(a,domain(X0))),compose(a,domain(X0))) = compose(a,domain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f16351]) ).
fof(f16432,plain,
ifeq(codomain(h),domain(a),compose(a,compose(h,compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f3694]) ).
fof(f16433,plain,
ifeq(codomain(h),domain(a),compose(a,compose(h,compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f3694]) ).
fof(f16434,plain,
! [X0] : ifeq(codomain(h),domain(X0),compose(a,compose(h,domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f3694]) ).
fof(f16435,plain,
ifeq(codomain(h),domain(b),compose(a,compose(h,g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(paramodulation,[status(thm)],[f55,f3694]) ).
fof(f16436,plain,
ifeq(codomain(h),domain(b),compose(a,compose(h,h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(paramodulation,[status(thm)],[f48,f3694]) ).
fof(f16437,plain,
! [X0] : ifeq(codomain(h),codomain(X0),compose(a,compose(h,codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(paramodulation,[status(thm)],[f17,f3694]) ).
fof(f16618,plain,
! [X0] : ifeq(domain(X0),domain(b),compose(domain(X0),h),compose(compose(domain(X0),h),codomain(h))) = compose(compose(domain(X0),h),codomain(h)),
inference(paramodulation,[status(thm)],[f48,f4357]) ).
fof(f16790,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(a,b))),compose(compose(domain(X1),domain(X0)),compose(a,b))),compose(compose(domain(X1),domain(X0)),compose(a,b))) = compose(compose(domain(X1),domain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f2159]) ).
fof(f16829,plain,
! [X0,X1] : ifeq(domain(X0),domain(codomain(compose(domain(X1),domain(X0)))),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),codomain(compose(domain(X1),domain(X0))))),compose(domain(X1),domain(X0))),compose(compose(domain(X1),domain(X0)),codomain(compose(domain(X1),domain(X0))))) = compose(compose(domain(X1),domain(X0)),codomain(compose(domain(X1),domain(X0)))),
inference(paramodulation,[status(thm)],[f19,f2159]) ).
fof(f17017,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(domain(X1),domain(X0))),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),codomain(compose(domain(X1),domain(X0))))),compose(domain(X1),domain(X0))),compose(compose(domain(X1),domain(X0)),codomain(compose(domain(X1),domain(X0))))) = compose(compose(domain(X1),domain(X0)),codomain(compose(domain(X1),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f16829]) ).
fof(f17018,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(domain(X1),domain(X0))),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),codomain(compose(domain(X1),domain(X0))))),compose(domain(X1),domain(X0))),compose(domain(X1),domain(X0))) = compose(compose(domain(X1),domain(X0)),codomain(compose(domain(X1),domain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f17017]) ).
fof(f17019,plain,
! [X0,X1] : ifeq(domain(X0),codomain(compose(domain(X1),domain(X0))),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),codomain(compose(domain(X1),domain(X0))))),compose(domain(X1),domain(X0))),compose(domain(X1),domain(X0))) = compose(domain(X1),domain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f17018]) ).
fof(f17146,plain,
ifeq(codomain(b),domain(b),compose(compose(a,b),h),compose(compose(compose(a,b),h),codomain(h))) = compose(compose(compose(a,b),h),codomain(h)),
inference(paramodulation,[status(thm)],[f959,f4718]) ).
fof(f17147,plain,
ifeq(codomain(h),domain(b),compose(compose(a,h),h),compose(compose(compose(a,h),h),codomain(h))) = compose(compose(compose(a,h),h),codomain(h)),
inference(paramodulation,[status(thm)],[f367,f4718]) ).
fof(f17149,plain,
! [X0] : ifeq(codomain(X0),domain(b),compose(codomain(X0),h),compose(compose(codomain(X0),h),codomain(h))) = compose(compose(codomain(X0),h),codomain(h)),
inference(paramodulation,[status(thm)],[f34,f4718]) ).
fof(f17302,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(compose(domain(X0),compose(a,b))),domain(X0),compose(domain(X0),compose(a,b)),compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b))),compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b))) = compose(compose(domain(compose(domain(X0),compose(a,b))),domain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f2262]) ).
fof(f18186,plain,
! [X0] : ifeq(domain(X0),codomain(compose(compose(a,b),domain(X0))),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),codomain(compose(compose(a,b),domain(X0))))),compose(compose(a,b),domain(X0))),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f2311]) ).
fof(f18188,plain,
! [X0] : ifeq(domain(X0),codomain(compose(g,domain(X0))),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),codomain(compose(g,domain(X0))))),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
inference(paramodulation,[status(thm)],[f359,f2311]) ).
fof(f18920,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),g)),compose(compose(compose(a,b),compose(a,h)),g)),compose(compose(compose(a,b),compose(a,h)),g)) = compose(compose(compose(a,b),compose(a,h)),g),
inference(paramodulation,[status(thm)],[f959,f2526]) ).
fof(f18921,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),g)),compose(compose(compose(a,h),compose(a,h)),g)),compose(compose(compose(a,h),compose(a,h)),g)) = compose(compose(compose(a,h),compose(a,h)),g),
inference(paramodulation,[status(thm)],[f367,f2526]) ).
fof(f18922,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),g)),compose(compose(g,compose(a,h)),g)),compose(compose(g,compose(a,h)),g)) = compose(compose(g,compose(a,h)),g),
inference(paramodulation,[status(thm)],[f359,f2526]) ).
fof(f18923,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),g)),compose(compose(codomain(X0),compose(a,h)),g)),compose(compose(codomain(X0),compose(a,h)),g)) = compose(compose(codomain(X0),compose(a,h)),g),
inference(paramodulation,[status(thm)],[f34,f2526]) ).
fof(f18924,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),g)),compose(compose(a,compose(a,h)),g)),compose(compose(a,compose(a,h)),g)) = compose(compose(a,compose(a,h)),g),
inference(paramodulation,[status(thm)],[f24,f2526]) ).
fof(f18925,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),g)),compose(compose(domain(X0),compose(a,h)),g)),compose(compose(domain(X0),compose(a,h)),g)) = compose(compose(domain(X0),compose(a,h)),g),
inference(paramodulation,[status(thm)],[f16,f2526]) ).
fof(f18926,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(compose(compose(a,h),g))),domain(a),compose(compose(a,h),g),compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g)),compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g)) = compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g),
inference(paramodulation,[status(thm)],[f18,f2526]) ).
fof(f18931,plain,
ifeq(codomain(h),domain(b),ifeq(domain(compose(compose(a,h),g)),domain(a),compose(compose(a,h),g),compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g)),compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g)) = compose(compose(domain(compose(compose(a,h),g)),compose(a,h)),g),
inference(forward_demodulation,[status(thm)],[f16,f18926]) ).
fof(f18957,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),g)),compose(compose(compose(a,b),codomain(X0)),g)),compose(compose(compose(a,b),codomain(X0)),g)) = compose(compose(compose(a,b),codomain(X0)),g),
inference(paramodulation,[status(thm)],[f959,f2528]) ).
fof(f18958,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),g)),compose(compose(compose(a,h),codomain(X0)),g)),compose(compose(compose(a,h),codomain(X0)),g)) = compose(compose(compose(a,h),codomain(X0)),g),
inference(paramodulation,[status(thm)],[f367,f2528]) ).
fof(f18959,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),g)),compose(compose(g,codomain(X0)),g)),compose(compose(g,codomain(X0)),g)) = compose(compose(g,codomain(X0)),g),
inference(paramodulation,[status(thm)],[f359,f2528]) ).
fof(f18960,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),g)),compose(compose(codomain(X1),codomain(X0)),g)),compose(compose(codomain(X1),codomain(X0)),g)) = compose(compose(codomain(X1),codomain(X0)),g),
inference(paramodulation,[status(thm)],[f34,f2528]) ).
fof(f18961,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),g)),compose(compose(a,codomain(X0)),g)),compose(compose(a,codomain(X0)),g)) = compose(compose(a,codomain(X0)),g),
inference(paramodulation,[status(thm)],[f24,f2528]) ).
fof(f18962,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),g)),compose(compose(domain(X1),codomain(X0)),g)),compose(compose(domain(X1),codomain(X0)),g)) = compose(compose(domain(X1),codomain(X0)),g),
inference(paramodulation,[status(thm)],[f16,f2528]) ).
fof(f18969,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(domain(compose(codomain(X0),g))),codomain(X0),compose(codomain(X0),g),compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g)),compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g)) = compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g),
inference(paramodulation,[status(thm)],[f18,f2528]) ).
fof(f19064,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(compose(codomain(X0),g)),codomain(X0),compose(codomain(X0),g),compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g)),compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g)) = compose(compose(domain(compose(codomain(X0),g)),codomain(X0)),g),
inference(forward_demodulation,[status(thm)],[f16,f18969]) ).
fof(f19385,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(compose(a,b),g)),compose(compose(compose(a,h),compose(a,b)),g)),compose(compose(compose(a,h),compose(a,b)),g)) = compose(compose(compose(a,h),compose(a,b)),g),
inference(paramodulation,[status(thm)],[f959,f2484]) ).
fof(f19387,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(g),compose(compose(a,h),compose(g,g)),compose(compose(compose(a,h),g),g)),compose(compose(compose(a,h),g),g)) = compose(compose(compose(a,h),g),g),
inference(paramodulation,[status(thm)],[f359,f2484]) ).
fof(f19395,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,g)),compose(compose(compose(a,h),h),g)),compose(compose(compose(a,h),h),g)) = compose(compose(compose(a,h),h),g),
inference(paramodulation,[status(thm)],[f48,f2484]) ).
fof(f19404,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),g)),compose(compose(compose(a,h),compose(a,b)),g)),compose(compose(compose(a,h),compose(a,b)),g)) = compose(compose(compose(a,h),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1163,f19385]) ).
fof(f19406,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,g)),compose(compose(compose(a,h),g),g)),compose(compose(compose(a,h),g),g)) = compose(compose(compose(a,h),g),g),
inference(forward_demodulation,[status(thm)],[f55,f19387]) ).
fof(f19452,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(codomain(X0),domain(compose(a,b)),compose(codomain(X0),compose(compose(a,b),g)),compose(compose(codomain(X0),compose(a,b)),g)),compose(compose(codomain(X0),compose(a,b)),g)) = compose(compose(codomain(X0),compose(a,b)),g),
inference(paramodulation,[status(thm)],[f959,f2486]) ).
fof(f19454,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(g),compose(codomain(X0),compose(g,g)),compose(compose(codomain(X0),g),g)),compose(compose(codomain(X0),g),g)) = compose(compose(codomain(X0),g),g),
inference(paramodulation,[status(thm)],[f359,f2486]) ).
fof(f19468,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(h,g)),compose(compose(codomain(X0),h),g)),compose(compose(codomain(X0),h),g)) = compose(compose(codomain(X0),h),g),
inference(paramodulation,[status(thm)],[f48,f2486]) ).
fof(f19495,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),g)),compose(compose(codomain(X0),compose(a,b)),g)),compose(compose(codomain(X0),compose(a,b)),g)) = compose(compose(codomain(X0),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1163,f19452]) ).
fof(f19497,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(g,g)),compose(compose(codomain(X0),g),g)),compose(compose(codomain(X0),g),g)) = compose(compose(codomain(X0),g),g),
inference(forward_demodulation,[status(thm)],[f55,f19454]) ).
fof(f19636,plain,
ifeq(codomain(b),domain(b),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(compose(a,b),g)),compose(compose(a,compose(a,b)),g)),compose(compose(a,compose(a,b)),g)) = compose(compose(a,compose(a,b)),g),
inference(paramodulation,[status(thm)],[f959,f2487]) ).
fof(f19658,plain,
ifeq(codomain(b),domain(b),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),g)),compose(compose(a,compose(a,b)),g)),compose(compose(a,compose(a,b)),g)) = compose(compose(a,compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1163,f19636]) ).
fof(f19732,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(compose(a,b),g)),compose(compose(domain(X0),compose(a,b)),g)),compose(compose(domain(X0),compose(a,b)),g)) = compose(compose(domain(X0),compose(a,b)),g),
inference(paramodulation,[status(thm)],[f959,f2488]) ).
fof(f19734,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(domain(X0),domain(g),compose(domain(X0),compose(g,g)),compose(compose(domain(X0),g),g)),compose(compose(domain(X0),g),g)) = compose(compose(domain(X0),g),g),
inference(paramodulation,[status(thm)],[f359,f2488]) ).
fof(f19749,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(domain(X0),domain(b),compose(domain(X0),compose(h,g)),compose(compose(domain(X0),h),g)),compose(compose(domain(X0),h),g)) = compose(compose(domain(X0),h),g),
inference(paramodulation,[status(thm)],[f48,f2488]) ).
fof(f19787,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),g)),compose(compose(domain(X0),compose(a,b)),g)),compose(compose(domain(X0),compose(a,b)),g)) = compose(compose(domain(X0),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1163,f19732]) ).
fof(f19789,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(domain(X0),domain(b),compose(domain(X0),compose(g,g)),compose(compose(domain(X0),g),g)),compose(compose(domain(X0),g),g)) = compose(compose(domain(X0),g),g),
inference(forward_demodulation,[status(thm)],[f55,f19734]) ).
fof(f19969,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(g,g)),compose(compose(compose(a,b),g),g)),compose(compose(compose(a,b),g),g)) = compose(compose(compose(a,b),g),g),
inference(paramodulation,[status(thm)],[f959,f2535]) ).
fof(f19971,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(b),compose(g,compose(g,g)),compose(compose(g,g),g)),compose(compose(g,g),g)) = compose(compose(g,g),g),
inference(paramodulation,[status(thm)],[f359,f2535]) ).
fof(f19975,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(compose(g,g))),domain(b),compose(g,g),compose(compose(domain(compose(g,g)),g),g)),compose(compose(domain(compose(g,g)),g),g)) = compose(compose(domain(compose(g,g)),g),g),
inference(paramodulation,[status(thm)],[f18,f2535]) ).
fof(f19985,plain,
ifeq(codomain(h),domain(b),ifeq(domain(compose(g,g)),domain(b),compose(g,g),compose(compose(domain(compose(g,g)),g),g)),compose(compose(domain(compose(g,g)),g),g)) = compose(compose(domain(compose(g,g)),g),g),
inference(forward_demodulation,[status(thm)],[f16,f19975]) ).
fof(f20011,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(h,g)),compose(compose(compose(a,b),h),g)),compose(compose(compose(a,b),h),g)) = compose(compose(compose(a,b),h),g),
inference(paramodulation,[status(thm)],[f959,f2493]) ).
fof(f20013,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(b),compose(g,compose(h,g)),compose(compose(g,h),g)),compose(compose(g,h),g)) = compose(compose(g,h),g),
inference(paramodulation,[status(thm)],[f359,f2493]) ).
fof(f20017,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(compose(h,g))),domain(b),compose(h,g),compose(compose(domain(compose(h,g)),h),g)),compose(compose(domain(compose(h,g)),h),g)) = compose(compose(domain(compose(h,g)),h),g),
inference(paramodulation,[status(thm)],[f18,f2493]) ).
fof(f20023,plain,
ifeq(codomain(h),domain(b),ifeq(domain(compose(h,g)),domain(b),compose(h,g),compose(compose(domain(compose(h,g)),h),g)),compose(compose(domain(compose(h,g)),h),g)) = compose(compose(domain(compose(h,g)),h),g),
inference(forward_demodulation,[status(thm)],[f16,f20017]) ).
fof(f20857,plain,
ifeq(codomain(b),domain(b),ifeq(domain(compose(compose(a,b),g)),domain(compose(a,b)),compose(compose(a,b),g),compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g)),compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g)) = compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g),
inference(paramodulation,[status(thm)],[f959,f2537]) ).
fof(f20881,plain,
ifeq(codomain(b),domain(b),ifeq(domain(compose(compose(a,b),g)),domain(a),compose(compose(a,b),g),compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g)),compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g)) = compose(compose(domain(compose(compose(a,b),g)),compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1163,f20857]) ).
fof(f21013,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),h)),compose(compose(compose(a,b),compose(a,h)),h)),compose(compose(compose(a,b),compose(a,h)),h)) = compose(compose(compose(a,b),compose(a,h)),h),
inference(paramodulation,[status(thm)],[f959,f2909]) ).
fof(f21014,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),h)),compose(compose(compose(a,h),compose(a,h)),h)),compose(compose(compose(a,h),compose(a,h)),h)) = compose(compose(compose(a,h),compose(a,h)),h),
inference(paramodulation,[status(thm)],[f367,f2909]) ).
fof(f21015,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),h)),compose(compose(g,compose(a,h)),h)),compose(compose(g,compose(a,h)),h)) = compose(compose(g,compose(a,h)),h),
inference(paramodulation,[status(thm)],[f359,f2909]) ).
fof(f21016,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),h)),compose(compose(codomain(X0),compose(a,h)),h)),compose(compose(codomain(X0),compose(a,h)),h)) = compose(compose(codomain(X0),compose(a,h)),h),
inference(paramodulation,[status(thm)],[f34,f2909]) ).
fof(f21017,plain,
ifeq(codomain(h),domain(b),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),h)),compose(compose(a,compose(a,h)),h)),compose(compose(a,compose(a,h)),h)) = compose(compose(a,compose(a,h)),h),
inference(paramodulation,[status(thm)],[f24,f2909]) ).
fof(f21018,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),h)),compose(compose(domain(X0),compose(a,h)),h)),compose(compose(domain(X0),compose(a,h)),h)) = compose(compose(domain(X0),compose(a,h)),h),
inference(paramodulation,[status(thm)],[f16,f2909]) ).
fof(f21019,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(compose(compose(a,h),h))),domain(a),compose(compose(a,h),h),compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h)),compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h)) = compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h),
inference(paramodulation,[status(thm)],[f18,f2909]) ).
fof(f21024,plain,
ifeq(codomain(h),domain(b),ifeq(domain(compose(compose(a,h),h)),domain(a),compose(compose(a,h),h),compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h)),compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h)) = compose(compose(domain(compose(compose(a,h),h)),compose(a,h)),h),
inference(forward_demodulation,[status(thm)],[f16,f21019]) ).
fof(f21050,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),h)),compose(compose(compose(a,b),codomain(X0)),h)),compose(compose(compose(a,b),codomain(X0)),h)) = compose(compose(compose(a,b),codomain(X0)),h),
inference(paramodulation,[status(thm)],[f959,f2911]) ).
fof(f21051,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),h)),compose(compose(compose(a,h),codomain(X0)),h)),compose(compose(compose(a,h),codomain(X0)),h)) = compose(compose(compose(a,h),codomain(X0)),h),
inference(paramodulation,[status(thm)],[f367,f2911]) ).
fof(f21052,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),h)),compose(compose(g,codomain(X0)),h)),compose(compose(g,codomain(X0)),h)) = compose(compose(g,codomain(X0)),h),
inference(paramodulation,[status(thm)],[f359,f2911]) ).
fof(f21053,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),h)),compose(compose(codomain(X1),codomain(X0)),h)),compose(compose(codomain(X1),codomain(X0)),h)) = compose(compose(codomain(X1),codomain(X0)),h),
inference(paramodulation,[status(thm)],[f34,f2911]) ).
fof(f21054,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),h)),compose(compose(a,codomain(X0)),h)),compose(compose(a,codomain(X0)),h)) = compose(compose(a,codomain(X0)),h),
inference(paramodulation,[status(thm)],[f24,f2911]) ).
fof(f21055,plain,
! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),h)),compose(compose(domain(X1),codomain(X0)),h)),compose(compose(domain(X1),codomain(X0)),h)) = compose(compose(domain(X1),codomain(X0)),h),
inference(paramodulation,[status(thm)],[f16,f2911]) ).
fof(f21062,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(codomain(domain(compose(codomain(X0),h))),codomain(X0),compose(codomain(X0),h),compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h)),compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h)) = compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h),
inference(paramodulation,[status(thm)],[f18,f2911]) ).
fof(f21157,plain,
! [X0] : ifeq(codomain(X0),domain(b),ifeq(domain(compose(codomain(X0),h)),codomain(X0),compose(codomain(X0),h),compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h)),compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h)) = compose(compose(domain(compose(codomain(X0),h)),codomain(X0)),h),
inference(forward_demodulation,[status(thm)],[f16,f21062]) ).
fof(f21296,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(compose(a,b),h)),compose(compose(compose(a,h),compose(a,b)),h)),compose(compose(compose(a,h),compose(a,b)),h)) = compose(compose(compose(a,h),compose(a,b)),h),
inference(paramodulation,[status(thm)],[f959,f2867]) ).
fof(f21298,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(g),compose(compose(a,h),compose(g,h)),compose(compose(compose(a,h),g),h)),compose(compose(compose(a,h),g),h)) = compose(compose(compose(a,h),g),h),
inference(paramodulation,[status(thm)],[f359,f2867]) ).
fof(f21306,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,h)),compose(compose(compose(a,h),h),h)),compose(compose(compose(a,h),h),h)) = compose(compose(compose(a,h),h),h),
inference(paramodulation,[status(thm)],[f48,f2867]) ).
fof(f21314,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),h)),compose(compose(compose(a,h),compose(a,b)),h)),compose(compose(compose(a,h),compose(a,b)),h)) = compose(compose(compose(a,h),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1163,f21296]) ).
fof(f21316,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,h)),compose(compose(compose(a,h),g),h)),compose(compose(compose(a,h),g),h)) = compose(compose(compose(a,h),g),h),
inference(forward_demodulation,[status(thm)],[f55,f21298]) ).
fof(f21359,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(codomain(X0),domain(compose(a,b)),compose(codomain(X0),compose(compose(a,b),h)),compose(compose(codomain(X0),compose(a,b)),h)),compose(compose(codomain(X0),compose(a,b)),h)) = compose(compose(codomain(X0),compose(a,b)),h),
inference(paramodulation,[status(thm)],[f959,f2869]) ).
fof(f21361,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(g),compose(codomain(X0),compose(g,h)),compose(compose(codomain(X0),g),h)),compose(compose(codomain(X0),g),h)) = compose(compose(codomain(X0),g),h),
inference(paramodulation,[status(thm)],[f359,f2869]) ).
fof(f21375,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(h,h)),compose(compose(codomain(X0),h),h)),compose(compose(codomain(X0),h),h)) = compose(compose(codomain(X0),h),h),
inference(paramodulation,[status(thm)],[f48,f2869]) ).
fof(f21401,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),h)),compose(compose(codomain(X0),compose(a,b)),h)),compose(compose(codomain(X0),compose(a,b)),h)) = compose(compose(codomain(X0),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1163,f21359]) ).
fof(f21403,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(g,h)),compose(compose(codomain(X0),g),h)),compose(compose(codomain(X0),g),h)) = compose(compose(codomain(X0),g),h),
inference(forward_demodulation,[status(thm)],[f55,f21361]) ).
fof(f21547,plain,
ifeq(codomain(b),domain(b),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(compose(a,b),h)),compose(compose(a,compose(a,b)),h)),compose(compose(a,compose(a,b)),h)) = compose(compose(a,compose(a,b)),h),
inference(paramodulation,[status(thm)],[f959,f2870]) ).
fof(f21568,plain,
ifeq(codomain(b),domain(b),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),h)),compose(compose(a,compose(a,b)),h)),compose(compose(a,compose(a,b)),h)) = compose(compose(a,compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1163,f21547]) ).
fof(f21629,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(compose(a,b),h)),compose(compose(domain(X0),compose(a,b)),h)),compose(compose(domain(X0),compose(a,b)),h)) = compose(compose(domain(X0),compose(a,b)),h),
inference(paramodulation,[status(thm)],[f959,f2871]) ).
fof(f21631,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(domain(X0),domain(g),compose(domain(X0),compose(g,h)),compose(compose(domain(X0),g),h)),compose(compose(domain(X0),g),h)) = compose(compose(domain(X0),g),h),
inference(paramodulation,[status(thm)],[f359,f2871]) ).
fof(f21646,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(domain(X0),domain(b),compose(domain(X0),compose(h,h)),compose(compose(domain(X0),h),h)),compose(compose(domain(X0),h),h)) = compose(compose(domain(X0),h),h),
inference(paramodulation,[status(thm)],[f48,f2871]) ).
fof(f21684,plain,
! [X0] : ifeq(codomain(b),domain(b),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),h)),compose(compose(domain(X0),compose(a,b)),h)),compose(compose(domain(X0),compose(a,b)),h)) = compose(compose(domain(X0),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1163,f21629]) ).
fof(f21686,plain,
! [X0] : ifeq(codomain(h),domain(b),ifeq(domain(X0),domain(b),compose(domain(X0),compose(g,h)),compose(compose(domain(X0),g),h)),compose(compose(domain(X0),g),h)) = compose(compose(domain(X0),g),h),
inference(forward_demodulation,[status(thm)],[f55,f21631]) ).
fof(f21867,plain,
ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(a,b),compose(a,b),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f959,f7662]) ).
fof(f21868,plain,
ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(a,b),compose(a,h),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f367,f7662]) ).
fof(f21869,plain,
ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(a,b),g,domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f359,f7662]) ).
fof(f21870,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(a,b),codomain(X0),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f34,f7662]) ).
fof(f21871,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(a,b),a,domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f24,f7662]) ).
fof(f21872,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(a,b),domain(X0),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f16,f7662]) ).
fof(f21883,plain,
ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(a,b),compose(a,b)),compose(a,b),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f959,f7705]) ).
fof(f21884,plain,
ifeq(codomain(h),domain(a),ifeq(compose(a,b),compose(compose(a,h),compose(a,b)),compose(a,h),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f367,f7705]) ).
fof(f21885,plain,
ifeq(codomain(h),domain(a),ifeq(compose(a,b),compose(g,compose(a,b)),g,domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f359,f7705]) ).
fof(f21886,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(codomain(X0),compose(a,b)),codomain(X0),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f34,f7705]) ).
fof(f21887,plain,
ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(a,compose(a,b)),a,domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f24,f7705]) ).
fof(f21888,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),compose(domain(X0),compose(a,b)),domain(X0),domain(a)),domain(a)) = domain(a),
inference(paramodulation,[status(thm)],[f16,f7705]) ).
fof(f22213,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(g,h)),compose(compose(compose(a,b),g),h)),compose(compose(compose(a,b),g),h)) = compose(compose(compose(a,b),g),h),
inference(paramodulation,[status(thm)],[f959,f2917]) ).
fof(f22215,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(b),compose(g,compose(g,h)),compose(compose(g,g),h)),compose(compose(g,g),h)) = compose(compose(g,g),h),
inference(paramodulation,[status(thm)],[f359,f2917]) ).
fof(f22219,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(compose(g,h))),domain(b),compose(g,h),compose(compose(domain(compose(g,h)),g),h)),compose(compose(domain(compose(g,h)),g),h)) = compose(compose(domain(compose(g,h)),g),h),
inference(paramodulation,[status(thm)],[f18,f2917]) ).
fof(f22229,plain,
ifeq(codomain(h),domain(b),ifeq(domain(compose(g,h)),domain(b),compose(g,h),compose(compose(domain(compose(g,h)),g),h)),compose(compose(domain(compose(g,h)),g),h)) = compose(compose(domain(compose(g,h)),g),h),
inference(forward_demodulation,[status(thm)],[f16,f22219]) ).
fof(f22420,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(h,h)),compose(compose(compose(a,b),h),h)),compose(compose(compose(a,b),h),h)) = compose(compose(compose(a,b),h),h),
inference(paramodulation,[status(thm)],[f959,f2876]) ).
fof(f22422,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(h),domain(b),compose(g,compose(h,h)),compose(compose(g,h),h)),compose(compose(g,h),h)) = compose(compose(g,h),h),
inference(paramodulation,[status(thm)],[f359,f2876]) ).
fof(f22426,plain,
ifeq(codomain(h),domain(b),ifeq(codomain(domain(compose(h,h))),domain(b),compose(h,h),compose(compose(domain(compose(h,h)),h),h)),compose(compose(domain(compose(h,h)),h),h)) = compose(compose(domain(compose(h,h)),h),h),
inference(paramodulation,[status(thm)],[f18,f2876]) ).
fof(f22432,plain,
ifeq(codomain(h),domain(b),ifeq(domain(compose(h,h)),domain(b),compose(h,h),compose(compose(domain(compose(h,h)),h),h)),compose(compose(domain(compose(h,h)),h),h)) = compose(compose(domain(compose(h,h)),h),h),
inference(forward_demodulation,[status(thm)],[f16,f22426]) ).
fof(f22604,plain,
ifeq(codomain(b),domain(b),ifeq(domain(compose(compose(a,b),h)),domain(compose(a,b)),compose(compose(a,b),h),compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h)),compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h)) = compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h),
inference(paramodulation,[status(thm)],[f959,f2923]) ).
fof(f22627,plain,
ifeq(codomain(b),domain(b),ifeq(domain(compose(compose(a,b),h)),domain(a),compose(compose(a,b),h),compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h)),compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h)) = compose(compose(domain(compose(compose(a,b),h)),compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1163,f22604]) ).
fof(f22742,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,b),compose(a,h)),codomain(X0))),compose(compose(compose(a,b),compose(a,h)),codomain(X0))) = compose(compose(compose(a,b),compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3155]) ).
fof(f22743,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),compose(a,h)),codomain(X0))),compose(compose(compose(a,h),compose(a,h)),codomain(X0))) = compose(compose(compose(a,h),compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f367,f3155]) ).
fof(f22744,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),codomain(X0))),compose(compose(g,compose(a,h)),codomain(X0))),compose(compose(g,compose(a,h)),codomain(X0))) = compose(compose(g,compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f3155]) ).
fof(f22745,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),codomain(X0))),compose(compose(codomain(X1),compose(a,h)),codomain(X0))),compose(compose(codomain(X1),compose(a,h)),codomain(X0))) = compose(compose(codomain(X1),compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f34,f3155]) ).
fof(f22746,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),codomain(X0))),compose(compose(a,compose(a,h)),codomain(X0))),compose(compose(a,compose(a,h)),codomain(X0))) = compose(compose(a,compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f24,f3155]) ).
fof(f22747,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),codomain(X0))),compose(compose(domain(X1),compose(a,h)),codomain(X0))),compose(compose(domain(X1),compose(a,h)),codomain(X0))) = compose(compose(domain(X1),compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f16,f3155]) ).
fof(f22748,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(domain(compose(compose(a,h),codomain(X0)))),domain(a),compose(compose(a,h),codomain(X0)),compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0))),compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0))) = compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0)),
inference(paramodulation,[status(thm)],[f18,f3155]) ).
fof(f22802,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(compose(compose(a,h),codomain(X0))),domain(a),compose(compose(a,h),codomain(X0)),compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0))),compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0))) = compose(compose(domain(compose(compose(a,h),codomain(X0))),compose(a,h)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f22748]) ).
fof(f22923,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),codomain(X1))),compose(compose(compose(a,b),codomain(X0)),codomain(X1))),compose(compose(compose(a,b),codomain(X0)),codomain(X1))) = compose(compose(compose(a,b),codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f959,f3157]) ).
fof(f22924,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),codomain(X1))),compose(compose(compose(a,h),codomain(X0)),codomain(X1))),compose(compose(compose(a,h),codomain(X0)),codomain(X1))) = compose(compose(compose(a,h),codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f367,f3157]) ).
fof(f22925,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))),compose(compose(g,codomain(X0)),codomain(X1))) = compose(compose(g,codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f359,f3157]) ).
fof(f22926,plain,
! [X0,X1,X2] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(X2),codomain(X0),compose(codomain(X2),compose(codomain(X0),codomain(X1))),compose(compose(codomain(X2),codomain(X0)),codomain(X1))),compose(compose(codomain(X2),codomain(X0)),codomain(X1))) = compose(compose(codomain(X2),codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f34,f3157]) ).
fof(f22927,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(X1))),compose(compose(a,codomain(X0)),codomain(X1))),compose(compose(a,codomain(X0)),codomain(X1))) = compose(compose(a,codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f24,f3157]) ).
fof(f22928,plain,
! [X0,X1,X2] : ifeq(codomain(X0),codomain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),codomain(X1))),compose(compose(domain(X2),codomain(X0)),codomain(X1))),compose(compose(domain(X2),codomain(X0)),codomain(X1))) = compose(compose(domain(X2),codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f16,f3157]) ).
fof(f22935,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(domain(compose(codomain(X0),codomain(X1)))),codomain(X0),compose(codomain(X0),codomain(X1)),compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1))),compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1))) = compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1)),
inference(paramodulation,[status(thm)],[f18,f3157]) ).
fof(f23076,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(compose(codomain(X0),codomain(X1))),codomain(X0),compose(codomain(X0),codomain(X1)),compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1))),compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1))) = compose(compose(domain(compose(codomain(X0),codomain(X1))),codomain(X0)),codomain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f22935]) ).
fof(f23294,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,h),compose(a,b)),codomain(X0))),compose(compose(compose(a,h),compose(a,b)),codomain(X0))) = compose(compose(compose(a,h),compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3084]) ).
fof(f23296,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(g),compose(compose(a,h),compose(g,codomain(X0))),compose(compose(compose(a,h),g),codomain(X0))),compose(compose(compose(a,h),g),codomain(X0))) = compose(compose(compose(a,h),g),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f3084]) ).
fof(f23310,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,codomain(X0))),compose(compose(compose(a,h),h),codomain(X0))),compose(compose(compose(a,h),h),codomain(X0))) = compose(compose(compose(a,h),h),codomain(X0)),
inference(paramodulation,[status(thm)],[f48,f3084]) ).
fof(f23344,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,h),compose(a,b)),codomain(X0))),compose(compose(compose(a,h),compose(a,b)),codomain(X0))) = compose(compose(compose(a,h),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f23294]) ).
fof(f23346,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,codomain(X0))),compose(compose(compose(a,h),g),codomain(X0))),compose(compose(compose(a,h),g),codomain(X0))) = compose(compose(compose(a,h),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f55,f23296]) ).
fof(f23500,plain,
! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(compose(a,b)),compose(codomain(X1),compose(compose(a,b),codomain(X0))),compose(compose(codomain(X1),compose(a,b)),codomain(X0))),compose(compose(codomain(X1),compose(a,b)),codomain(X0))) = compose(compose(codomain(X1),compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3086]) ).
fof(f23502,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(g),compose(codomain(X1),compose(g,codomain(X0))),compose(compose(codomain(X1),g),codomain(X0))),compose(compose(codomain(X1),g),codomain(X0))) = compose(compose(codomain(X1),g),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f3086]) ).
fof(f23522,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(b),compose(codomain(X1),compose(h,codomain(X0))),compose(compose(codomain(X1),h),codomain(X0))),compose(compose(codomain(X1),h),codomain(X0))) = compose(compose(codomain(X1),h),codomain(X0)),
inference(paramodulation,[status(thm)],[f48,f3086]) ).
fof(f23574,plain,
! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),codomain(X0))),compose(compose(codomain(X1),compose(a,b)),codomain(X0))),compose(compose(codomain(X1),compose(a,b)),codomain(X0))) = compose(compose(codomain(X1),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f23500]) ).
fof(f23576,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(codomain(X1),domain(b),compose(codomain(X1),compose(g,codomain(X0))),compose(compose(codomain(X1),g),codomain(X0))),compose(compose(codomain(X1),g),codomain(X0))) = compose(compose(codomain(X1),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f55,f23502]) ).
fof(f23823,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(compose(a,b),codomain(X0))),compose(compose(a,compose(a,b)),codomain(X0))),compose(compose(a,compose(a,b)),codomain(X0))) = compose(compose(a,compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3087]) ).
fof(f23880,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),codomain(X0))),compose(compose(a,compose(a,b)),codomain(X0))),compose(compose(a,compose(a,b)),codomain(X0))) = compose(compose(a,compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f23823]) ).
fof(f24066,plain,
! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(domain(X1),domain(compose(a,b)),compose(domain(X1),compose(compose(a,b),codomain(X0))),compose(compose(domain(X1),compose(a,b)),codomain(X0))),compose(compose(domain(X1),compose(a,b)),codomain(X0))) = compose(compose(domain(X1),compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3088]) ).
fof(f24068,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(domain(X1),domain(g),compose(domain(X1),compose(g,codomain(X0))),compose(compose(domain(X1),g),codomain(X0))),compose(compose(domain(X1),g),codomain(X0))) = compose(compose(domain(X1),g),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f3088]) ).
fof(f24089,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(domain(X1),domain(b),compose(domain(X1),compose(h,codomain(X0))),compose(compose(domain(X1),h),codomain(X0))),compose(compose(domain(X1),h),codomain(X0))) = compose(compose(domain(X1),h),codomain(X0)),
inference(paramodulation,[status(thm)],[f48,f3088]) ).
fof(f24152,plain,
! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),codomain(X0))),compose(compose(domain(X1),compose(a,b)),codomain(X0))),compose(compose(domain(X1),compose(a,b)),codomain(X0))) = compose(compose(domain(X1),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f24066]) ).
fof(f24154,plain,
! [X0,X1] : ifeq(codomain(h),codomain(X0),ifeq(domain(X1),domain(b),compose(domain(X1),compose(g,codomain(X0))),compose(compose(domain(X1),g),codomain(X0))),compose(compose(domain(X1),g),codomain(X0))) = compose(compose(domain(X1),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f55,f24068]) ).
fof(f24441,plain,
ifeq(codomain(b),domain(a),compose(domain(compose(a,b)),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f6391]) ).
fof(f24442,plain,
ifeq(codomain(h),domain(a),compose(domain(compose(a,h)),compose(compose(a,h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(paramodulation,[status(thm)],[f367,f6391]) ).
fof(f24457,plain,
ifeq(codomain(b),domain(a),compose(domain(a),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f24441]) ).
fof(f24458,plain,
ifeq(codomain(h),domain(a),compose(domain(a),compose(compose(a,h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f345,f24442]) ).
fof(f24523,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(codomain(compose(a,b)),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f6554]) ).
fof(f24524,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(codomain(compose(a,h)),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(paramodulation,[status(thm)],[f367,f6554]) ).
fof(f24537,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(codomain(b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f959,f24523]) ).
fof(f24538,plain,
ifeq(codomain(h),domain(a),compose(compose(a,h),compose(codomain(h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f367,f24524]) ).
fof(f24602,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(g,codomain(X0))),compose(compose(compose(a,b),g),codomain(X0))),compose(compose(compose(a,b),g),codomain(X0))) = compose(compose(compose(a,b),g),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3186]) ).
fof(f24604,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(b),compose(g,compose(g,codomain(X0))),compose(compose(g,g),codomain(X0))),compose(compose(g,g),codomain(X0))) = compose(compose(g,g),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f3186]) ).
fof(f24608,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(domain(compose(g,codomain(X0)))),domain(b),compose(g,codomain(X0)),compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0))),compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0))) = compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0)),
inference(paramodulation,[status(thm)],[f18,f3186]) ).
fof(f24667,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(compose(g,codomain(X0))),domain(b),compose(g,codomain(X0)),compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0))),compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0))) = compose(compose(domain(compose(g,codomain(X0))),g),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f24608]) ).
fof(f25039,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(h,codomain(X0))),compose(compose(compose(a,b),h),codomain(X0))),compose(compose(compose(a,b),h),codomain(X0))) = compose(compose(compose(a,b),h),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3093]) ).
fof(f25041,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(h),domain(b),compose(g,compose(h,codomain(X0))),compose(compose(g,h),codomain(X0))),compose(compose(g,h),codomain(X0))) = compose(compose(g,h),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f3093]) ).
fof(f25045,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(codomain(domain(compose(h,codomain(X0)))),domain(b),compose(h,codomain(X0)),compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0))),compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0))) = compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0)),
inference(paramodulation,[status(thm)],[f18,f3093]) ).
fof(f25102,plain,
! [X0] : ifeq(codomain(h),codomain(X0),ifeq(domain(compose(h,codomain(X0))),domain(b),compose(h,codomain(X0)),compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0))),compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0))) = compose(compose(domain(compose(h,codomain(X0))),h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f25045]) ).
fof(f25466,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(compose(compose(a,b),codomain(X0))),domain(compose(a,b)),compose(compose(a,b),codomain(X0)),compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0))),compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0))) = compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3188]) ).
fof(f25550,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(compose(compose(a,b),codomain(X0))),domain(a),compose(compose(a,b),codomain(X0)),compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0))),compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0))) = compose(compose(domain(compose(compose(a,b),codomain(X0))),compose(a,b)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f25466]) ).
fof(f28165,plain,
ifeq(codomain(h),domain(a),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),compose(a,b))),compose(compose(a,compose(a,h)),compose(a,b))),compose(compose(a,compose(a,h)),compose(a,b))) = compose(compose(a,compose(a,h)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f3680]) ).
fof(f28166,plain,
ifeq(codomain(h),domain(a),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),compose(a,h))),compose(compose(a,compose(a,h)),compose(a,h))),compose(compose(a,compose(a,h)),compose(a,h))) = compose(compose(a,compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f3680]) ).
fof(f28167,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),domain(X0))),compose(compose(a,compose(a,h)),domain(X0))),compose(compose(a,compose(a,h)),domain(X0))) = compose(compose(a,compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f3680]) ).
fof(f28173,plain,
ifeq(codomain(h),domain(codomain(compose(a,compose(a,h)))),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),codomain(compose(a,compose(a,h))))),compose(a,compose(a,h))),compose(compose(a,compose(a,h)),codomain(compose(a,compose(a,h))))) = compose(compose(a,compose(a,h)),codomain(compose(a,compose(a,h)))),
inference(paramodulation,[status(thm)],[f19,f3680]) ).
fof(f28182,plain,
ifeq(codomain(h),codomain(compose(a,compose(a,h))),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),codomain(compose(a,compose(a,h))))),compose(a,compose(a,h))),compose(compose(a,compose(a,h)),codomain(compose(a,compose(a,h))))) = compose(compose(a,compose(a,h)),codomain(compose(a,compose(a,h)))),
inference(forward_demodulation,[status(thm)],[f17,f28173]) ).
fof(f28183,plain,
ifeq(codomain(h),codomain(compose(a,compose(a,h))),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),codomain(compose(a,compose(a,h))))),compose(a,compose(a,h))),compose(a,compose(a,h))) = compose(compose(a,compose(a,h)),codomain(compose(a,compose(a,h)))),
inference(forward_demodulation,[status(thm)],[f19,f28182]) ).
fof(f28184,plain,
ifeq(codomain(h),codomain(compose(a,compose(a,h))),ifeq(domain(b),domain(a),compose(a,compose(compose(a,h),codomain(compose(a,compose(a,h))))),compose(a,compose(a,h))),compose(a,compose(a,h))) = compose(a,compose(a,h)),
inference(forward_demodulation,[status(thm)],[f19,f28183]) ).
fof(f28194,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(a,b))),compose(compose(a,codomain(X0)),compose(a,b))),compose(compose(a,codomain(X0)),compose(a,b))) = compose(compose(a,codomain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f3685]) ).
fof(f28195,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(a,h))),compose(compose(a,codomain(X0)),compose(a,h))),compose(compose(a,codomain(X0)),compose(a,h))) = compose(compose(a,codomain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f3685]) ).
fof(f28196,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),domain(X1))),compose(compose(a,codomain(X0)),domain(X1))),compose(compose(a,codomain(X0)),domain(X1))) = compose(compose(a,codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f33,f3685]) ).
fof(f28214,plain,
! [X0] : ifeq(codomain(X0),domain(codomain(compose(a,codomain(X0)))),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(compose(a,codomain(X0))))),compose(a,codomain(X0))),compose(compose(a,codomain(X0)),codomain(compose(a,codomain(X0))))) = compose(compose(a,codomain(X0)),codomain(compose(a,codomain(X0)))),
inference(paramodulation,[status(thm)],[f19,f3685]) ).
fof(f28327,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(a,codomain(X0))),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(compose(a,codomain(X0))))),compose(a,codomain(X0))),compose(compose(a,codomain(X0)),codomain(compose(a,codomain(X0))))) = compose(compose(a,codomain(X0)),codomain(compose(a,codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f28214]) ).
fof(f28328,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(a,codomain(X0))),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(compose(a,codomain(X0))))),compose(a,codomain(X0))),compose(a,codomain(X0))) = compose(compose(a,codomain(X0)),codomain(compose(a,codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f28327]) ).
fof(f28329,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(a,codomain(X0))),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),codomain(compose(a,codomain(X0))))),compose(a,codomain(X0))),compose(a,codomain(X0))) = compose(a,codomain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f28328]) ).
fof(f28752,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(compose(a,b),compose(a,h))),compose(compose(a,compose(a,b)),compose(a,h))),compose(compose(a,compose(a,b)),compose(a,h))) = compose(compose(a,compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f3642]) ).
fof(f28773,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(a,h))),compose(compose(a,compose(a,b)),compose(a,h))),compose(compose(a,compose(a,b)),compose(a,h))) = compose(compose(a,compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1163,f28752]) ).
fof(f28830,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(compose(a,b),domain(X0))),compose(compose(a,compose(a,b)),domain(X0))),compose(compose(a,compose(a,b)),domain(X0))) = compose(compose(a,compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f3643]) ).
fof(f28876,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),domain(X0))),compose(compose(a,compose(a,b)),domain(X0))),compose(compose(a,compose(a,b)),domain(X0))) = compose(compose(a,compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f28830]) ).
fof(f29535,plain,
ifeq(codomain(b),codomain(compose(a,compose(a,b))),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(compose(a,b),codomain(compose(a,compose(a,b))))),compose(a,compose(a,b))),compose(a,compose(a,b))) = compose(a,compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f3761]) ).
fof(f29564,plain,
ifeq(codomain(b),codomain(compose(a,compose(a,b))),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),codomain(compose(a,compose(a,b))))),compose(a,compose(a,b))),compose(a,compose(a,b))) = compose(a,compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f29535]) ).
fof(f29711,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),compose(a,b))),compose(compose(domain(X0),compose(a,h)),compose(a,b))),compose(compose(domain(X0),compose(a,h)),compose(a,b))) = compose(compose(domain(X0),compose(a,h)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4245]) ).
fof(f29712,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),compose(a,h))),compose(compose(domain(X0),compose(a,h)),compose(a,h))),compose(compose(domain(X0),compose(a,h)),compose(a,h))) = compose(compose(domain(X0),compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f4245]) ).
fof(f29713,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,h),domain(X0))),compose(compose(domain(X1),compose(a,h)),domain(X0))),compose(compose(domain(X1),compose(a,h)),domain(X0))) = compose(compose(domain(X1),compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f4245]) ).
fof(f29733,plain,
! [X0] : ifeq(codomain(h),domain(codomain(compose(domain(X0),compose(a,h)))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),codomain(compose(domain(X0),compose(a,h))))),compose(domain(X0),compose(a,h))),compose(compose(domain(X0),compose(a,h)),codomain(compose(domain(X0),compose(a,h))))) = compose(compose(domain(X0),compose(a,h)),codomain(compose(domain(X0),compose(a,h)))),
inference(paramodulation,[status(thm)],[f19,f4245]) ).
fof(f29812,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),compose(a,h))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),codomain(compose(domain(X0),compose(a,h))))),compose(domain(X0),compose(a,h))),compose(compose(domain(X0),compose(a,h)),codomain(compose(domain(X0),compose(a,h))))) = compose(compose(domain(X0),compose(a,h)),codomain(compose(domain(X0),compose(a,h)))),
inference(forward_demodulation,[status(thm)],[f17,f29733]) ).
fof(f29813,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),compose(a,h))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),codomain(compose(domain(X0),compose(a,h))))),compose(domain(X0),compose(a,h))),compose(domain(X0),compose(a,h))) = compose(compose(domain(X0),compose(a,h)),codomain(compose(domain(X0),compose(a,h)))),
inference(forward_demodulation,[status(thm)],[f19,f29812]) ).
fof(f29814,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),compose(a,h))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,h),codomain(compose(domain(X0),compose(a,h))))),compose(domain(X0),compose(a,h))),compose(domain(X0),compose(a,h))) = compose(domain(X0),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f19,f29813]) ).
fof(f29893,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(a,b))),compose(compose(domain(X1),codomain(X0)),compose(a,b))),compose(compose(domain(X1),codomain(X0)),compose(a,b))) = compose(compose(domain(X1),codomain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4247]) ).
fof(f29894,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(a,h))),compose(compose(domain(X1),codomain(X0)),compose(a,h))),compose(compose(domain(X1),codomain(X0)),compose(a,h))) = compose(compose(domain(X1),codomain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f4247]) ).
fof(f29895,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(domain(X2),codomain(X0),compose(domain(X2),compose(codomain(X0),domain(X1))),compose(compose(domain(X2),codomain(X0)),domain(X1))),compose(compose(domain(X2),codomain(X0)),domain(X1))) = compose(compose(domain(X2),codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f33,f4247]) ).
fof(f29926,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(compose(domain(X1),codomain(X0)))),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),codomain(compose(domain(X1),codomain(X0))))),compose(domain(X1),codomain(X0))),compose(compose(domain(X1),codomain(X0)),codomain(compose(domain(X1),codomain(X0))))) = compose(compose(domain(X1),codomain(X0)),codomain(compose(domain(X1),codomain(X0)))),
inference(paramodulation,[status(thm)],[f19,f4247]) ).
fof(f30101,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(domain(X1),codomain(X0))),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),codomain(compose(domain(X1),codomain(X0))))),compose(domain(X1),codomain(X0))),compose(compose(domain(X1),codomain(X0)),codomain(compose(domain(X1),codomain(X0))))) = compose(compose(domain(X1),codomain(X0)),codomain(compose(domain(X1),codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f29926]) ).
fof(f30102,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(domain(X1),codomain(X0))),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),codomain(compose(domain(X1),codomain(X0))))),compose(domain(X1),codomain(X0))),compose(domain(X1),codomain(X0))) = compose(compose(domain(X1),codomain(X0)),codomain(compose(domain(X1),codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f30101]) ).
fof(f30103,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(domain(X1),codomain(X0))),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),codomain(compose(domain(X1),codomain(X0))))),compose(domain(X1),codomain(X0))),compose(domain(X1),codomain(X0))) = compose(domain(X1),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f30102]) ).
fof(f30235,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(compose(a,b),compose(a,h))),compose(compose(domain(X0),compose(a,b)),compose(a,h))),compose(compose(domain(X0),compose(a,b)),compose(a,h))) = compose(compose(domain(X0),compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f4176]) ).
fof(f30237,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(g),compose(domain(X0),compose(g,compose(a,h))),compose(compose(domain(X0),g),compose(a,h))),compose(compose(domain(X0),g),compose(a,h))) = compose(compose(domain(X0),g),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f4176]) ).
fof(f30252,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(b),compose(domain(X0),compose(h,compose(a,h))),compose(compose(domain(X0),h),compose(a,h))),compose(compose(domain(X0),h),compose(a,h))) = compose(compose(domain(X0),h),compose(a,h)),
inference(paramodulation,[status(thm)],[f48,f4176]) ).
fof(f30289,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(a,h))),compose(compose(domain(X0),compose(a,b)),compose(a,h))),compose(compose(domain(X0),compose(a,b)),compose(a,h))) = compose(compose(domain(X0),compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1163,f30235]) ).
fof(f30291,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(b),compose(domain(X0),compose(g,compose(a,h))),compose(compose(domain(X0),g),compose(a,h))),compose(compose(domain(X0),g),compose(a,h))) = compose(compose(domain(X0),g),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f55,f30237]) ).
fof(f30467,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(compose(a,b)),compose(domain(X1),compose(compose(a,b),domain(X0))),compose(compose(domain(X1),compose(a,b)),domain(X0))),compose(compose(domain(X1),compose(a,b)),domain(X0))) = compose(compose(domain(X1),compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f4177]) ).
fof(f30469,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(g),compose(domain(X1),compose(g,domain(X0))),compose(compose(domain(X1),g),domain(X0))),compose(compose(domain(X1),g),domain(X0))) = compose(compose(domain(X1),g),domain(X0)),
inference(paramodulation,[status(thm)],[f359,f4177]) ).
fof(f30490,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(b),compose(domain(X1),compose(h,domain(X0))),compose(compose(domain(X1),h),domain(X0))),compose(compose(domain(X1),h),domain(X0))) = compose(compose(domain(X1),h),domain(X0)),
inference(paramodulation,[status(thm)],[f48,f4177]) ).
fof(f30546,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(a),compose(domain(X1),compose(compose(a,b),domain(X0))),compose(compose(domain(X1),compose(a,b)),domain(X0))),compose(compose(domain(X1),compose(a,b)),domain(X0))) = compose(compose(domain(X1),compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f30467]) ).
fof(f30548,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(domain(X1),domain(b),compose(domain(X1),compose(g,domain(X0))),compose(compose(domain(X1),g),domain(X0))),compose(compose(domain(X1),g),domain(X0))) = compose(compose(domain(X1),g),domain(X0)),
inference(forward_demodulation,[status(thm)],[f55,f30469]) ).
fof(f30822,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(b),compose(domain(X0),compose(g,compose(a,b))),compose(compose(domain(X0),g),compose(a,b))),compose(compose(domain(X0),g),compose(a,b))) = compose(compose(domain(X0),g),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4278]) ).
fof(f30844,plain,
! [X0] : ifeq(codomain(h),domain(codomain(compose(domain(X0),g))),ifeq(domain(X0),domain(b),compose(domain(X0),compose(g,codomain(compose(domain(X0),g)))),compose(domain(X0),g)),compose(compose(domain(X0),g),codomain(compose(domain(X0),g)))) = compose(compose(domain(X0),g),codomain(compose(domain(X0),g))),
inference(paramodulation,[status(thm)],[f19,f4278]) ).
fof(f30923,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),g)),ifeq(domain(X0),domain(b),compose(domain(X0),compose(g,codomain(compose(domain(X0),g)))),compose(domain(X0),g)),compose(compose(domain(X0),g),codomain(compose(domain(X0),g)))) = compose(compose(domain(X0),g),codomain(compose(domain(X0),g))),
inference(forward_demodulation,[status(thm)],[f17,f30844]) ).
fof(f30924,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),g)),ifeq(domain(X0),domain(b),compose(domain(X0),compose(g,codomain(compose(domain(X0),g)))),compose(domain(X0),g)),compose(domain(X0),g)) = compose(compose(domain(X0),g),codomain(compose(domain(X0),g))),
inference(forward_demodulation,[status(thm)],[f19,f30923]) ).
fof(f30925,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),g)),ifeq(domain(X0),domain(b),compose(domain(X0),compose(g,codomain(compose(domain(X0),g)))),compose(domain(X0),g)),compose(domain(X0),g)) = compose(domain(X0),g),
inference(forward_demodulation,[status(thm)],[f19,f30924]) ).
fof(f30998,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(b),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),h),compose(a,b))),compose(compose(domain(X0),h),compose(a,b))) = compose(compose(domain(X0),h),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4192]) ).
fof(f31019,plain,
! [X0] : ifeq(codomain(h),domain(codomain(compose(domain(X0),h))),ifeq(domain(X0),domain(b),compose(domain(X0),compose(h,codomain(compose(domain(X0),h)))),compose(domain(X0),h)),compose(compose(domain(X0),h),codomain(compose(domain(X0),h)))) = compose(compose(domain(X0),h),codomain(compose(domain(X0),h))),
inference(paramodulation,[status(thm)],[f19,f4192]) ).
fof(f31093,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),h)),ifeq(domain(X0),domain(b),compose(domain(X0),compose(h,codomain(compose(domain(X0),h)))),compose(domain(X0),h)),compose(compose(domain(X0),h),codomain(compose(domain(X0),h)))) = compose(compose(domain(X0),h),codomain(compose(domain(X0),h))),
inference(forward_demodulation,[status(thm)],[f17,f31019]) ).
fof(f31094,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),h)),ifeq(domain(X0),domain(b),compose(domain(X0),compose(h,codomain(compose(domain(X0),h)))),compose(domain(X0),h)),compose(domain(X0),h)) = compose(compose(domain(X0),h),codomain(compose(domain(X0),h))),
inference(forward_demodulation,[status(thm)],[f19,f31093]) ).
fof(f31095,plain,
! [X0] : ifeq(codomain(h),codomain(compose(domain(X0),h)),ifeq(domain(X0),domain(b),compose(domain(X0),compose(h,codomain(compose(domain(X0),h)))),compose(domain(X0),h)),compose(domain(X0),h)) = compose(domain(X0),h),
inference(forward_demodulation,[status(thm)],[f19,f31094]) ).
fof(f31431,plain,
! [X0] : ifeq(codomain(b),codomain(compose(domain(X0),compose(a,b))),ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(compose(a,b),codomain(compose(domain(X0),compose(a,b))))),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))) = compose(domain(X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f4360]) ).
fof(f31508,plain,
! [X0] : ifeq(codomain(b),codomain(compose(domain(X0),compose(a,b))),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),codomain(compose(domain(X0),compose(a,b))))),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))) = compose(domain(X0),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f31431]) ).
fof(f31906,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),domain(compose(a,b))),compose(a,b))) = compose(compose(compose(a,b),domain(compose(a,b))),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f5582]) ).
fof(f31907,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),domain(compose(a,h))),compose(a,h))) = compose(compose(compose(a,b),domain(compose(a,h))),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f5582]) ).
fof(f31920,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),domain(a)),compose(a,b))) = compose(compose(compose(a,b),domain(compose(a,b))),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f31906]) ).
fof(f31921,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),domain(a)),compose(a,b))) = compose(compose(compose(a,b),domain(a)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f31920]) ).
fof(f31922,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),domain(a)),compose(a,h))) = compose(compose(compose(a,b),domain(compose(a,h))),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f31907]) ).
fof(f31923,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),domain(a)),compose(a,h))) = compose(compose(compose(a,b),domain(a)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f345,f31922]) ).
fof(f32000,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),compose(a,b)),codomain(compose(a,b)))) = compose(compose(compose(a,b),compose(a,b)),codomain(compose(a,b))),
inference(paramodulation,[status(thm)],[f1163,f5714]) ).
fof(f32001,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),compose(a,h)),codomain(compose(a,h)))) = compose(compose(compose(a,b),compose(a,h)),codomain(compose(a,h))),
inference(paramodulation,[status(thm)],[f345,f5714]) ).
fof(f32016,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),compose(a,b)),codomain(b))) = compose(compose(compose(a,b),compose(a,b)),codomain(compose(a,b))),
inference(forward_demodulation,[status(thm)],[f959,f32000]) ).
fof(f32017,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(compose(a,b),compose(a,b)),codomain(b))) = compose(compose(compose(a,b),compose(a,b)),codomain(b)),
inference(forward_demodulation,[status(thm)],[f959,f32016]) ).
fof(f32018,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),compose(a,h)),codomain(h))) = compose(compose(compose(a,b),compose(a,h)),codomain(compose(a,h))),
inference(forward_demodulation,[status(thm)],[f367,f32001]) ).
fof(f32019,plain,
ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(compose(a,b),compose(a,h)),codomain(h))) = compose(compose(compose(a,b),compose(a,h)),codomain(h)),
inference(forward_demodulation,[status(thm)],[f367,f32018]) ).
fof(f32114,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(compose(a,b),compose(a,b)),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7530]) ).
fof(f32115,plain,
ifeq(codomain(h),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(compose(a,h),compose(a,b)),a,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7530]) ).
fof(f32116,plain,
ifeq(codomain(h),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(g,compose(a,b)),a,g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7530]) ).
fof(f32117,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(codomain(X0),compose(a,b)),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7530]) ).
fof(f32119,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(domain(X0),compose(a,b)),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7530]) ).
fof(f32134,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(a,compose(a,b)),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7533]) ).
fof(f32135,plain,
ifeq(codomain(h),domain(a),ifeq(domain(b),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(a,compose(a,b)),a,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7533]) ).
fof(f32136,plain,
ifeq(codomain(h),domain(a),ifeq(domain(b),domain(a),ifeq(compose(g,compose(a,b)),compose(a,compose(a,b)),a,g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7533]) ).
fof(f32137,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(a,compose(a,b)),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7533]) ).
fof(f32139,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(a,compose(a,b)),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7533]) ).
fof(f32154,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(compose(a,b),compose(a,b)),g,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7646]) ).
fof(f32155,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(compose(a,h),compose(a,b)),g,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7646]) ).
fof(f32157,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(codomain(X0),compose(a,b)),g,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7646]) ).
fof(f32158,plain,
ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(a,compose(a,b)),g,a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7646]) ).
fof(f32159,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(domain(X0),compose(a,b)),g,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7646]) ).
fof(f32173,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(g,compose(a,h))),compose(compose(compose(a,b),g),compose(a,h))),compose(compose(compose(a,b),g),compose(a,h))) = compose(compose(compose(a,b),g),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f4549]) ).
fof(f32174,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,compose(a,h))),compose(compose(compose(a,h),g),compose(a,h))),compose(compose(compose(a,h),g),compose(a,h))) = compose(compose(compose(a,h),g),compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f4549]) ).
fof(f32175,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(b),compose(g,compose(g,compose(a,h))),compose(compose(g,g),compose(a,h))),compose(compose(g,g),compose(a,h))) = compose(compose(g,g),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f4549]) ).
fof(f32176,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(g,compose(a,h))),compose(compose(codomain(X0),g),compose(a,h))),compose(compose(codomain(X0),g),compose(a,h))) = compose(compose(codomain(X0),g),compose(a,h)),
inference(paramodulation,[status(thm)],[f34,f4549]) ).
fof(f32179,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(domain(compose(g,compose(a,h)))),domain(b),compose(g,compose(a,h)),compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h))),compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h))) = compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h)),
inference(paramodulation,[status(thm)],[f18,f4549]) ).
fof(f32189,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(g,compose(a,h))),domain(b),compose(g,compose(a,h)),compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h))),compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h))) = compose(compose(domain(compose(g,compose(a,h))),g),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f32179]) ).
fof(f32216,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(g,compose(a,b)),g,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7725]) ).
fof(f32217,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(g,compose(a,b)),g,compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7725]) ).
fof(f32219,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(g,compose(a,b)),g,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7725]) ).
fof(f32220,plain,
ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(a,compose(a,b)),compose(g,compose(a,b)),g,a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7725]) ).
fof(f32221,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(g,compose(a,b)),g,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7725]) ).
fof(f32242,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(g,domain(X0))),compose(compose(compose(a,b),g),domain(X0))),compose(compose(compose(a,b),g),domain(X0))) = compose(compose(compose(a,b),g),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f4550]) ).
fof(f32243,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,domain(X0))),compose(compose(compose(a,h),g),domain(X0))),compose(compose(compose(a,h),g),domain(X0))) = compose(compose(compose(a,h),g),domain(X0)),
inference(paramodulation,[status(thm)],[f367,f4550]) ).
fof(f32244,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(b),compose(g,compose(g,domain(X0))),compose(compose(g,g),domain(X0))),compose(compose(g,g),domain(X0))) = compose(compose(g,g),domain(X0)),
inference(paramodulation,[status(thm)],[f359,f4550]) ).
fof(f32245,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(b),compose(codomain(X1),compose(g,domain(X0))),compose(compose(codomain(X1),g),domain(X0))),compose(compose(codomain(X1),g),domain(X0))) = compose(compose(codomain(X1),g),domain(X0)),
inference(paramodulation,[status(thm)],[f34,f4550]) ).
fof(f32248,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(compose(g,domain(X0)))),domain(b),compose(g,domain(X0)),compose(compose(domain(compose(g,domain(X0))),g),domain(X0))),compose(compose(domain(compose(g,domain(X0))),g),domain(X0))) = compose(compose(domain(compose(g,domain(X0))),g),domain(X0)),
inference(paramodulation,[status(thm)],[f18,f4550]) ).
fof(f32300,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(g,domain(X0))),domain(b),compose(g,domain(X0)),compose(compose(domain(compose(g,domain(X0))),g),domain(X0))),compose(compose(domain(compose(g,domain(X0))),g),domain(X0))) = compose(compose(domain(compose(g,domain(X0))),g),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f32248]) ).
fof(f32398,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,compose(a,b))),compose(compose(compose(a,h),g),compose(a,b))),compose(compose(compose(a,h),g),compose(a,b))) = compose(compose(compose(a,h),g),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4555]) ).
fof(f32406,plain,
ifeq(codomain(h),domain(codomain(compose(compose(a,h),g))),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,codomain(compose(compose(a,h),g)))),compose(compose(a,h),g)),compose(compose(compose(a,h),g),codomain(compose(compose(a,h),g)))) = compose(compose(compose(a,h),g),codomain(compose(compose(a,h),g))),
inference(paramodulation,[status(thm)],[f19,f4555]) ).
fof(f32415,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),g)),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,codomain(compose(compose(a,h),g)))),compose(compose(a,h),g)),compose(compose(compose(a,h),g),codomain(compose(compose(a,h),g)))) = compose(compose(compose(a,h),g),codomain(compose(compose(a,h),g))),
inference(forward_demodulation,[status(thm)],[f17,f32406]) ).
fof(f32416,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),g)),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,codomain(compose(compose(a,h),g)))),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(compose(a,h),g),codomain(compose(compose(a,h),g))),
inference(forward_demodulation,[status(thm)],[f19,f32415]) ).
fof(f32417,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),g)),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(g,codomain(compose(compose(a,h),g)))),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
inference(forward_demodulation,[status(thm)],[f19,f32416]) ).
fof(f32421,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(g,compose(a,b))),compose(compose(codomain(X0),g),compose(a,b))),compose(compose(codomain(X0),g),compose(a,b))) = compose(compose(codomain(X0),g),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4557]) ).
fof(f32441,plain,
! [X0] : ifeq(codomain(h),domain(codomain(compose(codomain(X0),g))),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(g,codomain(compose(codomain(X0),g)))),compose(codomain(X0),g)),compose(compose(codomain(X0),g),codomain(compose(codomain(X0),g)))) = compose(compose(codomain(X0),g),codomain(compose(codomain(X0),g))),
inference(paramodulation,[status(thm)],[f19,f4557]) ).
fof(f32514,plain,
! [X0] : ifeq(codomain(h),codomain(compose(codomain(X0),g)),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(g,codomain(compose(codomain(X0),g)))),compose(codomain(X0),g)),compose(compose(codomain(X0),g),codomain(compose(codomain(X0),g)))) = compose(compose(codomain(X0),g),codomain(compose(codomain(X0),g))),
inference(forward_demodulation,[status(thm)],[f17,f32441]) ).
fof(f32515,plain,
! [X0] : ifeq(codomain(h),codomain(compose(codomain(X0),g)),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(g,codomain(compose(codomain(X0),g)))),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(compose(codomain(X0),g),codomain(compose(codomain(X0),g))),
inference(forward_demodulation,[status(thm)],[f19,f32514]) ).
fof(f32516,plain,
! [X0] : ifeq(codomain(h),codomain(compose(codomain(X0),g)),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(g,codomain(compose(codomain(X0),g)))),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(codomain(X0),g),
inference(forward_demodulation,[status(thm)],[f19,f32515]) ).
fof(f32573,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(g,compose(a,b))),domain(b),compose(g,compose(a,b)),compose(compose(domain(compose(g,compose(a,b))),g),compose(a,b))),compose(compose(domain(compose(g,compose(a,b))),g),compose(a,b))) = compose(compose(domain(compose(g,compose(a,b))),g),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4574]) ).
fof(f32654,plain,
ifeq(codomain(h),codomain(compose(compose(a,b),g)),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(g,codomain(compose(compose(a,b),g)))),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
inference(paramodulation,[status(thm)],[f959,f4584]) ).
fof(f32656,plain,
ifeq(codomain(h),codomain(compose(g,g)),ifeq(codomain(h),domain(b),compose(g,compose(g,codomain(compose(g,g)))),compose(g,g)),compose(g,g)) = compose(g,g),
inference(paramodulation,[status(thm)],[f359,f4584]) ).
fof(f32761,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(h,compose(a,h))),compose(compose(compose(a,b),h),compose(a,h))),compose(compose(compose(a,b),h),compose(a,h))) = compose(compose(compose(a,b),h),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f4694]) ).
fof(f32762,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,compose(a,h))),compose(compose(compose(a,h),h),compose(a,h))),compose(compose(compose(a,h),h),compose(a,h))) = compose(compose(compose(a,h),h),compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f4694]) ).
fof(f32763,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(b),compose(g,compose(h,compose(a,h))),compose(compose(g,h),compose(a,h))),compose(compose(g,h),compose(a,h))) = compose(compose(g,h),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f4694]) ).
fof(f32764,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(h,compose(a,h))),compose(compose(codomain(X0),h),compose(a,h))),compose(compose(codomain(X0),h),compose(a,h))) = compose(compose(codomain(X0),h),compose(a,h)),
inference(paramodulation,[status(thm)],[f34,f4694]) ).
fof(f32767,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(domain(compose(h,compose(a,h)))),domain(b),compose(h,compose(a,h)),compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h))),compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h))) = compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h)),
inference(paramodulation,[status(thm)],[f18,f4694]) ).
fof(f32773,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(h,compose(a,h))),domain(b),compose(h,compose(a,h)),compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h))),compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h))) = compose(compose(domain(compose(h,compose(a,h))),h),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f32767]) ).
fof(f32797,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(h,domain(X0))),compose(compose(compose(a,b),h),domain(X0))),compose(compose(compose(a,b),h),domain(X0))) = compose(compose(compose(a,b),h),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f4695]) ).
fof(f32798,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,domain(X0))),compose(compose(compose(a,h),h),domain(X0))),compose(compose(compose(a,h),h),domain(X0))) = compose(compose(compose(a,h),h),domain(X0)),
inference(paramodulation,[status(thm)],[f367,f4695]) ).
fof(f32799,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(b),compose(g,compose(h,domain(X0))),compose(compose(g,h),domain(X0))),compose(compose(g,h),domain(X0))) = compose(compose(g,h),domain(X0)),
inference(paramodulation,[status(thm)],[f359,f4695]) ).
fof(f32800,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(b),compose(codomain(X1),compose(h,domain(X0))),compose(compose(codomain(X1),h),domain(X0))),compose(compose(codomain(X1),h),domain(X0))) = compose(compose(codomain(X1),h),domain(X0)),
inference(paramodulation,[status(thm)],[f34,f4695]) ).
fof(f32803,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(domain(compose(h,domain(X0)))),domain(b),compose(h,domain(X0)),compose(compose(domain(compose(h,domain(X0))),h),domain(X0))),compose(compose(domain(compose(h,domain(X0))),h),domain(X0))) = compose(compose(domain(compose(h,domain(X0))),h),domain(X0)),
inference(paramodulation,[status(thm)],[f18,f4695]) ).
fof(f32851,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(h,domain(X0))),domain(b),compose(h,domain(X0)),compose(compose(domain(compose(h,domain(X0))),h),domain(X0))),compose(compose(domain(compose(h,domain(X0))),h),domain(X0))) = compose(compose(domain(compose(h,domain(X0))),h),domain(X0)),
inference(forward_demodulation,[status(thm)],[f16,f32803]) ).
fof(f32941,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,compose(a,b))),compose(compose(compose(a,h),h),compose(a,b))),compose(compose(compose(a,h),h),compose(a,b))) = compose(compose(compose(a,h),h),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4700]) ).
fof(f32948,plain,
ifeq(codomain(h),domain(codomain(compose(compose(a,h),h))),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,codomain(compose(compose(a,h),h)))),compose(compose(a,h),h)),compose(compose(compose(a,h),h),codomain(compose(compose(a,h),h)))) = compose(compose(compose(a,h),h),codomain(compose(compose(a,h),h))),
inference(paramodulation,[status(thm)],[f19,f4700]) ).
fof(f32952,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),h)),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,codomain(compose(compose(a,h),h)))),compose(compose(a,h),h)),compose(compose(compose(a,h),h),codomain(compose(compose(a,h),h)))) = compose(compose(compose(a,h),h),codomain(compose(compose(a,h),h))),
inference(forward_demodulation,[status(thm)],[f17,f32948]) ).
fof(f32953,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),h)),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,codomain(compose(compose(a,h),h)))),compose(compose(a,h),h)),compose(compose(a,h),h)) = compose(compose(compose(a,h),h),codomain(compose(compose(a,h),h))),
inference(forward_demodulation,[status(thm)],[f19,f32952]) ).
fof(f32954,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),h)),ifeq(codomain(h),domain(b),compose(compose(a,h),compose(h,codomain(compose(compose(a,h),h)))),compose(compose(a,h),h)),compose(compose(a,h),h)) = compose(compose(a,h),h),
inference(forward_demodulation,[status(thm)],[f19,f32953]) ).
fof(f32958,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),h),compose(a,b))),compose(compose(codomain(X0),h),compose(a,b))) = compose(compose(codomain(X0),h),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4702]) ).
fof(f32977,plain,
! [X0] : ifeq(codomain(h),domain(codomain(compose(codomain(X0),h))),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(h,codomain(compose(codomain(X0),h)))),compose(codomain(X0),h)),compose(compose(codomain(X0),h),codomain(compose(codomain(X0),h)))) = compose(compose(codomain(X0),h),codomain(compose(codomain(X0),h))),
inference(paramodulation,[status(thm)],[f19,f4702]) ).
fof(f33045,plain,
! [X0] : ifeq(codomain(h),codomain(compose(codomain(X0),h)),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(h,codomain(compose(codomain(X0),h)))),compose(codomain(X0),h)),compose(compose(codomain(X0),h),codomain(compose(codomain(X0),h)))) = compose(compose(codomain(X0),h),codomain(compose(codomain(X0),h))),
inference(forward_demodulation,[status(thm)],[f17,f32977]) ).
fof(f33046,plain,
! [X0] : ifeq(codomain(h),codomain(compose(codomain(X0),h)),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(h,codomain(compose(codomain(X0),h)))),compose(codomain(X0),h)),compose(codomain(X0),h)) = compose(compose(codomain(X0),h),codomain(compose(codomain(X0),h))),
inference(forward_demodulation,[status(thm)],[f19,f33045]) ).
fof(f33047,plain,
! [X0] : ifeq(codomain(h),codomain(compose(codomain(X0),h)),ifeq(codomain(X0),domain(b),compose(codomain(X0),compose(h,codomain(compose(codomain(X0),h)))),compose(codomain(X0),h)),compose(codomain(X0),h)) = compose(codomain(X0),h),
inference(forward_demodulation,[status(thm)],[f19,f33046]) ).
fof(f33104,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(h,compose(a,b))),domain(b),compose(h,compose(a,b)),compose(compose(domain(compose(h,compose(a,b))),h),compose(a,b))),compose(compose(domain(compose(h,compose(a,b))),h),compose(a,b))) = compose(compose(domain(compose(h,compose(a,b))),h),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4716]) ).
fof(f33147,plain,
ifeq(codomain(h),codomain(compose(compose(a,b),h)),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(h,codomain(compose(compose(a,b),h)))),compose(compose(a,b),h)),compose(compose(a,b),h)) = compose(compose(a,b),h),
inference(paramodulation,[status(thm)],[f959,f4726]) ).
fof(f33149,plain,
ifeq(codomain(h),codomain(compose(g,h)),ifeq(codomain(h),domain(b),compose(g,compose(h,codomain(compose(g,h)))),compose(g,h)),compose(g,h)) = compose(g,h),
inference(paramodulation,[status(thm)],[f359,f4726]) ).
fof(f33231,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(a,h))),compose(compose(compose(a,b),codomain(X0)),compose(a,h))),compose(compose(compose(a,b),codomain(X0)),compose(a,h))) = compose(compose(compose(a,b),codomain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f4760]) ).
fof(f33232,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),compose(a,h))),compose(compose(compose(a,h),codomain(X0)),compose(a,h))),compose(compose(compose(a,h),codomain(X0)),compose(a,h))) = compose(compose(compose(a,h),codomain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f4760]) ).
fof(f33233,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),compose(a,h))),compose(compose(g,codomain(X0)),compose(a,h))),compose(compose(g,codomain(X0)),compose(a,h))) = compose(compose(g,codomain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f4760]) ).
fof(f33234,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(a,h))),compose(compose(codomain(X1),codomain(X0)),compose(a,h))),compose(compose(codomain(X1),codomain(X0)),compose(a,h))) = compose(compose(codomain(X1),codomain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f34,f4760]) ).
fof(f33243,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(compose(codomain(X0),compose(a,h)))),codomain(X0),compose(codomain(X0),compose(a,h)),compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h))),compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h))) = compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h)),
inference(paramodulation,[status(thm)],[f18,f4760]) ).
fof(f33336,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(compose(codomain(X0),compose(a,h))),codomain(X0),compose(codomain(X0),compose(a,h)),compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h))),compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h))) = compose(compose(domain(compose(codomain(X0),compose(a,h))),codomain(X0)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f16,f33243]) ).
fof(f33484,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),domain(X1))),compose(compose(compose(a,b),codomain(X0)),domain(X1))),compose(compose(compose(a,b),codomain(X0)),domain(X1))) = compose(compose(compose(a,b),codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f959,f4761]) ).
fof(f33485,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),domain(X1))),compose(compose(compose(a,h),codomain(X0)),domain(X1))),compose(compose(compose(a,h),codomain(X0)),domain(X1))) = compose(compose(compose(a,h),codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f367,f4761]) ).
fof(f33486,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),domain(X1))),compose(compose(g,codomain(X0)),domain(X1))),compose(compose(g,codomain(X0)),domain(X1))) = compose(compose(g,codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f359,f4761]) ).
fof(f33487,plain,
! [X0,X1,X2] : ifeq(codomain(X0),domain(X1),ifeq(codomain(X2),codomain(X0),compose(codomain(X2),compose(codomain(X0),domain(X1))),compose(compose(codomain(X2),codomain(X0)),domain(X1))),compose(compose(codomain(X2),codomain(X0)),domain(X1))) = compose(compose(codomain(X2),codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f34,f4761]) ).
fof(f33496,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(domain(compose(codomain(X0),domain(X1)))),codomain(X0),compose(codomain(X0),domain(X1)),compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1))),compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1))) = compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1)),
inference(paramodulation,[status(thm)],[f18,f4761]) ).
fof(f33631,plain,
! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(compose(codomain(X0),domain(X1))),codomain(X0),compose(codomain(X0),domain(X1)),compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1))),compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1))) = compose(compose(domain(compose(codomain(X0),domain(X1))),codomain(X0)),domain(X1)),
inference(forward_demodulation,[status(thm)],[f16,f33496]) ).
fof(f33838,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(compose(a,b),compose(a,b)),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7558]) ).
fof(f33839,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(compose(a,h),compose(a,b)),domain(X0),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7558]) ).
fof(f33840,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(g,compose(a,b)),domain(X0),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7558]) ).
fof(f33841,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X1),compose(a,b)),compose(codomain(X0),compose(a,b)),domain(X1),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7558]) ).
fof(f33842,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(a,compose(a,b)),domain(X0),a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7558]) ).
fof(f33843,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X1),compose(a,b)),compose(domain(X0),compose(a,b)),domain(X1),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7558]) ).
fof(f33934,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),compose(a,b))),compose(compose(compose(a,h),codomain(X0)),compose(a,b))),compose(compose(compose(a,h),codomain(X0)),compose(a,b))) = compose(compose(compose(a,h),codomain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4767]) ).
fof(f33955,plain,
! [X0] : ifeq(codomain(X0),domain(codomain(compose(compose(a,h),codomain(X0)))),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),codomain(compose(compose(a,h),codomain(X0))))),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),codomain(X0)),codomain(compose(compose(a,h),codomain(X0))))) = compose(compose(compose(a,h),codomain(X0)),codomain(compose(compose(a,h),codomain(X0)))),
inference(paramodulation,[status(thm)],[f19,f4767]) ).
fof(f34078,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(compose(a,h),codomain(X0))),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),codomain(compose(compose(a,h),codomain(X0))))),compose(compose(a,h),codomain(X0))),compose(compose(compose(a,h),codomain(X0)),codomain(compose(compose(a,h),codomain(X0))))) = compose(compose(compose(a,h),codomain(X0)),codomain(compose(compose(a,h),codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f33955]) ).
fof(f34079,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(compose(a,h),codomain(X0))),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),codomain(compose(compose(a,h),codomain(X0))))),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(compose(a,h),codomain(X0)),codomain(compose(compose(a,h),codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f34078]) ).
fof(f34080,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(compose(a,h),codomain(X0))),ifeq(codomain(h),codomain(X0),compose(compose(a,h),compose(codomain(X0),codomain(compose(compose(a,h),codomain(X0))))),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f34079]) ).
fof(f34168,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(domain(X0),compose(a,b)),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7561]) ).
fof(f34169,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(domain(X0),compose(a,b)),domain(X0),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7561]) ).
fof(f34170,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(g,compose(a,b)),compose(domain(X0),compose(a,b)),domain(X0),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7561]) ).
fof(f34171,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(domain(X1),compose(a,b)),domain(X1),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7561]) ).
fof(f34172,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(a),ifeq(compose(a,compose(a,b)),compose(domain(X0),compose(a,b)),domain(X0),a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7561]) ).
fof(f34173,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(domain(X1),compose(a,b)),domain(X1),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7561]) ).
fof(f34259,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(compose(a,b),compose(a,b)),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7647]) ).
fof(f34260,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(compose(a,h),compose(a,b)),codomain(X0),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7647]) ).
fof(f34261,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(g,compose(a,b)),codomain(X0),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7647]) ).
fof(f34262,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X1),compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X1),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7647]) ).
fof(f34263,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(a,compose(a,b)),codomain(X0),a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7647]) ).
fof(f34264,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X1),compose(a,b)),compose(domain(X0),compose(a,b)),codomain(X1),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7647]) ).
fof(f34332,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7726]) ).
fof(f34333,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X0),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f367,f7726]) ).
fof(f34334,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(g,compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X0),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f7726]) ).
fof(f34335,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(codomain(X1),compose(a,b)),codomain(X1),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f34,f7726]) ).
fof(f34336,plain,
! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(a,compose(a,b)),compose(codomain(X0),compose(a,b)),codomain(X0),a),a),a) = a,
inference(paramodulation,[status(thm)],[f24,f7726]) ).
fof(f34337,plain,
! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(codomain(X1),compose(a,b)),codomain(X1),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f16,f7726]) ).
fof(f34531,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(a,b))),compose(compose(codomain(X1),codomain(X0)),compose(a,b))),compose(compose(codomain(X1),codomain(X0)),compose(a,b))) = compose(compose(codomain(X1),codomain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4769]) ).
fof(f34564,plain,
! [X0,X1] : ifeq(codomain(X0),domain(codomain(compose(codomain(X1),codomain(X0)))),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),codomain(compose(codomain(X1),codomain(X0))))),compose(codomain(X1),codomain(X0))),compose(compose(codomain(X1),codomain(X0)),codomain(compose(codomain(X1),codomain(X0))))) = compose(compose(codomain(X1),codomain(X0)),codomain(compose(codomain(X1),codomain(X0)))),
inference(paramodulation,[status(thm)],[f19,f4769]) ).
fof(f34741,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(codomain(X1),codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),codomain(compose(codomain(X1),codomain(X0))))),compose(codomain(X1),codomain(X0))),compose(compose(codomain(X1),codomain(X0)),codomain(compose(codomain(X1),codomain(X0))))) = compose(compose(codomain(X1),codomain(X0)),codomain(compose(codomain(X1),codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f17,f34564]) ).
fof(f34742,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(codomain(X1),codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),codomain(compose(codomain(X1),codomain(X0))))),compose(codomain(X1),codomain(X0))),compose(codomain(X1),codomain(X0))) = compose(compose(codomain(X1),codomain(X0)),codomain(compose(codomain(X1),codomain(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f34741]) ).
fof(f34743,plain,
! [X0,X1] : ifeq(codomain(X0),codomain(compose(codomain(X1),codomain(X0))),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),codomain(compose(codomain(X1),codomain(X0))))),compose(codomain(X1),codomain(X0))),compose(codomain(X1),codomain(X0))) = compose(codomain(X1),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f19,f34742]) ).
fof(f35289,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(compose(codomain(X0),compose(a,b))),codomain(X0),compose(codomain(X0),compose(a,b)),compose(compose(domain(compose(codomain(X0),compose(a,b))),codomain(X0)),compose(a,b))),compose(compose(domain(compose(codomain(X0),compose(a,b))),codomain(X0)),compose(a,b))) = compose(compose(domain(compose(codomain(X0),compose(a,b))),codomain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4875]) ).
fof(f35860,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(compose(a,b),codomain(X0))),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),codomain(compose(compose(a,b),codomain(X0))))),compose(compose(a,b),codomain(X0))),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f4915]) ).
fof(f35862,plain,
! [X0] : ifeq(codomain(X0),codomain(compose(g,codomain(X0))),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),codomain(compose(g,codomain(X0))))),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f4915]) ).
fof(f36362,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(compose(a,h),compose(a,b))),domain(a),compose(compose(a,h),compose(a,b)),compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b))),compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b))) = compose(compose(domain(compose(compose(a,h),compose(a,b))),compose(a,h)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f5100]) ).
fof(f36363,plain,
ifeq(codomain(h),domain(a),ifeq(domain(compose(compose(a,h),compose(a,h))),domain(a),compose(compose(a,h),compose(a,h)),compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h))),compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h))) = compose(compose(domain(compose(compose(a,h),compose(a,h))),compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f5100]) ).
fof(f36364,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(domain(compose(compose(a,h),domain(X0))),domain(a),compose(compose(a,h),domain(X0)),compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0))),compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0))) = compose(compose(domain(compose(compose(a,h),domain(X0))),compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f33,f5100]) ).
fof(f36743,plain,
ifeq(codomain(b),domain(a),ifeq(domain(compose(compose(a,b),compose(a,h))),domain(compose(a,b)),compose(compose(a,b),compose(a,h)),compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h))),compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h))) = compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f5030]) ).
fof(f36763,plain,
ifeq(codomain(b),domain(a),ifeq(domain(compose(compose(a,b),compose(a,h))),domain(a),compose(compose(a,b),compose(a,h)),compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h))),compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h))) = compose(compose(domain(compose(compose(a,b),compose(a,h))),compose(a,b)),compose(a,h)),
inference(forward_demodulation,[status(thm)],[f1163,f36743]) ).
fof(f37052,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(a,b),domain(X0))),domain(compose(a,b)),compose(compose(a,b),domain(X0)),compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0))),compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0))) = compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f5031]) ).
fof(f37118,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(a,b),domain(X0))),domain(a),compose(compose(a,b),domain(X0)),compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0))),compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0))) = compose(compose(domain(compose(compose(a,b),domain(X0))),compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f37052]) ).
fof(f38232,plain,
ifeq(codomain(h),codomain(compose(compose(a,b),compose(a,h))),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),codomain(compose(compose(a,b),compose(a,h))))),compose(compose(a,b),compose(a,h))),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f5986]) ).
fof(f38233,plain,
ifeq(codomain(h),codomain(compose(compose(a,h),compose(a,h))),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),codomain(compose(compose(a,h),compose(a,h))))),compose(compose(a,h),compose(a,h))),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)),
inference(paramodulation,[status(thm)],[f367,f5986]) ).
fof(f38234,plain,
ifeq(codomain(h),codomain(compose(g,compose(a,h))),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),codomain(compose(g,compose(a,h))))),compose(g,compose(a,h))),compose(g,compose(a,h))) = compose(g,compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f5986]) ).
fof(f38235,plain,
! [X0] : ifeq(codomain(h),codomain(compose(codomain(X0),compose(a,h))),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),codomain(compose(codomain(X0),compose(a,h))))),compose(codomain(X0),compose(a,h))),compose(codomain(X0),compose(a,h))) = compose(codomain(X0),compose(a,h)),
inference(paramodulation,[status(thm)],[f34,f5986]) ).
fof(f38304,plain,
ifeq(codomain(b),codomain(compose(compose(a,h),compose(a,b))),ifeq(codomain(h),domain(compose(a,b)),compose(compose(a,h),compose(compose(a,b),codomain(compose(compose(a,h),compose(a,b))))),compose(compose(a,h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f5933]) ).
fof(f38324,plain,
ifeq(codomain(b),codomain(compose(compose(a,h),compose(a,b))),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),codomain(compose(compose(a,h),compose(a,b))))),compose(compose(a,h),compose(a,b))),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f38304]) ).
fof(f38408,plain,
! [X0] : ifeq(codomain(b),codomain(compose(codomain(X0),compose(a,b))),ifeq(codomain(X0),domain(compose(a,b)),compose(codomain(X0),compose(compose(a,b),codomain(compose(codomain(X0),compose(a,b))))),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))) = compose(codomain(X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f5935]) ).
fof(f38464,plain,
! [X0] : ifeq(codomain(b),codomain(compose(codomain(X0),compose(a,b))),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),codomain(compose(codomain(X0),compose(a,b))))),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))) = compose(codomain(X0),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f38408]) ).
fof(f38755,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(compose(a,b)),compose(g,compose(compose(a,b),X0)),compose(compose(g,compose(a,b)),X0)),compose(compose(g,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f959,f368]) ).
fof(f38761,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(g,compose(X0,compose(a,b))),compose(compose(g,X0),compose(a,b))),compose(compose(g,X0),compose(a,b))) = compose(compose(g,X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f368]) ).
fof(f38794,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),X0)),compose(compose(g,compose(a,b)),X0)),compose(compose(g,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f38755]) ).
fof(f38884,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(a,compose(a,b)),compose(a,b),a),a),a) = a,
inference(paramodulation,[status(thm)],[f959,f7012]) ).
fof(f38885,plain,
ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(a,compose(a,b)),compose(a,h),a),a),a) = a,
inference(paramodulation,[status(thm)],[f367,f7012]) ).
fof(f38902,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(a,compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),a),a),a) = a,
inference(paramodulation,[status(thm)],[f959,f7013]) ).
fof(f38903,plain,
ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(a,compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),a),a),a) = a,
inference(paramodulation,[status(thm)],[f367,f7013]) ).
fof(f38920,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(g,compose(a,b)),compose(a,b),g),g),g) = g,
inference(paramodulation,[status(thm)],[f959,f7640]) ).
fof(f38921,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(g,compose(a,b)),compose(a,h),g),g),g) = g,
inference(paramodulation,[status(thm)],[f367,f7640]) ).
fof(f38938,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(g,compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),g),g),g) = g,
inference(paramodulation,[status(thm)],[f959,f7719]) ).
fof(f38939,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),g),g),g) = g,
inference(paramodulation,[status(thm)],[f367,f7719]) ).
fof(f38956,plain,
ifeq(codomain(b),codomain(compose(g,compose(a,b))),ifeq(codomain(h),domain(compose(a,b)),compose(g,compose(compose(a,b),codomain(compose(g,compose(a,b))))),compose(g,compose(a,b))),compose(g,compose(a,b))) = compose(g,compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f5934]) ).
fof(f38976,plain,
ifeq(codomain(b),codomain(compose(g,compose(a,b))),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),codomain(compose(g,compose(a,b))))),compose(g,compose(a,b))),compose(g,compose(a,b))) = compose(g,compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f38956]) ).
fof(f39066,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(g,compose(a,b)),X0,g,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f1482]) ).
fof(f39068,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(g,compose(a,b)),X0,g,g),g),g),g) = g,
inference(paramodulation,[status(thm)],[f359,f1482]) ).
fof(f39683,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(domain(X0),compose(a,b)),compose(a,h),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f15,f7163]) ).
fof(f39692,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f15,f7163]) ).
fof(f41211,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(domain(X0),compose(a,b)),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f959,f7168]) ).
fof(f41428,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(domain(X0),compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f959,f7177]) ).
fof(f42294,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,b),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f959,f7639]) ).
fof(f42317,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(codomain(X0),compose(a,b)),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f959,f7641]) ).
fof(f42318,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(codomain(X0),compose(a,b)),compose(a,h),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f367,f7641]) ).
fof(f42507,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,h),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7645]) ).
fof(f42529,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,h),compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),compose(a,h)),compose(a,h)),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f959,f7718]) ).
fof(f42554,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(compose(a,b),compose(a,b)),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f959,f7720]) ).
fof(f42555,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(codomain(X0),compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f367,f7720]) ).
fof(f42746,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),ifeq(compose(compose(a,b),compose(a,b)),compose(compose(a,h),compose(a,b)),compose(a,h),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f7724]) ).
fof(f43110,plain,
! [X0,X1] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(g,compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,g),g),g),g) = g,
inference(forward_demodulation,[status(thm)],[f1163,f389]) ).
fof(f43111,plain,
! [X0,X1] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(g,compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,g),g),g),g) = g,
inference(forward_demodulation,[status(thm)],[f1163,f43110]) ).
fof(f43112,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(g,compose(a,b)),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),g),g),g),g) = g,
inference(paramodulation,[status(thm)],[f959,f43111]) ).
fof(f43292,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(compose(a,b)),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(compose(a,b),compose(a,b)),X1,compose(a,b),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f1023]) ).
fof(f43293,plain,
! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(X0,compose(a,b)),X1,ifeq(compose(compose(a,b),compose(a,b)),X1,compose(a,b),X0),X0),X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1163,f43292]) ).
fof(f43294,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X0,ifeq(compose(compose(a,b),compose(a,b)),X0,compose(a,b),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f959,f43293]) ).
fof(f43313,plain,
! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(compose(a,b)),ifeq(compose(compose(a,b),compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(forward_demodulation,[status(thm)],[f1163,f1024]) ).
fof(f43314,plain,
! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),ifeq(compose(compose(a,b),compose(a,b)),X1,ifeq(compose(X0,compose(a,b)),X1,X0,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
inference(forward_demodulation,[status(thm)],[f1163,f43313]) ).
fof(f43331,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(compose(a,b)),compose(compose(a,b),compose(compose(a,b),X0)),compose(compose(compose(a,b),compose(a,b)),X0)),compose(compose(compose(a,b),compose(a,b)),X0)) = compose(compose(compose(a,b),compose(a,b)),X0),
inference(paramodulation,[status(thm)],[f959,f1025]) ).
fof(f43337,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(a,b))),compose(compose(compose(a,b),X0),compose(a,b))),compose(compose(compose(a,b),X0),compose(a,b))) = compose(compose(compose(a,b),X0),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f1025]) ).
fof(f43370,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),X0)),compose(compose(compose(a,b),compose(a,b)),X0)),compose(compose(compose(a,b),compose(a,b)),X0)) = compose(compose(compose(a,b),compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f43331]) ).
fof(f43460,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(X1,compose(compose(a,b),X0)),compose(compose(X1,compose(a,b)),X0)),compose(compose(X1,compose(a,b)),X0)) = compose(compose(X1,compose(a,b)),X0),
inference(forward_demodulation,[status(thm)],[f1163,f1026]) ).
fof(f43461,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(a,b))),compose(compose(X0,compose(a,b)),compose(a,b))),compose(compose(X0,compose(a,b)),compose(a,b))) = compose(compose(X0,compose(a,b)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f43460]) ).
fof(f43514,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(h),domain(compose(a,b)),compose(g,compose(compose(a,b),g)),compose(compose(g,compose(a,b)),g)),compose(compose(g,compose(a,b)),g)) = compose(compose(g,compose(a,b)),g),
inference(paramodulation,[status(thm)],[f959,f2485]) ).
fof(f43533,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),g)),compose(compose(g,compose(a,b)),g)),compose(compose(g,compose(a,b)),g)) = compose(compose(g,compose(a,b)),g),
inference(forward_demodulation,[status(thm)],[f1163,f43514]) ).
fof(f43578,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(h),domain(compose(a,b)),compose(g,compose(compose(a,b),h)),compose(compose(g,compose(a,b)),h)),compose(compose(g,compose(a,b)),h)) = compose(compose(g,compose(a,b)),h),
inference(paramodulation,[status(thm)],[f959,f2868]) ).
fof(f43597,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),h)),compose(compose(g,compose(a,b)),h)),compose(compose(g,compose(a,b)),h)) = compose(compose(g,compose(a,b)),h),
inference(forward_demodulation,[status(thm)],[f1163,f43578]) ).
fof(f44586,plain,
ifeq(domain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(a,b))),compose(compose(compose(a,b),a),compose(a,b))),compose(compose(compose(a,b),a),compose(a,b))) = compose(compose(compose(a,b),a),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f1799]) ).
fof(f44588,plain,
ifeq(domain(b),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(a,compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
inference(paramodulation,[status(thm)],[f359,f1799]) ).
fof(f44674,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(a,b))),compose(compose(compose(a,b),domain(X0)),compose(a,b))),compose(compose(compose(a,b),domain(X0)),compose(a,b))) = compose(compose(compose(a,b),domain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f2148]) ).
fof(f44676,plain,
! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(h),domain(X0),compose(g,compose(domain(X0),compose(a,b))),compose(compose(g,domain(X0)),compose(a,b))),compose(compose(g,domain(X0)),compose(a,b))) = compose(compose(g,domain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f359,f2148]) ).
fof(f45345,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),g)),compose(compose(compose(a,b),compose(a,b)),g)),compose(compose(compose(a,b),compose(a,b)),g)) = compose(compose(compose(a,b),compose(a,b)),g),
inference(paramodulation,[status(thm)],[f959,f2525]) ).
fof(f45375,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(b),compose(g,compose(g,compose(a,b))),compose(compose(g,g),compose(a,b))),compose(compose(g,g),compose(a,b))) = compose(compose(g,g),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4556]) ).
fof(f45462,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(b),compose(g,compose(h,compose(a,b))),compose(compose(g,h),compose(a,b))),compose(compose(g,h),compose(a,b))) = compose(compose(g,h),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4701]) ).
fof(f45479,plain,
ifeq(codomain(b),domain(b),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),h)),compose(compose(compose(a,b),compose(a,b)),h)),compose(compose(compose(a,b),compose(a,b)),h)) = compose(compose(compose(a,b),compose(a,b)),h),
inference(paramodulation,[status(thm)],[f959,f2908]) ).
fof(f45958,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),codomain(X0))),compose(compose(compose(a,b),compose(a,b)),codomain(X0))),compose(compose(compose(a,b),compose(a,b)),codomain(X0))) = compose(compose(compose(a,b),compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f959,f3154]) ).
fof(f45960,plain,
! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0)),
inference(paramodulation,[status(thm)],[f359,f3154]) ).
fof(f47666,plain,
ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(a,b))),compose(compose(a,compose(a,b)),compose(a,b))),compose(compose(a,compose(a,b)),compose(a,b))) = compose(compose(a,compose(a,b)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f3679]) ).
fof(f47773,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(h),codomain(X0),compose(g,compose(codomain(X0),compose(a,b))),compose(compose(g,codomain(X0)),compose(a,b))),compose(compose(g,codomain(X0)),compose(a,b))) = compose(compose(g,codomain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4768]) ).
fof(f48006,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(compose(a,b)),compose(g,compose(compose(a,b),domain(X0))),compose(compose(g,compose(a,b)),domain(X0))),compose(compose(g,compose(a,b)),domain(X0))) = compose(compose(g,compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f8534]) ).
fof(f48007,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(compose(a,h)),compose(g,compose(compose(a,h),domain(X0))),compose(compose(g,compose(a,h)),domain(X0))),compose(compose(g,compose(a,h)),domain(X0))) = compose(compose(g,compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f367,f8534]) ).
fof(f48049,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),domain(X0))),compose(compose(g,compose(a,b)),domain(X0))),compose(compose(g,compose(a,b)),domain(X0))) = compose(compose(g,compose(a,b)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1163,f48006]) ).
fof(f48050,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),domain(X0))),compose(compose(g,compose(a,h)),domain(X0))),compose(compose(g,compose(a,h)),domain(X0))) = compose(compose(g,compose(a,h)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f345,f48007]) ).
fof(f48188,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(a,b))),compose(compose(domain(X0),compose(a,b)),compose(a,b))),compose(compose(domain(X0),compose(a,b)),compose(a,b))) = compose(compose(domain(X0),compose(a,b)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f4244]) ).
fof(f49121,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(g,compose(a,b))),compose(compose(compose(a,b),g),compose(a,b))),compose(compose(compose(a,b),g),compose(a,b))) = compose(compose(compose(a,b),g),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f4548]) ).
fof(f50693,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(b),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),h),compose(a,b))),compose(compose(compose(a,b),h),compose(a,b))) = compose(compose(compose(a,b),h),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f4693]) ).
fof(f50747,plain,
! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(a,b))),compose(compose(compose(a,b),codomain(X0)),compose(a,b))),compose(compose(compose(a,b),codomain(X0)),compose(a,b))) = compose(compose(compose(a,b),codomain(X0)),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f4759]) ).
fof(f51215,plain,
ifeq(codomain(b),domain(a),ifeq(domain(compose(compose(a,b),compose(a,b))),domain(a),compose(compose(a,b),compose(a,b)),compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b))),compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b))) = compose(compose(domain(compose(compose(a,b),compose(a,b))),compose(a,b)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f5099]) ).
fof(f51405,plain,
ifeq(codomain(b),codomain(compose(compose(a,b),compose(a,b))),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),codomain(compose(compose(a,b),compose(a,b))))),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f5985]) ).
fof(f52335,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),domain(X0))),compose(compose(compose(a,b),compose(a,b)),domain(X0))),compose(compose(compose(a,b),compose(a,b)),domain(X0))) = compose(compose(compose(a,b),compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f8592]) ).
fof(f52336,plain,
! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),domain(X0))),compose(compose(compose(a,h),compose(a,b)),domain(X0))),compose(compose(compose(a,h),compose(a,b)),domain(X0))) = compose(compose(compose(a,h),compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f367,f8592]) ).
fof(f52338,plain,
! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,b),domain(X0))),compose(compose(codomain(X1),compose(a,b)),domain(X0))),compose(compose(codomain(X1),compose(a,b)),domain(X0))) = compose(compose(codomain(X1),compose(a,b)),domain(X0)),
inference(paramodulation,[status(thm)],[f34,f8592]) ).
fof(f52485,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),domain(X0))),compose(compose(compose(a,b),compose(a,h)),domain(X0))),compose(compose(compose(a,b),compose(a,h)),domain(X0))) = compose(compose(compose(a,b),compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f959,f8593]) ).
fof(f52486,plain,
! [X0] : ifeq(codomain(h),domain(X0),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),domain(X0))),compose(compose(compose(a,h),compose(a,h)),domain(X0))),compose(compose(compose(a,h),compose(a,h)),domain(X0))) = compose(compose(compose(a,h),compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f367,f8593]) ).
fof(f52488,plain,
! [X0,X1] : ifeq(codomain(h),domain(X0),ifeq(codomain(X1),domain(a),compose(codomain(X1),compose(compose(a,h),domain(X0))),compose(compose(codomain(X1),compose(a,h)),domain(X0))),compose(compose(codomain(X1),compose(a,h)),domain(X0))) = compose(compose(codomain(X1),compose(a,h)),domain(X0)),
inference(paramodulation,[status(thm)],[f34,f8593]) ).
fof(f53355,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(a,b))),compose(compose(codomain(X0),compose(a,b)),compose(a,b))),compose(compose(codomain(X0),compose(a,b)),compose(a,b))) = compose(compose(codomain(X0),compose(a,b)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f8986]) ).
fof(f53356,plain,
! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(a,h))),compose(compose(codomain(X0),compose(a,b)),compose(a,h))),compose(compose(codomain(X0),compose(a,b)),compose(a,h))) = compose(compose(codomain(X0),compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f8986]) ).
fof(f53498,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),compose(a,b))),compose(compose(codomain(X0),compose(a,h)),compose(a,b))),compose(compose(codomain(X0),compose(a,h)),compose(a,b))) = compose(compose(codomain(X0),compose(a,h)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f8987]) ).
fof(f53499,plain,
! [X0] : ifeq(codomain(h),domain(a),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,h),compose(a,h))),compose(compose(codomain(X0),compose(a,h)),compose(a,h))),compose(compose(codomain(X0),compose(a,h)),compose(a,h))) = compose(compose(codomain(X0),compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f8987]) ).
fof(f53999,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,h),compose(a,b)),compose(a,b))),compose(compose(compose(a,h),compose(a,b)),compose(a,b))) = compose(compose(compose(a,h),compose(a,b)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f10369]) ).
fof(f54000,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,h),compose(a,b)),compose(a,h))),compose(compose(compose(a,h),compose(a,b)),compose(a,h))) = compose(compose(compose(a,h),compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f10369]) ).
fof(f54022,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),compose(a,b))),compose(compose(compose(a,h),compose(a,h)),compose(a,b))),compose(compose(compose(a,h),compose(a,h)),compose(a,b))) = compose(compose(compose(a,h),compose(a,h)),compose(a,b)),
inference(paramodulation,[status(thm)],[f1163,f10370]) ).
fof(f54023,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(compose(a,h),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,h),compose(a,h)),compose(a,h))),compose(compose(compose(a,h),compose(a,h)),compose(a,h))) = compose(compose(compose(a,h),compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f345,f10370]) ).
fof(f57535,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),compose(a,b))),compose(compose(compose(a,b),compose(a,h)),compose(a,b))),compose(compose(compose(a,b),compose(a,h)),compose(a,b))) = compose(compose(compose(a,b),compose(a,h)),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f10458]) ).
fof(f57537,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),compose(a,b))),compose(compose(g,compose(a,h)),compose(a,b))),compose(compose(g,compose(a,h)),compose(a,b))) = compose(compose(g,compose(a,h)),compose(a,b)),
inference(paramodulation,[status(thm)],[f359,f10458]) ).
fof(f57565,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,h),compose(a,h))),compose(compose(compose(a,b),compose(a,h)),compose(a,h))),compose(compose(compose(a,b),compose(a,h)),compose(a,h))) = compose(compose(compose(a,b),compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f10459]) ).
fof(f57567,plain,
ifeq(codomain(h),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,h),compose(a,h))),compose(compose(g,compose(a,h)),compose(a,h))),compose(compose(g,compose(a,h)),compose(a,h))) = compose(compose(g,compose(a,h)),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f10459]) ).
fof(f62863,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(a,h))),compose(compose(compose(a,b),compose(a,b)),compose(a,h))),compose(compose(compose(a,b),compose(a,b)),compose(a,h))) = compose(compose(compose(a,b),compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f959,f11251]) ).
fof(f62865,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),compose(a,h))),compose(compose(g,compose(a,b)),compose(a,h))),compose(compose(g,compose(a,b)),compose(a,h))) = compose(compose(g,compose(a,b)),compose(a,h)),
inference(paramodulation,[status(thm)],[f359,f11251]) ).
fof(f88415,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(compose(a,b)),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(g,compose(a,b)),compose(a,b))),compose(compose(g,compose(a,b)),compose(a,b))) = compose(compose(g,compose(a,b)),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f38761]) ).
fof(f88433,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(h),domain(a),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(g,compose(a,b)),compose(a,b))),compose(compose(g,compose(a,b)),compose(a,b))) = compose(compose(g,compose(a,b)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f88415]) ).
fof(f111244,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(compose(a,b)),compose(compose(a,b),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,b),compose(a,b)),compose(a,b))),compose(compose(compose(a,b),compose(a,b)),compose(a,b))) = compose(compose(compose(a,b),compose(a,b)),compose(a,b)),
inference(paramodulation,[status(thm)],[f959,f43337]) ).
fof(f111262,plain,
ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,b),compose(a,b)),compose(a,b))),compose(compose(compose(a,b),compose(a,b)),compose(a,b))) = compose(compose(compose(a,b),compose(a,b)),compose(a,b)),
inference(forward_demodulation,[status(thm)],[f1163,f111244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT001-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n016.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 13:59:39 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Drodi V4.1.1
% 28.68/4.28 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 28.68/4.28 % SZS output start Saturation for theBenchmark
% See solution above
% 8.97/4.49 % Elapsed time: 3.916791 seconds
% 8.97/4.49 % CPU time: 30.488226 seconds
% 8.97/4.49 % Total memory used: 865.455 MB
% 8.97/4.49 % Net memory used: 859.774 MB
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