Drodi-SAT---4.1.1.SAT-Sat.s

%------------------------------------------------------------------------------
% File     : Drodi-SAT---4.1.1
% Problem  : CAT002-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n010.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 12:07:38 PM UTC 2026

% Result   : Satisfiable 92.47s 22.69s
% Output   : Saturation 7.54s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B,C] : ifeq(A,A,B,C) = B,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X] : codomain(domain(X)) = domain(X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X] : domain(codomain(X)) = codomain(X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] : compose(domain(X),X) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X] : compose(X,codomain(X)) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y] : ifeq(codomain(X),domain(Y),domain(compose(X,Y)),domain(X)) = domain(X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y] : ifeq(codomain(X),domain(Y),codomain(compose(X,Y)),codomain(Y)) = codomain(Y),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,hypothesis,
    codomain(a) = domain(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,hypothesis,
    ! [X,Z,Y] : ifeq(codomain(X),domain(a),ifeq(codomain(Z),domain(b),ifeq(compose(Z,a),Y,ifeq(compose(X,a),Y,X,Z),Z),Z),Z) = Z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,hypothesis,
    ! [X,Z,Y] : ifeq(codomain(X),domain(a),ifeq(codomain(Z),domain(b),ifeq(compose(Z,b),Y,ifeq(compose(X,b),Y,X,Z),Z),Z),Z) = Z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,hypothesis,
    codomain(h) = domain(compose(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,hypothesis,
    codomain(g) = domain(compose(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,hypothesis,
    compose(h,compose(a,b)) = compose(g,compose(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,negated_conjecture,
    h != g,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,plain,
    ! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
    inference(cnf_transformation,[status(thm)],[f1]) ).

fof(f17,plain,
    ! [X0] : codomain(domain(X0)) = domain(X0),
    inference(cnf_transformation,[status(thm)],[f2]) ).

fof(f18,plain,
    ! [X0] : domain(codomain(X0)) = codomain(X0),
    inference(cnf_transformation,[status(thm)],[f3]) ).

fof(f19,plain,
    ! [X0] : compose(domain(X0),X0) = X0,
    inference(cnf_transformation,[status(thm)],[f4]) ).

fof(f20,plain,
    ! [X0] : compose(X0,codomain(X0)) = X0,
    inference(cnf_transformation,[status(thm)],[f5]) ).

fof(f21,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(X0,X1)),domain(X0)) = domain(X0),
    inference(cnf_transformation,[status(thm)],[f6]) ).

fof(f22,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,X1)),codomain(X1)) = codomain(X1),
    inference(cnf_transformation,[status(thm)],[f7]) ).

fof(f23,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(f24,plain,
    codomain(a) = domain(b),
    inference(cnf_transformation,[status(thm)],[f9]) ).

fof(f25,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),X2,ifeq(compose(X0,a),X2,X0,X1),X1),X1),X1) = X1,
    inference(cnf_transformation,[status(thm)],[f10]) ).

fof(f26,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),X2,ifeq(compose(X0,b),X2,X0,X1),X1),X1),X1) = X1,
    inference(cnf_transformation,[status(thm)],[f11]) ).

fof(f27,plain,
    codomain(h) = domain(compose(a,b)),
    inference(cnf_transformation,[status(thm)],[f12]) ).

fof(f28,plain,
    codomain(g) = domain(compose(a,b)),
    inference(cnf_transformation,[status(thm)],[f13]) ).

fof(f29,plain,
    compose(h,compose(a,b)) = compose(g,compose(a,b)),
    inference(cnf_transformation,[status(thm)],[f14]) ).

fof(f30,plain,
    h != g,
    inference(cnf_transformation,[status(thm)],[f15]) ).

fof(f31,plain,
    ! [X0] : compose(domain(X0),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f20]) ).

fof(f32,plain,
    ! [X0] : domain(domain(X0)) = codomain(domain(X0)),
    inference(paramodulation,[status(thm)],[f17,f18]) ).

fof(f33,plain,
    ! [X0] : codomain(codomain(X0)) = domain(codomain(X0)),
    inference(paramodulation,[status(thm)],[f18,f17]) ).

fof(f34,plain,
    ! [X0] : compose(codomain(X0),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f18,f19]) ).

fof(f35,plain,
    ! [X0] : domain(domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f17,f32]) ).

fof(f36,plain,
    ! [X0] : codomain(codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f18,f33]) ).

fof(f37,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),X1)),domain(domain(X0))) = domain(domain(X0)),
    inference(paramodulation,[status(thm)],[f17,f21]) ).

fof(f38,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),domain(compose(X0,codomain(X1))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f18,f21]) ).

fof(f46,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(a,X0)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f24,f21]) ).

fof(f48,plain,
    compose(a,domain(b)) = a,
    inference(paramodulation,[status(thm)],[f24,f20]) ).

fof(f53,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(X0,domain(X1))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f35,f21]) ).

fof(f62,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),X1)),domain(codomain(X0))) = domain(codomain(X0)),
    inference(paramodulation,[status(thm)],[f36,f21]) ).

fof(f66,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),X1)),codomain(X0)) = domain(codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f18,f62]) ).

fof(f67,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),X1)),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f18,f66]) ).

fof(f72,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f22]) ).

fof(f73,plain,
    ! [X0] : ifeq(domain(b),domain(X0),codomain(compose(a,X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f24,f22]) ).

fof(f74,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f17,f22]) ).

fof(f75,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,domain(X1))),codomain(domain(X1))) = codomain(domain(X1)),
    inference(paramodulation,[status(thm)],[f35,f22]) ).

fof(f76,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(X0,codomain(X1))),codomain(codomain(X1))) = codomain(codomain(X1)),
    inference(paramodulation,[status(thm)],[f18,f22]) ).

fof(f81,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,a)),domain(b)) = codomain(a),
    inference(paramodulation,[status(thm)],[f24,f22]) ).

fof(f83,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,domain(X1))),domain(X1)) = codomain(domain(X1)),
    inference(forward_demodulation,[status(thm)],[f17,f75]) ).

fof(f84,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(X0,domain(X1))),domain(X1)) = domain(X1),
    inference(forward_demodulation,[status(thm)],[f17,f83]) ).

fof(f85,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(X0,codomain(X1))),codomain(X1)) = codomain(codomain(X1)),
    inference(forward_demodulation,[status(thm)],[f36,f76]) ).

fof(f86,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(X0,codomain(X1))),codomain(X1)) = codomain(X1),
    inference(forward_demodulation,[status(thm)],[f36,f85]) ).

fof(f96,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,a)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f24,f81]) ).

fof(f137,plain,
    ifeq(codomain(a),domain(b),codomain(h),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f27,f21]) ).

fof(f140,plain,
    ! [X0] : ifeq(codomain(X0),codomain(h),codomain(compose(X0,compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
    inference(paramodulation,[status(thm)],[f27,f22]) ).

fof(f142,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),domain(X0),domain(compose(compose(a,b),X0)),codomain(h)) = domain(compose(a,b)),
    inference(paramodulation,[status(thm)],[f27,f21]) ).

fof(f143,plain,
    ! [X0] : ifeq(codomain(X0),codomain(h),domain(compose(X0,compose(a,b))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f27,f21]) ).

fof(f145,plain,
    compose(codomain(h),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f27,f19]) ).

fof(f146,plain,
    ifeq(domain(b),domain(b),codomain(h),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f24,f137]) ).

fof(f147,plain,
    codomain(h) = domain(a),
    inference(forward_demodulation,[status(thm)],[f16,f146]) ).

fof(f153,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),domain(X0),domain(compose(compose(a,b),X0)),codomain(h)) = codomain(h),
    inference(forward_demodulation,[status(thm)],[f27,f142]) ).

fof(f156,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,f23]) ).

fof(f157,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)],[f17,f23]) ).

fof(f158,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(h),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)],[f27,f23]) ).

fof(f159,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)],[f35,f23]) ).

fof(f160,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)],[f18,f23]) ).

fof(f161,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)],[f36,f23]) ).

fof(f162,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,f23]) ).

fof(f163,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)],[f17,f23]) ).

fof(f164,plain,
    ! [X0,X1] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(X1),codomain(h),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)],[f27,f23]) ).

fof(f166,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)],[f18,f23]) ).

fof(f167,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)],[f19,f23]) ).

fof(f168,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)],[f34,f23]) ).

fof(f169,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)],[f48,f23]) ).

fof(f170,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)],[f31,f23]) ).

fof(f171,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)],[f19,f23]) ).

fof(f172,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)],[f20,f23]) ).

fof(f173,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)],[f20,f23]) ).

fof(f174,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)],[f34,f23]) ).

fof(f175,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)],[f48,f23]) ).

fof(f176,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)],[f31,f23]) ).

fof(f177,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)],[f19,f23]) ).

fof(f178,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)],[f20,f23]) ).

fof(f186,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)],[f35,f157]) ).

fof(f188,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)],[f36,f166]) ).

fof(f189,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)],[f17,f167]) ).

fof(f190,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)],[f36,f168]) ).

fof(f191,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)],[f18,f190]) ).

fof(f192,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)],[f16,f191]) ).

fof(f193,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)],[f18,f192]) ).

fof(f194,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,f169]) ).

fof(f195,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)],[f35,f194]) ).

fof(f196,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)],[f16,f195]) ).

fof(f197,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)],[f17,f170]) ).

fof(f198,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)],[f35,f197]) ).

fof(f199,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)],[f16,f198]) ).

fof(f200,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)],[f35,f199]) ).

fof(f201,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)],[f17,f171]) ).

fof(f202,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)],[f16,f201]) ).

fof(f203,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)],[f35,f202]) ).

fof(f204,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)],[f18,f172]) ).

fof(f205,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)],[f16,f204]) ).

fof(f206,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)],[f18,f173]) ).

fof(f207,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)],[f20,f206]) ).

fof(f208,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)],[f20,f207]) ).

fof(f209,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)],[f36,f174]) ).

fof(f210,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)],[f36,f209]) ).

fof(f211,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)],[f18,f210]) ).

fof(f212,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)],[f16,f211]) ).

fof(f213,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)],[f34,f212]) ).

fof(f214,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)],[f34,f213]) ).

fof(f215,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)],[f17,f175]) ).

fof(f216,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,f215]) ).

fof(f217,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)],[f35,f216]) ).

fof(f218,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)],[f16,f217]) ).

fof(f219,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)],[f48,f218]) ).

fof(f220,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(a,compose(domain(b),X0)),compose(a,X0)) = compose(a,X0),
    inference(forward_demodulation,[status(thm)],[f48,f219]) ).

fof(f221,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)],[f17,f176]) ).

fof(f222,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)],[f17,f221]) ).

fof(f223,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)],[f35,f222]) ).

fof(f224,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)],[f16,f223]) ).

fof(f225,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)],[f31,f224]) ).

fof(f226,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)],[f31,f225]) ).

fof(f227,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)],[f17,f177]) ).

fof(f228,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)],[f16,f227]) ).

fof(f229,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)],[f19,f228]) ).

fof(f230,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)],[f19,f229]) ).

fof(f231,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)],[f36,f178]) ).

fof(f232,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)],[f18,f231]) ).

fof(f233,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)],[f16,f232]) ).

fof(f234,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)],[f20,f233]) ).

fof(f235,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)],[f20,f234]) ).

fof(f261,plain,
    domain(a) = domain(compose(a,b)),
    inference(backward_demodulation,[status(thm)],[f147,f27]) ).

fof(f262,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(X0,X1)),compose(compose(h,X0),X1)),compose(compose(h,X0),X1)) = compose(compose(h,X0),X1),
    inference(paramodulation,[status(thm)],[f147,f23]) ).

fof(f263,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(h,X0)),compose(compose(X1,h),X0)),compose(compose(X1,h),X0)) = compose(compose(X1,h),X0),
    inference(paramodulation,[status(thm)],[f147,f23]) ).

fof(f266,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,h)),domain(a)) = codomain(h),
    inference(paramodulation,[status(thm)],[f147,f22]) ).

fof(f267,plain,
    ! [X0] : ifeq(domain(a),domain(X0),codomain(compose(h,X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f147,f22]) ).

fof(f269,plain,
    ! [X0] : ifeq(domain(a),domain(X0),domain(compose(h,X0)),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f147,f21]) ).

fof(f271,plain,
    compose(h,domain(a)) = h,
    inference(paramodulation,[status(thm)],[f147,f20]) ).

fof(f276,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,h)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f147,f266]) ).

fof(f279,plain,
    ! [X0] : ifeq(codomain(domain(a)),domain(X0),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),X0)),compose(compose(h,domain(a)),X0)),compose(h,X0)) = compose(compose(h,domain(a)),X0),
    inference(paramodulation,[status(thm)],[f271,f23]) ).

fof(f281,plain,
    ! [X0] : ifeq(codomain(h),domain(domain(a)),ifeq(codomain(X0),domain(h),compose(X0,h),compose(compose(X0,h),domain(a))),compose(compose(X0,h),domain(a))) = compose(compose(X0,h),domain(a)),
    inference(paramodulation,[status(thm)],[f271,f23]) ).

fof(f284,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),X0)),compose(compose(h,domain(a)),X0)),compose(h,X0)) = compose(compose(h,domain(a)),X0),
    inference(forward_demodulation,[status(thm)],[f17,f279]) ).

fof(f285,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(domain(a)),compose(h,compose(domain(a),X0)),compose(compose(h,domain(a)),X0)),compose(h,X0)) = compose(compose(h,domain(a)),X0),
    inference(forward_demodulation,[status(thm)],[f147,f284]) ).

fof(f286,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(a),compose(h,compose(domain(a),X0)),compose(compose(h,domain(a)),X0)),compose(h,X0)) = compose(compose(h,domain(a)),X0),
    inference(forward_demodulation,[status(thm)],[f35,f285]) ).

fof(f287,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(h,compose(domain(a),X0)),compose(h,X0)) = compose(compose(h,domain(a)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f286]) ).

fof(f288,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(h,compose(domain(a),X0)),compose(h,X0)) = compose(h,X0),
    inference(forward_demodulation,[status(thm)],[f271,f287]) ).

fof(f295,plain,
    ! [X0] : ifeq(domain(a),domain(domain(a)),ifeq(codomain(X0),domain(h),compose(X0,h),compose(compose(X0,h),domain(a))),compose(compose(X0,h),domain(a))) = compose(compose(X0,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f147,f281]) ).

fof(f296,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(h),compose(X0,h),compose(compose(X0,h),domain(a))),compose(compose(X0,h),domain(a))) = compose(compose(X0,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f295]) ).

fof(f297,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,h),compose(compose(X0,h),domain(a))) = compose(compose(X0,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f296]) ).

fof(f304,plain,
    ifeq(codomain(a),domain(b),codomain(g),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f28,f21]) ).

fof(f315,plain,
    ifeq(domain(b),domain(b),codomain(g),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f24,f304]) ).

fof(f316,plain,
    codomain(g) = domain(a),
    inference(forward_demodulation,[status(thm)],[f16,f315]) ).

fof(f325,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),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)],[f316,f23]) ).

fof(f326,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(g),compose(X1,compose(g,X0)),compose(compose(X1,g),X0)),compose(compose(X1,g),X0)) = compose(compose(X1,g),X0),
    inference(paramodulation,[status(thm)],[f316,f23]) ).

fof(f329,plain,
    ! [X0] : ifeq(codomain(X0),domain(g),codomain(compose(X0,g)),domain(a)) = codomain(g),
    inference(paramodulation,[status(thm)],[f316,f22]) ).

fof(f330,plain,
    ! [X0] : ifeq(domain(a),domain(X0),codomain(compose(g,X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f316,f22]) ).

fof(f332,plain,
    ! [X0] : ifeq(domain(a),domain(X0),domain(compose(g,X0)),domain(g)) = domain(g),
    inference(paramodulation,[status(thm)],[f316,f21]) ).

fof(f334,plain,
    compose(g,domain(a)) = g,
    inference(paramodulation,[status(thm)],[f316,f20]) ).

fof(f339,plain,
    ! [X0] : ifeq(codomain(X0),domain(g),codomain(compose(X0,g)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f316,f329]) ).

fof(f342,plain,
    ! [X0] : ifeq(codomain(domain(a)),domain(X0),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),X0)),compose(compose(g,domain(a)),X0)),compose(g,X0)) = compose(compose(g,domain(a)),X0),
    inference(paramodulation,[status(thm)],[f334,f23]) ).

fof(f344,plain,
    ! [X0] : ifeq(codomain(g),domain(domain(a)),ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),domain(a))),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
    inference(paramodulation,[status(thm)],[f334,f23]) ).

fof(f347,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),X0)),compose(compose(g,domain(a)),X0)),compose(g,X0)) = compose(compose(g,domain(a)),X0),
    inference(forward_demodulation,[status(thm)],[f17,f342]) ).

fof(f348,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(domain(a)),compose(g,compose(domain(a),X0)),compose(compose(g,domain(a)),X0)),compose(g,X0)) = compose(compose(g,domain(a)),X0),
    inference(forward_demodulation,[status(thm)],[f316,f347]) ).

fof(f349,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(a),compose(g,compose(domain(a),X0)),compose(compose(g,domain(a)),X0)),compose(g,X0)) = compose(compose(g,domain(a)),X0),
    inference(forward_demodulation,[status(thm)],[f35,f348]) ).

fof(f350,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(g,compose(domain(a),X0)),compose(g,X0)) = compose(compose(g,domain(a)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f349]) ).

fof(f351,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(g,compose(domain(a),X0)),compose(g,X0)) = compose(g,X0),
    inference(forward_demodulation,[status(thm)],[f334,f350]) ).

fof(f358,plain,
    ! [X0] : ifeq(domain(a),domain(domain(a)),ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),domain(a))),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f316,f344]) ).

fof(f359,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),domain(a))),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f358]) ).

fof(f360,plain,
    ! [X0] : ifeq(codomain(X0),domain(g),compose(X0,g),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f359]) ).

fof(f386,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(g,a),X1,g,X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f316,f25]) ).

fof(f387,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(h,a),X1,h,X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f147,f25]) ).

fof(f388,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),X2,ifeq(compose(codomain(X0),a),X2,codomain(X0),X1),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f36,f25]) ).

fof(f389,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(a,a),X1,a,X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f24,f25]) ).

fof(f390,plain,
    ! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),X2,ifeq(compose(domain(X0),a),X2,domain(X0),X1),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f17,f25]) ).

fof(f391,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X1,ifeq(compose(X0,a),X1,X0,g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f25]) ).

fof(f392,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X1,ifeq(compose(X0,a),X1,X0,h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f25]) ).

fof(f393,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),X2,ifeq(compose(X0,a),X2,X0,codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f25]) ).

fof(f394,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,a),X1,ifeq(compose(X0,a),X1,X0,a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f24,f25]) ).

fof(f395,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),X2,ifeq(compose(X0,a),X2,X0,domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f25]) ).

fof(f396,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X0,a),compose(X1,a),X0,X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f16,f25]) ).

fof(f397,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(a,X1,ifeq(compose(X0,a),X1,X0,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f25]) ).

fof(f398,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),compose(X0,a),X0,X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f16,f25]) ).

fof(f399,plain,
    ! [X0,X1] : ifeq(codomain(domain(a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(a,X1,domain(a),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f19,f25]) ).

fof(f400,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(g,a),X1,g,X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f386]) ).

fof(f401,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(h,a),X1,h,X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f387]) ).

fof(f402,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,a),X1,ifeq(compose(X0,a),X1,X0,a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f394]) ).

fof(f403,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,X1,ifeq(compose(X0,a),X1,X0,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f397]) ).

fof(f404,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(a,X1,domain(a),X0),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f17,f399]) ).

fof(f405,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(a,X1,domain(a),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f404]) ).

fof(f406,plain,
    compose(domain(a),compose(a,b)) = compose(a,b),
    inference(forward_demodulation,[status(thm)],[f147,f145]) ).

fof(f408,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)],[f406,f23]) ).

fof(f410,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)],[f406,f23]) ).

fof(f417,plain,
    ! [X0] : ifeq(codomain(compose(a,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)],[f17,f408]) ).

fof(f418,plain,
    ! [X0] : ifeq(codomain(compose(a,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)],[f261,f417]) ).

fof(f419,plain,
    ! [X0] : ifeq(codomain(compose(a,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)],[f16,f418]) ).

fof(f420,plain,
    ! [X0] : ifeq(codomain(compose(a,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)],[f406,f419]) ).

fof(f426,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)],[f17,f410]) ).

fof(f427,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)],[f261,f426]) ).

fof(f428,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)],[f16,f427]) ).

fof(f429,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)],[f35,f428]) ).

fof(f437,plain,
    ifeq(codomain(a),domain(b),ifeq(codomain(g),domain(a),compose(h,compose(a,b)),compose(compose(g,a),b)),compose(compose(g,a),b)) = compose(compose(g,a),b),
    inference(paramodulation,[status(thm)],[f29,f23]) ).

fof(f438,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(codomain(g),domain(compose(a,b)),compose(g,compose(compose(a,b),X0)),compose(compose(g,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
    inference(paramodulation,[status(thm)],[f29,f23]) ).

fof(f440,plain,
    ! [X0] : ifeq(codomain(g),domain(compose(a,b)),ifeq(codomain(X0),domain(g),compose(X0,compose(h,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)],[f29,f23]) ).

fof(f441,plain,
    ifeq(codomain(g),domain(compose(a,b)),codomain(compose(h,compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
    inference(paramodulation,[status(thm)],[f29,f22]) ).

fof(f442,plain,
    ifeq(codomain(g),domain(compose(a,b)),domain(compose(h,compose(a,b))),domain(g)) = domain(g),
    inference(paramodulation,[status(thm)],[f29,f21]) ).

fof(f443,plain,
    ifeq(domain(b),domain(b),ifeq(codomain(g),domain(a),compose(h,compose(a,b)),compose(compose(g,a),b)),compose(compose(g,a),b)) = compose(compose(g,a),b),
    inference(forward_demodulation,[status(thm)],[f24,f437]) ).

fof(f444,plain,
    ifeq(codomain(g),domain(a),compose(h,compose(a,b)),compose(compose(g,a),b)) = compose(compose(g,a),b),
    inference(forward_demodulation,[status(thm)],[f16,f443]) ).

fof(f445,plain,
    ifeq(domain(a),domain(a),compose(h,compose(a,b)),compose(compose(g,a),b)) = compose(compose(g,a),b),
    inference(forward_demodulation,[status(thm)],[f316,f444]) ).

fof(f446,plain,
    compose(h,compose(a,b)) = compose(compose(g,a),b),
    inference(forward_demodulation,[status(thm)],[f16,f445]) ).

fof(f447,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(a),domain(compose(a,b)),compose(g,compose(compose(a,b),X0)),compose(compose(g,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f316,f438]) ).

fof(f448,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),domain(X0),ifeq(domain(a),domain(a),compose(g,compose(compose(a,b),X0)),compose(compose(g,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f261,f447]) ).

fof(f449,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),domain(X0),compose(g,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(g,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f448]) ).

fof(f450,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),domain(X0),compose(g,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f29,f449]) ).

fof(f456,plain,
    ! [X0] : ifeq(domain(a),domain(compose(a,b)),ifeq(codomain(X0),domain(g),compose(X0,compose(h,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(forward_demodulation,[status(thm)],[f316,f440]) ).

fof(f457,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(g),compose(X0,compose(h,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(forward_demodulation,[status(thm)],[f261,f456]) ).

fof(f458,plain,
    ! [X0] : ifeq(codomain(X0),domain(g),compose(X0,compose(h,compose(a,b))),compose(compose(X0,g),compose(a,b))) = compose(compose(X0,g),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f457]) ).

fof(f459,plain,
    ifeq(domain(a),domain(compose(a,b)),codomain(compose(h,compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f316,f441]) ).

fof(f460,plain,
    ifeq(domain(a),domain(a),codomain(compose(h,compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f261,f459]) ).

fof(f461,plain,
    codomain(compose(h,compose(a,b))) = codomain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f460]) ).

fof(f462,plain,
    ifeq(domain(a),domain(compose(a,b)),domain(compose(h,compose(a,b))),domain(g)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f316,f442]) ).

fof(f463,plain,
    ifeq(domain(a),domain(a),domain(compose(h,compose(a,b))),domain(g)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f261,f462]) ).

fof(f464,plain,
    domain(compose(h,compose(a,b))) = domain(g),
    inference(forward_demodulation,[status(thm)],[f16,f463]) ).

fof(f465,plain,
    ifeq(codomain(h),domain(compose(a,b)),domain(g),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f464,f21]) ).

fof(f466,plain,
    ! [X0,X1] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(codomain(X1),domain(g),compose(X1,compose(compose(h,compose(a,b)),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)) = compose(compose(X1,compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f464,f23]) ).

fof(f467,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(g),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(h,compose(a,b)))),compose(compose(X1,X0),compose(h,compose(a,b)))),compose(compose(X1,X0),compose(h,compose(a,b)))) = compose(compose(X1,X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f464,f23]) ).

fof(f470,plain,
    ! [X0] : ifeq(codomain(X0),domain(g),codomain(compose(X0,compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f464,f22]) ).

fof(f472,plain,
    ! [X0] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),domain(compose(compose(h,compose(a,b)),X0)),domain(g)) = domain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f464,f21]) ).

fof(f473,plain,
    ! [X0] : ifeq(codomain(X0),domain(g),domain(compose(X0,compose(h,compose(a,b)))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f464,f21]) ).

fof(f475,plain,
    compose(domain(g),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f464,f19]) ).

fof(f476,plain,
    ifeq(domain(a),domain(compose(a,b)),domain(g),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f147,f465]) ).

fof(f477,plain,
    ifeq(domain(a),domain(a),domain(g),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f261,f476]) ).

fof(f478,plain,
    domain(g) = domain(h),
    inference(forward_demodulation,[status(thm)],[f16,f477]) ).

fof(f484,plain,
    ! [X0] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),domain(compose(compose(h,compose(a,b)),X0)),domain(g)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f464,f472]) ).

fof(f486,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(g,b),X1,g,X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f316,f26]) ).

fof(f487,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,b),X1,h,X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f147,f26]) ).

fof(f488,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),X2,ifeq(compose(codomain(X0),b),X2,codomain(X0),X1),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f36,f26]) ).

fof(f489,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(a,b),X1,a,X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f24,f26]) ).

fof(f490,plain,
    ! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),X2,ifeq(compose(domain(X0),b),X2,domain(X0),X1),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f17,f26]) ).

fof(f491,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X1,ifeq(compose(X0,b),X1,X0,g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f26]) ).

fof(f492,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X1,ifeq(compose(X0,b),X1,X0,h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f26]) ).

fof(f493,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),X2,ifeq(compose(X0,b),X2,X0,codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f26]) ).

fof(f494,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,b),X1,ifeq(compose(X0,b),X1,X0,a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f24,f26]) ).

fof(f495,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),X2,ifeq(compose(X0,b),X2,X0,domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f26]) ).

fof(f496,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X0,b),compose(X1,b),X0,X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f16,f26]) ).

fof(f497,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(b)),domain(b),ifeq(b,X1,ifeq(compose(X0,b),X1,X0,domain(b)),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f26]) ).

fof(f498,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),compose(X0,b),X0,X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f16,f26]) ).

fof(f499,plain,
    ! [X0,X1] : ifeq(codomain(domain(b)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(b,X1,domain(b),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f19,f26]) ).

fof(f500,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(g,b),X1,g,X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f486]) ).

fof(f501,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,b),X1,h,X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f487]) ).

fof(f502,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(X0,b),X1,X0,a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f494]) ).

fof(f503,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(b,X1,ifeq(compose(X0,b),X1,X0,domain(b)),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f497]) ).

fof(f504,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(b,X1,ifeq(compose(X0,b),X1,X0,domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f503]) ).

fof(f505,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(b,X1,domain(b),X0),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f17,f499]) ).

fof(f506,plain,
    domain(compose(h,compose(a,b))) = domain(h),
    inference(backward_demodulation,[status(thm)],[f478,f464]) ).

fof(f508,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),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)],[f478,f23]) ).

fof(f514,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),domain(compose(X0,g)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f478,f21]) ).

fof(f516,plain,
    compose(domain(h),g) = g,
    inference(paramodulation,[status(thm)],[f478,f19]) ).

fof(f528,plain,
    ! [X0] : ifeq(codomain(g),domain(X0),ifeq(codomain(domain(h)),domain(g),compose(domain(h),compose(g,X0)),compose(compose(domain(h),g),X0)),compose(g,X0)) = compose(compose(domain(h),g),X0),
    inference(paramodulation,[status(thm)],[f516,f23]) ).

fof(f530,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(g),ifeq(codomain(X0),domain(domain(h)),compose(X0,g),compose(compose(X0,domain(h)),g)),compose(compose(X0,domain(h)),g)) = compose(compose(X0,domain(h)),g),
    inference(paramodulation,[status(thm)],[f516,f23]) ).

fof(f533,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(domain(h)),domain(g),compose(domain(h),compose(g,X0)),compose(compose(domain(h),g),X0)),compose(g,X0)) = compose(compose(domain(h),g),X0),
    inference(forward_demodulation,[status(thm)],[f316,f528]) ).

fof(f534,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(h),domain(g),compose(domain(h),compose(g,X0)),compose(compose(domain(h),g),X0)),compose(g,X0)) = compose(compose(domain(h),g),X0),
    inference(forward_demodulation,[status(thm)],[f17,f533]) ).

fof(f535,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(g,X0)),compose(compose(domain(h),g),X0)),compose(g,X0)) = compose(compose(domain(h),g),X0),
    inference(forward_demodulation,[status(thm)],[f478,f534]) ).

fof(f536,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(domain(h),compose(g,X0)),compose(g,X0)) = compose(compose(domain(h),g),X0),
    inference(forward_demodulation,[status(thm)],[f16,f535]) ).

fof(f537,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(domain(h),compose(g,X0)),compose(g,X0)) = compose(g,X0),
    inference(forward_demodulation,[status(thm)],[f516,f536]) ).

fof(f544,plain,
    ! [X0] : ifeq(domain(h),domain(g),ifeq(codomain(X0),domain(domain(h)),compose(X0,g),compose(compose(X0,domain(h)),g)),compose(compose(X0,domain(h)),g)) = compose(compose(X0,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f17,f530]) ).

fof(f545,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(X0,g),compose(compose(X0,domain(h)),g)),compose(compose(X0,domain(h)),g)) = compose(compose(X0,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f478,f544]) ).

fof(f546,plain,
    ! [X0] : ifeq(codomain(X0),domain(domain(h)),compose(X0,g),compose(compose(X0,domain(h)),g)) = compose(compose(X0,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f16,f545]) ).

fof(f547,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,g),compose(compose(X0,domain(h)),g)) = compose(compose(X0,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f35,f546]) ).

fof(f576,plain,
    ! [X0,X1] : ifeq(codomain(compose(g,a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f446,f26]) ).

fof(f577,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f446,f26]) ).

fof(f578,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(g,a)),domain(b),compose(compose(g,a),compose(b,X0)),compose(compose(compose(g,a),b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(g,a),b),X0),
    inference(paramodulation,[status(thm)],[f446,f23]) ).

fof(f580,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(b),ifeq(codomain(X0),domain(compose(g,a)),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(g,a)),b)),compose(compose(X0,compose(g,a)),b)) = compose(compose(X0,compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f446,f23]) ).

fof(f593,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(g,a)),domain(b),compose(compose(g,a),compose(b,X0)),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(g,a),b),X0),
    inference(forward_demodulation,[status(thm)],[f446,f578]) ).

fof(f594,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(g,a)),domain(b),compose(compose(g,a),compose(b,X0)),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f446,f593]) ).

fof(f599,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(compose(a,b)),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X1,ifeq(compose(X0,b),X1,X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f461,f26]) ).

fof(f600,plain,
    ! [X0,X1] : ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(compose(h,compose(a,b)),b),X1,compose(h,compose(a,b)),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f461,f26]) ).

fof(f601,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(compose(a,b)),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X1,ifeq(compose(X0,a),X1,X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f461,f25]) ).

fof(f602,plain,
    ! [X0,X1] : ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(h,compose(a,b)),a),X1,compose(h,compose(a,b)),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f461,f25]) ).

fof(f603,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(compose(a,b)),domain(X0),compose(compose(h,compose(a,b)),compose(X0,X1)),compose(compose(compose(h,compose(a,b)),X0),X1)),compose(compose(compose(h,compose(a,b)),X0),X1)) = compose(compose(compose(h,compose(a,b)),X0),X1),
    inference(paramodulation,[status(thm)],[f461,f23]) ).

fof(f627,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),codomain(X0),domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f461,f38]) ).

fof(f628,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),domain(compose(g,codomain(X0))),domain(g)) = domain(g),
    inference(paramodulation,[status(thm)],[f316,f38]) ).

fof(f629,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),domain(compose(h,codomain(X0))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f147,f38]) ).

fof(f630,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),domain(compose(codomain(X0),codomain(X1))),domain(codomain(X0))) = domain(codomain(X0)),
    inference(paramodulation,[status(thm)],[f36,f38]) ).

fof(f631,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),domain(compose(a,codomain(X0))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f24,f38]) ).

fof(f632,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),domain(compose(domain(X0),codomain(X1))),domain(domain(X0))) = domain(domain(X0)),
    inference(paramodulation,[status(thm)],[f17,f38]) ).

fof(f654,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),codomain(X0),domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(h)) = domain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f627]) ).

fof(f655,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),codomain(X0),domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f506,f654]) ).

fof(f656,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),domain(compose(g,codomain(X0))),domain(h)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f478,f628]) ).

fof(f657,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),domain(compose(g,codomain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f478,f656]) ).

fof(f658,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),domain(compose(codomain(X0),codomain(X1))),codomain(X0)) = domain(codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f18,f630]) ).

fof(f659,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),domain(compose(codomain(X0),codomain(X1))),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f18,f658]) ).

fof(f660,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),domain(compose(domain(X0),codomain(X1))),domain(X0)) = domain(domain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f632]) ).

fof(f661,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),domain(compose(domain(X0),codomain(X1))),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f35,f660]) ).

fof(f689,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),X1)),domain(X0)) = domain(domain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f37]) ).

fof(f690,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),X1)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f35,f689]) ).

fof(f697,plain,
    ! [X0] : ifeq(domain(X0),domain(h),domain(compose(domain(X0),g)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f478,f690]) ).

fof(f698,plain,
    ! [X0] : ifeq(domain(X0),domain(h),domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f506,f690]) ).

fof(f699,plain,
    ! [X0] : ifeq(domain(X0),domain(a),domain(compose(domain(X0),compose(a,b))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f261,f690]) ).

fof(f700,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),domain(compose(domain(X0),domain(X1))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f35,f690]) ).

fof(f773,plain,
    ! [X0] : ifeq(domain(a),domain(X0),domain(compose(g,domain(X0))),domain(g)) = domain(g),
    inference(paramodulation,[status(thm)],[f316,f53]) ).

fof(f774,plain,
    ! [X0] : ifeq(domain(a),domain(X0),domain(compose(h,domain(X0))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f147,f53]) ).

fof(f775,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),domain(X1))),domain(codomain(X0))) = domain(codomain(X0)),
    inference(paramodulation,[status(thm)],[f36,f53]) ).

fof(f776,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(a,domain(X0))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f24,f53]) ).

fof(f800,plain,
    ! [X0] : ifeq(domain(a),domain(X0),domain(compose(g,domain(X0))),domain(h)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f478,f773]) ).

fof(f801,plain,
    ! [X0] : ifeq(domain(a),domain(X0),domain(compose(g,domain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f478,f800]) ).

fof(f802,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),domain(X1))),codomain(X0)) = domain(codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f18,f775]) ).

fof(f803,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),domain(compose(codomain(X0),domain(X1))),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f18,f802]) ).

fof(f838,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),domain(compose(codomain(X0),g)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f478,f67]) ).

fof(f839,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f506,f67]) ).

fof(f840,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),domain(compose(codomain(X0),compose(a,b))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f261,f67]) ).

fof(f922,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),g)),codomain(g)) = codomain(g),
    inference(paramodulation,[status(thm)],[f478,f72]) ).

fof(f925,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),domain(X1))),codomain(domain(X1))) = codomain(domain(X1)),
    inference(paramodulation,[status(thm)],[f35,f72]) ).

fof(f926,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(codomain(X0),codomain(X1))),codomain(codomain(X1))) = codomain(codomain(X1)),
    inference(paramodulation,[status(thm)],[f18,f72]) ).

fof(f937,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),h)),domain(a)) = codomain(h),
    inference(paramodulation,[status(thm)],[f147,f72]) ).

fof(f939,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),a)),domain(b)) = codomain(a),
    inference(paramodulation,[status(thm)],[f24,f72]) ).

fof(f947,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),g)),domain(a)) = codomain(g),
    inference(forward_demodulation,[status(thm)],[f316,f922]) ).

fof(f948,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),g)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f316,f947]) ).

fof(f951,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),domain(X1))),domain(X1)) = codomain(domain(X1)),
    inference(forward_demodulation,[status(thm)],[f17,f925]) ).

fof(f952,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),codomain(compose(codomain(X0),domain(X1))),domain(X1)) = domain(X1),
    inference(forward_demodulation,[status(thm)],[f17,f951]) ).

fof(f953,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(codomain(X0),codomain(X1))),codomain(X1)) = codomain(codomain(X1)),
    inference(forward_demodulation,[status(thm)],[f36,f926]) ).

fof(f954,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),codomain(compose(codomain(X0),codomain(X1))),codomain(X1)) = codomain(X1),
    inference(forward_demodulation,[status(thm)],[f36,f953]) ).

fof(f969,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),h)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f147,f937]) ).

fof(f972,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),a)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f24,f939]) ).

fof(f975,plain,
    codomain(compose(a,b)) = codomain(b),
    inference(paramodulation,[status(thm)],[f16,f73]) ).

fof(f976,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,g)),codomain(g)) = codomain(g),
    inference(paramodulation,[status(thm)],[f478,f73]) ).

fof(f977,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f73]) ).

fof(f979,plain,
    ! [X0] : ifeq(domain(b),domain(X0),codomain(compose(a,domain(X0))),codomain(domain(X0))) = codomain(domain(X0)),
    inference(paramodulation,[status(thm)],[f35,f73]) ).

fof(f980,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),codomain(compose(a,codomain(X0))),codomain(codomain(X0))) = codomain(codomain(X0)),
    inference(paramodulation,[status(thm)],[f18,f73]) ).

fof(f985,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,h)),domain(a)) = codomain(h),
    inference(paramodulation,[status(thm)],[f147,f73]) ).

fof(f987,plain,
    ifeq(domain(b),domain(a),codomain(compose(a,a)),domain(b)) = codomain(a),
    inference(paramodulation,[status(thm)],[f24,f73]) ).

fof(f990,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,g)),domain(a)) = codomain(g),
    inference(forward_demodulation,[status(thm)],[f316,f976]) ).

fof(f991,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,g)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f316,f990]) ).

fof(f992,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(h,compose(a,b)))),codomain(compose(a,b))) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f461,f977]) ).

fof(f993,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(h,compose(a,b)))),codomain(compose(a,b))) = codomain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f461,f992]) ).

fof(f994,plain,
    ! [X0] : ifeq(domain(b),domain(X0),codomain(compose(a,domain(X0))),domain(X0)) = codomain(domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f979]) ).

fof(f995,plain,
    ! [X0] : ifeq(domain(b),domain(X0),codomain(compose(a,domain(X0))),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f17,f994]) ).

fof(f996,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),codomain(compose(a,codomain(X0))),codomain(X0)) = codomain(codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f36,f980]) ).

fof(f997,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),codomain(compose(a,codomain(X0))),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f36,f996]) ).

fof(f1010,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,h)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f147,f985]) ).

fof(f1013,plain,
    ifeq(domain(b),domain(a),codomain(compose(a,a)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f24,f987]) ).

fof(f1016,plain,
    codomain(compose(h,compose(a,b))) = codomain(b),
    inference(backward_demodulation,[status(thm)],[f975,f461]) ).

fof(f1019,plain,
    ifeq(domain(b),domain(compose(a,b)),codomain(compose(a,compose(a,b))),codomain(b)) = codomain(compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f73]) ).

fof(f1020,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(a,b)),codomain(compose(codomain(X0),compose(a,b))),codomain(b)) = codomain(compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f72]) ).

fof(f1026,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),domain(X0))),domain(compose(a,b))) = domain(compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f53]) ).

fof(f1029,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),domain(compose(compose(a,b),codomain(X0))),domain(compose(a,b))) = domain(compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f38]) ).

fof(f1030,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X1,ifeq(compose(X0,b),X1,X0,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f26]) ).

fof(f1031,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(compose(a,b),b),X1,compose(a,b),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f975,f26]) ).

fof(f1032,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X1,ifeq(compose(X0,a),X1,X0,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f25]) ).

fof(f1033,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(a,b),a),X1,compose(a,b),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f975,f25]) ).

fof(f1034,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)],[f975,f23]) ).

fof(f1039,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),codomain(compose(compose(a,b),X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f975,f22]) ).

fof(f1043,plain,
    compose(compose(a,b),codomain(b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f20]) ).

fof(f1045,plain,
    ifeq(domain(b),domain(a),codomain(compose(a,compose(a,b))),codomain(b)) = codomain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f261,f1019]) ).

fof(f1046,plain,
    ifeq(domain(b),domain(a),codomain(compose(a,compose(a,b))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f975,f1045]) ).

fof(f1047,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)],[f261,f1020]) ).

fof(f1048,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(codomain(X0),compose(a,b))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f975,f1047]) ).

fof(f1060,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)],[f261,f1026]) ).

fof(f1061,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),domain(X0))),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f261,f1060]) ).

fof(f1064,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)],[f261,f1029]) ).

fof(f1065,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),domain(compose(compose(a,b),codomain(X0))),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f261,f1064]) ).

fof(f1080,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(h,compose(a,b))),codomain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f72]) ).

fof(f1086,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),domain(X0))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f53]) ).

fof(f1099,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),codomain(compose(compose(h,compose(a,b)),X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1016,f22]) ).

fof(f1103,plain,
    compose(compose(h,compose(a,b)),codomain(b)) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f20]) ).

fof(f1109,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f1080]) ).

fof(f1110,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f1016,f1109]) ).

fof(f1122,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),domain(X0))),domain(h)) = domain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f1086]) ).

fof(f1123,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),domain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f506,f1122]) ).

fof(f1142,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)],[f1043,f23]) ).

fof(f1158,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)],[f36,f1142]) ).

fof(f1159,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)],[f975,f1158]) ).

fof(f1160,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)],[f18,f1159]) ).

fof(f1161,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)],[f16,f1160]) ).

fof(f1162,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)],[f1043,f1161]) ).

fof(f1185,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),g)),codomain(g)) = codomain(g),
    inference(paramodulation,[status(thm)],[f478,f74]) ).

fof(f1186,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f74]) ).

fof(f1187,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)],[f261,f74]) ).

fof(f1188,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),domain(X1))),codomain(domain(X1))) = codomain(domain(X1)),
    inference(paramodulation,[status(thm)],[f35,f74]) ).

fof(f1189,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),codomain(compose(domain(X0),codomain(X1))),codomain(codomain(X1))) = codomain(codomain(X1)),
    inference(paramodulation,[status(thm)],[f18,f74]) ).

fof(f1203,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),h)),domain(a)) = codomain(h),
    inference(paramodulation,[status(thm)],[f147,f74]) ).

fof(f1205,plain,
    ! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),a)),domain(b)) = codomain(a),
    inference(paramodulation,[status(thm)],[f24,f74]) ).

fof(f1213,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),g)),domain(a)) = codomain(g),
    inference(forward_demodulation,[status(thm)],[f316,f1185]) ).

fof(f1214,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),g)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f316,f1213]) ).

fof(f1215,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f1186]) ).

fof(f1216,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f1016,f1215]) ).

fof(f1217,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)],[f975,f1187]) ).

fof(f1218,plain,
    ! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),compose(a,b))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f975,f1217]) ).

fof(f1219,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),domain(X1))),domain(X1)) = codomain(domain(X1)),
    inference(forward_demodulation,[status(thm)],[f17,f1188]) ).

fof(f1220,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),codomain(compose(domain(X0),domain(X1))),domain(X1)) = domain(X1),
    inference(forward_demodulation,[status(thm)],[f17,f1219]) ).

fof(f1221,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),codomain(compose(domain(X0),codomain(X1))),codomain(X1)) = codomain(codomain(X1)),
    inference(forward_demodulation,[status(thm)],[f36,f1189]) ).

fof(f1222,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),codomain(compose(domain(X0),codomain(X1))),codomain(X1)) = codomain(X1),
    inference(forward_demodulation,[status(thm)],[f36,f1221]) ).

fof(f1242,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),h)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f147,f1203]) ).

fof(f1245,plain,
    ! [X0] : ifeq(domain(X0),domain(a),codomain(compose(domain(X0),a)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f24,f1205]) ).

fof(f1248,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1016,f84]) ).

fof(f1249,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),codomain(compose(compose(a,b),domain(X0))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f975,f84]) ).

fof(f1250,plain,
    ! [X0] : ifeq(domain(a),domain(X0),codomain(compose(g,domain(X0))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f316,f84]) ).

fof(f1251,plain,
    ! [X0] : ifeq(domain(a),domain(X0),codomain(compose(h,domain(X0))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f147,f84]) ).

fof(f1332,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1016,f86]) ).

fof(f1333,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),codomain(compose(compose(a,b),codomain(X0))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f975,f86]) ).

fof(f1334,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),codomain(compose(g,codomain(X0))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f316,f86]) ).

fof(f1335,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),codomain(compose(h,codomain(X0))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f147,f86]) ).

fof(f1436,plain,
    ifeq(domain(b),domain(h),domain(compose(a,g)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f478,f46]) ).

fof(f1437,plain,
    ifeq(domain(b),domain(h),domain(compose(a,compose(h,compose(a,b)))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f506,f46]) ).

fof(f1438,plain,
    ifeq(domain(b),domain(a),domain(compose(a,compose(a,b))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f261,f46]) ).

fof(f1448,plain,
    codomain(compose(h,a)) = codomain(a),
    inference(paramodulation,[status(thm)],[f16,f267]) ).

fof(f1449,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,g)),codomain(g)) = codomain(g),
    inference(paramodulation,[status(thm)],[f478,f267]) ).

fof(f1450,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f267]) ).

fof(f1460,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,h)),domain(a)) = codomain(h),
    inference(paramodulation,[status(thm)],[f147,f267]) ).

fof(f1465,plain,
    codomain(compose(h,a)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f24,f1448]) ).

fof(f1466,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,g)),domain(a)) = codomain(g),
    inference(forward_demodulation,[status(thm)],[f316,f1449]) ).

fof(f1467,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,g)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f316,f1466]) ).

fof(f1468,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f1450]) ).

fof(f1469,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f1016,f1468]) ).

fof(f1493,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,h)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f147,f1460]) ).

fof(f1507,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),codomain(compose(compose(h,a),codomain(X0))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1465,f86]) ).

fof(f1508,plain,
    ! [X0] : ifeq(domain(b),domain(X0),codomain(compose(compose(h,a),domain(X0))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1465,f84]) ).

fof(f1521,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X1,ifeq(compose(X0,b),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f26]) ).

fof(f1522,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(compose(h,a),b),X1,compose(h,a),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1465,f26]) ).

fof(f1523,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X1,ifeq(compose(X0,a),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f25]) ).

fof(f1524,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(h,a),a),X1,compose(h,a),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1465,f25]) ).

fof(f1525,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,X1)),compose(compose(compose(h,a),X0),X1)),compose(compose(compose(h,a),X0),X1)) = compose(compose(compose(h,a),X0),X1),
    inference(paramodulation,[status(thm)],[f1465,f23]) ).

fof(f1530,plain,
    ! [X0] : ifeq(domain(b),domain(X0),codomain(compose(compose(h,a),X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1465,f22]) ).

fof(f1534,plain,
    compose(compose(h,a),domain(b)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f20]) ).

fof(f1564,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),b),X1,ifeq(compose(X0,b),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f1521]) ).

fof(f1565,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),a),X1,ifeq(compose(X0,a),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f1523]) ).

fof(f1573,plain,
    ifeq(domain(b),domain(a),codomain(compose(compose(h,a),a)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1465,f96]) ).

fof(f1574,plain,
    ifeq(codomain(b),domain(a),codomain(compose(compose(h,compose(a,b)),a)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1016,f96]) ).

fof(f1575,plain,
    ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),a)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f975,f96]) ).

fof(f1576,plain,
    ifeq(domain(a),domain(a),codomain(compose(g,a)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f316,f96]) ).

fof(f1583,plain,
    codomain(compose(g,a)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f1576]) ).

fof(f1590,plain,
    ifeq(domain(b),domain(a),codomain(compose(compose(g,a),a)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1583,f96]) ).

fof(f1595,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),codomain(compose(compose(g,a),codomain(X0))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1583,f86]) ).

fof(f1596,plain,
    ! [X0] : ifeq(domain(b),domain(X0),codomain(compose(compose(g,a),domain(X0))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1583,f84]) ).

fof(f1611,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X1,ifeq(compose(X0,a),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f25]) ).

fof(f1612,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(g,a),a),X1,compose(g,a),X0),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1583,f25]) ).

fof(f1613,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,X1)),compose(compose(compose(g,a),X0),X1)),compose(compose(compose(g,a),X0),X1)) = compose(compose(compose(g,a),X0),X1),
    inference(paramodulation,[status(thm)],[f1583,f23]) ).

fof(f1614,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(compose(g,a)),compose(X1,compose(compose(g,a),X0)),compose(compose(X1,compose(g,a)),X0)),compose(compose(X1,compose(g,a)),X0)) = compose(compose(X1,compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f23]) ).

fof(f1618,plain,
    ! [X0] : ifeq(domain(b),domain(X0),codomain(compose(compose(g,a),X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1583,f22]) ).

fof(f1622,plain,
    compose(compose(g,a),domain(b)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f20]) ).

fof(f1655,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),a),X1,ifeq(compose(X0,a),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f1611]) ).

fof(f1667,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(X0),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),X0)),compose(compose(compose(h,a),domain(b)),X0)),compose(compose(h,a),X0)) = compose(compose(compose(h,a),domain(b)),X0),
    inference(paramodulation,[status(thm)],[f1534,f23]) ).

fof(f1687,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),X0)),compose(compose(compose(h,a),domain(b)),X0)),compose(compose(h,a),X0)) = compose(compose(compose(h,a),domain(b)),X0),
    inference(forward_demodulation,[status(thm)],[f17,f1667]) ).

fof(f1688,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(domain(b)),compose(compose(h,a),compose(domain(b),X0)),compose(compose(compose(h,a),domain(b)),X0)),compose(compose(h,a),X0)) = compose(compose(compose(h,a),domain(b)),X0),
    inference(forward_demodulation,[status(thm)],[f1465,f1687]) ).

fof(f1689,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(b),compose(compose(h,a),compose(domain(b),X0)),compose(compose(compose(h,a),domain(b)),X0)),compose(compose(h,a),X0)) = compose(compose(compose(h,a),domain(b)),X0),
    inference(forward_demodulation,[status(thm)],[f35,f1688]) ).

fof(f1690,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(b),X0)),compose(compose(h,a),X0)) = compose(compose(compose(h,a),domain(b)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f1689]) ).

fof(f1691,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(b),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
    inference(forward_demodulation,[status(thm)],[f1534,f1690]) ).

fof(f1711,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(X0),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),X0)),compose(compose(compose(g,a),domain(b)),X0)),compose(compose(g,a),X0)) = compose(compose(compose(g,a),domain(b)),X0),
    inference(paramodulation,[status(thm)],[f1622,f23]) ).

fof(f1731,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),X0)),compose(compose(compose(g,a),domain(b)),X0)),compose(compose(g,a),X0)) = compose(compose(compose(g,a),domain(b)),X0),
    inference(forward_demodulation,[status(thm)],[f17,f1711]) ).

fof(f1732,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(domain(b)),compose(compose(g,a),compose(domain(b),X0)),compose(compose(compose(g,a),domain(b)),X0)),compose(compose(g,a),X0)) = compose(compose(compose(g,a),domain(b)),X0),
    inference(forward_demodulation,[status(thm)],[f1583,f1731]) ).

fof(f1733,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(b),compose(compose(g,a),compose(domain(b),X0)),compose(compose(compose(g,a),domain(b)),X0)),compose(compose(g,a),X0)) = compose(compose(compose(g,a),domain(b)),X0),
    inference(forward_demodulation,[status(thm)],[f35,f1732]) ).

fof(f1734,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(b),X0)),compose(compose(g,a),X0)) = compose(compose(compose(g,a),domain(b)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f1733]) ).

fof(f1735,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(b),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
    inference(forward_demodulation,[status(thm)],[f1622,f1734]) ).

fof(f1752,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,g)),codomain(g)) = codomain(g),
    inference(paramodulation,[status(thm)],[f478,f330]) ).

fof(f1753,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f330]) ).

fof(f1766,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,h)),domain(a)) = codomain(h),
    inference(paramodulation,[status(thm)],[f147,f330]) ).

fof(f1772,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,g)),domain(a)) = codomain(g),
    inference(forward_demodulation,[status(thm)],[f316,f1752]) ).

fof(f1773,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,g)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f316,f1772]) ).

fof(f1774,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f1753]) ).

fof(f1775,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f1016,f1774]) ).

fof(f1802,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,h)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f147,f1766]) ).

fof(f1812,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),g)),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f514]) ).

fof(f1813,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(a,b),g)),domain(compose(a,b))) = domain(compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f514]) ).

fof(f1814,plain,
    ifeq(domain(a),domain(h),domain(compose(g,g)),domain(g)) = domain(g),
    inference(paramodulation,[status(thm)],[f316,f514]) ).

fof(f1815,plain,
    ifeq(domain(a),domain(h),domain(compose(h,g)),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f147,f514]) ).

fof(f1826,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),g)),domain(h)) = domain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f1812]) ).

fof(f1827,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),g)),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f506,f1826]) ).

fof(f1828,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(a,b),g)),domain(a)) = domain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f261,f1813]) ).

fof(f1829,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(a,b),g)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f261,f1828]) ).

fof(f1830,plain,
    ifeq(domain(a),domain(h),domain(compose(g,g)),domain(h)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f478,f1814]) ).

fof(f1831,plain,
    ifeq(domain(a),domain(h),domain(compose(g,g)),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f478,f1830]) ).

fof(f1854,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,b))),codomain(compose(a,b))) = codomain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f147,f140]) ).

fof(f1855,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,b))),codomain(b)) = codomain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f975,f1854]) ).

fof(f1856,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),codomain(compose(X0,compose(a,b))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f975,f1855]) ).

fof(f1857,plain,
    ifeq(domain(b),domain(a),codomain(compose(compose(g,a),compose(a,b))),codomain(b)) = codomain(b),
    inference(paramodulation,[status(thm)],[f1583,f1856]) ).

fof(f1858,plain,
    ifeq(domain(b),domain(a),codomain(compose(compose(h,a),compose(a,b))),codomain(b)) = codomain(b),
    inference(paramodulation,[status(thm)],[f1465,f1856]) ).

fof(f1859,plain,
    ifeq(codomain(b),domain(a),codomain(compose(compose(h,compose(a,b)),compose(a,b))),codomain(b)) = codomain(b),
    inference(paramodulation,[status(thm)],[f1016,f1856]) ).

fof(f1860,plain,
    ifeq(codomain(b),domain(a),codomain(compose(compose(a,b),compose(a,b))),codomain(b)) = codomain(b),
    inference(paramodulation,[status(thm)],[f975,f1856]) ).

fof(f1881,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),X0)),codomain(h)) = codomain(h),
    inference(forward_demodulation,[status(thm)],[f975,f153]) ).

fof(f1882,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),X0)),domain(a)) = codomain(h),
    inference(forward_demodulation,[status(thm)],[f147,f1881]) ).

fof(f1883,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(a,b),X0)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f147,f1882]) ).

fof(f1885,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(a,b),compose(h,compose(a,b)))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f506,f1883]) ).

fof(f1886,plain,
    ifeq(codomain(b),domain(a),domain(compose(compose(a,b),compose(a,b))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f261,f1883]) ).

fof(f1896,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),h)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1583,f276]) ).

fof(f1897,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),h)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1465,f276]) ).

fof(f1898,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),h)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1016,f276]) ).

fof(f1899,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),h)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f975,f276]) ).

fof(f1908,plain,
    domain(compose(h,a)) = domain(h),
    inference(paramodulation,[status(thm)],[f16,f269]) ).

fof(f1910,plain,
    ifeq(domain(a),domain(h),domain(compose(h,compose(h,compose(a,b)))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f506,f269]) ).

fof(f1925,plain,
    ifeq(domain(a),domain(h),domain(compose(h,compose(h,a))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f1908,f269]) ).

fof(f1926,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(a,b),compose(h,a))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1908,f1883]) ).

fof(f1927,plain,
    ifeq(codomain(compose(h,a)),domain(h),domain(compose(compose(h,a),g)),domain(h)) = domain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f514]) ).

fof(f1928,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f330]) ).

fof(f1929,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f267]) ).

fof(f1930,plain,
    ifeq(domain(b),domain(h),domain(compose(a,compose(h,a))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1908,f46]) ).

fof(f1935,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f74]) ).

fof(f1937,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f73]) ).

fof(f1938,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f72]) ).

fof(f1939,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),domain(compose(codomain(X0),compose(h,a))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1908,f67]) ).

fof(f1940,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(X0),domain(compose(compose(h,a),domain(X0))),domain(h)) = domain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f53]) ).

fof(f1945,plain,
    ! [X0] : ifeq(domain(X0),domain(h),domain(compose(domain(X0),compose(h,a))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1908,f690]) ).

fof(f1947,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),codomain(X0),domain(compose(compose(h,a),codomain(X0))),domain(h)) = domain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f38]) ).

fof(f1948,plain,
    ! [X0,X1] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,a),X0)),compose(compose(X1,compose(h,a)),X0)),compose(compose(X1,compose(h,a)),X0)) = compose(compose(X1,compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1908,f23]) ).

fof(f1949,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(h,a))),compose(compose(X1,X0),compose(h,a))),compose(compose(X1,X0),compose(h,a))) = compose(compose(X1,X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f23]) ).

fof(f1952,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f22]) ).

fof(f1954,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(X0),domain(compose(compose(h,a),X0)),domain(h)) = domain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f21]) ).

fof(f1955,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),domain(compose(X0,compose(h,a))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1908,f21]) ).

fof(f1957,plain,
    compose(domain(h),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1908,f19]) ).

fof(f1959,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),g)),domain(h)) = domain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1927]) ).

fof(f1960,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),g)),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f1908,f1959]) ).

fof(f1961,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1928]) ).

fof(f1962,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f1961]) ).

fof(f1963,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1929]) ).

fof(f1964,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f1963]) ).

fof(f1975,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1935]) ).

fof(f1976,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f1975]) ).

fof(f1978,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1937]) ).

fof(f1979,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f1978]) ).

fof(f1980,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1938]) ).

fof(f1981,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f1980]) ).

fof(f1982,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(compose(h,a),domain(X0))),domain(h)) = domain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1940]) ).

fof(f1983,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(compose(h,a),domain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f1908,f1982]) ).

fof(f1995,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),domain(compose(compose(h,a),codomain(X0))),domain(h)) = domain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1947]) ).

fof(f1996,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),domain(compose(compose(h,a),codomain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f1908,f1995]) ).

fof(f1997,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,a),X0)),compose(compose(X1,compose(h,a)),X0)),compose(compose(X1,compose(h,a)),X0)) = compose(compose(X1,compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1465,f1948]) ).

fof(f2002,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1952]) ).

fof(f2003,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f2002]) ).

fof(f2005,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(compose(h,a),X0)),domain(h)) = domain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f1954]) ).

fof(f2006,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(compose(h,a),X0)),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f1908,f2005]) ).

fof(f2008,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),domain(compose(X0,compose(a,b))),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f147,f143]) ).

fof(f2010,plain,
    ifeq(domain(b),domain(a),domain(compose(compose(h,a),compose(a,b))),domain(compose(h,a))) = domain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f2008]) ).

fof(f2011,plain,
    ifeq(codomain(b),domain(a),domain(compose(compose(h,compose(a,b)),compose(a,b))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f2008]) ).

fof(f2028,plain,
    ifeq(domain(b),domain(a),domain(compose(compose(h,a),compose(a,b))),domain(h)) = domain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f2010]) ).

fof(f2029,plain,
    ifeq(domain(b),domain(a),domain(compose(compose(h,a),compose(a,b))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f1908,f2028]) ).

fof(f2030,plain,
    ifeq(codomain(b),domain(a),domain(compose(compose(h,compose(a,b)),compose(a,b))),domain(h)) = domain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f2011]) ).

fof(f2031,plain,
    ifeq(codomain(b),domain(a),domain(compose(compose(h,compose(a,b)),compose(a,b))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f506,f2030]) ).

fof(f2071,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),X0)),compose(compose(domain(h),compose(h,a)),X0)),compose(compose(h,a),X0)) = compose(compose(domain(h),compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1957,f23]) ).

fof(f2073,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(compose(h,a)),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(h,a)),compose(compose(X0,domain(h)),compose(h,a))),compose(compose(X0,domain(h)),compose(h,a))) = compose(compose(X0,domain(h)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1957,f23]) ).

fof(f2083,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),X0)),compose(compose(domain(h),compose(h,a)),X0)),compose(compose(h,a),X0)) = compose(compose(domain(h),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1465,f2071]) ).

fof(f2084,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(h),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),X0)),compose(compose(domain(h),compose(h,a)),X0)),compose(compose(h,a),X0)) = compose(compose(domain(h),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f17,f2083]) ).

fof(f2085,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,a),X0)),compose(compose(domain(h),compose(h,a)),X0)),compose(compose(h,a),X0)) = compose(compose(domain(h),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f2084]) ).

fof(f2086,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(domain(h),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f2085]) ).

fof(f2087,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
    inference(forward_demodulation,[status(thm)],[f1957,f2086]) ).

fof(f2094,plain,
    ! [X0] : ifeq(domain(h),domain(compose(h,a)),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(h,a)),compose(compose(X0,domain(h)),compose(h,a))),compose(compose(X0,domain(h)),compose(h,a))) = compose(compose(X0,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f17,f2073]) ).

fof(f2095,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(h,a)),compose(compose(X0,domain(h)),compose(h,a))),compose(compose(X0,domain(h)),compose(h,a))) = compose(compose(X0,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f2094]) ).

fof(f2096,plain,
    ! [X0] : ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(h,a)),compose(compose(X0,domain(h)),compose(h,a))) = compose(compose(X0,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f16,f2095]) ).

fof(f2097,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,domain(h)),compose(h,a))) = compose(compose(X0,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f35,f2096]) ).

fof(f2104,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,g)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f478,f339]) ).

fof(f2105,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),g)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1583,f2104]) ).

fof(f2106,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),g)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1465,f2104]) ).

fof(f2107,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),g)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1016,f2104]) ).

fof(f2108,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),g)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f975,f2104]) ).

fof(f2121,plain,
    ! [X0] : ifeq(domain(a),domain(X0),domain(compose(g,X0)),domain(h)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f478,f332]) ).

fof(f2122,plain,
    ! [X0] : ifeq(domain(a),domain(X0),domain(compose(g,X0)),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f478,f2121]) ).

fof(f2123,plain,
    domain(compose(g,a)) = domain(h),
    inference(paramodulation,[status(thm)],[f16,f2122]) ).

fof(f2125,plain,
    ifeq(domain(a),domain(h),domain(compose(g,compose(h,a))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f1908,f2122]) ).

fof(f2126,plain,
    ifeq(domain(a),domain(h),domain(compose(g,compose(h,compose(a,b)))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f506,f2122]) ).

fof(f2143,plain,
    ifeq(domain(a),domain(h),domain(compose(g,compose(g,a))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f2123,f2122]) ).

fof(f2144,plain,
    ifeq(codomain(compose(g,a)),domain(a),domain(compose(compose(g,a),compose(a,b))),domain(h)) = domain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2008]) ).

fof(f2145,plain,
    ifeq(domain(a),domain(h),domain(compose(h,compose(g,a))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f2123,f269]) ).

fof(f2146,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(a,b),compose(g,a))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f2123,f1883]) ).

fof(f2147,plain,
    ifeq(codomain(compose(g,a)),domain(h),domain(compose(compose(g,a),g)),domain(h)) = domain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f514]) ).

fof(f2148,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f330]) ).

fof(f2149,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f267]) ).

fof(f2150,plain,
    ifeq(domain(b),domain(h),domain(compose(a,compose(g,a))),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f2123,f46]) ).

fof(f2155,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f74]) ).

fof(f2157,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f73]) ).

fof(f2158,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f72]) ).

fof(f2159,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),domain(compose(codomain(X0),compose(g,a))),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f2123,f67]) ).

fof(f2160,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(X0),domain(compose(compose(g,a),domain(X0))),domain(h)) = domain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f53]) ).

fof(f2165,plain,
    ! [X0] : ifeq(domain(X0),domain(h),domain(compose(domain(X0),compose(g,a))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f2123,f690]) ).

fof(f2167,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),codomain(X0),domain(compose(compose(g,a),codomain(X0))),domain(h)) = domain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f38]) ).

fof(f2169,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(g,a))),compose(compose(X1,X0),compose(g,a))),compose(compose(X1,X0),compose(g,a))) = compose(compose(X1,X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f23]) ).

fof(f2172,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f22]) ).

fof(f2174,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(X0),domain(compose(compose(g,a),X0)),domain(h)) = domain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f21]) ).

fof(f2175,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),domain(compose(X0,compose(g,a))),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f2123,f21]) ).

fof(f2177,plain,
    compose(domain(h),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f2123,f19]) ).

fof(f2180,plain,
    ifeq(domain(b),domain(a),domain(compose(compose(g,a),compose(a,b))),domain(h)) = domain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2144]) ).

fof(f2181,plain,
    ifeq(domain(b),domain(a),domain(compose(compose(g,a),compose(a,b))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f2123,f2180]) ).

fof(f2182,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),g)),domain(h)) = domain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2147]) ).

fof(f2183,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),g)),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f2123,f2182]) ).

fof(f2184,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2148]) ).

fof(f2185,plain,
    ifeq(domain(a),domain(h),codomain(compose(g,compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f2184]) ).

fof(f2186,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2149]) ).

fof(f2187,plain,
    ifeq(domain(a),domain(h),codomain(compose(h,compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f2186]) ).

fof(f2198,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2155]) ).

fof(f2199,plain,
    ! [X0] : ifeq(domain(X0),domain(h),codomain(compose(domain(X0),compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f2198]) ).

fof(f2201,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2157]) ).

fof(f2202,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f2201]) ).

fof(f2203,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2158]) ).

fof(f2204,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(codomain(X0),compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f2203]) ).

fof(f2205,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(compose(g,a),domain(X0))),domain(h)) = domain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2160]) ).

fof(f2206,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(compose(g,a),domain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f2123,f2205]) ).

fof(f2218,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),domain(compose(compose(g,a),codomain(X0))),domain(h)) = domain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2167]) ).

fof(f2219,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),domain(compose(compose(g,a),codomain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f2123,f2218]) ).

fof(f2225,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2172]) ).

fof(f2226,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f2225]) ).

fof(f2228,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(compose(g,a),X0)),domain(h)) = domain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f2174]) ).

fof(f2229,plain,
    ! [X0] : ifeq(domain(b),domain(X0),domain(compose(compose(g,a),X0)),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f2123,f2228]) ).

fof(f2234,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),X0)),compose(compose(domain(h),compose(g,a)),X0)),compose(compose(g,a),X0)) = compose(compose(domain(h),compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f2177,f23]) ).

fof(f2236,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(compose(g,a)),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(g,a)),compose(compose(X0,domain(h)),compose(g,a))),compose(compose(X0,domain(h)),compose(g,a))) = compose(compose(X0,domain(h)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2177,f23]) ).

fof(f2247,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),X0)),compose(compose(domain(h),compose(g,a)),X0)),compose(compose(g,a),X0)) = compose(compose(domain(h),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1583,f2234]) ).

fof(f2248,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(h),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),X0)),compose(compose(domain(h),compose(g,a)),X0)),compose(compose(g,a),X0)) = compose(compose(domain(h),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f17,f2247]) ).

fof(f2249,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(g,a),X0)),compose(compose(domain(h),compose(g,a)),X0)),compose(compose(g,a),X0)) = compose(compose(domain(h),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f2248]) ).

fof(f2250,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(domain(h),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f2249]) ).

fof(f2251,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
    inference(forward_demodulation,[status(thm)],[f2177,f2250]) ).

fof(f2258,plain,
    ! [X0] : ifeq(domain(h),domain(compose(g,a)),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(g,a)),compose(compose(X0,domain(h)),compose(g,a))),compose(compose(X0,domain(h)),compose(g,a))) = compose(compose(X0,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f17,f2236]) ).

fof(f2259,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(g,a)),compose(compose(X0,domain(h)),compose(g,a))),compose(compose(X0,domain(h)),compose(g,a))) = compose(compose(X0,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f2258]) ).

fof(f2260,plain,
    ! [X0] : ifeq(codomain(X0),domain(domain(h)),compose(X0,compose(g,a)),compose(compose(X0,domain(h)),compose(g,a))) = compose(compose(X0,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f2259]) ).

fof(f2261,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,domain(h)),compose(g,a))) = compose(compose(X0,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f35,f2260]) ).

fof(f2268,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)],[f16,f156]) ).

fof(f2269,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(a,g)),compose(compose(X0,a),g)),compose(compose(X0,a),g)) = compose(compose(X0,a),g),
    inference(paramodulation,[status(thm)],[f478,f156]) ).

fof(f2270,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(g,a))),compose(compose(X0,a),compose(g,a))),compose(compose(X0,a),compose(g,a))) = compose(compose(X0,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f156]) ).

fof(f2271,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(h,a))),compose(compose(X0,a),compose(h,a))),compose(compose(X0,a),compose(h,a))) = compose(compose(X0,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f156]) ).

fof(f2272,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(a,compose(h,compose(a,b)))),compose(compose(X0,a),compose(h,compose(a,b)))),compose(compose(X0,a),compose(h,compose(a,b)))) = compose(compose(X0,a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f156]) ).

fof(f2273,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)],[f261,f156]) ).

fof(f2274,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)],[f35,f156]) ).

fof(f2275,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)],[f18,f156]) ).

fof(f2276,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,X0)),compose(compose(compose(g,a),a),X0)),compose(compose(compose(g,a),a),X0)) = compose(compose(compose(g,a),a),X0),
    inference(paramodulation,[status(thm)],[f1583,f156]) ).

fof(f2277,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,X0)),compose(compose(compose(h,a),a),X0)),compose(compose(compose(h,a),a),X0)) = compose(compose(compose(h,a),a),X0),
    inference(paramodulation,[status(thm)],[f1465,f156]) ).

fof(f2278,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,X0)),compose(compose(compose(h,compose(a,b)),a),X0)),compose(compose(compose(h,compose(a,b)),a),X0)) = compose(compose(compose(h,compose(a,b)),a),X0),
    inference(paramodulation,[status(thm)],[f1016,f156]) ).

fof(f2279,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)],[f975,f156]) ).

fof(f2280,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),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)],[f316,f156]) ).

fof(f2281,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(a),compose(h,compose(a,X0)),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
    inference(paramodulation,[status(thm)],[f147,f156]) ).

fof(f2282,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)],[f36,f156]) ).

fof(f2283,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,f156]) ).

fof(f2284,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)],[f17,f156]) ).

fof(f2287,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)],[f19,f156]) ).

fof(f2293,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)],[f20,f156]) ).

fof(f2294,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)],[f19,f156]) ).

fof(f2301,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(g,compose(a,X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
    inference(forward_demodulation,[status(thm)],[f16,f2280]) ).

fof(f2302,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(h,compose(a,X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
    inference(forward_demodulation,[status(thm)],[f16,f2281]) ).

fof(f2309,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)],[f17,f2287]) ).

fof(f2331,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)],[f18,f2293]) ).

fof(f2332,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)],[f20,f2331]) ).

fof(f2333,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)],[f20,f2332]) ).

fof(f2334,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)],[f17,f2294]) ).

fof(f2335,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)],[f16,f2334]) ).

fof(f2336,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)],[f19,f2335]) ).

fof(f2337,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(a),compose(a,X0)),compose(a,X0)) = compose(a,X0),
    inference(forward_demodulation,[status(thm)],[f19,f2336]) ).

fof(f2644,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),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)],[f478,f186]) ).

fof(f2645,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(g,a))),compose(compose(X1,domain(X0)),compose(g,a))),compose(compose(X1,domain(X0)),compose(g,a))) = compose(compose(X1,domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f186]) ).

fof(f2646,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(h,a))),compose(compose(X1,domain(X0)),compose(h,a))),compose(compose(X1,domain(X0)),compose(h,a))) = compose(compose(X1,domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f186]) ).

fof(f2647,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(X1,domain(X0)),compose(h,compose(a,b)))),compose(compose(X1,domain(X0)),compose(h,compose(a,b)))) = compose(compose(X1,domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f186]) ).

fof(f2648,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)],[f261,f186]) ).

fof(f2649,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)],[f35,f186]) ).

fof(f2650,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)],[f18,f186]) ).

fof(f2651,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),X1)),compose(compose(compose(g,a),domain(X0)),X1)),compose(compose(compose(g,a),domain(X0)),X1)) = compose(compose(compose(g,a),domain(X0)),X1),
    inference(paramodulation,[status(thm)],[f1583,f186]) ).

fof(f2652,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),X1)),compose(compose(compose(h,a),domain(X0)),X1)),compose(compose(compose(h,a),domain(X0)),X1)) = compose(compose(compose(h,a),domain(X0)),X1),
    inference(paramodulation,[status(thm)],[f1465,f186]) ).

fof(f2653,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),X1)),compose(compose(compose(h,compose(a,b)),domain(X0)),X1)),compose(compose(compose(h,compose(a,b)),domain(X0)),X1)) = compose(compose(compose(h,compose(a,b)),domain(X0)),X1),
    inference(paramodulation,[status(thm)],[f1016,f186]) ).

fof(f2654,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)],[f975,f186]) ).

fof(f2655,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(a),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)],[f316,f186]) ).

fof(f2656,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),X1)),compose(compose(h,domain(X0)),X1)),compose(compose(h,domain(X0)),X1)) = compose(compose(h,domain(X0)),X1),
    inference(paramodulation,[status(thm)],[f147,f186]) ).

fof(f2657,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)],[f36,f186]) ).

fof(f2658,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,f186]) ).

fof(f2659,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)],[f17,f186]) ).

fof(f2667,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)],[f19,f186]) ).

fof(f2682,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)],[f20,f186]) ).

fof(f2784,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)],[f17,f2667]) ).

fof(f2836,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)],[f18,f2682]) ).

fof(f2837,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)],[f20,f2836]) ).

fof(f2838,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)],[f20,f2837]) ).

fof(f2966,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(forward_demodulation,[status(thm)],[f147,f158]) ).

fof(f2967,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(compose(g,a)),compose(X0,compose(compose(g,a),compose(a,b))),compose(compose(X0,compose(g,a)),compose(a,b))),compose(compose(X0,compose(g,a)),compose(a,b))) = compose(compose(X0,compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2966]) ).

fof(f2968,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(compose(h,a),compose(a,b))),compose(compose(X0,compose(h,a)),compose(a,b))),compose(compose(X0,compose(h,a)),compose(a,b))) = compose(compose(X0,compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2966]) ).

fof(f2969,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(compose(h,compose(a,b))),compose(X0,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),compose(a,b))) = compose(compose(X0,compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f2966]) ).

fof(f2972,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(h),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)],[f147,f2966]) ).

fof(f2973,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(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)],[f36,f2966]) ).

fof(f2976,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,compose(a,b))),compose(compose(compose(g,a),X0),compose(a,b))),compose(compose(compose(g,a),X0),compose(a,b))) = compose(compose(compose(g,a),X0),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2966]) ).

fof(f2977,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,compose(a,b))),compose(compose(compose(h,a),X0),compose(a,b))),compose(compose(compose(h,a),X0),compose(a,b))) = compose(compose(compose(h,a),X0),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2966]) ).

fof(f2978,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,compose(a,b))),compose(compose(compose(h,compose(a,b)),X0),compose(a,b))),compose(compose(compose(h,compose(a,b)),X0),compose(a,b))) = compose(compose(compose(h,compose(a,b)),X0),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f2966]) ).

fof(f2979,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)],[f975,f2966]) ).

fof(f2980,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),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)],[f316,f2966]) ).

fof(f2981,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(X0),compose(h,compose(X0,compose(a,b))),compose(compose(h,X0),compose(a,b))),compose(compose(h,X0),compose(a,b))) = compose(compose(h,X0),compose(a,b)),
    inference(paramodulation,[status(thm)],[f147,f2966]) ).

fof(f2982,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)],[f36,f2966]) ).

fof(f2983,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)],[f24,f2966]) ).

fof(f2984,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)],[f17,f2966]) ).

fof(f2989,plain,
    ! [X0] : ifeq(codomain(compose(a,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)],[f261,f2966]) ).

fof(f2992,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(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)],[f19,f2966]) ).

fof(f2996,plain,
    ifeq(codomain(domain(b)),domain(a),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,a),domain(b)),compose(a,b))) = compose(compose(compose(h,a),domain(b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1534,f2966]) ).

fof(f2997,plain,
    ifeq(codomain(codomain(b)),domain(a),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(a,b))),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,b),codomain(b)),compose(a,b))) = compose(compose(compose(a,b),codomain(b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1043,f2966]) ).

fof(f2998,plain,
    ifeq(codomain(domain(b)),domain(a),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(compose(g,a),domain(b)),compose(a,b))) = compose(compose(compose(g,a),domain(b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1622,f2966]) ).

fof(f2999,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(compose(g,a)),domain(b),compose(compose(g,a),compose(b,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(g,a),b),compose(a,b))) = compose(compose(compose(g,a),b),compose(a,b)),
    inference(paramodulation,[status(thm)],[f446,f2966]) ).

fof(f3000,plain,
    ifeq(codomain(compose(a,b)),domain(a),ifeq(codomain(g),domain(compose(a,b)),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(h,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)],[f29,f2966]) ).

fof(f3003,plain,
    ! [X0] : ifeq(codomain(codomain(X0)),domain(a),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))),compose(compose(codomain(X0),codomain(X0)),compose(a,b))) = compose(compose(codomain(X0),codomain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f34,f2966]) ).

fof(f3004,plain,
    ifeq(codomain(domain(b)),domain(a),ifeq(codomain(a),domain(domain(b)),compose(a,compose(domain(b),compose(a,b))),compose(a,compose(a,b))),compose(compose(a,domain(b)),compose(a,b))) = compose(compose(a,domain(b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f48,f2966]) ).

fof(f3005,plain,
    ifeq(codomain(compose(g,a)),domain(a),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(domain(h),compose(g,a)),compose(a,b))) = compose(compose(domain(h),compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f2177,f2966]) ).

fof(f3006,plain,
    ifeq(codomain(compose(h,a)),domain(a),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(domain(h),compose(h,a)),compose(a,b))) = compose(compose(domain(h),compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1957,f2966]) ).

fof(f3008,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,b))),compose(compose(a,b),compose(a,b))),compose(compose(domain(a),compose(a,b)),compose(a,b))) = compose(compose(domain(a),compose(a,b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f406,f2966]) ).

fof(f3009,plain,
    ! [X0] : ifeq(codomain(domain(X0)),domain(a),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))),compose(compose(domain(X0),domain(X0)),compose(a,b))) = compose(compose(domain(X0),domain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f31,f2966]) ).

fof(f3010,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(X0)),domain(X0),compose(domain(X0),compose(X0,compose(a,b))),compose(X0,compose(a,b))),compose(compose(domain(X0),X0),compose(a,b))) = compose(compose(domain(X0),X0),compose(a,b)),
    inference(paramodulation,[status(thm)],[f19,f2966]) ).

fof(f3011,plain,
    ! [X0] : ifeq(codomain(codomain(X0)),domain(a),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),compose(a,b))),compose(X0,compose(a,b))),compose(compose(X0,codomain(X0)),compose(a,b))) = compose(compose(X0,codomain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f20,f2966]) ).

fof(f3028,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(a,b))),compose(compose(X0,compose(g,a)),compose(a,b))),compose(compose(X0,compose(g,a)),compose(a,b))) = compose(compose(X0,compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f2967]) ).

fof(f3029,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(a,b))),compose(compose(X0,compose(h,a)),compose(a,b))),compose(compose(X0,compose(h,a)),compose(a,b))) = compose(compose(X0,compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f2968]) ).

fof(f3030,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),compose(a,b))) = compose(compose(X0,compose(h,compose(a,b))),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f506,f2969]) ).

fof(f3035,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,h),compose(a,b))) = compose(compose(X0,h),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f2972]) ).

fof(f3036,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(forward_demodulation,[status(thm)],[f18,f2973]) ).

fof(f3044,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(forward_demodulation,[status(thm)],[f975,f2989]) ).

fof(f3047,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(forward_demodulation,[status(thm)],[f17,f2992]) ).

fof(f3061,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,a),domain(b)),compose(a,b))) = compose(compose(compose(h,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f2996]) ).

fof(f3062,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(domain(b)),compose(compose(h,a),compose(domain(b),compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,a),domain(b)),compose(a,b))) = compose(compose(compose(h,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1465,f3061]) ).

fof(f3063,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),compose(compose(h,a),compose(domain(b),compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,a),domain(b)),compose(a,b))) = compose(compose(compose(h,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f35,f3062]) ).

fof(f3064,plain,
    ifeq(domain(b),domain(a),compose(compose(h,a),compose(domain(b),compose(a,b))),compose(compose(compose(h,a),domain(b)),compose(a,b))) = compose(compose(compose(h,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3063]) ).

fof(f3065,plain,
    ifeq(domain(b),domain(a),compose(compose(h,a),compose(domain(b),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(compose(h,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1534,f3064]) ).

fof(f3066,plain,
    ifeq(domain(b),domain(a),compose(compose(h,a),compose(domain(b),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1534,f3065]) ).

fof(f3067,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(a,b))),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,b),codomain(b)),compose(a,b))) = compose(compose(compose(a,b),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f36,f2997]) ).

fof(f3068,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(a,b))),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,b),codomain(b)),compose(a,b))) = compose(compose(compose(a,b),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f975,f3067]) ).

fof(f3069,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),codomain(b),compose(compose(a,b),compose(codomain(b),compose(a,b))),compose(compose(a,b),compose(a,b))),compose(compose(compose(a,b),codomain(b)),compose(a,b))) = compose(compose(compose(a,b),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f18,f3068]) ).

fof(f3070,plain,
    ifeq(codomain(b),domain(a),compose(compose(a,b),compose(codomain(b),compose(a,b))),compose(compose(compose(a,b),codomain(b)),compose(a,b))) = compose(compose(compose(a,b),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3069]) ).

fof(f3071,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(compose(a,b),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1043,f3070]) ).

fof(f3072,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)],[f1043,f3071]) ).

fof(f3073,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(compose(g,a),domain(b)),compose(a,b))) = compose(compose(compose(g,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f2998]) ).

fof(f3074,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(domain(b)),compose(compose(g,a),compose(domain(b),compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(compose(g,a),domain(b)),compose(a,b))) = compose(compose(compose(g,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1583,f3073]) ).

fof(f3075,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),compose(compose(g,a),compose(domain(b),compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(compose(g,a),domain(b)),compose(a,b))) = compose(compose(compose(g,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f35,f3074]) ).

fof(f3076,plain,
    ifeq(domain(b),domain(a),compose(compose(g,a),compose(domain(b),compose(a,b))),compose(compose(compose(g,a),domain(b)),compose(a,b))) = compose(compose(compose(g,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3075]) ).

fof(f3077,plain,
    ifeq(domain(b),domain(a),compose(compose(g,a),compose(domain(b),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(compose(g,a),domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1622,f3076]) ).

fof(f3078,plain,
    ifeq(domain(b),domain(a),compose(compose(g,a),compose(domain(b),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1622,f3077]) ).

fof(f3079,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(b),domain(b),compose(compose(g,a),compose(b,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(g,a),b),compose(a,b))) = compose(compose(compose(g,a),b),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1583,f2999]) ).

fof(f3080,plain,
    ifeq(codomain(b),domain(a),compose(compose(g,a),compose(b,compose(a,b))),compose(compose(compose(g,a),b),compose(a,b))) = compose(compose(compose(g,a),b),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3079]) ).

fof(f3081,plain,
    ifeq(codomain(b),domain(a),compose(compose(g,a),compose(b,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),b),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f446,f3080]) ).

fof(f3082,plain,
    ifeq(codomain(b),domain(a),compose(compose(g,a),compose(b,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f446,f3081]) ).

fof(f3083,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(g),domain(compose(a,b)),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(h,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)],[f975,f3000]) ).

fof(f3084,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(compose(a,b)),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(h,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)],[f316,f3083]) ).

fof(f3085,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(a),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(h,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)],[f261,f3084]) ).

fof(f3086,plain,
    ifeq(codomain(b),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)),
    inference(forward_demodulation,[status(thm)],[f16,f3085]) ).

fof(f3087,plain,
    ifeq(codomain(b),domain(a),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(g,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f29,f3086]) ).

fof(f3088,plain,
    ifeq(codomain(b),domain(a),compose(g,compose(compose(a,b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f29,f3087]) ).

fof(f3103,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(codomain(X0)),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))),compose(compose(codomain(X0),codomain(X0)),compose(a,b))) = compose(compose(codomain(X0),codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f36,f3003]) ).

fof(f3104,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(codomain(X0)),compose(codomain(X0),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))),compose(compose(codomain(X0),codomain(X0)),compose(a,b))) = compose(compose(codomain(X0),codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f36,f3103]) ).

fof(f3105,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),codomain(X0),compose(codomain(X0),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))),compose(compose(codomain(X0),codomain(X0)),compose(a,b))) = compose(compose(codomain(X0),codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f18,f3104]) ).

fof(f3106,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(codomain(X0),compose(a,b))),compose(compose(codomain(X0),codomain(X0)),compose(a,b))) = compose(compose(codomain(X0),codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3105]) ).

fof(f3107,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(codomain(X0),compose(a,b))),compose(codomain(X0),compose(a,b))) = compose(compose(codomain(X0),codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f34,f3106]) ).

fof(f3108,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(forward_demodulation,[status(thm)],[f34,f3107]) ).

fof(f3109,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(a),domain(domain(b)),compose(a,compose(domain(b),compose(a,b))),compose(a,compose(a,b))),compose(compose(a,domain(b)),compose(a,b))) = compose(compose(a,domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f3004]) ).

fof(f3110,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(domain(b)),compose(a,compose(domain(b),compose(a,b))),compose(a,compose(a,b))),compose(compose(a,domain(b)),compose(a,b))) = compose(compose(a,domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f24,f3109]) ).

fof(f3111,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),compose(a,compose(domain(b),compose(a,b))),compose(a,compose(a,b))),compose(compose(a,domain(b)),compose(a,b))) = compose(compose(a,domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f35,f3110]) ).

fof(f3112,plain,
    ifeq(domain(b),domain(a),compose(a,compose(domain(b),compose(a,b))),compose(compose(a,domain(b)),compose(a,b))) = compose(compose(a,domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3111]) ).

fof(f3113,plain,
    ifeq(domain(b),domain(a),compose(a,compose(domain(b),compose(a,b))),compose(a,compose(a,b))) = compose(compose(a,domain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f48,f3112]) ).

fof(f3114,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(forward_demodulation,[status(thm)],[f48,f3113]) ).

fof(f3115,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(domain(h),compose(g,a)),compose(a,b))) = compose(compose(domain(h),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1583,f3005]) ).

fof(f3116,plain,
    ifeq(domain(b),domain(a),ifeq(domain(h),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(domain(h),compose(g,a)),compose(a,b))) = compose(compose(domain(h),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f3115]) ).

fof(f3117,plain,
    ifeq(domain(b),domain(a),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))),compose(compose(domain(h),compose(g,a)),compose(a,b))) = compose(compose(domain(h),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f3116]) ).

fof(f3118,plain,
    ifeq(domain(b),domain(a),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(domain(h),compose(g,a)),compose(a,b))) = compose(compose(domain(h),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3117]) ).

fof(f3119,plain,
    ifeq(domain(b),domain(a),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(domain(h),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2177,f3118]) ).

fof(f3120,plain,
    ifeq(domain(b),domain(a),compose(domain(h),compose(compose(g,a),compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2177,f3119]) ).

fof(f3121,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(domain(h),compose(h,a)),compose(a,b))) = compose(compose(domain(h),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1465,f3006]) ).

fof(f3122,plain,
    ifeq(domain(b),domain(a),ifeq(domain(h),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(domain(h),compose(h,a)),compose(a,b))) = compose(compose(domain(h),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f3121]) ).

fof(f3123,plain,
    ifeq(domain(b),domain(a),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(domain(h),compose(h,a)),compose(a,b))) = compose(compose(domain(h),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f3122]) ).

fof(f3124,plain,
    ifeq(domain(b),domain(a),compose(domain(h),compose(compose(h,a),compose(a,b))),compose(compose(domain(h),compose(h,a)),compose(a,b))) = compose(compose(domain(h),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3123]) ).

fof(f3125,plain,
    ifeq(domain(b),domain(a),compose(domain(h),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(domain(h),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1957,f3124]) ).

fof(f3126,plain,
    ifeq(domain(b),domain(a),compose(domain(h),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1957,f3125]) ).

fof(f3135,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(domain(a)),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))),compose(compose(domain(a),compose(a,b)),compose(a,b))) = compose(compose(domain(a),compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f975,f3008]) ).

fof(f3136,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(compose(a,b)),compose(domain(a),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))),compose(compose(domain(a),compose(a,b)),compose(a,b))) = compose(compose(domain(a),compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f3135]) ).

fof(f3137,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(a),compose(domain(a),compose(compose(a,b),compose(a,b))),compose(compose(a,b),compose(a,b))),compose(compose(domain(a),compose(a,b)),compose(a,b))) = compose(compose(domain(a),compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f261,f3136]) ).

fof(f3138,plain,
    ifeq(codomain(b),domain(a),compose(domain(a),compose(compose(a,b),compose(a,b))),compose(compose(domain(a),compose(a,b)),compose(a,b))) = compose(compose(domain(a),compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3137]) ).

fof(f3139,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(domain(a),compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f406,f3138]) ).

fof(f3140,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)],[f406,f3139]) ).

fof(f3141,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(X0)),domain(domain(X0)),compose(domain(X0),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))),compose(compose(domain(X0),domain(X0)),compose(a,b))) = compose(compose(domain(X0),domain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f3009]) ).

fof(f3142,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(X0),domain(domain(X0)),compose(domain(X0),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))),compose(compose(domain(X0),domain(X0)),compose(a,b))) = compose(compose(domain(X0),domain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f3141]) ).

fof(f3143,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))),compose(compose(domain(X0),domain(X0)),compose(a,b))) = compose(compose(domain(X0),domain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f35,f3142]) ).

fof(f3144,plain,
    ! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(domain(X0),compose(a,b))),compose(compose(domain(X0),domain(X0)),compose(a,b))) = compose(compose(domain(X0),domain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3143]) ).

fof(f3145,plain,
    ! [X0] : ifeq(domain(X0),domain(a),compose(domain(X0),compose(domain(X0),compose(a,b))),compose(domain(X0),compose(a,b))) = compose(compose(domain(X0),domain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f31,f3144]) ).

fof(f3146,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(forward_demodulation,[status(thm)],[f31,f3145]) ).

fof(f3147,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(X0),domain(X0),compose(domain(X0),compose(X0,compose(a,b))),compose(X0,compose(a,b))),compose(compose(domain(X0),X0),compose(a,b))) = compose(compose(domain(X0),X0),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f3010]) ).

fof(f3148,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),compose(domain(X0),compose(X0,compose(a,b))),compose(compose(domain(X0),X0),compose(a,b))) = compose(compose(domain(X0),X0),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3147]) ).

fof(f3149,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),compose(domain(X0),compose(X0,compose(a,b))),compose(X0,compose(a,b))) = compose(compose(domain(X0),X0),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f19,f3148]) ).

fof(f3150,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(forward_demodulation,[status(thm)],[f19,f3149]) ).

fof(f3151,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(codomain(X0)),compose(X0,compose(codomain(X0),compose(a,b))),compose(X0,compose(a,b))),compose(compose(X0,codomain(X0)),compose(a,b))) = compose(compose(X0,codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f36,f3011]) ).

fof(f3152,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),codomain(X0),compose(X0,compose(codomain(X0),compose(a,b))),compose(X0,compose(a,b))),compose(compose(X0,codomain(X0)),compose(a,b))) = compose(compose(X0,codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f18,f3151]) ).

fof(f3153,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(codomain(X0),compose(a,b))),compose(compose(X0,codomain(X0)),compose(a,b))) = compose(compose(X0,codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f3152]) ).

fof(f3154,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(codomain(X0),compose(a,b))),compose(X0,compose(a,b))) = compose(compose(X0,codomain(X0)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f20,f3153]) ).

fof(f3155,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(forward_demodulation,[status(thm)],[f20,f3154]) ).

fof(f3591,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(compose(g,a)),compose(X1,compose(compose(g,a),codomain(X0))),compose(compose(X1,compose(g,a)),codomain(X0))),compose(compose(X1,compose(g,a)),codomain(X0))) = compose(compose(X1,compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f160]) ).

fof(f3592,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(compose(h,a)),compose(X1,compose(compose(h,a),codomain(X0))),compose(compose(X1,compose(h,a)),codomain(X0))),compose(compose(X1,compose(h,a)),codomain(X0))) = compose(compose(X1,compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f160]) ).

fof(f3593,plain,
    ! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(compose(h,compose(a,b))),compose(X1,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(X1,compose(h,compose(a,b))),codomain(X0))),compose(compose(X1,compose(h,compose(a,b))),codomain(X0))) = compose(compose(X1,compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f160]) ).

fof(f3595,plain,
    ! [X0,X1] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(g),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)],[f316,f160]) ).

fof(f3596,plain,
    ! [X0,X1] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(h),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)],[f147,f160]) ).

fof(f3597,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)],[f36,f160]) ).

fof(f3609,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,codomain(X1))),compose(compose(compose(g,a),X0),codomain(X1))),compose(compose(compose(g,a),X0),codomain(X1))) = compose(compose(compose(g,a),X0),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1583,f160]) ).

fof(f3610,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,codomain(X1))),compose(compose(compose(h,a),X0),codomain(X1))),compose(compose(compose(h,a),X0),codomain(X1))) = compose(compose(compose(h,a),X0),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1465,f160]) ).

fof(f3611,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,codomain(X1))),compose(compose(compose(h,compose(a,b)),X0),codomain(X1))),compose(compose(compose(h,compose(a,b)),X0),codomain(X1))) = compose(compose(compose(h,compose(a,b)),X0),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1016,f160]) ).

fof(f3612,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)],[f975,f160]) ).

fof(f3613,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(a),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)],[f316,f160]) ).

fof(f3614,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(a),domain(X0),compose(h,compose(X0,codomain(X1))),compose(compose(h,X0),codomain(X1))),compose(compose(h,X0),codomain(X1))) = compose(compose(h,X0),codomain(X1)),
    inference(paramodulation,[status(thm)],[f147,f160]) ).

fof(f3615,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)],[f36,f160]) ).

fof(f3616,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,f160]) ).

fof(f3617,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)],[f17,f160]) ).

fof(f3622,plain,
    ! [X0,X1] : ifeq(codomain(compose(a,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(paramodulation,[status(thm)],[f261,f160]) ).

fof(f3625,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)],[f19,f160]) ).

fof(f3641,plain,
    ! [X0] : ifeq(codomain(domain(b)),codomain(X0),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,a),domain(b)),codomain(X0))) = compose(compose(compose(h,a),domain(b)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1534,f160]) ).

fof(f3642,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)],[f1043,f160]) ).

fof(f3643,plain,
    ! [X0] : ifeq(codomain(domain(b)),codomain(X0),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(compose(g,a),domain(b)),codomain(X0))) = compose(compose(compose(g,a),domain(b)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1622,f160]) ).

fof(f3644,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(compose(g,a)),domain(b),compose(compose(g,a),compose(b,codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(g,a),b),codomain(X0))) = compose(compose(compose(g,a),b),codomain(X0)),
    inference(paramodulation,[status(thm)],[f446,f160]) ).

fof(f3645,plain,
    ! [X0] : ifeq(codomain(compose(a,b)),codomain(X0),ifeq(codomain(g),domain(compose(a,b)),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(h,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)],[f29,f160]) ).

fof(f3646,plain,
    ! [X0] : ifeq(codomain(domain(a)),codomain(X0),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),codomain(X0))),compose(g,codomain(X0))),compose(compose(g,domain(a)),codomain(X0))) = compose(compose(g,domain(a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f334,f160]) ).

fof(f3647,plain,
    ! [X0] : ifeq(codomain(domain(a)),codomain(X0),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),codomain(X0))),compose(h,codomain(X0))),compose(compose(h,domain(a)),codomain(X0))) = compose(compose(h,domain(a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f271,f160]) ).

fof(f3648,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)],[f34,f160]) ).

fof(f3649,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)],[f48,f160]) ).

fof(f3650,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),codomain(X0),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(domain(h),compose(g,a)),codomain(X0))) = compose(compose(domain(h),compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f2177,f160]) ).

fof(f3651,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),codomain(X0),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(domain(h),compose(h,a)),codomain(X0))) = compose(compose(domain(h),compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1957,f160]) ).

fof(f3652,plain,
    ! [X0] : ifeq(codomain(g),codomain(X0),ifeq(codomain(domain(h)),domain(g),compose(domain(h),compose(g,codomain(X0))),compose(g,codomain(X0))),compose(compose(domain(h),g),codomain(X0))) = compose(compose(domain(h),g),codomain(X0)),
    inference(paramodulation,[status(thm)],[f516,f160]) ).

fof(f3653,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)],[f406,f160]) ).

fof(f3654,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)],[f31,f160]) ).

fof(f3655,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)],[f19,f160]) ).

fof(f3656,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)],[f20,f160]) ).

fof(f3695,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(g,a),codomain(X0))),compose(compose(X1,compose(g,a)),codomain(X0))),compose(compose(X1,compose(g,a)),codomain(X0))) = compose(compose(X1,compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f3591]) ).

fof(f3696,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,a),codomain(X0))),compose(compose(X1,compose(h,a)),codomain(X0))),compose(compose(X1,compose(h,a)),codomain(X0))) = compose(compose(X1,compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f3592]) ).

fof(f3697,plain,
    ! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(X1,compose(h,compose(a,b))),codomain(X0))),compose(compose(X1,compose(h,compose(a,b))),codomain(X0))) = compose(compose(X1,compose(h,compose(a,b))),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f506,f3593]) ).

fof(f3699,plain,
    ! [X0,X1] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(h),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)],[f478,f3595]) ).

fof(f3700,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)],[f18,f3597]) ).

fof(f3742,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)],[f975,f3622]) ).

fof(f3745,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)],[f17,f3625]) ).

fof(f3802,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,a),domain(b)),codomain(X0))) = compose(compose(compose(h,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f3641]) ).

fof(f3803,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(domain(b)),compose(compose(h,a),compose(domain(b),codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,a),domain(b)),codomain(X0))) = compose(compose(compose(h,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1465,f3802]) ).

fof(f3804,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(b),compose(compose(h,a),compose(domain(b),codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,a),domain(b)),codomain(X0))) = compose(compose(compose(h,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f3803]) ).

fof(f3805,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(domain(b),codomain(X0))),compose(compose(compose(h,a),domain(b)),codomain(X0))) = compose(compose(compose(h,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3804]) ).

fof(f3806,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(domain(b),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(compose(h,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1534,f3805]) ).

fof(f3807,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(domain(b),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1534,f3806]) ).

fof(f3808,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)],[f36,f3642]) ).

fof(f3809,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)],[f975,f3808]) ).

fof(f3810,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)],[f18,f3809]) ).

fof(f3811,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)],[f16,f3810]) ).

fof(f3812,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)],[f1043,f3811]) ).

fof(f3813,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)],[f1043,f3812]) ).

fof(f3814,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(compose(g,a),domain(b)),codomain(X0))) = compose(compose(compose(g,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f3643]) ).

fof(f3815,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(domain(b)),compose(compose(g,a),compose(domain(b),codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(compose(g,a),domain(b)),codomain(X0))) = compose(compose(compose(g,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1583,f3814]) ).

fof(f3816,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(b),compose(compose(g,a),compose(domain(b),codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(compose(g,a),domain(b)),codomain(X0))) = compose(compose(compose(g,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f3815]) ).

fof(f3817,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(domain(b),codomain(X0))),compose(compose(compose(g,a),domain(b)),codomain(X0))) = compose(compose(compose(g,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3816]) ).

fof(f3818,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(domain(b),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(compose(g,a),domain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1622,f3817]) ).

fof(f3819,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(domain(b),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1622,f3818]) ).

fof(f3820,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(b),compose(compose(g,a),compose(b,codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(g,a),b),codomain(X0))) = compose(compose(compose(g,a),b),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1583,f3644]) ).

fof(f3821,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(g,a),compose(b,codomain(X0))),compose(compose(compose(g,a),b),codomain(X0))) = compose(compose(compose(g,a),b),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3820]) ).

fof(f3822,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(g,a),compose(b,codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),b),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f446,f3821]) ).

fof(f3823,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(g,a),compose(b,codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f446,f3822]) ).

fof(f3824,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(g),domain(compose(a,b)),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f975,f3645]) ).

fof(f3825,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(compose(a,b)),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f316,f3824]) ).

fof(f3826,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(a),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f261,f3825]) ).

fof(f3827,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(g,compose(a,b)),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3826]) ).

fof(f3828,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(g,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f29,f3827]) ).

fof(f3829,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(g,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f29,f3828]) ).

fof(f3830,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),codomain(X0))),compose(g,codomain(X0))),compose(compose(g,domain(a)),codomain(X0))) = compose(compose(g,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f3646]) ).

fof(f3831,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(domain(a)),compose(g,compose(domain(a),codomain(X0))),compose(g,codomain(X0))),compose(compose(g,domain(a)),codomain(X0))) = compose(compose(g,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f316,f3830]) ).

fof(f3832,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(a),compose(g,compose(domain(a),codomain(X0))),compose(g,codomain(X0))),compose(compose(g,domain(a)),codomain(X0))) = compose(compose(g,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f3831]) ).

fof(f3833,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(g,compose(domain(a),codomain(X0))),compose(compose(g,domain(a)),codomain(X0))) = compose(compose(g,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3832]) ).

fof(f3834,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(g,compose(domain(a),codomain(X0))),compose(g,codomain(X0))) = compose(compose(g,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f334,f3833]) ).

fof(f3835,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(g,compose(domain(a),codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f334,f3834]) ).

fof(f3836,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),codomain(X0))),compose(h,codomain(X0))),compose(compose(h,domain(a)),codomain(X0))) = compose(compose(h,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f3647]) ).

fof(f3837,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(domain(a)),compose(h,compose(domain(a),codomain(X0))),compose(h,codomain(X0))),compose(compose(h,domain(a)),codomain(X0))) = compose(compose(h,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f147,f3836]) ).

fof(f3838,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(a),compose(h,compose(domain(a),codomain(X0))),compose(h,codomain(X0))),compose(compose(h,domain(a)),codomain(X0))) = compose(compose(h,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f3837]) ).

fof(f3839,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(h,compose(domain(a),codomain(X0))),compose(compose(h,domain(a)),codomain(X0))) = compose(compose(h,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3838]) ).

fof(f3840,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(h,compose(domain(a),codomain(X0))),compose(h,codomain(X0))) = compose(compose(h,domain(a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f271,f3839]) ).

fof(f3841,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(h,compose(domain(a),codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f271,f3840]) ).

fof(f3842,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)],[f36,f3648]) ).

fof(f3843,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)],[f36,f3842]) ).

fof(f3844,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)],[f18,f3843]) ).

fof(f3845,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)],[f16,f3844]) ).

fof(f3846,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)],[f34,f3845]) ).

fof(f3847,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)],[f34,f3846]) ).

fof(f3848,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)],[f17,f3649]) ).

fof(f3849,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,f3848]) ).

fof(f3850,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)],[f35,f3849]) ).

fof(f3851,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)],[f16,f3850]) ).

fof(f3852,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)],[f48,f3851]) ).

fof(f3853,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)],[f48,f3852]) ).

fof(f3854,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(domain(h),compose(g,a)),codomain(X0))) = compose(compose(domain(h),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1583,f3650]) ).

fof(f3855,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(h),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(domain(h),compose(g,a)),codomain(X0))) = compose(compose(domain(h),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f3854]) ).

fof(f3856,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))),compose(compose(domain(h),compose(g,a)),codomain(X0))) = compose(compose(domain(h),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f3855]) ).

fof(f3857,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(domain(h),compose(g,a)),codomain(X0))) = compose(compose(domain(h),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3856]) ).

fof(f3858,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(domain(h),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2177,f3857]) ).

fof(f3859,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(domain(h),compose(compose(g,a),codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2177,f3858]) ).

fof(f3860,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(domain(h),compose(h,a)),codomain(X0))) = compose(compose(domain(h),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1465,f3651]) ).

fof(f3861,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(h),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(domain(h),compose(h,a)),codomain(X0))) = compose(compose(domain(h),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f3860]) ).

fof(f3862,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(domain(h),compose(h,a)),codomain(X0))) = compose(compose(domain(h),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f3861]) ).

fof(f3863,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(domain(h),compose(compose(h,a),codomain(X0))),compose(compose(domain(h),compose(h,a)),codomain(X0))) = compose(compose(domain(h),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3862]) ).

fof(f3864,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(domain(h),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(domain(h),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1957,f3863]) ).

fof(f3865,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(domain(h),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1957,f3864]) ).

fof(f3866,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(domain(h)),domain(g),compose(domain(h),compose(g,codomain(X0))),compose(g,codomain(X0))),compose(compose(domain(h),g),codomain(X0))) = compose(compose(domain(h),g),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f316,f3652]) ).

fof(f3867,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(h),domain(g),compose(domain(h),compose(g,codomain(X0))),compose(g,codomain(X0))),compose(compose(domain(h),g),codomain(X0))) = compose(compose(domain(h),g),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f3866]) ).

fof(f3868,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(g,codomain(X0))),compose(g,codomain(X0))),compose(compose(domain(h),g),codomain(X0))) = compose(compose(domain(h),g),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f478,f3867]) ).

fof(f3869,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(domain(h),compose(g,codomain(X0))),compose(compose(domain(h),g),codomain(X0))) = compose(compose(domain(h),g),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f3868]) ).

fof(f3870,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(domain(h),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(compose(domain(h),g),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f516,f3869]) ).

fof(f3871,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(domain(h),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(g,codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f516,f3870]) ).

fof(f3872,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)],[f975,f3653]) ).

fof(f3873,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)],[f17,f3872]) ).

fof(f3874,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)],[f261,f3873]) ).

fof(f3875,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)],[f16,f3874]) ).

fof(f3876,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)],[f406,f3875]) ).

fof(f3877,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)],[f406,f3876]) ).

fof(f3878,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)],[f17,f3654]) ).

fof(f3879,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)],[f17,f3878]) ).

fof(f3880,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)],[f35,f3879]) ).

fof(f3881,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)],[f16,f3880]) ).

fof(f3882,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)],[f31,f3881]) ).

fof(f3883,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)],[f31,f3882]) ).

fof(f3884,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)],[f17,f3655]) ).

fof(f3885,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)],[f16,f3884]) ).

fof(f3886,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)],[f19,f3885]) ).

fof(f3887,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)],[f19,f3886]) ).

fof(f3888,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)],[f36,f3656]) ).

fof(f3889,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)],[f18,f3888]) ).

fof(f3890,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)],[f16,f3889]) ).

fof(f3891,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)],[f20,f3890]) ).

fof(f3892,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)],[f20,f3891]) ).

fof(f4155,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(compose(g,a),X0)),compose(compose(a,compose(g,a)),X0)),compose(compose(a,compose(g,a)),X0)) = compose(compose(a,compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f162]) ).

fof(f4156,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),X0)),compose(compose(a,compose(h,a)),X0)),compose(compose(a,compose(h,a)),X0)) = compose(compose(a,compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f162]) ).

fof(f4157,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(compose(h,compose(a,b))),compose(a,compose(compose(h,compose(a,b)),X0)),compose(compose(a,compose(h,compose(a,b))),X0)),compose(compose(a,compose(h,compose(a,b))),X0)) = compose(compose(a,compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1016,f162]) ).

fof(f4159,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(g),compose(a,compose(g,X0)),compose(compose(a,g),X0)),compose(compose(a,g),X0)) = compose(compose(a,g),X0),
    inference(paramodulation,[status(thm)],[f316,f162]) ).

fof(f4160,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(h,X0)),compose(compose(a,h),X0)),compose(compose(a,h),X0)) = compose(compose(a,h),X0),
    inference(paramodulation,[status(thm)],[f147,f162]) ).

fof(f4161,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)],[f36,f162]) ).

fof(f4164,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),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)],[f478,f162]) ).

fof(f4165,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(g,a))),compose(compose(a,X0),compose(g,a))),compose(compose(a,X0),compose(g,a))) = compose(compose(a,X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f162]) ).

fof(f4166,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(h,a))),compose(compose(a,X0),compose(h,a))),compose(compose(a,X0),compose(h,a))) = compose(compose(a,X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f162]) ).

fof(f4167,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(X0,compose(h,compose(a,b)))),compose(compose(a,X0),compose(h,compose(a,b)))),compose(compose(a,X0),compose(h,compose(a,b)))) = compose(compose(a,X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f162]) ).

fof(f4169,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)],[f35,f162]) ).

fof(f4171,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)],[f16,f162]) ).

fof(f4176,plain,
    ! [X0] : ifeq(codomain(compose(a,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(paramodulation,[status(thm)],[f261,f162]) ).

fof(f4179,plain,
    ifeq(codomain(compose(h,a)),domain(domain(b)),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(h,a)),compose(compose(a,compose(h,a)),domain(b))),compose(compose(a,compose(h,a)),domain(b))) = compose(compose(a,compose(h,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1534,f162]) ).

fof(f4180,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)],[f1043,f162]) ).

fof(f4181,plain,
    ifeq(codomain(compose(g,a)),domain(domain(b)),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(g,a)),compose(compose(a,compose(g,a)),domain(b))),compose(compose(a,compose(g,a)),domain(b))) = compose(compose(a,compose(g,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1622,f162]) ).

fof(f4182,plain,
    ifeq(codomain(compose(g,a)),domain(b),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(g,a)),b)),compose(compose(a,compose(g,a)),b)) = compose(compose(a,compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f446,f162]) ).

fof(f4183,plain,
    ifeq(codomain(g),domain(compose(a,b)),ifeq(domain(b),domain(g),compose(a,compose(h,compose(a,b))),compose(compose(a,g),compose(a,b))),compose(compose(a,g),compose(a,b))) = compose(compose(a,g),compose(a,b)),
    inference(paramodulation,[status(thm)],[f29,f162]) ).

fof(f4184,plain,
    ifeq(codomain(g),domain(domain(a)),ifeq(domain(b),domain(g),compose(a,g),compose(compose(a,g),domain(a))),compose(compose(a,g),domain(a))) = compose(compose(a,g),domain(a)),
    inference(paramodulation,[status(thm)],[f334,f162]) ).

fof(f4185,plain,
    ifeq(codomain(h),domain(domain(a)),ifeq(domain(b),domain(h),compose(a,h),compose(compose(a,h),domain(a))),compose(compose(a,h),domain(a))) = compose(compose(a,h),domain(a)),
    inference(paramodulation,[status(thm)],[f271,f162]) ).

fof(f4186,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)],[f34,f162]) ).

fof(f4187,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)],[f48,f162]) ).

fof(f4188,plain,
    ifeq(codomain(domain(h)),domain(compose(g,a)),ifeq(domain(b),domain(domain(h)),compose(a,compose(g,a)),compose(compose(a,domain(h)),compose(g,a))),compose(compose(a,domain(h)),compose(g,a))) = compose(compose(a,domain(h)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2177,f162]) ).

fof(f4189,plain,
    ifeq(codomain(domain(h)),domain(compose(h,a)),ifeq(domain(b),domain(domain(h)),compose(a,compose(h,a)),compose(compose(a,domain(h)),compose(h,a))),compose(compose(a,domain(h)),compose(h,a))) = compose(compose(a,domain(h)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1957,f162]) ).

fof(f4190,plain,
    ifeq(codomain(domain(h)),domain(g),ifeq(domain(b),domain(domain(h)),compose(a,g),compose(compose(a,domain(h)),g)),compose(compose(a,domain(h)),g)) = compose(compose(a,domain(h)),g),
    inference(paramodulation,[status(thm)],[f516,f162]) ).

fof(f4191,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)],[f406,f162]) ).

fof(f4192,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)],[f31,f162]) ).

fof(f4193,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)],[f19,f162]) ).

fof(f4194,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)],[f20,f162]) ).

fof(f4196,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)],[f20,f162]) ).

fof(f4203,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),X0)),compose(compose(a,compose(g,a)),X0)),compose(compose(a,compose(g,a)),X0)) = compose(compose(a,compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f4155]) ).

fof(f4204,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),X0)),compose(compose(a,compose(h,a)),X0)),compose(compose(a,compose(h,a)),X0)) = compose(compose(a,compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f4156]) ).

fof(f4205,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),X0)),compose(compose(a,compose(h,compose(a,b))),X0)),compose(compose(a,compose(h,compose(a,b))),X0)) = compose(compose(a,compose(h,compose(a,b))),X0),
    inference(forward_demodulation,[status(thm)],[f506,f4157]) ).

fof(f4207,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(g,X0)),compose(compose(a,g),X0)),compose(compose(a,g),X0)) = compose(compose(a,g),X0),
    inference(forward_demodulation,[status(thm)],[f478,f4159]) ).

fof(f4208,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)],[f18,f4161]) ).

fof(f4214,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)],[f975,f4176]) ).

fof(f4217,plain,
    ifeq(domain(b),domain(domain(b)),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(h,a)),compose(compose(a,compose(h,a)),domain(b))),compose(compose(a,compose(h,a)),domain(b))) = compose(compose(a,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f4179]) ).

fof(f4218,plain,
    ifeq(domain(b),domain(b),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(h,a)),compose(compose(a,compose(h,a)),domain(b))),compose(compose(a,compose(h,a)),domain(b))) = compose(compose(a,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f4217]) ).

fof(f4219,plain,
    ifeq(domain(b),domain(compose(h,a)),compose(a,compose(h,a)),compose(compose(a,compose(h,a)),domain(b))) = compose(compose(a,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f4218]) ).

fof(f4220,plain,
    ifeq(domain(b),domain(h),compose(a,compose(h,a)),compose(compose(a,compose(h,a)),domain(b))) = compose(compose(a,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1908,f4219]) ).

fof(f4221,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)],[f975,f4180]) ).

fof(f4222,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)],[f18,f4221]) ).

fof(f4223,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)],[f16,f4222]) ).

fof(f4224,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)],[f261,f4223]) ).

fof(f4225,plain,
    ifeq(domain(b),domain(domain(b)),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(g,a)),compose(compose(a,compose(g,a)),domain(b))),compose(compose(a,compose(g,a)),domain(b))) = compose(compose(a,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f4181]) ).

fof(f4226,plain,
    ifeq(domain(b),domain(b),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(g,a)),compose(compose(a,compose(g,a)),domain(b))),compose(compose(a,compose(g,a)),domain(b))) = compose(compose(a,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f4225]) ).

fof(f4227,plain,
    ifeq(domain(b),domain(compose(g,a)),compose(a,compose(g,a)),compose(compose(a,compose(g,a)),domain(b))) = compose(compose(a,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f4226]) ).

fof(f4228,plain,
    ifeq(domain(b),domain(h),compose(a,compose(g,a)),compose(compose(a,compose(g,a)),domain(b))) = compose(compose(a,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f2123,f4227]) ).

fof(f4229,plain,
    ifeq(domain(b),domain(b),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(g,a)),b)),compose(compose(a,compose(g,a)),b)) = compose(compose(a,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f1583,f4182]) ).

fof(f4230,plain,
    ifeq(domain(b),domain(compose(g,a)),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(g,a)),b)) = compose(compose(a,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f4229]) ).

fof(f4231,plain,
    ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(g,a)),b)) = compose(compose(a,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f2123,f4230]) ).

fof(f4232,plain,
    ifeq(domain(a),domain(compose(a,b)),ifeq(domain(b),domain(g),compose(a,compose(h,compose(a,b))),compose(compose(a,g),compose(a,b))),compose(compose(a,g),compose(a,b))) = compose(compose(a,g),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f316,f4183]) ).

fof(f4233,plain,
    ifeq(domain(a),domain(a),ifeq(domain(b),domain(g),compose(a,compose(h,compose(a,b))),compose(compose(a,g),compose(a,b))),compose(compose(a,g),compose(a,b))) = compose(compose(a,g),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f261,f4232]) ).

fof(f4234,plain,
    ifeq(domain(b),domain(g),compose(a,compose(h,compose(a,b))),compose(compose(a,g),compose(a,b))) = compose(compose(a,g),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f4233]) ).

fof(f4235,plain,
    ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,g),compose(a,b))) = compose(compose(a,g),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f478,f4234]) ).

fof(f4236,plain,
    ifeq(domain(a),domain(domain(a)),ifeq(domain(b),domain(g),compose(a,g),compose(compose(a,g),domain(a))),compose(compose(a,g),domain(a))) = compose(compose(a,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f316,f4184]) ).

fof(f4237,plain,
    ifeq(domain(a),domain(a),ifeq(domain(b),domain(g),compose(a,g),compose(compose(a,g),domain(a))),compose(compose(a,g),domain(a))) = compose(compose(a,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f4236]) ).

fof(f4238,plain,
    ifeq(domain(b),domain(g),compose(a,g),compose(compose(a,g),domain(a))) = compose(compose(a,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f4237]) ).

fof(f4239,plain,
    ifeq(domain(b),domain(h),compose(a,g),compose(compose(a,g),domain(a))) = compose(compose(a,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f478,f4238]) ).

fof(f4240,plain,
    ifeq(domain(a),domain(domain(a)),ifeq(domain(b),domain(h),compose(a,h),compose(compose(a,h),domain(a))),compose(compose(a,h),domain(a))) = compose(compose(a,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f147,f4185]) ).

fof(f4241,plain,
    ifeq(domain(a),domain(a),ifeq(domain(b),domain(h),compose(a,h),compose(compose(a,h),domain(a))),compose(compose(a,h),domain(a))) = compose(compose(a,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f4240]) ).

fof(f4242,plain,
    ifeq(domain(b),domain(h),compose(a,h),compose(compose(a,h),domain(a))) = compose(compose(a,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f4241]) ).

fof(f4243,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)],[f36,f4186]) ).

fof(f4244,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)],[f18,f4243]) ).

fof(f4245,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)],[f16,f4244]) ).

fof(f4246,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)],[f18,f4245]) ).

fof(f4247,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,f4187]) ).

fof(f4248,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)],[f35,f4247]) ).

fof(f4249,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)],[f16,f4248]) ).

fof(f4250,plain,
    ifeq(domain(h),domain(compose(g,a)),ifeq(domain(b),domain(domain(h)),compose(a,compose(g,a)),compose(compose(a,domain(h)),compose(g,a))),compose(compose(a,domain(h)),compose(g,a))) = compose(compose(a,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f17,f4188]) ).

fof(f4251,plain,
    ifeq(domain(h),domain(h),ifeq(domain(b),domain(domain(h)),compose(a,compose(g,a)),compose(compose(a,domain(h)),compose(g,a))),compose(compose(a,domain(h)),compose(g,a))) = compose(compose(a,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f4250]) ).

fof(f4252,plain,
    ifeq(domain(b),domain(domain(h)),compose(a,compose(g,a)),compose(compose(a,domain(h)),compose(g,a))) = compose(compose(a,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f4251]) ).

fof(f4253,plain,
    ifeq(domain(b),domain(h),compose(a,compose(g,a)),compose(compose(a,domain(h)),compose(g,a))) = compose(compose(a,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f35,f4252]) ).

fof(f4254,plain,
    ifeq(domain(h),domain(compose(h,a)),ifeq(domain(b),domain(domain(h)),compose(a,compose(h,a)),compose(compose(a,domain(h)),compose(h,a))),compose(compose(a,domain(h)),compose(h,a))) = compose(compose(a,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f17,f4189]) ).

fof(f4255,plain,
    ifeq(domain(h),domain(h),ifeq(domain(b),domain(domain(h)),compose(a,compose(h,a)),compose(compose(a,domain(h)),compose(h,a))),compose(compose(a,domain(h)),compose(h,a))) = compose(compose(a,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f4254]) ).

fof(f4256,plain,
    ifeq(domain(b),domain(domain(h)),compose(a,compose(h,a)),compose(compose(a,domain(h)),compose(h,a))) = compose(compose(a,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f16,f4255]) ).

fof(f4257,plain,
    ifeq(domain(b),domain(h),compose(a,compose(h,a)),compose(compose(a,domain(h)),compose(h,a))) = compose(compose(a,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f35,f4256]) ).

fof(f4258,plain,
    ifeq(domain(h),domain(g),ifeq(domain(b),domain(domain(h)),compose(a,g),compose(compose(a,domain(h)),g)),compose(compose(a,domain(h)),g)) = compose(compose(a,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f17,f4190]) ).

fof(f4259,plain,
    ifeq(domain(h),domain(h),ifeq(domain(b),domain(domain(h)),compose(a,g),compose(compose(a,domain(h)),g)),compose(compose(a,domain(h)),g)) = compose(compose(a,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f478,f4258]) ).

fof(f4260,plain,
    ifeq(domain(b),domain(domain(h)),compose(a,g),compose(compose(a,domain(h)),g)) = compose(compose(a,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f16,f4259]) ).

fof(f4261,plain,
    ifeq(domain(b),domain(h),compose(a,g),compose(compose(a,domain(h)),g)) = compose(compose(a,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f35,f4260]) ).

fof(f4262,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)],[f17,f4191]) ).

fof(f4263,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)],[f261,f4262]) ).

fof(f4264,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)],[f16,f4263]) ).

fof(f4265,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)],[f35,f4264]) ).

fof(f4266,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)],[f17,f4192]) ).

fof(f4267,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)],[f35,f4266]) ).

fof(f4268,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)],[f16,f4267]) ).

fof(f4269,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)],[f35,f4268]) ).

fof(f4270,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)],[f17,f4193]) ).

fof(f4271,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)],[f16,f4270]) ).

fof(f4272,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)],[f35,f4271]) ).

fof(f4273,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)],[f18,f4194]) ).

fof(f4274,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)],[f16,f4273]) ).

fof(f4279,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)],[f18,f4196]) ).

fof(f4280,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)],[f20,f4279]) ).

fof(f4281,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)],[f20,f4280]) ).

fof(f4581,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(compose(g,a)),compose(domain(X1),compose(compose(g,a),X0)),compose(compose(domain(X1),compose(g,a)),X0)),compose(compose(domain(X1),compose(g,a)),X0)) = compose(compose(domain(X1),compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f163]) ).

fof(f4582,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(compose(h,a)),compose(domain(X1),compose(compose(h,a),X0)),compose(compose(domain(X1),compose(h,a)),X0)),compose(compose(domain(X1),compose(h,a)),X0)) = compose(compose(domain(X1),compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f163]) ).

fof(f4583,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(compose(h,compose(a,b))),compose(domain(X1),compose(compose(h,compose(a,b)),X0)),compose(compose(domain(X1),compose(h,compose(a,b))),X0)),compose(compose(domain(X1),compose(h,compose(a,b))),X0)) = compose(compose(domain(X1),compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1016,f163]) ).

fof(f4585,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(g),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)],[f316,f163]) ).

fof(f4586,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(h),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)],[f147,f163]) ).

fof(f4587,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)],[f36,f163]) ).

fof(f4590,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),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)],[f478,f163]) ).

fof(f4591,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(g,a))),compose(compose(domain(X1),X0),compose(g,a))),compose(compose(domain(X1),X0),compose(g,a))) = compose(compose(domain(X1),X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f163]) ).

fof(f4592,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(h,a))),compose(compose(domain(X1),X0),compose(h,a))),compose(compose(domain(X1),X0),compose(h,a))) = compose(compose(domain(X1),X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f163]) ).

fof(f4593,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(X0,compose(h,compose(a,b)))),compose(compose(domain(X1),X0),compose(h,compose(a,b)))),compose(compose(domain(X1),X0),compose(h,compose(a,b)))) = compose(compose(domain(X1),X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f163]) ).

fof(f4595,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)],[f35,f163]) ).

fof(f4609,plain,
    ! [X0,X1] : ifeq(codomain(compose(a,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(paramodulation,[status(thm)],[f261,f163]) ).

fof(f4623,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(domain(b)),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),compose(h,a)),domain(b))),compose(compose(domain(X0),compose(h,a)),domain(b))) = compose(compose(domain(X0),compose(h,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1534,f163]) ).

fof(f4624,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)],[f1043,f163]) ).

fof(f4625,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(domain(b)),ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),compose(g,a)),domain(b))),compose(compose(domain(X0),compose(g,a)),domain(b))) = compose(compose(domain(X0),compose(g,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1622,f163]) ).

fof(f4626,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(b),ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(g,a)),b)),compose(compose(domain(X0),compose(g,a)),b)) = compose(compose(domain(X0),compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f446,f163]) ).

fof(f4627,plain,
    ! [X0] : ifeq(codomain(g),domain(compose(a,b)),ifeq(domain(X0),domain(g),compose(domain(X0),compose(h,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)],[f29,f163]) ).

fof(f4628,plain,
    ! [X0] : ifeq(codomain(g),domain(domain(a)),ifeq(domain(X0),domain(g),compose(domain(X0),g),compose(compose(domain(X0),g),domain(a))),compose(compose(domain(X0),g),domain(a))) = compose(compose(domain(X0),g),domain(a)),
    inference(paramodulation,[status(thm)],[f334,f163]) ).

fof(f4629,plain,
    ! [X0] : ifeq(codomain(h),domain(domain(a)),ifeq(domain(X0),domain(h),compose(domain(X0),h),compose(compose(domain(X0),h),domain(a))),compose(compose(domain(X0),h),domain(a))) = compose(compose(domain(X0),h),domain(a)),
    inference(paramodulation,[status(thm)],[f271,f163]) ).

fof(f4630,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)],[f34,f163]) ).

fof(f4631,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)],[f48,f163]) ).

fof(f4632,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(compose(g,a)),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),domain(h)),compose(g,a))),compose(compose(domain(X0),domain(h)),compose(g,a))) = compose(compose(domain(X0),domain(h)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2177,f163]) ).

fof(f4633,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(compose(h,a)),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),domain(h)),compose(h,a))),compose(compose(domain(X0),domain(h)),compose(h,a))) = compose(compose(domain(X0),domain(h)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1957,f163]) ).

fof(f4634,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(g),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),g),compose(compose(domain(X0),domain(h)),g)),compose(compose(domain(X0),domain(h)),g)) = compose(compose(domain(X0),domain(h)),g),
    inference(paramodulation,[status(thm)],[f516,f163]) ).

fof(f4635,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)],[f406,f163]) ).

fof(f4636,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)],[f31,f163]) ).

fof(f4637,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)],[f19,f163]) ).

fof(f4638,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)],[f20,f163]) ).

fof(f4639,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)],[f20,f163]) ).

fof(f4669,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(g,a),X0)),compose(compose(domain(X1),compose(g,a)),X0)),compose(compose(domain(X1),compose(g,a)),X0)) = compose(compose(domain(X1),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f4581]) ).

fof(f4670,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,a),X0)),compose(compose(domain(X1),compose(h,a)),X0)),compose(compose(domain(X1),compose(h,a)),X0)) = compose(compose(domain(X1),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f4582]) ).

fof(f4671,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,compose(a,b)),X0)),compose(compose(domain(X1),compose(h,compose(a,b))),X0)),compose(compose(domain(X1),compose(h,compose(a,b))),X0)) = compose(compose(domain(X1),compose(h,compose(a,b))),X0),
    inference(forward_demodulation,[status(thm)],[f506,f4583]) ).

fof(f4673,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(h),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)],[f478,f4585]) ).

fof(f4674,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)],[f18,f4587]) ).

fof(f4710,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)],[f975,f4609]) ).

fof(f4751,plain,
    ! [X0] : ifeq(domain(b),domain(domain(b)),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),compose(h,a)),domain(b))),compose(compose(domain(X0),compose(h,a)),domain(b))) = compose(compose(domain(X0),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f4623]) ).

fof(f4752,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),compose(h,a)),domain(b))),compose(compose(domain(X0),compose(h,a)),domain(b))) = compose(compose(domain(X0),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f4751]) ).

fof(f4753,plain,
    ! [X0] : ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),compose(h,a)),domain(b))) = compose(compose(domain(X0),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f4752]) ).

fof(f4754,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),compose(h,a)),domain(b))) = compose(compose(domain(X0),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1908,f4753]) ).

fof(f4755,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)],[f975,f4624]) ).

fof(f4756,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)],[f18,f4755]) ).

fof(f4757,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)],[f16,f4756]) ).

fof(f4758,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)],[f261,f4757]) ).

fof(f4759,plain,
    ! [X0] : ifeq(domain(b),domain(domain(b)),ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),compose(g,a)),domain(b))),compose(compose(domain(X0),compose(g,a)),domain(b))) = compose(compose(domain(X0),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f4625]) ).

fof(f4760,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),compose(g,a)),domain(b))),compose(compose(domain(X0),compose(g,a)),domain(b))) = compose(compose(domain(X0),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f4759]) ).

fof(f4761,plain,
    ! [X0] : ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),compose(g,a)),domain(b))) = compose(compose(domain(X0),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f4760]) ).

fof(f4762,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),compose(g,a)),domain(b))) = compose(compose(domain(X0),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f2123,f4761]) ).

fof(f4763,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(g,a)),b)),compose(compose(domain(X0),compose(g,a)),b)) = compose(compose(domain(X0),compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f1583,f4626]) ).

fof(f4764,plain,
    ! [X0] : ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(g,a)),b)) = compose(compose(domain(X0),compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f4763]) ).

fof(f4765,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(g,a)),b)) = compose(compose(domain(X0),compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f2123,f4764]) ).

fof(f4766,plain,
    ! [X0] : ifeq(domain(a),domain(compose(a,b)),ifeq(domain(X0),domain(g),compose(domain(X0),compose(h,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(forward_demodulation,[status(thm)],[f316,f4627]) ).

fof(f4767,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(g),compose(domain(X0),compose(h,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(forward_demodulation,[status(thm)],[f261,f4766]) ).

fof(f4768,plain,
    ! [X0] : ifeq(domain(X0),domain(g),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),g),compose(a,b))) = compose(compose(domain(X0),g),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f4767]) ).

fof(f4769,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),g),compose(a,b))) = compose(compose(domain(X0),g),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f478,f4768]) ).

fof(f4770,plain,
    ! [X0] : ifeq(domain(a),domain(domain(a)),ifeq(domain(X0),domain(g),compose(domain(X0),g),compose(compose(domain(X0),g),domain(a))),compose(compose(domain(X0),g),domain(a))) = compose(compose(domain(X0),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f316,f4628]) ).

fof(f4771,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(g),compose(domain(X0),g),compose(compose(domain(X0),g),domain(a))),compose(compose(domain(X0),g),domain(a))) = compose(compose(domain(X0),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f4770]) ).

fof(f4772,plain,
    ! [X0] : ifeq(domain(X0),domain(g),compose(domain(X0),g),compose(compose(domain(X0),g),domain(a))) = compose(compose(domain(X0),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f4771]) ).

fof(f4773,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),g),compose(compose(domain(X0),g),domain(a))) = compose(compose(domain(X0),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f478,f4772]) ).

fof(f4774,plain,
    ! [X0] : ifeq(domain(a),domain(domain(a)),ifeq(domain(X0),domain(h),compose(domain(X0),h),compose(compose(domain(X0),h),domain(a))),compose(compose(domain(X0),h),domain(a))) = compose(compose(domain(X0),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f147,f4629]) ).

fof(f4775,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(h),compose(domain(X0),h),compose(compose(domain(X0),h),domain(a))),compose(compose(domain(X0),h),domain(a))) = compose(compose(domain(X0),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f4774]) ).

fof(f4776,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),h),compose(compose(domain(X0),h),domain(a))) = compose(compose(domain(X0),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f4775]) ).

fof(f4777,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)],[f36,f4630]) ).

fof(f4778,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)],[f18,f4777]) ).

fof(f4779,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)],[f16,f4778]) ).

fof(f4780,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)],[f18,f4779]) ).

fof(f4781,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,f4631]) ).

fof(f4782,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)],[f35,f4781]) ).

fof(f4783,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)],[f16,f4782]) ).

fof(f4784,plain,
    ! [X0] : ifeq(domain(h),domain(compose(g,a)),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),domain(h)),compose(g,a))),compose(compose(domain(X0),domain(h)),compose(g,a))) = compose(compose(domain(X0),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f17,f4632]) ).

fof(f4785,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),domain(h)),compose(g,a))),compose(compose(domain(X0),domain(h)),compose(g,a))) = compose(compose(domain(X0),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f4784]) ).

fof(f4786,plain,
    ! [X0] : ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),domain(h)),compose(g,a))) = compose(compose(domain(X0),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f4785]) ).

fof(f4787,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),domain(h)),compose(g,a))) = compose(compose(domain(X0),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f35,f4786]) ).

fof(f4788,plain,
    ! [X0] : ifeq(domain(h),domain(compose(h,a)),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),domain(h)),compose(h,a))),compose(compose(domain(X0),domain(h)),compose(h,a))) = compose(compose(domain(X0),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f17,f4633]) ).

fof(f4789,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),domain(h)),compose(h,a))),compose(compose(domain(X0),domain(h)),compose(h,a))) = compose(compose(domain(X0),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f4788]) ).

fof(f4790,plain,
    ! [X0] : ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),domain(h)),compose(h,a))) = compose(compose(domain(X0),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f16,f4789]) ).

fof(f4791,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),domain(h)),compose(h,a))) = compose(compose(domain(X0),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f35,f4790]) ).

fof(f4792,plain,
    ! [X0] : ifeq(domain(h),domain(g),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),g),compose(compose(domain(X0),domain(h)),g)),compose(compose(domain(X0),domain(h)),g)) = compose(compose(domain(X0),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f17,f4634]) ).

fof(f4793,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),g),compose(compose(domain(X0),domain(h)),g)),compose(compose(domain(X0),domain(h)),g)) = compose(compose(domain(X0),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f478,f4792]) ).

fof(f4794,plain,
    ! [X0] : ifeq(domain(X0),domain(domain(h)),compose(domain(X0),g),compose(compose(domain(X0),domain(h)),g)) = compose(compose(domain(X0),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f16,f4793]) ).

fof(f4795,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),g),compose(compose(domain(X0),domain(h)),g)) = compose(compose(domain(X0),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f35,f4794]) ).

fof(f4796,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)],[f17,f4635]) ).

fof(f4797,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)],[f261,f4796]) ).

fof(f4798,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)],[f16,f4797]) ).

fof(f4799,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)],[f35,f4798]) ).

fof(f4800,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)],[f17,f4636]) ).

fof(f4801,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)],[f35,f4800]) ).

fof(f4802,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)],[f16,f4801]) ).

fof(f4803,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)],[f35,f4802]) ).

fof(f4804,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)],[f17,f4637]) ).

fof(f4805,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)],[f16,f4804]) ).

fof(f4806,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)],[f35,f4805]) ).

fof(f4807,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)],[f18,f4638]) ).

fof(f4808,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)],[f16,f4807]) ).

fof(f4809,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)],[f18,f4639]) ).

fof(f4810,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)],[f20,f4809]) ).

fof(f4811,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)],[f20,f4810]) ).

fof(f5140,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),codomain(h),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)],[f975,f164]) ).

fof(f5141,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)],[f147,f5140]) ).

fof(f5142,plain,
    ! [X0] : ifeq(codomain(b),domain(h),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(paramodulation,[status(thm)],[f478,f5141]) ).

fof(f5143,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(g,a))),compose(compose(X0,compose(a,b)),compose(g,a))),compose(compose(X0,compose(a,b)),compose(g,a))) = compose(compose(X0,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5141]) ).

fof(f5144,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(h,a))),compose(compose(X0,compose(a,b)),compose(h,a))),compose(compose(X0,compose(a,b)),compose(h,a))) = compose(compose(X0,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5141]) ).

fof(f5145,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(X0,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(X0,compose(a,b)),compose(h,compose(a,b)))),compose(compose(X0,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(X0,compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f5141]) ).

fof(f5147,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(paramodulation,[status(thm)],[f35,f5141]) ).

fof(f5149,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),X0)),compose(compose(compose(g,a),compose(a,b)),X0)),compose(compose(compose(g,a),compose(a,b)),X0)) = compose(compose(compose(g,a),compose(a,b)),X0),
    inference(paramodulation,[status(thm)],[f1583,f5141]) ).

fof(f5150,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),X0)),compose(compose(compose(h,a),compose(a,b)),X0)),compose(compose(compose(h,a),compose(a,b)),X0)) = compose(compose(compose(h,a),compose(a,b)),X0),
    inference(paramodulation,[status(thm)],[f1465,f5141]) ).

fof(f5151,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),X0)),compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)),compose(compose(compose(h,compose(a,b)),compose(a,b)),X0)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),X0),
    inference(paramodulation,[status(thm)],[f1016,f5141]) ).

fof(f5152,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(paramodulation,[status(thm)],[f975,f5141]) ).

fof(f5154,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(a),compose(h,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(paramodulation,[status(thm)],[f147,f5141]) ).

fof(f5155,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(paramodulation,[status(thm)],[f36,f5141]) ).

fof(f5158,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(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(paramodulation,[status(thm)],[f19,f5141]) ).

fof(f5160,plain,
    ! [X0] : ifeq(codomain(b),domain(codomain(compose(a,b))),ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(compose(a,b)))),compose(compose(X0,compose(a,b)),codomain(compose(a,b)))) = compose(compose(X0,compose(a,b)),codomain(compose(a,b))),
    inference(paramodulation,[status(thm)],[f20,f5141]) ).

fof(f5161,plain,
    ! [X0] : ifeq(codomain(b),domain(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(compose(X0,compose(a,b)),codomain(compose(X0,compose(a,b))))) = compose(compose(X0,compose(a,b)),codomain(compose(X0,compose(a,b)))),
    inference(paramodulation,[status(thm)],[f20,f5141]) ).

fof(f5172,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(h,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f5154]) ).

fof(f5173,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)],[f17,f5158]) ).

fof(f5176,plain,
    ! [X0] : ifeq(codomain(b),codomain(compose(a,b)),ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(compose(a,b)))),compose(compose(X0,compose(a,b)),codomain(compose(a,b)))) = compose(compose(X0,compose(a,b)),codomain(compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f18,f5160]) ).

fof(f5177,plain,
    ! [X0] : ifeq(codomain(b),codomain(b),ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(compose(a,b)))),compose(compose(X0,compose(a,b)),codomain(compose(a,b)))) = compose(compose(X0,compose(a,b)),codomain(compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f975,f5176]) ).

fof(f5178,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),compose(X0,compose(a,b)),compose(compose(X0,compose(a,b)),codomain(compose(a,b)))) = compose(compose(X0,compose(a,b)),codomain(compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f5177]) ).

fof(f5179,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(compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f975,f5178]) ).

fof(f5180,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)],[f975,f5179]) ).

fof(f5181,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(compose(X0,compose(a,b)),codomain(compose(X0,compose(a,b))))) = compose(compose(X0,compose(a,b)),codomain(compose(X0,compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f18,f5161]) ).

fof(f5182,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(compose(X0,compose(a,b)),codomain(compose(X0,compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f20,f5181]) ).

fof(f5183,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)],[f20,f5182]) ).

fof(f5671,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),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(paramodulation,[status(thm)],[f478,f188]) ).

fof(f5672,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(g,a))),compose(compose(X1,codomain(X0)),compose(g,a))),compose(compose(X1,codomain(X0)),compose(g,a))) = compose(compose(X1,codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f188]) ).

fof(f5673,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(h,a))),compose(compose(X1,codomain(X0)),compose(h,a))),compose(compose(X1,codomain(X0)),compose(h,a))) = compose(compose(X1,codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f188]) ).

fof(f5674,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(X1,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(X1,codomain(X0)),compose(h,compose(a,b)))),compose(compose(X1,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(X1,codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f188]) ).

fof(f5676,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)],[f35,f188]) ).

fof(f5679,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),X1)),compose(compose(compose(g,a),codomain(X0)),X1)),compose(compose(compose(g,a),codomain(X0)),X1)) = compose(compose(compose(g,a),codomain(X0)),X1),
    inference(paramodulation,[status(thm)],[f1583,f188]) ).

fof(f5680,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),X1)),compose(compose(compose(h,a),codomain(X0)),X1)),compose(compose(compose(h,a),codomain(X0)),X1)) = compose(compose(compose(h,a),codomain(X0)),X1),
    inference(paramodulation,[status(thm)],[f1465,f188]) ).

fof(f5681,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),X1)),compose(compose(compose(h,compose(a,b)),codomain(X0)),X1)),compose(compose(compose(h,compose(a,b)),codomain(X0)),X1)) = compose(compose(compose(h,compose(a,b)),codomain(X0)),X1),
    inference(paramodulation,[status(thm)],[f1016,f188]) ).

fof(f5682,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)],[f975,f188]) ).

fof(f5683,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),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)],[f316,f188]) ).

fof(f5684,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),X1)),compose(compose(h,codomain(X0)),X1)),compose(compose(h,codomain(X0)),X1)) = compose(compose(h,codomain(X0)),X1),
    inference(paramodulation,[status(thm)],[f147,f188]) ).

fof(f5685,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)],[f36,f188]) ).

fof(f5697,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)],[f19,f188]) ).

fof(f5709,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)],[f20,f188]) ).

fof(f5829,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)],[f17,f5697]) ).

fof(f5882,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)],[f18,f5709]) ).

fof(f5883,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)],[f20,f5882]) ).

fof(f5884,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)],[f20,f5883]) ).

fof(f6228,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(g,a),X0)),domain(compose(g,a)),compose(compose(g,a),X0),compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0)),compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0)) = compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f189]) ).

fof(f6229,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(h,a),X0)),domain(compose(h,a)),compose(compose(h,a),X0),compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0)),compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0)) = compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f189]) ).

fof(f6230,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(h,compose(a,b)),X0)),domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),X0),compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0)),compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0)) = compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1016,f189]) ).

fof(f6232,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(compose(g,X0)),domain(g),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)],[f316,f189]) ).

fof(f6233,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(compose(h,X0)),domain(h),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)],[f147,f189]) ).

fof(f6237,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),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(paramodulation,[status(thm)],[f478,f189]) ).

fof(f6238,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(X0,compose(g,a))),domain(X0),compose(X0,compose(g,a)),compose(compose(domain(compose(X0,compose(g,a))),X0),compose(g,a))),compose(compose(domain(compose(X0,compose(g,a))),X0),compose(g,a))) = compose(compose(domain(compose(X0,compose(g,a))),X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f189]) ).

fof(f6239,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(X0,compose(h,a))),domain(X0),compose(X0,compose(h,a)),compose(compose(domain(compose(X0,compose(h,a))),X0),compose(h,a))),compose(compose(domain(compose(X0,compose(h,a))),X0),compose(h,a))) = compose(compose(domain(compose(X0,compose(h,a))),X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f189]) ).

fof(f6240,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(X0,compose(h,compose(a,b)))),domain(X0),compose(X0,compose(h,compose(a,b))),compose(compose(domain(compose(X0,compose(h,compose(a,b)))),X0),compose(h,compose(a,b)))),compose(compose(domain(compose(X0,compose(h,compose(a,b)))),X0),compose(h,compose(a,b)))) = compose(compose(domain(compose(X0,compose(h,compose(a,b)))),X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f189]) ).

fof(f6242,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)],[f35,f189]) ).

fof(f6327,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(g,a),X0)),domain(h),compose(compose(g,a),X0),compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0)),compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0)) = compose(compose(domain(compose(compose(g,a),X0)),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f6228]) ).

fof(f6328,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(h,a),X0)),domain(h),compose(compose(h,a),X0),compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0)),compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0)) = compose(compose(domain(compose(compose(h,a),X0)),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f6229]) ).

fof(f6329,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(h,compose(a,b)),X0)),domain(h),compose(compose(h,compose(a,b)),X0),compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0)),compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0)) = compose(compose(domain(compose(compose(h,compose(a,b)),X0)),compose(h,compose(a,b))),X0),
    inference(forward_demodulation,[status(thm)],[f506,f6230]) ).

fof(f6331,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(compose(g,X0)),domain(h),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)],[f478,f6232]) ).

fof(f6947,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(g,a),X0),compose(compose(compose(g,a),domain(X0)),X0)) = compose(compose(compose(g,a),domain(X0)),X0),
    inference(paramodulation,[status(thm)],[f1583,f203]) ).

fof(f6948,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(h,a),X0),compose(compose(compose(h,a),domain(X0)),X0)) = compose(compose(compose(h,a),domain(X0)),X0),
    inference(paramodulation,[status(thm)],[f1465,f203]) ).

fof(f6949,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),X0),compose(compose(compose(h,compose(a,b)),domain(X0)),X0)) = compose(compose(compose(h,compose(a,b)),domain(X0)),X0),
    inference(paramodulation,[status(thm)],[f1016,f203]) ).

fof(f6950,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)],[f975,f203]) ).

fof(f6951,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(g,X0),compose(compose(g,domain(X0)),X0)) = compose(compose(g,domain(X0)),X0),
    inference(paramodulation,[status(thm)],[f316,f203]) ).

fof(f6952,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(h,X0),compose(compose(h,domain(X0)),X0)) = compose(compose(h,domain(X0)),X0),
    inference(paramodulation,[status(thm)],[f147,f203]) ).

fof(f6953,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)],[f36,f203]) ).

fof(f6959,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,domain(compose(h,compose(a,b)))),compose(h,compose(a,b)))) = compose(compose(X0,domain(compose(h,compose(a,b)))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f203]) ).

fof(f6999,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,domain(h)),compose(h,compose(a,b)))) = compose(compose(X0,domain(compose(h,compose(a,b)))),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f6959]) ).

fof(f7000,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,domain(h)),compose(h,compose(a,b)))) = compose(compose(X0,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f6999]) ).

fof(f7118,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(g,a),X0),compose(compose(compose(g,a),X0),codomain(X0))) = compose(compose(compose(g,a),X0),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f205]) ).

fof(f7119,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(h,a),X0),compose(compose(compose(h,a),X0),codomain(X0))) = compose(compose(compose(h,a),X0),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f205]) ).

fof(f7120,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),X0),compose(compose(compose(h,compose(a,b)),X0),codomain(X0))) = compose(compose(compose(h,compose(a,b)),X0),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f205]) ).

fof(f7121,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)],[f975,f205]) ).

fof(f7122,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(g,X0),compose(compose(g,X0),codomain(X0))) = compose(compose(g,X0),codomain(X0)),
    inference(paramodulation,[status(thm)],[f316,f205]) ).

fof(f7123,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(h,X0),compose(compose(h,X0),codomain(X0))) = compose(compose(h,X0),codomain(X0)),
    inference(paramodulation,[status(thm)],[f147,f205]) ).

fof(f7124,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)],[f36,f205]) ).

fof(f7128,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,compose(g,a)),codomain(compose(g,a)))) = compose(compose(X0,compose(g,a)),codomain(compose(g,a))),
    inference(paramodulation,[status(thm)],[f2123,f205]) ).

fof(f7129,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,compose(h,a)),codomain(compose(h,a)))) = compose(compose(X0,compose(h,a)),codomain(compose(h,a))),
    inference(paramodulation,[status(thm)],[f1908,f205]) ).

fof(f7130,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),codomain(compose(h,compose(a,b))))) = compose(compose(X0,compose(h,compose(a,b))),codomain(compose(h,compose(a,b)))),
    inference(paramodulation,[status(thm)],[f506,f205]) ).

fof(f7178,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,compose(g,a)),domain(b))) = compose(compose(X0,compose(g,a)),codomain(compose(g,a))),
    inference(forward_demodulation,[status(thm)],[f1583,f7128]) ).

fof(f7179,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,compose(g,a)),domain(b))) = compose(compose(X0,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f7178]) ).

fof(f7180,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,compose(h,a)),domain(b))) = compose(compose(X0,compose(h,a)),codomain(compose(h,a))),
    inference(forward_demodulation,[status(thm)],[f1465,f7129]) ).

fof(f7181,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,compose(h,a)),domain(b))) = compose(compose(X0,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f7180]) ).

fof(f7182,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),codomain(b))) = compose(compose(X0,compose(h,compose(a,b))),codomain(compose(h,compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f1016,f7130]) ).

fof(f7183,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,compose(a,b))),codomain(b))) = compose(compose(X0,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f1016,f7182]) ).

fof(f7362,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(X0,compose(g,a))),ifeq(codomain(X0),domain(compose(g,a)),compose(X0,compose(compose(g,a),codomain(compose(X0,compose(g,a))))),compose(X0,compose(g,a))),compose(X0,compose(g,a))) = compose(X0,compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f208]) ).

fof(f7363,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(X0,compose(h,a))),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(compose(h,a),codomain(compose(X0,compose(h,a))))),compose(X0,compose(h,a))),compose(X0,compose(h,a))) = compose(X0,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f208]) ).

fof(f7364,plain,
    ! [X0] : ifeq(codomain(b),codomain(compose(X0,compose(h,compose(a,b)))),ifeq(codomain(X0),domain(compose(h,compose(a,b))),compose(X0,compose(compose(h,compose(a,b)),codomain(compose(X0,compose(h,compose(a,b)))))),compose(X0,compose(h,compose(a,b)))),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f208]) ).

fof(f7366,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(X0,g)),ifeq(codomain(X0),domain(g),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(X0,g)) = compose(X0,g),
    inference(paramodulation,[status(thm)],[f316,f208]) ).

fof(f7367,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(X0,h)),ifeq(codomain(X0),domain(h),compose(X0,compose(h,codomain(compose(X0,h)))),compose(X0,h)),compose(X0,h)) = compose(X0,h),
    inference(paramodulation,[status(thm)],[f147,f208]) ).

fof(f7391,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(compose(g,a),X0)),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,codomain(compose(compose(g,a),X0)))),compose(compose(g,a),X0)),compose(compose(g,a),X0)) = compose(compose(g,a),X0),
    inference(paramodulation,[status(thm)],[f1583,f208]) ).

fof(f7392,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(compose(h,a),X0)),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,codomain(compose(compose(h,a),X0)))),compose(compose(h,a),X0)),compose(compose(h,a),X0)) = compose(compose(h,a),X0),
    inference(paramodulation,[status(thm)],[f1465,f208]) ).

fof(f7393,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(compose(h,compose(a,b)),X0)),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,codomain(compose(compose(h,compose(a,b)),X0)))),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(paramodulation,[status(thm)],[f1016,f208]) ).

fof(f7394,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)],[f975,f208]) ).

fof(f7395,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(g,X0)),ifeq(domain(a),domain(X0),compose(g,compose(X0,codomain(compose(g,X0)))),compose(g,X0)),compose(g,X0)) = compose(g,X0),
    inference(paramodulation,[status(thm)],[f316,f208]) ).

fof(f7396,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(h,X0)),ifeq(domain(a),domain(X0),compose(h,compose(X0,codomain(compose(h,X0)))),compose(h,X0)),compose(h,X0)) = compose(h,X0),
    inference(paramodulation,[status(thm)],[f147,f208]) ).

fof(f7397,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)],[f36,f208]) ).

fof(f7459,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(X0,compose(g,a))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),codomain(compose(X0,compose(g,a))))),compose(X0,compose(g,a))),compose(X0,compose(g,a))) = compose(X0,compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f7362]) ).

fof(f7460,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(X0,compose(h,a))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),codomain(compose(X0,compose(h,a))))),compose(X0,compose(h,a))),compose(X0,compose(h,a))) = compose(X0,compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f7363]) ).

fof(f7461,plain,
    ! [X0] : ifeq(codomain(b),codomain(compose(X0,compose(h,compose(a,b)))),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),codomain(compose(X0,compose(h,compose(a,b)))))),compose(X0,compose(h,compose(a,b)))),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f7364]) ).

fof(f7463,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(X0,g)),ifeq(codomain(X0),domain(h),compose(X0,compose(g,codomain(compose(X0,g)))),compose(X0,g)),compose(X0,g)) = compose(X0,g),
    inference(forward_demodulation,[status(thm)],[f478,f7366]) ).

fof(f7987,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(paramodulation,[status(thm)],[f1016,f230]) ).

fof(f7990,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(domain(h),compose(h,X0)),compose(h,X0)) = compose(h,X0),
    inference(paramodulation,[status(thm)],[f147,f230]) ).

fof(f7994,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(domain(X0),compose(X0,g)),compose(X0,g)) = compose(X0,g),
    inference(paramodulation,[status(thm)],[f478,f230]) ).

fof(f7995,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(domain(X0),compose(X0,compose(g,a))),compose(X0,compose(g,a))) = compose(X0,compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f230]) ).

fof(f7996,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(domain(X0),compose(X0,compose(h,a))),compose(X0,compose(h,a))) = compose(X0,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f230]) ).

fof(f7997,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(domain(X0),compose(X0,compose(h,compose(a,b)))),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f230]) ).

fof(f7999,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)],[f35,f230]) ).

fof(f8044,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(domain(h),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f506,f7987]) ).

fof(f8194,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(paramodulation,[status(thm)],[f1016,f235]) ).

fof(f8201,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(codomain(X0),g)),compose(X0,g)) = compose(X0,g),
    inference(paramodulation,[status(thm)],[f478,f235]) ).

fof(f8202,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(codomain(X0),compose(g,a))),compose(X0,compose(g,a))) = compose(X0,compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f235]) ).

fof(f8203,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(codomain(X0),compose(h,a))),compose(X0,compose(h,a))) = compose(X0,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f235]) ).

fof(f8204,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(codomain(X0),compose(h,compose(a,b)))),compose(X0,compose(h,compose(a,b)))) = compose(X0,compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f235]) ).

fof(f8206,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)],[f35,f235]) ).

fof(f8237,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f1016,f8194]) ).

fof(f8322,plain,
    compose(domain(h),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f478,f475]) ).

fof(f8346,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(domain(X0),domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f8322,f163]) ).

fof(f8347,plain,
    ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),ifeq(domain(b),domain(domain(h)),compose(a,compose(h,compose(a,b))),compose(compose(a,domain(h)),compose(h,compose(a,b)))),compose(compose(a,domain(h)),compose(h,compose(a,b)))) = compose(compose(a,domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f8322,f162]) ).

fof(f8348,plain,
    ! [X0] : ifeq(codomain(compose(h,compose(a,b))),codomain(X0),ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f8322,f160]) ).

fof(f8350,plain,
    ifeq(codomain(compose(h,compose(a,b))),domain(a),ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f8322,f2966]) ).

fof(f8481,plain,
    ! [X0] : ifeq(domain(h),domain(compose(h,compose(a,b))),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(domain(X0),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f8346]) ).

fof(f8482,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(domain(X0),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f8481]) ).

fof(f8483,plain,
    ! [X0] : ifeq(domain(X0),domain(domain(h)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(domain(X0),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f8482]) ).

fof(f8484,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(domain(X0),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f8483]) ).

fof(f8485,plain,
    ifeq(domain(h),domain(compose(h,compose(a,b))),ifeq(domain(b),domain(domain(h)),compose(a,compose(h,compose(a,b))),compose(compose(a,domain(h)),compose(h,compose(a,b)))),compose(compose(a,domain(h)),compose(h,compose(a,b)))) = compose(compose(a,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f8347]) ).

fof(f8486,plain,
    ifeq(domain(h),domain(h),ifeq(domain(b),domain(domain(h)),compose(a,compose(h,compose(a,b))),compose(compose(a,domain(h)),compose(h,compose(a,b)))),compose(compose(a,domain(h)),compose(h,compose(a,b)))) = compose(compose(a,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f8485]) ).

fof(f8487,plain,
    ifeq(domain(b),domain(domain(h)),compose(a,compose(h,compose(a,b))),compose(compose(a,domain(h)),compose(h,compose(a,b)))) = compose(compose(a,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f8486]) ).

fof(f8488,plain,
    ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,domain(h)),compose(h,compose(a,b)))) = compose(compose(a,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f8487]) ).

fof(f8489,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1016,f8348]) ).

fof(f8490,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(h),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f8489]) ).

fof(f8491,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f506,f8490]) ).

fof(f8492,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f8491]) ).

fof(f8493,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(domain(h),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f8322,f8492]) ).

fof(f8500,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1016,f8350]) ).

fof(f8501,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(h),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f8500]) ).

fof(f8502,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f506,f8501]) ).

fof(f8503,plain,
    ifeq(codomain(b),domain(a),compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f8502]) ).

fof(f8504,plain,
    ifeq(codomain(b),domain(a),compose(domain(h),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f8322,f8503]) ).

fof(f8873,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f1039]) ).

fof(f8874,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f1039]) ).

fof(f8875,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f1039]) ).

fof(f8892,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f8873]) ).

fof(f8893,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f8892]) ).

fof(f8894,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f8874]) ).

fof(f8895,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f8894]) ).

fof(f8896,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f8875]) ).

fof(f8897,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(a,b),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f1016,f8896]) ).

fof(f8954,plain,
    ! [X0] : ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),ifeq(domain(X0),domain(compose(h,compose(a,b))),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f1103,f163]) ).

fof(f8955,plain,
    ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),ifeq(domain(b),domain(compose(h,compose(a,b))),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f1103,f162]) ).

fof(f8956,plain,
    ! [X0] : ifeq(codomain(codomain(b)),codomain(X0),ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),codomain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1103,f160]) ).

fof(f8958,plain,
    ifeq(codomain(codomain(b)),domain(a),ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1103,f2966]) ).

fof(f9108,plain,
    ! [X0] : ifeq(codomain(b),domain(codomain(b)),ifeq(domain(X0),domain(compose(h,compose(a,b))),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f1016,f8954]) ).

fof(f9109,plain,
    ! [X0] : ifeq(codomain(b),codomain(b),ifeq(domain(X0),domain(compose(h,compose(a,b))),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f18,f9108]) ).

fof(f9110,plain,
    ! [X0] : ifeq(domain(X0),domain(compose(h,compose(a,b))),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f9109]) ).

fof(f9111,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f506,f9110]) ).

fof(f9112,plain,
    ifeq(codomain(b),domain(codomain(b)),ifeq(domain(b),domain(compose(h,compose(a,b))),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f1016,f8955]) ).

fof(f9113,plain,
    ifeq(codomain(b),codomain(b),ifeq(domain(b),domain(compose(h,compose(a,b))),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f18,f9112]) ).

fof(f9114,plain,
    ifeq(domain(b),domain(compose(h,compose(a,b))),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f9113]) ).

fof(f9115,plain,
    ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,compose(a,b))),codomain(b))) = compose(compose(a,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f506,f9114]) ).

fof(f9116,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),codomain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f36,f8956]) ).

fof(f9117,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),codomain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1016,f9116]) ).

fof(f9118,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),codomain(b),compose(compose(h,compose(a,b)),compose(codomain(b),codomain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f18,f9117]) ).

fof(f9119,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f9118]) ).

fof(f9120,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1103,f9119]) ).

fof(f9127,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f36,f8958]) ).

fof(f9128,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1016,f9127]) ).

fof(f9129,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),codomain(b),compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f18,f9128]) ).

fof(f9130,plain,
    ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f9129]) ).

fof(f9131,plain,
    ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(codomain(b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1103,f9130]) ).

fof(f9281,plain,
    codomain(compose(compose(h,a),b)) = codomain(b),
    inference(paramodulation,[status(thm)],[f16,f1530]) ).

fof(f9283,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f1530]) ).

fof(f9284,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f1530]) ).

fof(f9285,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f1530]) ).

fof(f9303,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f9283]) ).

fof(f9304,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f9303]) ).

fof(f9305,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f9284]) ).

fof(f9306,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f9305]) ).

fof(f9307,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f9285]) ).

fof(f9308,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(h,a),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f1016,f9307]) ).

fof(f9641,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f1618]) ).

fof(f9642,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(h,a))),codomain(compose(h,a))) = codomain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f1618]) ).

fof(f9643,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f1618]) ).

fof(f9664,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(g,a))),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f9641]) ).

fof(f9665,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f9664]) ).

fof(f9666,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(h,a))),domain(b)) = codomain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f9642]) ).

fof(f9667,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1465,f9666]) ).

fof(f9668,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f9643]) ).

fof(f9669,plain,
    ifeq(domain(b),domain(h),codomain(compose(compose(g,a),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f1016,f9668]) ).

fof(f9705,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(compose(a,a),X0,a,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f389]) ).

fof(f9706,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(a,a),X0,a,compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f389]) ).

fof(f9707,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(a,a),X0,a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f389]) ).

fof(f9708,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(a,a),X0,a,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f389]) ).

fof(f9709,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(a,a),X0,a,g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f389]) ).

fof(f9710,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(a,a),X0,a,h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f389]) ).

fof(f9711,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(a,a),X1,a,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f389]) ).

fof(f9712,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,a),X0,ifeq(compose(a,a),X0,a,a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f24,f389]) ).

fof(f9713,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(a,a),X1,a,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f389]) ).

fof(f9714,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(a,a),compose(X0,a),a,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f16,f389]) ).

fof(f9715,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(a,X0,ifeq(compose(a,a),X0,a,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f389]) ).

fof(f9716,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(a,a),a,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f16,f389]) ).

fof(f9717,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(a,a),X0,a,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f9705]) ).

fof(f9718,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(a,a),X0,a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f9706]) ).

fof(f9719,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(a,a),X0,a,a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f9712]) ).

fof(f9720,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(a,a),X0,a,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f9715]) ).

fof(f9730,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f390]) ).

fof(f9731,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f390]) ).

fof(f9732,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f390]) ).

fof(f9733,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f390]) ).

fof(f9734,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f390]) ).

fof(f9735,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f390]) ).

fof(f9736,plain,
    ! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),X2,ifeq(compose(domain(X0),a),X2,domain(X0),codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f390]) ).

fof(f9737,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f24,f390]) ).

fof(f9738,plain,
    ! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),X2,ifeq(compose(domain(X0),a),X2,domain(X0),domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f390]) ).

fof(f9739,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(domain(X0),a),compose(X1,a),domain(X0),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f16,f390]) ).

fof(f9740,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(a,X1,ifeq(compose(domain(X0),a),X1,domain(X0),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f390]) ).

fof(f9741,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),compose(domain(X0),a),domain(X0),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f16,f390]) ).

fof(f9775,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(compose(g,a),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f9730]) ).

fof(f9776,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(compose(h,a),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f9731]) ).

fof(f9777,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(a,a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f9737]) ).

fof(f9778,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,X1,ifeq(compose(domain(X0),a),X1,domain(X0),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f9740]) ).

fof(f9814,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(h,a))),domain(compose(g,a))) = domain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f1955]) ).

fof(f9815,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(h,a))),domain(compose(h,a))) = domain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f1955]) ).

fof(f9816,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(h,a))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f1955]) ).

fof(f9832,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(h,a))),domain(h)) = domain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f9814]) ).

fof(f9833,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(h,a))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f2123,f9832]) ).

fof(f9834,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(h,a))),domain(h)) = domain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f9815]) ).

fof(f9835,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(h,a))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f1908,f9834]) ).

fof(f9836,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(h,a))),domain(h)) = domain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f9816]) ).

fof(f9837,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(h,a))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f506,f9836]) ).

fof(f9869,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1583,f402]) ).

fof(f9870,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1465,f402]) ).

fof(f9871,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1016,f402]) ).

fof(f9872,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(a,a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f975,f402]) ).

fof(f9873,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(compose(a,a),X0,ifeq(compose(g,a),X0,g,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f316,f402]) ).

fof(f9874,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(compose(a,a),X0,ifeq(compose(h,a),X0,h,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f147,f402]) ).

fof(f9875,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f36,f402]) ).

fof(f9878,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,a),compose(a,a),X0,a),a) = a,
    inference(paramodulation,[status(thm)],[f16,f402]) ).

fof(f9879,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(a,a),compose(X0,a),X0,a),a) = a,
    inference(paramodulation,[status(thm)],[f16,f402]) ).

fof(f9880,plain,
    ! [X0] : ifeq(codomain(domain(a)),domain(a),ifeq(compose(a,a),X0,ifeq(a,X0,domain(a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f19,f402]) ).

fof(f9881,plain,
    ! [X0] : ifeq(compose(a,a),X0,ifeq(compose(g,a),X0,g,a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f9873]) ).

fof(f9882,plain,
    ! [X0] : ifeq(compose(a,a),X0,ifeq(compose(h,a),X0,h,a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f9874]) ).

fof(f9883,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(compose(a,a),X0,ifeq(a,X0,domain(a),a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f17,f9880]) ).

fof(f9884,plain,
    ! [X0] : ifeq(compose(a,a),X0,ifeq(a,X0,domain(a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f9883]) ).

fof(f9885,plain,
    ifeq(a,compose(a,a),domain(a),a) = a,
    inference(paramodulation,[status(thm)],[f16,f9884]) ).

fof(f9886,plain,
    ifeq(compose(a,a),a,domain(a),a) = a,
    inference(paramodulation,[status(thm)],[f16,f9884]) ).

fof(f9890,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(compose(g,a),a),X1,compose(g,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1583,f395]) ).

fof(f9891,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(compose(h,a),a),X1,compose(h,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1465,f395]) ).

fof(f9892,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(compose(h,compose(a,b)),a),X1,compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1016,f395]) ).

fof(f9893,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(compose(a,b),a),X1,compose(a,b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f975,f395]) ).

fof(f9894,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(g,a),X1,g,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f316,f395]) ).

fof(f9895,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(h,a),X1,h,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f147,f395]) ).

fof(f9896,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),X2,ifeq(compose(codomain(X0),a),X2,codomain(X0),domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f36,f395]) ).

fof(f9899,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(X0,a),X1,X0,domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f395]) ).

fof(f9907,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(X0,a),compose(domain(X1),a),X0,domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f16,f395]) ).

fof(f9916,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),compose(X0,a),X0,domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f16,f395]) ).

fof(f9917,plain,
    ! [X0,X1] : ifeq(codomain(domain(a)),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(a,X1,domain(a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f19,f395]) ).

fof(f9946,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(g,a),X1,g,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f16,f9894]) ).

fof(f9947,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(compose(h,a),X1,h,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f16,f9895]) ).

fof(f10034,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(a,X1,domain(a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f17,f9917]) ).

fof(f10035,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),X1,ifeq(a,X1,domain(a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f16,f10034]) ).

fof(f10209,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(g,a))),domain(compose(g,a))) = domain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f2175]) ).

fof(f10210,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(g,a))),domain(compose(h,a))) = domain(compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f2175]) ).

fof(f10211,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(g,a))),domain(compose(h,compose(a,b)))) = domain(compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f2175]) ).

fof(f10227,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(g,a))),domain(h)) = domain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f10209]) ).

fof(f10228,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(g,a))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f2123,f10227]) ).

fof(f10229,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(g,a))),domain(h)) = domain(compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f10210]) ).

fof(f10230,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(g,a))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f1908,f10229]) ).

fof(f10231,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(g,a))),domain(h)) = domain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f10211]) ).

fof(f10232,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(g,a))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f506,f10231]) ).

fof(f10264,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(g,a),a),compose(X0,a),compose(g,a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1583,f396]) ).

fof(f10265,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,a),a),compose(X0,a),compose(h,a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1465,f396]) ).

fof(f10266,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(X0,a),compose(h,compose(a,b)),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1016,f396]) ).

fof(f10267,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(a,b),a),compose(X0,a),compose(a,b),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f975,f396]) ).

fof(f10268,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(g,a),compose(X0,a),g,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f316,f396]) ).

fof(f10269,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,a),compose(X0,a),h,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f147,f396]) ).

fof(f10270,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X0),a),compose(X1,a),codomain(X0),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f36,f396]) ).

fof(f10274,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,a),compose(compose(g,a),a),X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f396]) ).

fof(f10275,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,a),compose(compose(h,a),a),X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f396]) ).

fof(f10276,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(X0,a),compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f396]) ).

fof(f10277,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(X0,a),compose(compose(a,b),a),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f396]) ).

fof(f10278,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,a),compose(g,a),X0,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f396]) ).

fof(f10279,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,a),compose(h,a),X0,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f396]) ).

fof(f10280,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X0,a),compose(codomain(X1),a),X0,codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f396]) ).

fof(f10283,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(b),X0,X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f16,f396]) ).

fof(f10284,plain,
    ! [X0] : ifeq(codomain(domain(a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(a,compose(X0,a),domain(a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f19,f396]) ).

fof(f10285,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(compose(X0,a),a,X0,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f396]) ).

fof(f10286,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(g,a),compose(X0,a),g,X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f10268]) ).

fof(f10287,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(h,a),compose(X0,a),h,X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f10269]) ).

fof(f10288,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,a),compose(compose(g,a),a),X0,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10274]) ).

fof(f10289,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,a),compose(compose(h,a),a),X0,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10275]) ).

fof(f10291,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(a,compose(X0,a),domain(a),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f17,f10284]) ).

fof(f10292,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(a,compose(X0,a),domain(a),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f10291]) ).

fof(f10293,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,a),a,X0,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f10285]) ).

fof(f10295,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(compose(g,a)),domain(b),compose(g,a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10283]) ).

fof(f10296,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(compose(h,a)),domain(b),compose(h,a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10283]) ).

fof(f10297,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(compose(h,compose(a,b))),domain(b),compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10283]) ).

fof(f10298,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(compose(a,b)),domain(b),compose(a,b),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10283]) ).

fof(f10299,plain,
    ifeq(domain(a),domain(a),ifeq(codomain(g),domain(b),g,g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10283]) ).

fof(f10300,plain,
    ifeq(domain(a),domain(a),ifeq(codomain(h),domain(b),h,h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10283]) ).

fof(f10301,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(codomain(X0)),domain(b),codomain(X0),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10283]) ).

fof(f10302,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(a),domain(b),a,a),a) = a,
    inference(paramodulation,[status(thm)],[f24,f10283]) ).

fof(f10303,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(X0)),domain(b),domain(X0),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10283]) ).

fof(f10315,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),compose(g,a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f1583,f10295]) ).

fof(f10316,plain,
    ifeq(domain(b),domain(a),compose(g,a),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10315]) ).

fof(f10317,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),compose(h,a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f1465,f10296]) ).

fof(f10318,plain,
    ifeq(domain(b),domain(a),compose(h,a),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10317]) ).

fof(f10319,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1016,f10297]) ).

fof(f10320,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),compose(a,b),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(forward_demodulation,[status(thm)],[f975,f10298]) ).

fof(f10321,plain,
    ifeq(codomain(g),domain(b),g,g) = g,
    inference(forward_demodulation,[status(thm)],[f16,f10299]) ).

fof(f10322,plain,
    ifeq(domain(a),domain(b),g,g) = g,
    inference(forward_demodulation,[status(thm)],[f316,f10321]) ).

fof(f10323,plain,
    ifeq(codomain(h),domain(b),h,h) = h,
    inference(forward_demodulation,[status(thm)],[f16,f10300]) ).

fof(f10324,plain,
    ifeq(domain(a),domain(b),h,h) = h,
    inference(forward_demodulation,[status(thm)],[f147,f10323]) ).

fof(f10325,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(X0),domain(b),codomain(X0),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f36,f10301]) ).

fof(f10326,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),a,a),a) = a,
    inference(forward_demodulation,[status(thm)],[f24,f10302]) ).

fof(f10327,plain,
    ifeq(domain(b),domain(a),a,a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f10326]) ).

fof(f10328,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(X0),domain(b),domain(X0),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f17,f10303]) ).

fof(f10345,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1583,f403]) ).

fof(f10346,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1465,f403]) ).

fof(f10347,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1016,f403]) ).

fof(f10348,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f975,f403]) ).

fof(f10349,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(g,a),X0,g,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f316,f403]) ).

fof(f10350,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(h,a),X0,h,domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f147,f403]) ).

fof(f10351,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f36,f403]) ).

fof(f10355,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(X0,a),X0,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f16,f403]) ).

fof(f10356,plain,
    ! [X0] : ifeq(codomain(domain(a)),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(a,X0,domain(a),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f403]) ).

fof(f10357,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(g,a),X0,g,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f16,f10349]) ).

fof(f10358,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(compose(h,a),X0,h,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f16,f10350]) ).

fof(f10359,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(a,X0,domain(a),domain(a)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f10356]) ).

fof(f10360,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(a,X0,ifeq(a,X0,domain(a),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f16,f10359]) ).

fof(f10362,plain,
    ifeq(domain(b),domain(b),ifeq(a,compose(compose(g,a),a),domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10292]) ).

fof(f10363,plain,
    ifeq(domain(b),domain(b),ifeq(a,compose(compose(h,a),a),domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10292]) ).

fof(f10364,plain,
    ifeq(codomain(b),domain(b),ifeq(a,compose(compose(h,compose(a,b)),a),domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10292]) ).

fof(f10365,plain,
    ifeq(codomain(b),domain(b),ifeq(a,compose(compose(a,b),a),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10292]) ).

fof(f10366,plain,
    ifeq(domain(a),domain(b),ifeq(a,compose(g,a),domain(a),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10292]) ).

fof(f10367,plain,
    ifeq(domain(a),domain(b),ifeq(a,compose(h,a),domain(a),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10292]) ).

fof(f10368,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(a,compose(codomain(X0),a),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10292]) ).

fof(f10370,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(a,compose(domain(X0),a),domain(a),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10292]) ).

fof(f10372,plain,
    ifeq(codomain(domain(a)),domain(b),ifeq(a,a,domain(a),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f10292]) ).

fof(f10373,plain,
    ifeq(a,compose(compose(g,a),a),domain(a),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10362]) ).

fof(f10374,plain,
    ifeq(a,compose(compose(h,a),a),domain(a),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10363]) ).

fof(f10377,plain,
    ifeq(domain(a),domain(b),ifeq(a,a,domain(a),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f10372]) ).

fof(f10378,plain,
    ifeq(domain(a),domain(b),domain(a),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f16,f10377]) ).

fof(f10381,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(compose(g,a),a),compose(g,a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1583,f398]) ).

fof(f10382,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(compose(h,a),a),compose(h,a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1465,f398]) ).

fof(f10383,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1016,f398]) ).

fof(f10384,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(compose(a,b),a),compose(a,b),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f975,f398]) ).

fof(f10385,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(g,a),g,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f316,f398]) ).

fof(f10386,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(h,a),h,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f147,f398]) ).

fof(f10387,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,a),compose(codomain(X0),a),codomain(X0),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f36,f398]) ).

fof(f10391,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),compose(X0,a),X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f398]) ).

fof(f10392,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),compose(X0,a),X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f398]) ).

fof(f10393,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(X0,a),X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f398]) ).

fof(f10394,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(X0,a),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f398]) ).

fof(f10395,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(X0,a),X0,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f398]) ).

fof(f10396,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(X0,a),X0,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f398]) ).

fof(f10397,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),compose(X0,a),X0,codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f398]) ).

fof(f10402,plain,
    ! [X0] : ifeq(codomain(domain(a)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),a,domain(a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f19,f398]) ).

fof(f10404,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(g,a),g,X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f10385]) ).

fof(f10405,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),compose(h,a),h,X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f10386]) ).

fof(f10406,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),a),compose(X0,a),X0,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10391]) ).

fof(f10407,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),a),compose(X0,a),X0,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10392]) ).

fof(f10410,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),a,domain(a),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f17,f10402]) ).

fof(f10411,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),a,domain(a),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f10410]) ).

fof(f10413,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),a,domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10411]) ).

fof(f10414,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),a,domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10411]) ).

fof(f10415,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),a,domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10411]) ).

fof(f10416,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),a,domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10411]) ).

fof(f10417,plain,
    ifeq(domain(a),domain(b),ifeq(compose(g,a),a,domain(a),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10411]) ).

fof(f10418,plain,
    ifeq(domain(a),domain(b),ifeq(compose(h,a),a,domain(a),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10411]) ).

fof(f10419,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),a,domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10411]) ).

fof(f10421,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),a,domain(a),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10411]) ).

fof(f10424,plain,
    ifeq(compose(compose(g,a),a),a,domain(a),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10413]) ).

fof(f10425,plain,
    ifeq(compose(compose(h,a),a),a,domain(a),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10414]) ).

fof(f10431,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(a,X0,domain(a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f405]) ).

fof(f10432,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(a,X0,domain(a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f405]) ).

fof(f10433,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(a,X0,domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f405]) ).

fof(f10434,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(a,X0,domain(a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f405]) ).

fof(f10435,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(a,X0,domain(a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f405]) ).

fof(f10436,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(a,X0,domain(a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f405]) ).

fof(f10437,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(a,X1,domain(a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f405]) ).

fof(f10445,plain,
    ! [X0] : ifeq(compose(compose(g,a),a),X0,ifeq(a,X0,domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10431]) ).

fof(f10446,plain,
    ! [X0] : ifeq(compose(compose(h,a),a),X0,ifeq(a,X0,domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10432]) ).

fof(f10452,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(g,compose(compose(a,b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f975,f450]) ).

fof(f10453,plain,
    ifeq(codomain(b),domain(h),compose(g,compose(compose(a,b),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
    inference(paramodulation,[status(thm)],[f478,f10452]) ).

fof(f10454,plain,
    ifeq(codomain(b),domain(h),compose(g,compose(compose(a,b),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f10452]) ).

fof(f10455,plain,
    ifeq(codomain(b),domain(h),compose(g,compose(compose(a,b),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f10452]) ).

fof(f10456,plain,
    ifeq(codomain(b),domain(h),compose(g,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f10452]) ).

fof(f10458,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(g,compose(compose(a,b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
    inference(paramodulation,[status(thm)],[f35,f10452]) ).

fof(f10483,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,g),compose(a,b))) = compose(compose(X0,g),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f478,f458]) ).

fof(f10485,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),g),compose(a,b))) = compose(compose(compose(g,a),g),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f10483]) ).

fof(f10486,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),g),compose(a,b))) = compose(compose(compose(h,a),g),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f10483]) ).

fof(f10487,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),g),compose(a,b))) = compose(compose(compose(h,compose(a,b)),g),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10483]) ).

fof(f10488,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,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)],[f975,f10483]) ).

fof(f10489,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,g),compose(a,b))) = compose(compose(g,g),compose(a,b)),
    inference(paramodulation,[status(thm)],[f316,f10483]) ).

fof(f10490,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,g),compose(a,b))) = compose(compose(h,g),compose(a,b)),
    inference(paramodulation,[status(thm)],[f147,f10483]) ).

fof(f10491,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),g),compose(a,b))) = compose(compose(codomain(X0),g),compose(a,b)),
    inference(paramodulation,[status(thm)],[f36,f10483]) ).

fof(f10518,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(a,b),X0,a,compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f489]) ).

fof(f10519,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(a,b),X0,a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f489]) ).

fof(f10520,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(a,b),X0,a,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f489]) ).

fof(f10521,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(a,b),X0,a,g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f489]) ).

fof(f10522,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(a,b),X0,a,h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f489]) ).

fof(f10523,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(a,b),X1,a,codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f489]) ).

fof(f10524,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,b),X0,ifeq(compose(a,b),X0,a,a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f24,f489]) ).

fof(f10525,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(a,b),X1,a,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f489]) ).

fof(f10526,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(a,b),compose(X0,b),a,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f16,f489]) ).

fof(f10527,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(a,b),X0,a,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f446,f489]) ).

fof(f10528,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(domain(b)),domain(b),ifeq(b,X0,ifeq(compose(a,b),X0,a,domain(b)),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f489]) ).

fof(f10529,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(a,b),a,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f16,f489]) ).

fof(f10532,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),X0,ifeq(compose(a,b),X0,a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10518]) ).

fof(f10533,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(a,b),X0,a,a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f10524]) ).

fof(f10534,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(a,b),X0,a,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f1583,f10527]) ).

fof(f10535,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(a,b),X0,a,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10534]) ).

fof(f10536,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(b,X0,ifeq(compose(a,b),X0,a,domain(b)),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f10528]) ).

fof(f10537,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(a,b),X0,a,domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f10536]) ).

fof(f10538,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(domain(a),b),X1,domain(a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f16,f490]) ).

fof(f10548,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f490]) ).

fof(f10549,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f490]) ).

fof(f10550,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f490]) ).

fof(f10551,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f490]) ).

fof(f10552,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f490]) ).

fof(f10553,plain,
    ! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),X2,ifeq(compose(domain(X0),b),X2,domain(X0),codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f490]) ).

fof(f10554,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f24,f490]) ).

fof(f10555,plain,
    ! [X0,X1,X2] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),X2,ifeq(compose(domain(X0),b),X2,domain(X0),domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f490]) ).

fof(f10556,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(domain(X0),b),compose(X1,b),domain(X0),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f16,f490]) ).

fof(f10557,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f446,f490]) ).

fof(f10558,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(b)),domain(b),ifeq(b,X1,ifeq(compose(domain(X0),b),X1,domain(X0),domain(b)),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f490]) ).

fof(f10559,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),compose(domain(X0),b),domain(X0),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f16,f490]) ).

fof(f10593,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(compose(h,a),b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10548]) ).

fof(f10594,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(domain(X0),b),X1,domain(X0),a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f10554]) ).

fof(f10595,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f1583,f10557]) ).

fof(f10596,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10595]) ).

fof(f10597,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(b,X1,ifeq(compose(domain(X0),b),X1,domain(X0),domain(b)),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f10558]) ).

fof(f10598,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(b,X1,ifeq(compose(domain(X0),b),X1,domain(X0),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f10597]) ).

fof(f10630,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(g,a),b),X0,compose(g,a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1583,f502]) ).

fof(f10631,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1465,f502]) ).

fof(f10632,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1016,f502]) ).

fof(f10633,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f975,f502]) ).

fof(f10634,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(compose(a,b),X0,ifeq(compose(g,b),X0,g,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f316,f502]) ).

fof(f10635,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(compose(a,b),X0,ifeq(compose(h,b),X0,h,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f147,f502]) ).

fof(f10636,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f36,f502]) ).

fof(f10639,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),compose(a,b),X0,a),a) = a,
    inference(paramodulation,[status(thm)],[f16,f502]) ).

fof(f10640,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(X0,b),X0,a),a) = a,
    inference(paramodulation,[status(thm)],[f16,f502]) ).

fof(f10642,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(a),ifeq(compose(a,b),X0,ifeq(b,X0,domain(b),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f19,f502]) ).

fof(f10643,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f446,f10630]) ).

fof(f10644,plain,
    ! [X0] : ifeq(compose(a,b),X0,ifeq(compose(g,b),X0,g,a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f10634]) ).

fof(f10645,plain,
    ! [X0] : ifeq(compose(a,b),X0,ifeq(compose(h,b),X0,h,a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f10635]) ).

fof(f10647,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(b,X0,domain(b),a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f17,f10642]) ).

fof(f10650,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(compose(h,a),b),X1,compose(h,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1465,f495]) ).

fof(f10651,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(compose(h,compose(a,b)),b),X1,compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1016,f495]) ).

fof(f10652,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(compose(a,b),b),X1,compose(a,b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f975,f495]) ).

fof(f10653,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(g,b),X1,g,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f316,f495]) ).

fof(f10654,plain,
    ! [X0,X1] : ifeq(domain(a),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(h,b),X1,h,domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f147,f495]) ).

fof(f10655,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),X2,ifeq(compose(codomain(X0),b),X2,codomain(X0),domain(X1)),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f36,f495]) ).

fof(f10666,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(X0,b),compose(domain(X1),b),X0,domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f16,f495]) ).

fof(f10675,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),compose(X0,b),X0,domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f16,f495]) ).

fof(f10676,plain,
    ! [X0,X1] : ifeq(codomain(compose(g,a)),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f446,f495]) ).

fof(f10677,plain,
    ! [X0,X1] : ifeq(codomain(domain(b)),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(b,X1,domain(b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f19,f495]) ).

fof(f10707,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(g,b),X1,g,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f16,f10653]) ).

fof(f10708,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(h,b),X1,h,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f16,f10654]) ).

fof(f10795,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f1583,f10676]) ).

fof(f10796,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(b,X1,domain(b),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f17,f10677]) ).

fof(f10966,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(g,a),b),compose(X0,b),compose(g,a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1583,f496]) ).

fof(f10967,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,a),b),compose(X0,b),compose(h,a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1465,f496]) ).

fof(f10968,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(X0,b),compose(h,compose(a,b)),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1016,f496]) ).

fof(f10969,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(a,b),b),compose(X0,b),compose(a,b),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f975,f496]) ).

fof(f10970,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(g,b),compose(X0,b),g,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f316,f496]) ).

fof(f10971,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,b),compose(X0,b),h,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f147,f496]) ).

fof(f10972,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X0),b),compose(X1,b),codomain(X0),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f36,f496]) ).

fof(f10976,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,b),compose(compose(g,a),b),X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f496]) ).

fof(f10977,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,b),compose(compose(h,a),b),X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f496]) ).

fof(f10978,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(X0,b),compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f496]) ).

fof(f10979,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(X0,b),compose(compose(a,b),b),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f496]) ).

fof(f10980,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,b),compose(g,b),X0,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f496]) ).

fof(f10981,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(X0,b),compose(h,b),X0,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f496]) ).

fof(f10982,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X0,b),compose(codomain(X1),b),X0,codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f496]) ).

fof(f10987,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(a),ifeq(codomain(X0),domain(b),ifeq(b,compose(X0,b),domain(b),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f19,f496]) ).

fof(f10989,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(b)),domain(b),ifeq(compose(X0,b),b,X0,domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f496]) ).

fof(f10990,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(X0,b),compose(g,a),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f446,f10966]) ).

fof(f10991,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(g,b),compose(X0,b),g,X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f10970]) ).

fof(f10992,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(h,b),compose(X0,b),h,X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f10971]) ).

fof(f10993,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),compose(compose(g,a),b),X0,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f10976]) ).

fof(f10994,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),compose(h,compose(a,b)),X0,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f10993]) ).

fof(f10995,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),compose(compose(h,a),b),X0,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f10977]) ).

fof(f10998,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(b,compose(X0,b),domain(b),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f17,f10987]) ).

fof(f11001,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(X0,b),b,X0,domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f10989]) ).

fof(f11002,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),b,X0,domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f11001]) ).

fof(f11211,plain,
    ifeq(compose(g,a),compose(a,a),g,a) = a,
    inference(paramodulation,[status(thm)],[f16,f9881]) ).

fof(f11212,plain,
    ifeq(compose(a,a),compose(g,a),g,a) = a,
    inference(paramodulation,[status(thm)],[f16,f9881]) ).

fof(f11239,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1465,f504]) ).

fof(f11240,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(b,X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1016,f504]) ).

fof(f11241,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(b,X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f975,f504]) ).

fof(f11242,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(b,X0,ifeq(compose(g,b),X0,g,domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f316,f504]) ).

fof(f11243,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(b,X0,ifeq(compose(h,b),X0,h,domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f147,f504]) ).

fof(f11244,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(b,X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f36,f504]) ).

fof(f11248,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(b,compose(X0,b),X0,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f504]) ).

fof(f11249,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(a),ifeq(b,X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f446,f504]) ).

fof(f11250,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(a),ifeq(b,X0,ifeq(b,X0,domain(b),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f504]) ).

fof(f11252,plain,
    ! [X0] : ifeq(b,X0,ifeq(compose(g,b),X0,g,domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f11242]) ).

fof(f11253,plain,
    ! [X0] : ifeq(b,X0,ifeq(compose(h,b),X0,h,domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f11243]) ).

fof(f11254,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f11249]) ).

fof(f11255,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(b,X0,domain(b),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f11250]) ).

fof(f11256,plain,
    ifeq(compose(h,a),compose(a,a),h,a) = a,
    inference(paramodulation,[status(thm)],[f16,f9882]) ).

fof(f11257,plain,
    ifeq(compose(a,a),compose(h,a),h,a) = a,
    inference(paramodulation,[status(thm)],[f16,f9882]) ).

fof(f11282,plain,
    ifeq(compose(g,b),compose(a,b),g,a) = a,
    inference(paramodulation,[status(thm)],[f16,f10644]) ).

fof(f11283,plain,
    ifeq(compose(a,b),compose(g,b),g,a) = a,
    inference(paramodulation,[status(thm)],[f16,f10644]) ).

fof(f11293,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(compose(g,a),b),compose(g,a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1583,f498]) ).

fof(f11294,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(compose(h,a),b),compose(h,a),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1465,f498]) ).

fof(f11295,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f1016,f498]) ).

fof(f11296,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(compose(a,b),b),compose(a,b),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f975,f498]) ).

fof(f11297,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(g,b),g,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f316,f498]) ).

fof(f11298,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(h,b),h,X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f147,f498]) ).

fof(f11299,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(X1,b),compose(codomain(X0),b),codomain(X0),X1),X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f36,f498]) ).

fof(f11303,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(X0,b),X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f498]) ).

fof(f11304,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(X0,b),X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f498]) ).

fof(f11305,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(X0,b),X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f498]) ).

fof(f11306,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(X0,b),X0,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f498]) ).

fof(f11307,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(X0,b),X0,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f498]) ).

fof(f11308,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(X0,b),X0,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f498]) ).

fof(f11309,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),compose(X0,b),X0,codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f498]) ).

fof(f11316,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),b,domain(b),X0),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f19,f498]) ).

fof(f11318,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(h,compose(a,b)),compose(g,a),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f446,f11293]) ).

fof(f11319,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(g,b),g,X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f11297]) ).

fof(f11320,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(h,b),h,X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f16,f11298]) ).

fof(f11321,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),b),compose(X0,b),X0,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11303]) ).

fof(f11322,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(X0,b),X0,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f11321]) ).

fof(f11323,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),b),compose(X0,b),X0,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11304]) ).

fof(f11330,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),b,domain(b),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f17,f11316]) ).

fof(f11348,plain,
    ifeq(compose(h,b),compose(a,b),h,a) = a,
    inference(paramodulation,[status(thm)],[f16,f10645]) ).

fof(f11349,plain,
    ifeq(compose(a,b),compose(h,b),h,a) = a,
    inference(paramodulation,[status(thm)],[f16,f10645]) ).

fof(f11376,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(b,X0,domain(b),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f505]) ).

fof(f11377,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(b,X0,domain(b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f505]) ).

fof(f11378,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(b,X0,domain(b),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f505]) ).

fof(f11379,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(b,X0,domain(b),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f505]) ).

fof(f11380,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(b,X0,domain(b),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f505]) ).

fof(f11381,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(b,X1,domain(b),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f505]) ).

fof(f11385,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(compose(g,a)),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(b,X0,domain(b),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f446,f505]) ).

fof(f11390,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),X0,ifeq(b,X0,domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11376]) ).

fof(f11392,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X0,ifeq(b,X0,domain(b),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f1583,f11385]) ).

fof(f11393,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(b,X0,domain(b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11392]) ).

fof(f11397,plain,
    ifeq(domain(b),domain(b),ifeq(compose(g,a),compose(compose(g,a),a),g,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10286]) ).

fof(f11398,plain,
    ifeq(domain(b),domain(b),ifeq(compose(g,a),compose(compose(h,a),a),g,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10286]) ).

fof(f11399,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(g,a),compose(compose(h,compose(a,b)),a),g,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10286]) ).

fof(f11400,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(g,a),compose(compose(a,b),a),g,compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10286]) ).

fof(f11402,plain,
    ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(h,a),g,h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10286]) ).

fof(f11403,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(g,a),compose(codomain(X0),a),g,codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10286]) ).

fof(f11405,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(g,a),compose(domain(X0),a),g,domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10286]) ).

fof(f11408,plain,
    ifeq(codomain(domain(a)),domain(b),ifeq(compose(g,a),a,g,domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f10286]) ).

fof(f11411,plain,
    ifeq(compose(g,a),compose(compose(g,a),a),g,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11397]) ).

fof(f11412,plain,
    ifeq(compose(g,a),compose(compose(h,a),a),g,compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11398]) ).

fof(f11417,plain,
    ifeq(domain(a),domain(b),ifeq(compose(g,a),a,g,domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f11408]) ).

fof(f11421,plain,
    ifeq(domain(b),domain(b),ifeq(compose(h,a),compose(compose(g,a),a),h,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10287]) ).

fof(f11422,plain,
    ifeq(domain(b),domain(b),ifeq(compose(h,a),compose(compose(h,a),a),h,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10287]) ).

fof(f11423,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(h,a),compose(compose(h,compose(a,b)),a),h,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10287]) ).

fof(f11424,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(h,a),compose(compose(a,b),a),h,compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10287]) ).

fof(f11425,plain,
    ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(g,a),h,g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10287]) ).

fof(f11427,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(h,a),compose(codomain(X0),a),h,codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10287]) ).

fof(f11429,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(h,a),compose(domain(X0),a),h,domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10287]) ).

fof(f11432,plain,
    ifeq(codomain(domain(a)),domain(b),ifeq(compose(h,a),a,h,domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f10287]) ).

fof(f11435,plain,
    ifeq(compose(h,a),compose(compose(g,a),a),h,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11421]) ).

fof(f11436,plain,
    ifeq(compose(h,a),compose(compose(h,a),a),h,compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11422]) ).

fof(f11441,plain,
    ifeq(domain(a),domain(b),ifeq(compose(h,a),a,h,domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f11432]) ).

fof(f11446,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),compose(g,a),g,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10404]) ).

fof(f11447,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),compose(g,a),g,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10404]) ).

fof(f11448,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(g,a),g,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10404]) ).

fof(f11449,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(g,a),g,compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10404]) ).

fof(f11451,plain,
    ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(g,a),g,h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10404]) ).

fof(f11452,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(g,a),g,codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10404]) ).

fof(f11454,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(g,a),g,domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10404]) ).

fof(f11457,plain,
    ifeq(codomain(domain(a)),domain(b),ifeq(a,compose(g,a),g,domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f10404]) ).

fof(f11461,plain,
    ifeq(compose(compose(g,a),a),compose(g,a),g,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11446]) ).

fof(f11462,plain,
    ifeq(compose(compose(h,a),a),compose(g,a),g,compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11447]) ).

fof(f11467,plain,
    ifeq(domain(a),domain(b),ifeq(a,compose(g,a),g,domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f11457]) ).

fof(f11472,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),compose(h,a),h,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10405]) ).

fof(f11473,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),compose(h,a),h,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10405]) ).

fof(f11474,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(h,a),h,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10405]) ).

fof(f11475,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(h,a),h,compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10405]) ).

fof(f11476,plain,
    ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(h,a),h,g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10405]) ).

fof(f11478,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(h,a),h,codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10405]) ).

fof(f11480,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(h,a),h,domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10405]) ).

fof(f11483,plain,
    ifeq(codomain(domain(a)),domain(b),ifeq(a,compose(h,a),h,domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f10405]) ).

fof(f11487,plain,
    ifeq(compose(compose(g,a),a),compose(h,a),h,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11472]) ).

fof(f11488,plain,
    ifeq(compose(compose(h,a),a),compose(h,a),h,compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11473]) ).

fof(f11493,plain,
    ifeq(domain(a),domain(b),ifeq(a,compose(h,a),h,domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f11483]) ).

fof(f11497,plain,
    ifeq(domain(b),domain(b),ifeq(compose(g,b),compose(compose(g,a),b),g,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10991]) ).

fof(f11498,plain,
    ifeq(domain(b),domain(b),ifeq(compose(g,b),compose(compose(h,a),b),g,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10991]) ).

fof(f11499,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(g,b),compose(compose(h,compose(a,b)),b),g,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10991]) ).

fof(f11500,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(g,b),compose(compose(a,b),b),g,compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10991]) ).

fof(f11502,plain,
    ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(h,b),g,h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10991]) ).

fof(f11503,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(g,b),compose(codomain(X0),b),g,codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10991]) ).

fof(f11505,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(g,b),compose(domain(X0),b),g,domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10991]) ).

fof(f11509,plain,
    ifeq(codomain(domain(b)),domain(b),ifeq(compose(g,b),b,g,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f10991]) ).

fof(f11512,plain,
    ifeq(compose(g,b),compose(compose(g,a),b),g,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11497]) ).

fof(f11513,plain,
    ifeq(compose(g,b),compose(h,compose(a,b)),g,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f11512]) ).

fof(f11514,plain,
    ifeq(compose(g,b),compose(compose(h,a),b),g,compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11498]) ).

fof(f11521,plain,
    ifeq(domain(b),domain(b),ifeq(compose(g,b),b,g,domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f11509]) ).

fof(f11522,plain,
    ifeq(compose(g,b),b,g,domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f11521]) ).

fof(f11540,plain,
    ifeq(domain(b),domain(b),ifeq(compose(h,b),compose(compose(g,a),b),h,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10992]) ).

fof(f11541,plain,
    ifeq(domain(b),domain(b),ifeq(compose(h,b),compose(compose(h,a),b),h,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10992]) ).

fof(f11542,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(h,b),compose(compose(h,compose(a,b)),b),h,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10992]) ).

fof(f11543,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(h,b),compose(compose(a,b),b),h,compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10992]) ).

fof(f11544,plain,
    ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(g,b),h,g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10992]) ).

fof(f11546,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(h,b),compose(codomain(X0),b),h,codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10992]) ).

fof(f11548,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(h,b),compose(domain(X0),b),h,domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10992]) ).

fof(f11552,plain,
    ifeq(codomain(domain(b)),domain(b),ifeq(compose(h,b),b,h,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f10992]) ).

fof(f11555,plain,
    ifeq(compose(h,b),compose(compose(g,a),b),h,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11540]) ).

fof(f11556,plain,
    ifeq(compose(h,b),compose(h,compose(a,b)),h,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f11555]) ).

fof(f11557,plain,
    ifeq(compose(h,b),compose(compose(h,a),b),h,compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11541]) ).

fof(f11564,plain,
    ifeq(domain(b),domain(b),ifeq(compose(h,b),b,h,domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f11552]) ).

fof(f11565,plain,
    ifeq(compose(h,b),b,h,domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f11564]) ).

fof(f11584,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(g,b),g,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f11319]) ).

fof(f11585,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(g,b),g,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f11319]) ).

fof(f11586,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(g,b),g,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f11319]) ).

fof(f11587,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(g,b),g,compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f11319]) ).

fof(f11589,plain,
    ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(g,b),g,h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f11319]) ).

fof(f11590,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(g,b),g,codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f11319]) ).

fof(f11592,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(g,b),g,domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f11319]) ).

fof(f11596,plain,
    ifeq(codomain(domain(b)),domain(b),ifeq(b,compose(g,b),g,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f11319]) ).

fof(f11600,plain,
    ifeq(compose(compose(g,a),b),compose(g,b),g,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11584]) ).

fof(f11601,plain,
    ifeq(compose(h,compose(a,b)),compose(g,b),g,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f11600]) ).

fof(f11602,plain,
    ifeq(compose(compose(h,a),b),compose(g,b),g,compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11585]) ).

fof(f11609,plain,
    ifeq(domain(b),domain(b),ifeq(b,compose(g,b),g,domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f11596]) ).

fof(f11610,plain,
    ifeq(b,compose(g,b),g,domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f11609]) ).

fof(f11615,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(h,b),h,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f11320]) ).

fof(f11616,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(h,b),h,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f11320]) ).

fof(f11617,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(h,b),h,compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f11320]) ).

fof(f11618,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(h,b),h,compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f11320]) ).

fof(f11619,plain,
    ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(h,b),h,g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f11320]) ).

fof(f11621,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(h,b),h,codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f11320]) ).

fof(f11623,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(h,b),h,domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f11320]) ).

fof(f11627,plain,
    ifeq(codomain(domain(b)),domain(b),ifeq(b,compose(h,b),h,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f11320]) ).

fof(f11631,plain,
    ifeq(compose(compose(g,a),b),compose(h,b),h,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f11615]) ).

fof(f11632,plain,
    ifeq(compose(h,compose(a,b)),compose(h,b),h,compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f11631]) ).

fof(f11633,plain,
    ifeq(compose(compose(h,a),b),compose(h,b),h,compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f11616]) ).

fof(f11640,plain,
    ifeq(domain(b),domain(b),ifeq(b,compose(h,b),h,domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f11627]) ).

fof(f11641,plain,
    ifeq(b,compose(h,b),h,domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f11640]) ).

fof(f11645,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(compose(g,a)),compose(X1,compose(compose(g,a),domain(X0))),compose(compose(X1,compose(g,a)),domain(X0))),compose(compose(X1,compose(g,a)),domain(X0))) = compose(compose(X1,compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f159]) ).

fof(f11646,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(compose(h,a)),compose(X1,compose(compose(h,a),domain(X0))),compose(compose(X1,compose(h,a)),domain(X0))),compose(compose(X1,compose(h,a)),domain(X0))) = compose(compose(X1,compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f159]) ).

fof(f11647,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(compose(h,compose(a,b))),compose(X1,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(X1,compose(h,compose(a,b))),domain(X0))),compose(compose(X1,compose(h,compose(a,b))),domain(X0))) = compose(compose(X1,compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f159]) ).

fof(f11649,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(g),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)],[f316,f159]) ).

fof(f11650,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),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)],[f147,f159]) ).

fof(f11662,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,domain(X1))),compose(compose(compose(g,a),X0),domain(X1))),compose(compose(compose(g,a),X0),domain(X1))) = compose(compose(compose(g,a),X0),domain(X1)),
    inference(paramodulation,[status(thm)],[f1583,f159]) ).

fof(f11663,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,domain(X1))),compose(compose(compose(h,a),X0),domain(X1))),compose(compose(compose(h,a),X0),domain(X1))) = compose(compose(compose(h,a),X0),domain(X1)),
    inference(paramodulation,[status(thm)],[f1465,f159]) ).

fof(f11664,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,domain(X1))),compose(compose(compose(h,compose(a,b)),X0),domain(X1))),compose(compose(compose(h,compose(a,b)),X0),domain(X1))) = compose(compose(compose(h,compose(a,b)),X0),domain(X1)),
    inference(paramodulation,[status(thm)],[f1016,f159]) ).

fof(f11665,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)],[f975,f159]) ).

fof(f11666,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),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)],[f316,f159]) ).

fof(f11667,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(X0,domain(X1))),compose(compose(h,X0),domain(X1))),compose(compose(h,X0),domain(X1))) = compose(compose(h,X0),domain(X1)),
    inference(paramodulation,[status(thm)],[f147,f159]) ).

fof(f11668,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)],[f36,f159]) ).

fof(f11696,plain,
    ! [X0] : ifeq(codomain(codomain(b)),domain(X0),ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1103,f159]) ).

fof(f11697,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(X0),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(compose(h,a),domain(b)),domain(X0))) = compose(compose(compose(h,a),domain(b)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1534,f159]) ).

fof(f11698,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)],[f1043,f159]) ).

fof(f11699,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(X0),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(compose(g,a),domain(b)),domain(X0))) = compose(compose(compose(g,a),domain(b)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1622,f159]) ).

fof(f11700,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(g,a)),domain(b),compose(compose(g,a),compose(b,domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(g,a),b),domain(X0))) = compose(compose(compose(g,a),b),domain(X0)),
    inference(paramodulation,[status(thm)],[f446,f159]) ).

fof(f11702,plain,
    ! [X0] : ifeq(codomain(domain(a)),domain(X0),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),domain(X0))),compose(g,domain(X0))),compose(compose(g,domain(a)),domain(X0))) = compose(compose(g,domain(a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f334,f159]) ).

fof(f11703,plain,
    ! [X0] : ifeq(codomain(domain(a)),domain(X0),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),domain(X0))),compose(h,domain(X0))),compose(compose(h,domain(a)),domain(X0))) = compose(compose(h,domain(a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f271,f159]) ).

fof(f11704,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)],[f34,f159]) ).

fof(f11705,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)],[f48,f159]) ).

fof(f11706,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(X0),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(domain(h),compose(g,a)),domain(X0))) = compose(compose(domain(h),compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f2177,f159]) ).

fof(f11707,plain,
    ! [X0] : ifeq(codomain(compose(h,compose(a,b))),domain(X0),ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f8322,f159]) ).

fof(f11708,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(X0),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(domain(h),compose(h,a)),domain(X0))) = compose(compose(domain(h),compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1957,f159]) ).

fof(f11709,plain,
    ! [X0] : ifeq(codomain(g),domain(X0),ifeq(codomain(domain(h)),domain(g),compose(domain(h),compose(g,domain(X0))),compose(g,domain(X0))),compose(compose(domain(h),g),domain(X0))) = compose(compose(domain(h),g),domain(X0)),
    inference(paramodulation,[status(thm)],[f516,f159]) ).

fof(f11710,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)],[f406,f159]) ).

fof(f11711,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)],[f31,f159]) ).

fof(f11749,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(g,a),domain(X0))),compose(compose(X1,compose(g,a)),domain(X0))),compose(compose(X1,compose(g,a)),domain(X0))) = compose(compose(X1,compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f11645]) ).

fof(f11750,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,a),domain(X0))),compose(compose(X1,compose(h,a)),domain(X0))),compose(compose(X1,compose(h,a)),domain(X0))) = compose(compose(X1,compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f11646]) ).

fof(f11751,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(X1,compose(h,compose(a,b))),domain(X0))),compose(compose(X1,compose(h,compose(a,b))),domain(X0))) = compose(compose(X1,compose(h,compose(a,b))),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f506,f11647]) ).

fof(f11753,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),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(forward_demodulation,[status(thm)],[f478,f11649]) ).

fof(f11856,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f36,f11696]) ).

fof(f11857,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1016,f11856]) ).

fof(f11858,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),codomain(b),compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f18,f11857]) ).

fof(f11859,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))),compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11858]) ).

fof(f11860,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1103,f11859]) ).

fof(f11861,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(codomain(b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1103,f11860]) ).

fof(f11862,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(compose(h,a),domain(b)),domain(X0))) = compose(compose(compose(h,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f11697]) ).

fof(f11863,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(domain(b)),compose(compose(h,a),compose(domain(b),domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(compose(h,a),domain(b)),domain(X0))) = compose(compose(compose(h,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1465,f11862]) ).

fof(f11864,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(b),compose(compose(h,a),compose(domain(b),domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(compose(h,a),domain(b)),domain(X0))) = compose(compose(compose(h,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f11863]) ).

fof(f11865,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(b),domain(X0))),compose(compose(compose(h,a),domain(b)),domain(X0))) = compose(compose(compose(h,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11864]) ).

fof(f11866,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(b),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(compose(h,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1534,f11865]) ).

fof(f11867,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(b),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1534,f11866]) ).

fof(f11868,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)],[f36,f11698]) ).

fof(f11869,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)],[f975,f11868]) ).

fof(f11870,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)],[f18,f11869]) ).

fof(f11871,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)],[f16,f11870]) ).

fof(f11872,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)],[f1043,f11871]) ).

fof(f11873,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)],[f1043,f11872]) ).

fof(f11874,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(compose(g,a),domain(b)),domain(X0))) = compose(compose(compose(g,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f11699]) ).

fof(f11875,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(domain(b)),compose(compose(g,a),compose(domain(b),domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(compose(g,a),domain(b)),domain(X0))) = compose(compose(compose(g,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1583,f11874]) ).

fof(f11876,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(b),compose(compose(g,a),compose(domain(b),domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(compose(g,a),domain(b)),domain(X0))) = compose(compose(compose(g,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f11875]) ).

fof(f11877,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(b),domain(X0))),compose(compose(compose(g,a),domain(b)),domain(X0))) = compose(compose(compose(g,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11876]) ).

fof(f11878,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(b),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(compose(g,a),domain(b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1622,f11877]) ).

fof(f11879,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(b),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1622,f11878]) ).

fof(f11880,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(b),compose(compose(g,a),compose(b,domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(g,a),b),domain(X0))) = compose(compose(compose(g,a),b),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1583,f11700]) ).

fof(f11881,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(g,a),compose(b,domain(X0))),compose(compose(compose(g,a),b),domain(X0))) = compose(compose(compose(g,a),b),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11880]) ).

fof(f11882,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(g,a),compose(b,domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(g,a),b),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f446,f11881]) ).

fof(f11883,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(g,a),compose(b,domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f446,f11882]) ).

fof(f11890,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),domain(X0))),compose(g,domain(X0))),compose(compose(g,domain(a)),domain(X0))) = compose(compose(g,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f11702]) ).

fof(f11891,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(domain(a)),compose(g,compose(domain(a),domain(X0))),compose(g,domain(X0))),compose(compose(g,domain(a)),domain(X0))) = compose(compose(g,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f316,f11890]) ).

fof(f11892,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(a),compose(g,compose(domain(a),domain(X0))),compose(g,domain(X0))),compose(compose(g,domain(a)),domain(X0))) = compose(compose(g,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f11891]) ).

fof(f11893,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(g,compose(domain(a),domain(X0))),compose(compose(g,domain(a)),domain(X0))) = compose(compose(g,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11892]) ).

fof(f11894,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(g,compose(domain(a),domain(X0))),compose(g,domain(X0))) = compose(compose(g,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f334,f11893]) ).

fof(f11895,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(g,compose(domain(a),domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
    inference(forward_demodulation,[status(thm)],[f334,f11894]) ).

fof(f11896,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),domain(X0))),compose(h,domain(X0))),compose(compose(h,domain(a)),domain(X0))) = compose(compose(h,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f11703]) ).

fof(f11897,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(domain(a)),compose(h,compose(domain(a),domain(X0))),compose(h,domain(X0))),compose(compose(h,domain(a)),domain(X0))) = compose(compose(h,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f147,f11896]) ).

fof(f11898,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(a),compose(h,compose(domain(a),domain(X0))),compose(h,domain(X0))),compose(compose(h,domain(a)),domain(X0))) = compose(compose(h,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f35,f11897]) ).

fof(f11899,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(h,compose(domain(a),domain(X0))),compose(compose(h,domain(a)),domain(X0))) = compose(compose(h,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11898]) ).

fof(f11900,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(h,compose(domain(a),domain(X0))),compose(h,domain(X0))) = compose(compose(h,domain(a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f271,f11899]) ).

fof(f11901,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(h,compose(domain(a),domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
    inference(forward_demodulation,[status(thm)],[f271,f11900]) ).

fof(f11902,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)],[f36,f11704]) ).

fof(f11903,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)],[f36,f11902]) ).

fof(f11904,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)],[f18,f11903]) ).

fof(f11905,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)],[f16,f11904]) ).

fof(f11906,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)],[f34,f11905]) ).

fof(f11907,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)],[f34,f11906]) ).

fof(f11908,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)],[f17,f11705]) ).

fof(f11909,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,f11908]) ).

fof(f11910,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)],[f35,f11909]) ).

fof(f11911,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)],[f16,f11910]) ).

fof(f11912,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)],[f48,f11911]) ).

fof(f11913,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)],[f48,f11912]) ).

fof(f11914,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(domain(h),compose(g,a)),domain(X0))) = compose(compose(domain(h),compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1583,f11706]) ).

fof(f11915,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(h),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(domain(h),compose(g,a)),domain(X0))) = compose(compose(domain(h),compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f11914]) ).

fof(f11916,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))),compose(compose(domain(h),compose(g,a)),domain(X0))) = compose(compose(domain(h),compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f11915]) ).

fof(f11917,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(domain(h),compose(g,a)),domain(X0))) = compose(compose(domain(h),compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11916]) ).

fof(f11918,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(domain(h),compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f2177,f11917]) ).

fof(f11919,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(g,a),domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f2177,f11918]) ).

fof(f11920,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1016,f11707]) ).

fof(f11921,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(h),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f11920]) ).

fof(f11922,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f506,f11921]) ).

fof(f11923,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(domain(h),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11922]) ).

fof(f11924,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(domain(h),compose(h,compose(a,b))),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f8322,f11923]) ).

fof(f11925,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(domain(h),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f8322,f11924]) ).

fof(f11926,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(domain(h),compose(h,a)),domain(X0))) = compose(compose(domain(h),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1465,f11708]) ).

fof(f11927,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(h),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(domain(h),compose(h,a)),domain(X0))) = compose(compose(domain(h),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f11926]) ).

fof(f11928,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(domain(h),compose(h,a)),domain(X0))) = compose(compose(domain(h),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f11927]) ).

fof(f11929,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(h,a),domain(X0))),compose(compose(domain(h),compose(h,a)),domain(X0))) = compose(compose(domain(h),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11928]) ).

fof(f11930,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(domain(h),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1957,f11929]) ).

fof(f11931,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(domain(h),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1957,f11930]) ).

fof(f11932,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(domain(h)),domain(g),compose(domain(h),compose(g,domain(X0))),compose(g,domain(X0))),compose(compose(domain(h),g),domain(X0))) = compose(compose(domain(h),g),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f316,f11709]) ).

fof(f11933,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(h),domain(g),compose(domain(h),compose(g,domain(X0))),compose(g,domain(X0))),compose(compose(domain(h),g),domain(X0))) = compose(compose(domain(h),g),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f11932]) ).

fof(f11934,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(h),domain(h),compose(domain(h),compose(g,domain(X0))),compose(g,domain(X0))),compose(compose(domain(h),g),domain(X0))) = compose(compose(domain(h),g),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f478,f11933]) ).

fof(f11935,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(domain(h),compose(g,domain(X0))),compose(compose(domain(h),g),domain(X0))) = compose(compose(domain(h),g),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f11934]) ).

fof(f11936,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(domain(h),compose(g,domain(X0))),compose(g,domain(X0))) = compose(compose(domain(h),g),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f516,f11935]) ).

fof(f11937,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(domain(h),compose(g,domain(X0))),compose(g,domain(X0))) = compose(g,domain(X0)),
    inference(forward_demodulation,[status(thm)],[f516,f11936]) ).

fof(f11938,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)],[f975,f11710]) ).

fof(f11939,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)],[f17,f11938]) ).

fof(f11940,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)],[f261,f11939]) ).

fof(f11941,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)],[f16,f11940]) ).

fof(f11942,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)],[f406,f11941]) ).

fof(f11943,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)],[f406,f11942]) ).

fof(f11944,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)],[f17,f11711]) ).

fof(f11945,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)],[f17,f11944]) ).

fof(f11946,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)],[f35,f11945]) ).

fof(f11947,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)],[f16,f11946]) ).

fof(f11948,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)],[f31,f11947]) ).

fof(f11949,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)],[f31,f11948]) ).

fof(f12416,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(compose(g,a)),compose(codomain(X1),compose(compose(g,a),X0)),compose(compose(codomain(X1),compose(g,a)),X0)),compose(compose(codomain(X1),compose(g,a)),X0)) = compose(compose(codomain(X1),compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f161]) ).

fof(f12417,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(compose(h,a)),compose(codomain(X1),compose(compose(h,a),X0)),compose(compose(codomain(X1),compose(h,a)),X0)),compose(compose(codomain(X1),compose(h,a)),X0)) = compose(compose(codomain(X1),compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f161]) ).

fof(f12418,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(compose(h,compose(a,b))),compose(codomain(X1),compose(compose(h,compose(a,b)),X0)),compose(compose(codomain(X1),compose(h,compose(a,b))),X0)),compose(compose(codomain(X1),compose(h,compose(a,b))),X0)) = compose(compose(codomain(X1),compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1016,f161]) ).

fof(f12420,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(g),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)],[f316,f161]) ).

fof(f12421,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),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)],[f147,f161]) ).

fof(f12425,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),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)],[f478,f161]) ).

fof(f12426,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(g,a))),compose(compose(codomain(X1),X0),compose(g,a))),compose(compose(codomain(X1),X0),compose(g,a))) = compose(compose(codomain(X1),X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f161]) ).

fof(f12427,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(h,a))),compose(compose(codomain(X1),X0),compose(h,a))),compose(compose(codomain(X1),X0),compose(h,a))) = compose(compose(codomain(X1),X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f161]) ).

fof(f12428,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(X0,compose(h,compose(a,b)))),compose(compose(codomain(X1),X0),compose(h,compose(a,b)))),compose(compose(codomain(X1),X0),compose(h,compose(a,b)))) = compose(compose(codomain(X1),X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f161]) ).

fof(f12460,plain,
    ! [X0] : ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),ifeq(codomain(X0),domain(compose(h,compose(a,b))),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f1103,f161]) ).

fof(f12461,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(domain(b)),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),compose(h,a)),domain(b))),compose(compose(codomain(X0),compose(h,a)),domain(b))) = compose(compose(codomain(X0),compose(h,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1534,f161]) ).

fof(f12462,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)],[f1043,f161]) ).

fof(f12463,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(domain(b)),ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),compose(g,a)),domain(b))),compose(compose(codomain(X0),compose(g,a)),domain(b))) = compose(compose(codomain(X0),compose(g,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1622,f161]) ).

fof(f12464,plain,
    ! [X0] : ifeq(codomain(compose(g,a)),domain(b),ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(g,a)),b)),compose(compose(codomain(X0),compose(g,a)),b)) = compose(compose(codomain(X0),compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f446,f161]) ).

fof(f12466,plain,
    ! [X0] : ifeq(codomain(g),domain(domain(a)),ifeq(codomain(X0),domain(g),compose(codomain(X0),g),compose(compose(codomain(X0),g),domain(a))),compose(compose(codomain(X0),g),domain(a))) = compose(compose(codomain(X0),g),domain(a)),
    inference(paramodulation,[status(thm)],[f334,f161]) ).

fof(f12467,plain,
    ! [X0] : ifeq(codomain(h),domain(domain(a)),ifeq(codomain(X0),domain(h),compose(codomain(X0),h),compose(compose(codomain(X0),h),domain(a))),compose(compose(codomain(X0),h),domain(a))) = compose(compose(codomain(X0),h),domain(a)),
    inference(paramodulation,[status(thm)],[f271,f161]) ).

fof(f12468,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)],[f34,f161]) ).

fof(f12469,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)],[f48,f161]) ).

fof(f12470,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(compose(g,a)),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),domain(h)),compose(g,a))),compose(compose(codomain(X0),domain(h)),compose(g,a))) = compose(compose(codomain(X0),domain(h)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2177,f161]) ).

fof(f12471,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f8322,f161]) ).

fof(f12472,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(compose(h,a)),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),domain(h)),compose(h,a))),compose(compose(codomain(X0),domain(h)),compose(h,a))) = compose(compose(codomain(X0),domain(h)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1957,f161]) ).

fof(f12473,plain,
    ! [X0] : ifeq(codomain(domain(h)),domain(g),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),g),compose(compose(codomain(X0),domain(h)),g)),compose(compose(codomain(X0),domain(h)),g)) = compose(compose(codomain(X0),domain(h)),g),
    inference(paramodulation,[status(thm)],[f516,f161]) ).

fof(f12474,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)],[f406,f161]) ).

fof(f12475,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)],[f31,f161]) ).

fof(f12504,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(g,a),X0)),compose(compose(codomain(X1),compose(g,a)),X0)),compose(compose(codomain(X1),compose(g,a)),X0)) = compose(compose(codomain(X1),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f12416]) ).

fof(f12505,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,a),X0)),compose(compose(codomain(X1),compose(h,a)),X0)),compose(compose(codomain(X1),compose(h,a)),X0)) = compose(compose(codomain(X1),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f12417]) ).

fof(f12506,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,compose(a,b)),X0)),compose(compose(codomain(X1),compose(h,compose(a,b))),X0)),compose(compose(codomain(X1),compose(h,compose(a,b))),X0)) = compose(compose(codomain(X1),compose(h,compose(a,b))),X0),
    inference(forward_demodulation,[status(thm)],[f506,f12418]) ).

fof(f12508,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),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(forward_demodulation,[status(thm)],[f478,f12420]) ).

fof(f12601,plain,
    ! [X0] : ifeq(codomain(b),domain(codomain(b)),ifeq(codomain(X0),domain(compose(h,compose(a,b))),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f1016,f12460]) ).

fof(f12602,plain,
    ! [X0] : ifeq(codomain(b),codomain(b),ifeq(codomain(X0),domain(compose(h,compose(a,b))),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f18,f12601]) ).

fof(f12603,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(h,compose(a,b))),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f12602]) ).

fof(f12604,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f506,f12603]) ).

fof(f12605,plain,
    ! [X0] : ifeq(domain(b),domain(domain(b)),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),compose(h,a)),domain(b))),compose(compose(codomain(X0),compose(h,a)),domain(b))) = compose(compose(codomain(X0),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f12461]) ).

fof(f12606,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),compose(h,a)),domain(b))),compose(compose(codomain(X0),compose(h,a)),domain(b))) = compose(compose(codomain(X0),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f12605]) ).

fof(f12607,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),compose(h,a)),domain(b))) = compose(compose(codomain(X0),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f12606]) ).

fof(f12608,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),compose(h,a)),domain(b))) = compose(compose(codomain(X0),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1908,f12607]) ).

fof(f12609,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)],[f975,f12462]) ).

fof(f12610,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)],[f18,f12609]) ).

fof(f12611,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)],[f16,f12610]) ).

fof(f12612,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)],[f261,f12611]) ).

fof(f12613,plain,
    ! [X0] : ifeq(domain(b),domain(domain(b)),ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),compose(g,a)),domain(b))),compose(compose(codomain(X0),compose(g,a)),domain(b))) = compose(compose(codomain(X0),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f12463]) ).

fof(f12614,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),compose(g,a)),domain(b))),compose(compose(codomain(X0),compose(g,a)),domain(b))) = compose(compose(codomain(X0),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f12613]) ).

fof(f12615,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),compose(g,a)),domain(b))) = compose(compose(codomain(X0),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f12614]) ).

fof(f12616,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),compose(g,a)),domain(b))) = compose(compose(codomain(X0),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f2123,f12615]) ).

fof(f12617,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(g,a)),b)),compose(compose(codomain(X0),compose(g,a)),b)) = compose(compose(codomain(X0),compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f1583,f12464]) ).

fof(f12618,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(g,a)),b)) = compose(compose(codomain(X0),compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f12617]) ).

fof(f12619,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(g,a)),b)) = compose(compose(codomain(X0),compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f2123,f12618]) ).

fof(f12624,plain,
    ! [X0] : ifeq(domain(a),domain(domain(a)),ifeq(codomain(X0),domain(g),compose(codomain(X0),g),compose(compose(codomain(X0),g),domain(a))),compose(compose(codomain(X0),g),domain(a))) = compose(compose(codomain(X0),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f316,f12466]) ).

fof(f12625,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(g),compose(codomain(X0),g),compose(compose(codomain(X0),g),domain(a))),compose(compose(codomain(X0),g),domain(a))) = compose(compose(codomain(X0),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f12624]) ).

fof(f12626,plain,
    ! [X0] : ifeq(codomain(X0),domain(g),compose(codomain(X0),g),compose(compose(codomain(X0),g),domain(a))) = compose(compose(codomain(X0),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f12625]) ).

fof(f12627,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),g),compose(compose(codomain(X0),g),domain(a))) = compose(compose(codomain(X0),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f478,f12626]) ).

fof(f12628,plain,
    ! [X0] : ifeq(domain(a),domain(domain(a)),ifeq(codomain(X0),domain(h),compose(codomain(X0),h),compose(compose(codomain(X0),h),domain(a))),compose(compose(codomain(X0),h),domain(a))) = compose(compose(codomain(X0),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f147,f12467]) ).

fof(f12629,plain,
    ! [X0] : ifeq(domain(a),domain(a),ifeq(codomain(X0),domain(h),compose(codomain(X0),h),compose(compose(codomain(X0),h),domain(a))),compose(compose(codomain(X0),h),domain(a))) = compose(compose(codomain(X0),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f12628]) ).

fof(f12630,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),h),compose(compose(codomain(X0),h),domain(a))) = compose(compose(codomain(X0),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f12629]) ).

fof(f12631,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)],[f36,f12468]) ).

fof(f12632,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)],[f18,f12631]) ).

fof(f12633,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)],[f16,f12632]) ).

fof(f12634,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)],[f18,f12633]) ).

fof(f12635,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,f12469]) ).

fof(f12636,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)],[f35,f12635]) ).

fof(f12637,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)],[f16,f12636]) ).

fof(f12638,plain,
    ! [X0] : ifeq(domain(h),domain(compose(g,a)),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),domain(h)),compose(g,a))),compose(compose(codomain(X0),domain(h)),compose(g,a))) = compose(compose(codomain(X0),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f17,f12470]) ).

fof(f12639,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),domain(h)),compose(g,a))),compose(compose(codomain(X0),domain(h)),compose(g,a))) = compose(compose(codomain(X0),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f12638]) ).

fof(f12640,plain,
    ! [X0] : ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),domain(h)),compose(g,a))) = compose(compose(codomain(X0),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f12639]) ).

fof(f12641,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),domain(h)),compose(g,a))) = compose(compose(codomain(X0),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f35,f12640]) ).

fof(f12642,plain,
    ! [X0] : ifeq(domain(h),domain(compose(h,compose(a,b))),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f12471]) ).

fof(f12643,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f12642]) ).

fof(f12644,plain,
    ! [X0] : ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f12643]) ).

fof(f12645,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f12644]) ).

fof(f12646,plain,
    ! [X0] : ifeq(domain(h),domain(compose(h,a)),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),domain(h)),compose(h,a))),compose(compose(codomain(X0),domain(h)),compose(h,a))) = compose(compose(codomain(X0),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f17,f12472]) ).

fof(f12647,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),domain(h)),compose(h,a))),compose(compose(codomain(X0),domain(h)),compose(h,a))) = compose(compose(codomain(X0),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f12646]) ).

fof(f12648,plain,
    ! [X0] : ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),domain(h)),compose(h,a))) = compose(compose(codomain(X0),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f16,f12647]) ).

fof(f12649,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),domain(h)),compose(h,a))) = compose(compose(codomain(X0),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f35,f12648]) ).

fof(f12650,plain,
    ! [X0] : ifeq(domain(h),domain(g),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),g),compose(compose(codomain(X0),domain(h)),g)),compose(compose(codomain(X0),domain(h)),g)) = compose(compose(codomain(X0),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f17,f12473]) ).

fof(f12651,plain,
    ! [X0] : ifeq(domain(h),domain(h),ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),g),compose(compose(codomain(X0),domain(h)),g)),compose(compose(codomain(X0),domain(h)),g)) = compose(compose(codomain(X0),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f478,f12650]) ).

fof(f12652,plain,
    ! [X0] : ifeq(codomain(X0),domain(domain(h)),compose(codomain(X0),g),compose(compose(codomain(X0),domain(h)),g)) = compose(compose(codomain(X0),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f16,f12651]) ).

fof(f12653,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),g),compose(compose(codomain(X0),domain(h)),g)) = compose(compose(codomain(X0),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f35,f12652]) ).

fof(f12654,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)],[f17,f12474]) ).

fof(f12655,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)],[f261,f12654]) ).

fof(f12656,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)],[f16,f12655]) ).

fof(f12657,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)],[f35,f12656]) ).

fof(f12658,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)],[f17,f12475]) ).

fof(f12659,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)],[f35,f12658]) ).

fof(f12660,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)],[f16,f12659]) ).

fof(f12661,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)],[f35,f12660]) ).

fof(f13561,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(compose(h,a),b),compose(h,a))),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f9281,f2003]) ).

fof(f13578,plain,
    domain(compose(compose(h,a),b)) = domain(h),
    inference(paramodulation,[status(thm)],[f16,f2006]) ).

fof(f13582,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(h,a),compose(h,compose(a,b)))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f506,f2006]) ).

fof(f14359,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(compose(g,a),codomain(X0)),compose(compose(compose(g,a),codomain(X0)),codomain(X0))) = compose(compose(compose(g,a),codomain(X0)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f193]) ).

fof(f14360,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(compose(h,a),codomain(X0)),compose(compose(compose(h,a),codomain(X0)),codomain(X0))) = compose(compose(compose(h,a),codomain(X0)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f193]) ).

fof(f14361,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),codomain(X0)),compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f193]) ).

fof(f14362,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)],[f975,f193]) ).

fof(f14363,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(g,codomain(X0)),compose(compose(g,codomain(X0)),codomain(X0))) = compose(compose(g,codomain(X0)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f316,f193]) ).

fof(f14364,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(h,codomain(X0)),compose(compose(h,codomain(X0)),codomain(X0))) = compose(compose(h,codomain(X0)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f147,f193]) ).

fof(f14902,plain,
    ifeq(domain(b),domain(a),compose(compose(g,a),a),compose(compose(compose(g,a),a),domain(b))) = compose(compose(compose(g,a),a),domain(b)),
    inference(paramodulation,[status(thm)],[f1583,f196]) ).

fof(f14903,plain,
    ifeq(domain(b),domain(a),compose(compose(h,a),a),compose(compose(compose(h,a),a),domain(b))) = compose(compose(compose(h,a),a),domain(b)),
    inference(paramodulation,[status(thm)],[f1465,f196]) ).

fof(f14904,plain,
    ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),a),compose(compose(compose(h,compose(a,b)),a),domain(b))) = compose(compose(compose(h,compose(a,b)),a),domain(b)),
    inference(paramodulation,[status(thm)],[f1016,f196]) ).

fof(f14905,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)],[f975,f196]) ).

fof(f14928,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(compose(h,a),b),compose(g,a))),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f9281,f2226]) ).

fof(f14947,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(compose(h,a),b))),domain(h)) = domain(h),
    inference(paramodulation,[status(thm)],[f13578,f2229]) ).

fof(f14967,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(g,a),domain(X0)),compose(compose(compose(g,a),domain(X0)),domain(X0))) = compose(compose(compose(g,a),domain(X0)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f200]) ).

fof(f14968,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(compose(h,a),domain(X0)),compose(compose(compose(h,a),domain(X0)),domain(X0))) = compose(compose(compose(h,a),domain(X0)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f200]) ).

fof(f14969,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),domain(X0)),compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X0))) = compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f200]) ).

fof(f14970,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)],[f975,f200]) ).

fof(f14971,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(g,domain(X0)),compose(compose(g,domain(X0)),domain(X0))) = compose(compose(g,domain(X0)),domain(X0)),
    inference(paramodulation,[status(thm)],[f316,f200]) ).

fof(f14972,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(h,domain(X0)),compose(compose(h,domain(X0)),domain(X0))) = compose(compose(h,domain(X0)),domain(X0)),
    inference(paramodulation,[status(thm)],[f147,f200]) ).

fof(f15243,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(codomain(X0),g),
    inference(paramodulation,[status(thm)],[f478,f214]) ).

fof(f15245,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(codomain(X0),compose(g,a))),compose(codomain(X0),compose(g,a))) = compose(codomain(X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f214]) ).

fof(f15246,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(codomain(X0),compose(h,a))),compose(codomain(X0),compose(h,a))) = compose(codomain(X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f214]) ).

fof(f15247,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(codomain(X0),compose(h,compose(a,b)))),compose(codomain(X0),compose(h,compose(a,b)))) = compose(codomain(X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f214]) ).

fof(f15458,plain,
    ifeq(domain(b),domain(h),compose(a,compose(domain(b),g)),compose(a,g)) = compose(a,g),
    inference(paramodulation,[status(thm)],[f478,f220]) ).

fof(f15460,plain,
    ifeq(domain(b),domain(h),compose(a,compose(domain(b),compose(g,a))),compose(a,compose(g,a))) = compose(a,compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f220]) ).

fof(f15461,plain,
    ifeq(domain(b),domain(h),compose(a,compose(domain(b),compose(h,a))),compose(a,compose(h,a))) = compose(a,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f220]) ).

fof(f15462,plain,
    ifeq(domain(b),domain(h),compose(a,compose(domain(b),compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f220]) ).

fof(f15495,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(domain(X0),g)),compose(domain(X0),g)) = compose(domain(X0),g),
    inference(paramodulation,[status(thm)],[f478,f226]) ).

fof(f15497,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(domain(X0),compose(g,a))),compose(domain(X0),compose(g,a))) = compose(domain(X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f226]) ).

fof(f15498,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(domain(X0),compose(h,a))),compose(domain(X0),compose(h,a))) = compose(domain(X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f226]) ).

fof(f15499,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(domain(X0),compose(h,compose(a,b)))),compose(domain(X0),compose(h,compose(a,b)))) = compose(domain(X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f226]) ).

fof(f15708,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(compose(g,a),X0)),compose(compose(h,compose(g,a)),X0)),compose(compose(h,compose(g,a)),X0)) = compose(compose(h,compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f262]) ).

fof(f15709,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),X0)),compose(compose(h,compose(h,a)),X0)),compose(compose(h,compose(h,a)),X0)) = compose(compose(h,compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f262]) ).

fof(f15710,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(h,compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(h,compose(a,b))),X0)),compose(compose(h,compose(h,compose(a,b))),X0)) = compose(compose(h,compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1016,f262]) ).

fof(f15712,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(g),compose(h,compose(g,X0)),compose(compose(h,g),X0)),compose(compose(h,g),X0)) = compose(compose(h,g),X0),
    inference(paramodulation,[status(thm)],[f316,f262]) ).

fof(f15713,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(h,X0)),compose(compose(h,h),X0)),compose(compose(h,h),X0)) = compose(compose(h,h),X0),
    inference(paramodulation,[status(thm)],[f147,f262]) ).

fof(f15717,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(X0,g)),compose(compose(h,X0),g)),compose(compose(h,X0),g)) = compose(compose(h,X0),g),
    inference(paramodulation,[status(thm)],[f478,f262]) ).

fof(f15719,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(X0,compose(g,a))),compose(compose(h,X0),compose(g,a))),compose(compose(h,X0),compose(g,a))) = compose(compose(h,X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f262]) ).

fof(f15720,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(X0,compose(h,a))),compose(compose(h,X0),compose(h,a))),compose(compose(h,X0),compose(h,a))) = compose(compose(h,X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f262]) ).

fof(f15721,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(X0,compose(h,compose(a,b)))),compose(compose(h,X0),compose(h,compose(a,b)))),compose(compose(h,X0),compose(h,compose(a,b)))) = compose(compose(h,X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f262]) ).

fof(f15735,plain,
    ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f1103,f262]) ).

fof(f15736,plain,
    ifeq(codomain(compose(h,a)),domain(domain(b)),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(h,a)),compose(compose(h,compose(h,a)),domain(b))),compose(compose(h,compose(h,a)),domain(b))) = compose(compose(h,compose(h,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1534,f262]) ).

fof(f15738,plain,
    ifeq(codomain(compose(g,a)),domain(domain(b)),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(g,a)),compose(compose(h,compose(g,a)),domain(b))),compose(compose(h,compose(g,a)),domain(b))) = compose(compose(h,compose(g,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1622,f262]) ).

fof(f15739,plain,
    ifeq(codomain(compose(g,a)),domain(b),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(g,a)),b)),compose(compose(h,compose(g,a)),b)) = compose(compose(h,compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f446,f262]) ).

fof(f15741,plain,
    ifeq(codomain(g),domain(domain(a)),ifeq(domain(a),domain(g),compose(h,g),compose(compose(h,g),domain(a))),compose(compose(h,g),domain(a))) = compose(compose(h,g),domain(a)),
    inference(paramodulation,[status(thm)],[f334,f262]) ).

fof(f15742,plain,
    ifeq(codomain(h),domain(domain(a)),ifeq(domain(a),domain(h),compose(h,h),compose(compose(h,h),domain(a))),compose(compose(h,h),domain(a))) = compose(compose(h,h),domain(a)),
    inference(paramodulation,[status(thm)],[f271,f262]) ).

fof(f15746,plain,
    ifeq(codomain(domain(h)),domain(compose(g,a)),ifeq(domain(a),domain(domain(h)),compose(h,compose(g,a)),compose(compose(h,domain(h)),compose(g,a))),compose(compose(h,domain(h)),compose(g,a))) = compose(compose(h,domain(h)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2177,f262]) ).

fof(f15747,plain,
    ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),ifeq(domain(a),domain(domain(h)),compose(h,compose(h,compose(a,b))),compose(compose(h,domain(h)),compose(h,compose(a,b)))),compose(compose(h,domain(h)),compose(h,compose(a,b)))) = compose(compose(h,domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f8322,f262]) ).

fof(f15748,plain,
    ifeq(codomain(domain(h)),domain(compose(h,a)),ifeq(domain(a),domain(domain(h)),compose(h,compose(h,a)),compose(compose(h,domain(h)),compose(h,a))),compose(compose(h,domain(h)),compose(h,a))) = compose(compose(h,domain(h)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1957,f262]) ).

fof(f15749,plain,
    ifeq(codomain(domain(h)),domain(g),ifeq(domain(a),domain(domain(h)),compose(h,g),compose(compose(h,domain(h)),g)),compose(compose(h,domain(h)),g)) = compose(compose(h,domain(h)),g),
    inference(paramodulation,[status(thm)],[f516,f262]) ).

fof(f15765,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),X0)),compose(compose(h,compose(g,a)),X0)),compose(compose(h,compose(g,a)),X0)) = compose(compose(h,compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f15708]) ).

fof(f15766,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),X0)),compose(compose(h,compose(h,a)),X0)),compose(compose(h,compose(h,a)),X0)) = compose(compose(h,compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f15709]) ).

fof(f15767,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(h,compose(a,b))),X0)),compose(compose(h,compose(h,compose(a,b))),X0)) = compose(compose(h,compose(h,compose(a,b))),X0),
    inference(forward_demodulation,[status(thm)],[f506,f15710]) ).

fof(f15770,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(g,X0)),compose(compose(h,g),X0)),compose(compose(h,g),X0)) = compose(compose(h,g),X0),
    inference(forward_demodulation,[status(thm)],[f478,f15712]) ).

fof(f15788,plain,
    ifeq(codomain(b),domain(codomain(b)),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f1016,f15735]) ).

fof(f15789,plain,
    ifeq(codomain(b),codomain(b),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f18,f15788]) ).

fof(f15790,plain,
    ifeq(domain(a),domain(compose(h,compose(a,b))),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f15789]) ).

fof(f15791,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,compose(a,b))),codomain(b))) = compose(compose(h,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f506,f15790]) ).

fof(f15792,plain,
    ifeq(domain(b),domain(domain(b)),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(h,a)),compose(compose(h,compose(h,a)),domain(b))),compose(compose(h,compose(h,a)),domain(b))) = compose(compose(h,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f15736]) ).

fof(f15793,plain,
    ifeq(domain(b),domain(b),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(h,a)),compose(compose(h,compose(h,a)),domain(b))),compose(compose(h,compose(h,a)),domain(b))) = compose(compose(h,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f15792]) ).

fof(f15794,plain,
    ifeq(domain(a),domain(compose(h,a)),compose(h,compose(h,a)),compose(compose(h,compose(h,a)),domain(b))) = compose(compose(h,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f15793]) ).

fof(f15795,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,a)),compose(compose(h,compose(h,a)),domain(b))) = compose(compose(h,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1908,f15794]) ).

fof(f15801,plain,
    ifeq(domain(b),domain(domain(b)),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(g,a)),compose(compose(h,compose(g,a)),domain(b))),compose(compose(h,compose(g,a)),domain(b))) = compose(compose(h,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f15738]) ).

fof(f15802,plain,
    ifeq(domain(b),domain(b),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(g,a)),compose(compose(h,compose(g,a)),domain(b))),compose(compose(h,compose(g,a)),domain(b))) = compose(compose(h,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f15801]) ).

fof(f15803,plain,
    ifeq(domain(a),domain(compose(g,a)),compose(h,compose(g,a)),compose(compose(h,compose(g,a)),domain(b))) = compose(compose(h,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f15802]) ).

fof(f15804,plain,
    ifeq(domain(a),domain(h),compose(h,compose(g,a)),compose(compose(h,compose(g,a)),domain(b))) = compose(compose(h,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f2123,f15803]) ).

fof(f15805,plain,
    ifeq(domain(b),domain(b),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(g,a)),b)),compose(compose(h,compose(g,a)),b)) = compose(compose(h,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f1583,f15739]) ).

fof(f15806,plain,
    ifeq(domain(a),domain(compose(g,a)),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(g,a)),b)) = compose(compose(h,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f15805]) ).

fof(f15807,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(g,a)),b)) = compose(compose(h,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f2123,f15806]) ).

fof(f15812,plain,
    ifeq(domain(a),domain(domain(a)),ifeq(domain(a),domain(g),compose(h,g),compose(compose(h,g),domain(a))),compose(compose(h,g),domain(a))) = compose(compose(h,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f316,f15741]) ).

fof(f15813,plain,
    ifeq(domain(a),domain(a),ifeq(domain(a),domain(g),compose(h,g),compose(compose(h,g),domain(a))),compose(compose(h,g),domain(a))) = compose(compose(h,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f15812]) ).

fof(f15814,plain,
    ifeq(domain(a),domain(g),compose(h,g),compose(compose(h,g),domain(a))) = compose(compose(h,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f15813]) ).

fof(f15815,plain,
    ifeq(domain(a),domain(h),compose(h,g),compose(compose(h,g),domain(a))) = compose(compose(h,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f478,f15814]) ).

fof(f15816,plain,
    ifeq(domain(a),domain(domain(a)),ifeq(domain(a),domain(h),compose(h,h),compose(compose(h,h),domain(a))),compose(compose(h,h),domain(a))) = compose(compose(h,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f147,f15742]) ).

fof(f15817,plain,
    ifeq(domain(a),domain(a),ifeq(domain(a),domain(h),compose(h,h),compose(compose(h,h),domain(a))),compose(compose(h,h),domain(a))) = compose(compose(h,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f15816]) ).

fof(f15818,plain,
    ifeq(domain(a),domain(h),compose(h,h),compose(compose(h,h),domain(a))) = compose(compose(h,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f15817]) ).

fof(f15831,plain,
    ifeq(domain(h),domain(compose(g,a)),ifeq(domain(a),domain(domain(h)),compose(h,compose(g,a)),compose(compose(h,domain(h)),compose(g,a))),compose(compose(h,domain(h)),compose(g,a))) = compose(compose(h,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f17,f15746]) ).

fof(f15832,plain,
    ifeq(domain(h),domain(h),ifeq(domain(a),domain(domain(h)),compose(h,compose(g,a)),compose(compose(h,domain(h)),compose(g,a))),compose(compose(h,domain(h)),compose(g,a))) = compose(compose(h,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f15831]) ).

fof(f15833,plain,
    ifeq(domain(a),domain(domain(h)),compose(h,compose(g,a)),compose(compose(h,domain(h)),compose(g,a))) = compose(compose(h,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f15832]) ).

fof(f15834,plain,
    ifeq(domain(a),domain(h),compose(h,compose(g,a)),compose(compose(h,domain(h)),compose(g,a))) = compose(compose(h,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f35,f15833]) ).

fof(f15835,plain,
    ifeq(domain(h),domain(compose(h,compose(a,b))),ifeq(domain(a),domain(domain(h)),compose(h,compose(h,compose(a,b))),compose(compose(h,domain(h)),compose(h,compose(a,b)))),compose(compose(h,domain(h)),compose(h,compose(a,b)))) = compose(compose(h,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f15747]) ).

fof(f15836,plain,
    ifeq(domain(h),domain(h),ifeq(domain(a),domain(domain(h)),compose(h,compose(h,compose(a,b))),compose(compose(h,domain(h)),compose(h,compose(a,b)))),compose(compose(h,domain(h)),compose(h,compose(a,b)))) = compose(compose(h,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f15835]) ).

fof(f15837,plain,
    ifeq(domain(a),domain(domain(h)),compose(h,compose(h,compose(a,b))),compose(compose(h,domain(h)),compose(h,compose(a,b)))) = compose(compose(h,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f15836]) ).

fof(f15838,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,domain(h)),compose(h,compose(a,b)))) = compose(compose(h,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f15837]) ).

fof(f15839,plain,
    ifeq(domain(h),domain(compose(h,a)),ifeq(domain(a),domain(domain(h)),compose(h,compose(h,a)),compose(compose(h,domain(h)),compose(h,a))),compose(compose(h,domain(h)),compose(h,a))) = compose(compose(h,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f17,f15748]) ).

fof(f15840,plain,
    ifeq(domain(h),domain(h),ifeq(domain(a),domain(domain(h)),compose(h,compose(h,a)),compose(compose(h,domain(h)),compose(h,a))),compose(compose(h,domain(h)),compose(h,a))) = compose(compose(h,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f15839]) ).

fof(f15841,plain,
    ifeq(domain(a),domain(domain(h)),compose(h,compose(h,a)),compose(compose(h,domain(h)),compose(h,a))) = compose(compose(h,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f16,f15840]) ).

fof(f15842,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,a)),compose(compose(h,domain(h)),compose(h,a))) = compose(compose(h,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f35,f15841]) ).

fof(f15843,plain,
    ifeq(domain(h),domain(g),ifeq(domain(a),domain(domain(h)),compose(h,g),compose(compose(h,domain(h)),g)),compose(compose(h,domain(h)),g)) = compose(compose(h,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f17,f15749]) ).

fof(f15844,plain,
    ifeq(domain(h),domain(h),ifeq(domain(a),domain(domain(h)),compose(h,g),compose(compose(h,domain(h)),g)),compose(compose(h,domain(h)),g)) = compose(compose(h,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f478,f15843]) ).

fof(f15845,plain,
    ifeq(domain(a),domain(domain(h)),compose(h,g),compose(compose(h,domain(h)),g)) = compose(compose(h,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f16,f15844]) ).

fof(f15846,plain,
    ifeq(domain(a),domain(h),compose(h,g),compose(compose(h,domain(h)),g)) = compose(compose(h,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f35,f15845]) ).

fof(f15913,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,a)),compose(compose(X0,h),a)) = compose(compose(X0,h),a),
    inference(paramodulation,[status(thm)],[f16,f263]) ).

fof(f15914,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(h,g)),compose(compose(X0,h),g)),compose(compose(X0,h),g)) = compose(compose(X0,h),g),
    inference(paramodulation,[status(thm)],[f478,f263]) ).

fof(f15916,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(g,a))),compose(compose(X0,h),compose(g,a))),compose(compose(X0,h),compose(g,a))) = compose(compose(X0,h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f263]) ).

fof(f15917,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(h,a))),compose(compose(X0,h),compose(h,a))),compose(compose(X0,h),compose(h,a))) = compose(compose(X0,h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f263]) ).

fof(f15918,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(h,compose(a,b)))),compose(compose(X0,h),compose(h,compose(a,b)))),compose(compose(X0,h),compose(h,compose(a,b)))) = compose(compose(X0,h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f263]) ).

fof(f15923,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,X0)),compose(compose(compose(g,a),h),X0)),compose(compose(compose(g,a),h),X0)) = compose(compose(compose(g,a),h),X0),
    inference(paramodulation,[status(thm)],[f1583,f263]) ).

fof(f15924,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,X0)),compose(compose(compose(h,a),h),X0)),compose(compose(compose(h,a),h),X0)) = compose(compose(compose(h,a),h),X0),
    inference(paramodulation,[status(thm)],[f1465,f263]) ).

fof(f15925,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,X0)),compose(compose(compose(h,compose(a,b)),h),X0)),compose(compose(compose(h,compose(a,b)),h),X0)) = compose(compose(compose(h,compose(a,b)),h),X0),
    inference(paramodulation,[status(thm)],[f1016,f263]) ).

fof(f15926,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),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)],[f975,f263]) ).

fof(f15927,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(h,X0)),compose(compose(g,h),X0)),compose(compose(g,h),X0)) = compose(compose(g,h),X0),
    inference(paramodulation,[status(thm)],[f316,f263]) ).

fof(f15970,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(compose(g,a),X0)),compose(compose(g,compose(g,a)),X0)),compose(compose(g,compose(g,a)),X0)) = compose(compose(g,compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f325]) ).

fof(f15971,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),X0)),compose(compose(g,compose(h,a)),X0)),compose(compose(g,compose(h,a)),X0)) = compose(compose(g,compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f325]) ).

fof(f15972,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(g,compose(compose(h,compose(a,b)),X0)),compose(compose(g,compose(h,compose(a,b))),X0)),compose(compose(g,compose(h,compose(a,b))),X0)) = compose(compose(g,compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1016,f325]) ).

fof(f15974,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(g),compose(g,compose(g,X0)),compose(compose(g,g),X0)),compose(compose(g,g),X0)) = compose(compose(g,g),X0),
    inference(paramodulation,[status(thm)],[f316,f325]) ).

fof(f15979,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),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)],[f478,f325]) ).

fof(f15981,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(X0,compose(g,a))),compose(compose(g,X0),compose(g,a))),compose(compose(g,X0),compose(g,a))) = compose(compose(g,X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f325]) ).

fof(f15982,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(X0,compose(h,a))),compose(compose(g,X0),compose(h,a))),compose(compose(g,X0),compose(h,a))) = compose(compose(g,X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f325]) ).

fof(f15983,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(X0,compose(h,compose(a,b)))),compose(compose(g,X0),compose(h,compose(a,b)))),compose(compose(g,X0),compose(h,compose(a,b)))) = compose(compose(g,X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f325]) ).

fof(f15998,plain,
    ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f1103,f325]) ).

fof(f15999,plain,
    ifeq(codomain(compose(h,a)),domain(domain(b)),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(h,a)),compose(compose(g,compose(h,a)),domain(b))),compose(compose(g,compose(h,a)),domain(b))) = compose(compose(g,compose(h,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1534,f325]) ).

fof(f16001,plain,
    ifeq(codomain(compose(g,a)),domain(domain(b)),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(g,a)),compose(compose(g,compose(g,a)),domain(b))),compose(compose(g,compose(g,a)),domain(b))) = compose(compose(g,compose(g,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1622,f325]) ).

fof(f16002,plain,
    ifeq(codomain(compose(g,a)),domain(b),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(g,a)),b)),compose(compose(g,compose(g,a)),b)) = compose(compose(g,compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f446,f325]) ).

fof(f16004,plain,
    ifeq(codomain(g),domain(domain(a)),ifeq(domain(a),domain(g),compose(g,g),compose(compose(g,g),domain(a))),compose(compose(g,g),domain(a))) = compose(compose(g,g),domain(a)),
    inference(paramodulation,[status(thm)],[f334,f325]) ).

fof(f16005,plain,
    ifeq(codomain(h),domain(domain(a)),ifeq(domain(a),domain(h),compose(g,h),compose(compose(g,h),domain(a))),compose(compose(g,h),domain(a))) = compose(compose(g,h),domain(a)),
    inference(paramodulation,[status(thm)],[f271,f325]) ).

fof(f16009,plain,
    ifeq(codomain(domain(h)),domain(compose(g,a)),ifeq(domain(a),domain(domain(h)),compose(g,compose(g,a)),compose(compose(g,domain(h)),compose(g,a))),compose(compose(g,domain(h)),compose(g,a))) = compose(compose(g,domain(h)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2177,f325]) ).

fof(f16010,plain,
    ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),ifeq(domain(a),domain(domain(h)),compose(g,compose(h,compose(a,b))),compose(compose(g,domain(h)),compose(h,compose(a,b)))),compose(compose(g,domain(h)),compose(h,compose(a,b)))) = compose(compose(g,domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f8322,f325]) ).

fof(f16011,plain,
    ifeq(codomain(domain(h)),domain(compose(h,a)),ifeq(domain(a),domain(domain(h)),compose(g,compose(h,a)),compose(compose(g,domain(h)),compose(h,a))),compose(compose(g,domain(h)),compose(h,a))) = compose(compose(g,domain(h)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1957,f325]) ).

fof(f16012,plain,
    ifeq(codomain(domain(h)),domain(g),ifeq(domain(a),domain(domain(h)),compose(g,g),compose(compose(g,domain(h)),g)),compose(compose(g,domain(h)),g)) = compose(compose(g,domain(h)),g),
    inference(paramodulation,[status(thm)],[f516,f325]) ).

fof(f16030,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),X0)),compose(compose(g,compose(g,a)),X0)),compose(compose(g,compose(g,a)),X0)) = compose(compose(g,compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f15970]) ).

fof(f16031,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),X0)),compose(compose(g,compose(h,a)),X0)),compose(compose(g,compose(h,a)),X0)) = compose(compose(g,compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f15971]) ).

fof(f16032,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),X0)),compose(compose(g,compose(h,compose(a,b))),X0)),compose(compose(g,compose(h,compose(a,b))),X0)) = compose(compose(g,compose(h,compose(a,b))),X0),
    inference(forward_demodulation,[status(thm)],[f506,f15972]) ).

fof(f16037,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(g,X0)),compose(compose(g,g),X0)),compose(compose(g,g),X0)) = compose(compose(g,g),X0),
    inference(forward_demodulation,[status(thm)],[f478,f15974]) ).

fof(f16060,plain,
    ifeq(codomain(b),domain(codomain(b)),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f1016,f15998]) ).

fof(f16061,plain,
    ifeq(codomain(b),codomain(b),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f18,f16060]) ).

fof(f16062,plain,
    ifeq(domain(a),domain(compose(h,compose(a,b))),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f16061]) ).

fof(f16063,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,compose(a,b))),codomain(b))) = compose(compose(g,compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f506,f16062]) ).

fof(f16064,plain,
    ifeq(domain(b),domain(domain(b)),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(h,a)),compose(compose(g,compose(h,a)),domain(b))),compose(compose(g,compose(h,a)),domain(b))) = compose(compose(g,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f15999]) ).

fof(f16065,plain,
    ifeq(domain(b),domain(b),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(h,a)),compose(compose(g,compose(h,a)),domain(b))),compose(compose(g,compose(h,a)),domain(b))) = compose(compose(g,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f16064]) ).

fof(f16066,plain,
    ifeq(domain(a),domain(compose(h,a)),compose(g,compose(h,a)),compose(compose(g,compose(h,a)),domain(b))) = compose(compose(g,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f16065]) ).

fof(f16067,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,a)),compose(compose(g,compose(h,a)),domain(b))) = compose(compose(g,compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1908,f16066]) ).

fof(f16075,plain,
    ifeq(domain(b),domain(domain(b)),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(g,a)),compose(compose(g,compose(g,a)),domain(b))),compose(compose(g,compose(g,a)),domain(b))) = compose(compose(g,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f16001]) ).

fof(f16076,plain,
    ifeq(domain(b),domain(b),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(g,a)),compose(compose(g,compose(g,a)),domain(b))),compose(compose(g,compose(g,a)),domain(b))) = compose(compose(g,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f16075]) ).

fof(f16077,plain,
    ifeq(domain(a),domain(compose(g,a)),compose(g,compose(g,a)),compose(compose(g,compose(g,a)),domain(b))) = compose(compose(g,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f16076]) ).

fof(f16078,plain,
    ifeq(domain(a),domain(h),compose(g,compose(g,a)),compose(compose(g,compose(g,a)),domain(b))) = compose(compose(g,compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f2123,f16077]) ).

fof(f16079,plain,
    ifeq(domain(b),domain(b),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(g,a)),b)),compose(compose(g,compose(g,a)),b)) = compose(compose(g,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f1583,f16002]) ).

fof(f16080,plain,
    ifeq(domain(a),domain(compose(g,a)),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(g,a)),b)) = compose(compose(g,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f16079]) ).

fof(f16081,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(g,a)),b)) = compose(compose(g,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f2123,f16080]) ).

fof(f16086,plain,
    ifeq(domain(a),domain(domain(a)),ifeq(domain(a),domain(g),compose(g,g),compose(compose(g,g),domain(a))),compose(compose(g,g),domain(a))) = compose(compose(g,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f316,f16004]) ).

fof(f16087,plain,
    ifeq(domain(a),domain(a),ifeq(domain(a),domain(g),compose(g,g),compose(compose(g,g),domain(a))),compose(compose(g,g),domain(a))) = compose(compose(g,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f16086]) ).

fof(f16088,plain,
    ifeq(domain(a),domain(g),compose(g,g),compose(compose(g,g),domain(a))) = compose(compose(g,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f16087]) ).

fof(f16089,plain,
    ifeq(domain(a),domain(h),compose(g,g),compose(compose(g,g),domain(a))) = compose(compose(g,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f478,f16088]) ).

fof(f16090,plain,
    ifeq(domain(a),domain(domain(a)),ifeq(domain(a),domain(h),compose(g,h),compose(compose(g,h),domain(a))),compose(compose(g,h),domain(a))) = compose(compose(g,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f147,f16005]) ).

fof(f16091,plain,
    ifeq(domain(a),domain(a),ifeq(domain(a),domain(h),compose(g,h),compose(compose(g,h),domain(a))),compose(compose(g,h),domain(a))) = compose(compose(g,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f16090]) ).

fof(f16092,plain,
    ifeq(domain(a),domain(h),compose(g,h),compose(compose(g,h),domain(a))) = compose(compose(g,h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f16091]) ).

fof(f16105,plain,
    ifeq(domain(h),domain(compose(g,a)),ifeq(domain(a),domain(domain(h)),compose(g,compose(g,a)),compose(compose(g,domain(h)),compose(g,a))),compose(compose(g,domain(h)),compose(g,a))) = compose(compose(g,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f17,f16009]) ).

fof(f16106,plain,
    ifeq(domain(h),domain(h),ifeq(domain(a),domain(domain(h)),compose(g,compose(g,a)),compose(compose(g,domain(h)),compose(g,a))),compose(compose(g,domain(h)),compose(g,a))) = compose(compose(g,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f16105]) ).

fof(f16107,plain,
    ifeq(domain(a),domain(domain(h)),compose(g,compose(g,a)),compose(compose(g,domain(h)),compose(g,a))) = compose(compose(g,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f16106]) ).

fof(f16108,plain,
    ifeq(domain(a),domain(h),compose(g,compose(g,a)),compose(compose(g,domain(h)),compose(g,a))) = compose(compose(g,domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f35,f16107]) ).

fof(f16109,plain,
    ifeq(domain(h),domain(compose(h,compose(a,b))),ifeq(domain(a),domain(domain(h)),compose(g,compose(h,compose(a,b))),compose(compose(g,domain(h)),compose(h,compose(a,b)))),compose(compose(g,domain(h)),compose(h,compose(a,b)))) = compose(compose(g,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f16010]) ).

fof(f16110,plain,
    ifeq(domain(h),domain(h),ifeq(domain(a),domain(domain(h)),compose(g,compose(h,compose(a,b))),compose(compose(g,domain(h)),compose(h,compose(a,b)))),compose(compose(g,domain(h)),compose(h,compose(a,b)))) = compose(compose(g,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f16109]) ).

fof(f16111,plain,
    ifeq(domain(a),domain(domain(h)),compose(g,compose(h,compose(a,b))),compose(compose(g,domain(h)),compose(h,compose(a,b)))) = compose(compose(g,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f16110]) ).

fof(f16112,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,domain(h)),compose(h,compose(a,b)))) = compose(compose(g,domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f16111]) ).

fof(f16113,plain,
    ifeq(domain(h),domain(compose(h,a)),ifeq(domain(a),domain(domain(h)),compose(g,compose(h,a)),compose(compose(g,domain(h)),compose(h,a))),compose(compose(g,domain(h)),compose(h,a))) = compose(compose(g,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f17,f16011]) ).

fof(f16114,plain,
    ifeq(domain(h),domain(h),ifeq(domain(a),domain(domain(h)),compose(g,compose(h,a)),compose(compose(g,domain(h)),compose(h,a))),compose(compose(g,domain(h)),compose(h,a))) = compose(compose(g,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f16113]) ).

fof(f16115,plain,
    ifeq(domain(a),domain(domain(h)),compose(g,compose(h,a)),compose(compose(g,domain(h)),compose(h,a))) = compose(compose(g,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f16,f16114]) ).

fof(f16116,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,a)),compose(compose(g,domain(h)),compose(h,a))) = compose(compose(g,domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f35,f16115]) ).

fof(f16117,plain,
    ifeq(domain(h),domain(g),ifeq(domain(a),domain(domain(h)),compose(g,g),compose(compose(g,domain(h)),g)),compose(compose(g,domain(h)),g)) = compose(compose(g,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f17,f16012]) ).

fof(f16118,plain,
    ifeq(domain(h),domain(h),ifeq(domain(a),domain(domain(h)),compose(g,g),compose(compose(g,domain(h)),g)),compose(compose(g,domain(h)),g)) = compose(compose(g,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f478,f16117]) ).

fof(f16119,plain,
    ifeq(domain(a),domain(domain(h)),compose(g,g),compose(compose(g,domain(h)),g)) = compose(compose(g,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f16,f16118]) ).

fof(f16120,plain,
    ifeq(domain(a),domain(h),compose(g,g),compose(compose(g,domain(h)),g)) = compose(compose(g,domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f35,f16119]) ).

fof(f16194,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),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)],[f478,f326]) ).

fof(f16195,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(g,a)),compose(compose(X0,g),a)) = compose(compose(X0,g),a),
    inference(paramodulation,[status(thm)],[f16,f16194]) ).

fof(f16196,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,g)),compose(compose(X0,g),g)),compose(compose(X0,g),g)) = compose(compose(X0,g),g),
    inference(paramodulation,[status(thm)],[f478,f16194]) ).

fof(f16198,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,compose(g,a))),compose(compose(X0,g),compose(g,a))),compose(compose(X0,g),compose(g,a))) = compose(compose(X0,g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f16194]) ).

fof(f16199,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,compose(h,a))),compose(compose(X0,g),compose(h,a))),compose(compose(X0,g),compose(h,a))) = compose(compose(X0,g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f16194]) ).

fof(f16200,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(g,compose(h,compose(a,b)))),compose(compose(X0,g),compose(h,compose(a,b)))),compose(compose(X0,g),compose(h,compose(a,b)))) = compose(compose(X0,g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f16194]) ).

fof(f16205,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,X0)),compose(compose(compose(g,a),g),X0)),compose(compose(compose(g,a),g),X0)) = compose(compose(compose(g,a),g),X0),
    inference(paramodulation,[status(thm)],[f1583,f16194]) ).

fof(f16206,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,X0)),compose(compose(compose(h,a),g),X0)),compose(compose(compose(h,a),g),X0)) = compose(compose(compose(h,a),g),X0),
    inference(paramodulation,[status(thm)],[f1465,f16194]) ).

fof(f16207,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,X0)),compose(compose(compose(h,compose(a,b)),g),X0)),compose(compose(compose(h,compose(a,b)),g),X0)) = compose(compose(compose(h,compose(a,b)),g),X0),
    inference(paramodulation,[status(thm)],[f1016,f16194]) ).

fof(f16208,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),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)],[f975,f16194]) ).

fof(f16266,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(compose(g,a),X0,g,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f400]) ).

fof(f16267,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(g,a),X0,g,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f400]) ).

fof(f16268,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(g,a),X0,g,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f400]) ).

fof(f16269,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(g,a),X0,g,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f400]) ).

fof(f16270,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(g,a),X0,g,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f400]) ).

fof(f16271,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(g,a),X0,g,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f400]) ).

fof(f16272,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(g,a),X1,g,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f400]) ).

fof(f16281,plain,
    ! [X0] : ifeq(compose(compose(g,a),a),X0,ifeq(compose(g,a),X0,g,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f16266]) ).

fof(f16282,plain,
    ! [X0] : ifeq(compose(compose(h,a),a),X0,ifeq(compose(g,a),X0,g,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f16267]) ).

fof(f16290,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(compose(h,a),X0,h,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f401]) ).

fof(f16291,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(h,a),X0,h,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f401]) ).

fof(f16292,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(h,a),X0,h,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f401]) ).

fof(f16293,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(h,a),X0,h,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f401]) ).

fof(f16294,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(h,a),X0,h,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f401]) ).

fof(f16295,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(h,a),X0,h,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f401]) ).

fof(f16296,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(h,a),X1,h,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f401]) ).

fof(f16305,plain,
    ! [X0] : ifeq(compose(compose(g,a),a),X0,ifeq(compose(h,a),X0,h,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f16290]) ).

fof(f16306,plain,
    ! [X0] : ifeq(compose(compose(h,a),a),X0,ifeq(compose(h,a),X0,h,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f16291]) ).

fof(f16330,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f388]) ).

fof(f16331,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f388]) ).

fof(f16332,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f388]) ).

fof(f16333,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f388]) ).

fof(f16334,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f388]) ).

fof(f16335,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f388]) ).

fof(f16336,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),X2,ifeq(compose(codomain(X0),a),X2,codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f388]) ).

fof(f16386,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f16330]) ).

fof(f16387,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f16331]) ).

fof(f16445,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1583,f391]) ).

fof(f16446,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1465,f391]) ).

fof(f16447,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1016,f391]) ).

fof(f16448,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f975,f391]) ).

fof(f16462,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1583,f392]) ).

fof(f16463,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1465,f392]) ).

fof(f16464,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1016,f392]) ).

fof(f16465,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f975,f392]) ).

fof(f16479,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(compose(g,a),a),X1,compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1583,f393]) ).

fof(f16480,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(compose(h,a),a),X1,compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1465,f393]) ).

fof(f16481,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(compose(h,compose(a,b)),a),X1,compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1016,f393]) ).

fof(f16482,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),X1,ifeq(compose(compose(a,b),a),X1,compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f975,f393]) ).

fof(f16930,plain,
    ifeq(codomain(b),domain(h),compose(domain(compose(compose(h,a),b)),compose(compose(compose(h,a),b),g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(paramodulation,[status(thm)],[f9281,f7994]) ).

fof(f16931,plain,
    ifeq(domain(b),domain(h),compose(domain(compose(g,a)),compose(compose(g,a),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
    inference(paramodulation,[status(thm)],[f1583,f7994]) ).

fof(f16932,plain,
    ifeq(domain(b),domain(h),compose(domain(compose(h,a)),compose(compose(h,a),g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
    inference(paramodulation,[status(thm)],[f1465,f7994]) ).

fof(f16934,plain,
    ifeq(codomain(b),domain(h),compose(domain(compose(a,b)),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
    inference(paramodulation,[status(thm)],[f975,f7994]) ).

fof(f16935,plain,
    ifeq(domain(a),domain(h),compose(domain(g),compose(g,g)),compose(g,g)) = compose(g,g),
    inference(paramodulation,[status(thm)],[f316,f7994]) ).

fof(f16936,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(h,g)),compose(h,g)) = compose(h,g),
    inference(paramodulation,[status(thm)],[f147,f7994]) ).

fof(f16938,plain,
    ifeq(domain(b),domain(h),compose(domain(a),compose(a,g)),compose(a,g)) = compose(a,g),
    inference(paramodulation,[status(thm)],[f24,f7994]) ).

fof(f16952,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(compose(h,a),b),g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f13578,f16930]) ).

fof(f16953,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
    inference(forward_demodulation,[status(thm)],[f2123,f16931]) ).

fof(f16954,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
    inference(forward_demodulation,[status(thm)],[f1908,f16932]) ).

fof(f16956,plain,
    ifeq(codomain(b),domain(h),compose(domain(a),compose(compose(a,b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
    inference(forward_demodulation,[status(thm)],[f261,f16934]) ).

fof(f16957,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(g,g)),compose(g,g)) = compose(g,g),
    inference(forward_demodulation,[status(thm)],[f478,f16935]) ).

fof(f16983,plain,
    ifeq(codomain(b),domain(h),compose(compose(compose(h,a),b),compose(codomain(compose(compose(h,a),b)),g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(paramodulation,[status(thm)],[f9281,f8201]) ).

fof(f16984,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(codomain(compose(g,a)),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
    inference(paramodulation,[status(thm)],[f1583,f8201]) ).

fof(f16985,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(codomain(compose(h,a)),g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
    inference(paramodulation,[status(thm)],[f1465,f8201]) ).

fof(f16987,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(compose(a,b)),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
    inference(paramodulation,[status(thm)],[f975,f8201]) ).

fof(f16988,plain,
    ifeq(domain(a),domain(h),compose(g,compose(codomain(g),g)),compose(g,g)) = compose(g,g),
    inference(paramodulation,[status(thm)],[f316,f8201]) ).

fof(f16989,plain,
    ifeq(domain(a),domain(h),compose(h,compose(codomain(h),g)),compose(h,g)) = compose(h,g),
    inference(paramodulation,[status(thm)],[f147,f8201]) ).

fof(f17005,plain,
    ifeq(codomain(b),domain(h),compose(compose(compose(h,a),b),compose(codomain(b),g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f9281,f16983]) ).

fof(f17006,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
    inference(forward_demodulation,[status(thm)],[f1583,f16984]) ).

fof(f17007,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
    inference(forward_demodulation,[status(thm)],[f1465,f16985]) ).

fof(f17009,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
    inference(forward_demodulation,[status(thm)],[f975,f16987]) ).

fof(f17010,plain,
    ifeq(domain(a),domain(h),compose(g,compose(domain(a),g)),compose(g,g)) = compose(g,g),
    inference(forward_demodulation,[status(thm)],[f316,f16988]) ).

fof(f17011,plain,
    ifeq(domain(a),domain(h),compose(h,compose(domain(a),g)),compose(h,g)) = compose(h,g),
    inference(forward_demodulation,[status(thm)],[f147,f16989]) ).

fof(f17035,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(compose(h,a),b),a),compose(a,a),compose(compose(h,a),b),a),a) = a,
    inference(paramodulation,[status(thm)],[f9281,f9878]) ).

fof(f17036,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(a,a),compose(g,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1583,f9878]) ).

fof(f17037,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(a,a),compose(h,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1465,f9878]) ).

fof(f17039,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),a),compose(a,a),compose(a,b),a),a) = a,
    inference(paramodulation,[status(thm)],[f975,f9878]) ).

fof(f17042,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),a),compose(a,a),codomain(X0),a),a) = a,
    inference(paramodulation,[status(thm)],[f36,f9878]) ).

fof(f17044,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),a),compose(a,a),domain(X0),a),a) = a,
    inference(paramodulation,[status(thm)],[f17,f9878]) ).

fof(f17058,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(a,a),compose(compose(compose(h,a),b),a),compose(compose(h,a),b),a),a) = a,
    inference(paramodulation,[status(thm)],[f9281,f9879]) ).

fof(f17059,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(compose(g,a),a),compose(g,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1583,f9879]) ).

fof(f17060,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(compose(h,a),a),compose(h,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1465,f9879]) ).

fof(f17062,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(a,a),compose(compose(a,b),a),compose(a,b),a),a) = a,
    inference(paramodulation,[status(thm)],[f975,f9879]) ).

fof(f17065,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(a,a),compose(codomain(X0),a),codomain(X0),a),a) = a,
    inference(paramodulation,[status(thm)],[f36,f9879]) ).

fof(f17067,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(a,a),compose(domain(X0),a),domain(X0),a),a) = a,
    inference(paramodulation,[status(thm)],[f17,f9879]) ).

fof(f17081,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)],[f975,f420]) ).

fof(f17084,plain,
    ifeq(codomain(b),domain(h),compose(domain(a),compose(compose(a,b),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f17081]) ).

fof(f17085,plain,
    ifeq(codomain(b),domain(h),compose(domain(a),compose(compose(a,b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f17081]) ).

fof(f17086,plain,
    ifeq(codomain(b),domain(h),compose(domain(a),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f17081]) ).

fof(f17110,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(compose(h,a),b),b),compose(a,b),compose(compose(h,a),b),a),a) = a,
    inference(paramodulation,[status(thm)],[f9281,f10639]) ).

fof(f17111,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),compose(a,b),compose(g,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1583,f10639]) ).

fof(f17112,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),compose(a,b),compose(h,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1465,f10639]) ).

fof(f17114,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),b),compose(a,b),compose(a,b),a),a) = a,
    inference(paramodulation,[status(thm)],[f975,f10639]) ).

fof(f17117,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),compose(a,b),codomain(X0),a),a) = a,
    inference(paramodulation,[status(thm)],[f36,f10639]) ).

fof(f17119,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),compose(a,b),domain(X0),a),a) = a,
    inference(paramodulation,[status(thm)],[f17,f10639]) ).

fof(f17124,plain,
    ifeq(codomain(domain(b)),domain(a),ifeq(b,compose(a,b),domain(b),a),a) = a,
    inference(paramodulation,[status(thm)],[f19,f10639]) ).

fof(f17125,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(a,b),compose(g,a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f446,f17111]) ).

fof(f17133,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(a,b),domain(b),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f17,f17124]) ).

fof(f17135,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(compose(h,a),b),b),compose(compose(h,a),b),a),a) = a,
    inference(paramodulation,[status(thm)],[f9281,f10640]) ).

fof(f17136,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(compose(g,a),b),compose(g,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1583,f10640]) ).

fof(f17137,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(compose(h,a),b),compose(h,a),a),a) = a,
    inference(paramodulation,[status(thm)],[f1465,f10640]) ).

fof(f17139,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(a,b),b),compose(a,b),a),a) = a,
    inference(paramodulation,[status(thm)],[f975,f10640]) ).

fof(f17142,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(a,b),compose(codomain(X0),b),codomain(X0),a),a) = a,
    inference(paramodulation,[status(thm)],[f36,f10640]) ).

fof(f17144,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(a,b),compose(domain(X0),b),domain(X0),a),a) = a,
    inference(paramodulation,[status(thm)],[f17,f10640]) ).

fof(f17149,plain,
    ifeq(codomain(domain(b)),domain(a),ifeq(compose(a,b),b,domain(b),a),a) = a,
    inference(paramodulation,[status(thm)],[f19,f10640]) ).

fof(f17151,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(h,compose(a,b)),compose(g,a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f446,f17136]) ).

fof(f17159,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),b,domain(b),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f17,f17149]) ).

fof(f17163,plain,
    ifeq(domain(a),domain(h),compose(h,compose(domain(a),compose(g,a))),compose(h,compose(g,a))) = compose(h,compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f288]) ).

fof(f17164,plain,
    ifeq(domain(a),domain(h),compose(h,compose(domain(a),compose(h,a))),compose(h,compose(h,a))) = compose(h,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f288]) ).

fof(f17196,plain,
    ifeq(domain(a),domain(h),compose(g,compose(domain(a),compose(g,a))),compose(g,compose(g,a))) = compose(g,compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f351]) ).

fof(f17197,plain,
    ifeq(domain(a),domain(h),compose(g,compose(domain(a),compose(h,a))),compose(g,compose(h,a))) = compose(g,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f351]) ).

fof(f17228,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),domain(compose(X0,compose(h,compose(a,b)))),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f478,f473]) ).

fof(f17229,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(compose(h,a),b),compose(h,compose(a,b)))),domain(compose(compose(h,a),b))) = domain(compose(compose(h,a),b)),
    inference(paramodulation,[status(thm)],[f9281,f17228]) ).

fof(f17249,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(compose(h,a),b),compose(h,compose(a,b)))),domain(h)) = domain(compose(compose(h,a),b)),
    inference(forward_demodulation,[status(thm)],[f13578,f17229]) ).

fof(f17250,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(compose(h,a),b),compose(h,compose(a,b)))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f13578,f17249]) ).

fof(f17291,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(compose(h,a),b))),compose(g,compose(compose(h,a),b))) = compose(g,compose(compose(h,a),b)),
    inference(paramodulation,[status(thm)],[f13578,f537]) ).

fof(f17292,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(g,a))),compose(g,compose(g,a))) = compose(g,compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f537]) ).

fof(f17293,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(h,a))),compose(g,compose(h,a))) = compose(g,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f537]) ).

fof(f17333,plain,
    ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,b)),compose(compose(compose(g,a),domain(a)),compose(a,b))) = compose(compose(compose(g,a),domain(a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f429]) ).

fof(f17334,plain,
    ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,b)),compose(compose(compose(h,a),domain(a)),compose(a,b))) = compose(compose(compose(h,a),domain(a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f429]) ).

fof(f17335,plain,
    ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),domain(a)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),domain(a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f429]) ).

fof(f17336,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(paramodulation,[status(thm)],[f975,f429]) ).

fof(f17511,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(g),compose(X1,compose(compose(h,compose(a,b)),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)) = compose(compose(X1,compose(h,compose(a,b))),X0),
    inference(forward_demodulation,[status(thm)],[f1016,f466]) ).

fof(f17512,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(h,compose(a,b)),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)),compose(compose(X1,compose(h,compose(a,b))),X0)) = compose(compose(X1,compose(h,compose(a,b))),X0),
    inference(forward_demodulation,[status(thm)],[f478,f17511]) ).

fof(f17513,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),g)),compose(compose(X0,compose(h,compose(a,b))),g)),compose(compose(X0,compose(h,compose(a,b))),g)) = compose(compose(X0,compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f478,f17512]) ).

fof(f17515,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(X0,compose(h,compose(a,b))),compose(g,a))),compose(compose(X0,compose(h,compose(a,b))),compose(g,a))) = compose(compose(X0,compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f17512]) ).

fof(f17516,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(X0,compose(h,compose(a,b))),compose(h,a))),compose(compose(X0,compose(h,compose(a,b))),compose(h,a))) = compose(compose(X0,compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f17512]) ).

fof(f17517,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(X0,compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f17512]) ).

fof(f17522,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(g,a),compose(h,compose(a,b))),X0)),compose(compose(compose(g,a),compose(h,compose(a,b))),X0)) = compose(compose(compose(g,a),compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1583,f17512]) ).

fof(f17523,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(h,a),compose(h,compose(a,b))),X0)),compose(compose(compose(h,a),compose(h,compose(a,b))),X0)) = compose(compose(compose(h,a),compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1465,f17512]) ).

fof(f17524,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f1016,f17512]) ).

fof(f17525,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),X0)),compose(compose(compose(a,b),compose(h,compose(a,b))),X0)),compose(compose(compose(a,b),compose(h,compose(a,b))),X0)) = compose(compose(compose(a,b),compose(h,compose(a,b))),X0),
    inference(paramodulation,[status(thm)],[f975,f17512]) ).

fof(f17573,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(compose(h,a),b))),codomain(compose(compose(h,a),b))) = codomain(compose(compose(h,a),b)),
    inference(paramodulation,[status(thm)],[f13578,f1099]) ).

fof(f17594,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(compose(h,a),b))),codomain(b)) = codomain(compose(compose(h,a),b)),
    inference(forward_demodulation,[status(thm)],[f9281,f17573]) ).

fof(f17595,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(compose(h,a),b))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f9281,f17594]) ).

fof(f17676,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(X1,compose(X0,compose(h,compose(a,b)))),compose(compose(X1,X0),compose(h,compose(a,b)))),compose(compose(X1,X0),compose(h,compose(a,b)))) = compose(compose(X1,X0),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f478,f467]) ).

fof(f17678,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(g,a)),compose(X0,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(X0,compose(g,a)),compose(h,compose(a,b)))),compose(compose(X0,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(X0,compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f17676]) ).

fof(f17679,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(X0,compose(h,a)),compose(h,compose(a,b)))),compose(compose(X0,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(X0,compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f17676]) ).

fof(f17688,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,compose(h,compose(a,b)))),compose(compose(compose(g,a),X0),compose(h,compose(a,b)))),compose(compose(compose(g,a),X0),compose(h,compose(a,b)))) = compose(compose(compose(g,a),X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f17676]) ).

fof(f17689,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,compose(h,compose(a,b)))),compose(compose(compose(h,a),X0),compose(h,compose(a,b)))),compose(compose(compose(h,a),X0),compose(h,compose(a,b)))) = compose(compose(compose(h,a),X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f17676]) ).

fof(f17690,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),X0),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),X0),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f17676]) ).

fof(f17691,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(h,compose(a,b)))),compose(compose(compose(a,b),X0),compose(h,compose(a,b)))),compose(compose(compose(a,b),X0),compose(h,compose(a,b)))) = compose(compose(compose(a,b),X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f17676]) ).

fof(f17709,plain,
    ifeq(codomain(codomain(b)),domain(h),ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1103,f17676]) ).

fof(f17710,plain,
    ifeq(codomain(domain(b)),domain(h),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1534,f17676]) ).

fof(f17711,plain,
    ifeq(codomain(codomain(b)),domain(h),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1043,f17676]) ).

fof(f17712,plain,
    ifeq(codomain(domain(b)),domain(h),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1622,f17676]) ).

fof(f17713,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(compose(g,a)),domain(b),compose(compose(g,a),compose(b,compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(g,a),b),compose(h,compose(a,b)))) = compose(compose(compose(g,a),b),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f446,f17676]) ).

fof(f17715,plain,
    ifeq(codomain(domain(a)),domain(h),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))),compose(compose(g,domain(a)),compose(h,compose(a,b)))) = compose(compose(g,domain(a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f334,f17676]) ).

fof(f17716,plain,
    ifeq(codomain(domain(a)),domain(h),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))),compose(compose(h,domain(a)),compose(h,compose(a,b)))) = compose(compose(h,domain(a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f271,f17676]) ).

fof(f17720,plain,
    ifeq(codomain(compose(g,a)),domain(h),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f2177,f17676]) ).

fof(f17721,plain,
    ifeq(codomain(compose(h,compose(a,b))),domain(h),ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f8322,f17676]) ).

fof(f17722,plain,
    ifeq(codomain(compose(h,a)),domain(h),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1957,f17676]) ).

fof(f17749,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(X0,compose(g,a)),compose(h,compose(a,b)))),compose(compose(X0,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(X0,compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f2123,f17678]) ).

fof(f17750,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(X0,compose(h,a)),compose(h,compose(a,b)))),compose(compose(X0,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(X0,compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f17679]) ).

fof(f17778,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f36,f17709]) ).

fof(f17779,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(codomain(b)),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f17778]) ).

fof(f17780,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),codomain(b),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f18,f17779]) ).

fof(f17781,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17780]) ).

fof(f17782,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1103,f17781]) ).

fof(f17783,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1103,f17782]) ).

fof(f17784,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(compose(h,a)),domain(domain(b)),compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f17710]) ).

fof(f17785,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(domain(b)),compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1465,f17784]) ).

fof(f17786,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(b),compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f17785]) ).

fof(f17787,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17786]) ).

fof(f17788,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1534,f17787]) ).

fof(f17789,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1534,f17788]) ).

fof(f17790,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(compose(a,b)),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f36,f17711]) ).

fof(f17791,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(codomain(b)),compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f975,f17790]) ).

fof(f17792,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),codomain(b),compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f18,f17791]) ).

fof(f17793,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17792]) ).

fof(f17794,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(compose(a,b),codomain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1043,f17793]) ).

fof(f17795,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1043,f17794]) ).

fof(f17796,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(compose(g,a)),domain(domain(b)),compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f17712]) ).

fof(f17797,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(domain(b)),compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1583,f17796]) ).

fof(f17798,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(b),compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f17797]) ).

fof(f17799,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17798]) ).

fof(f17800,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1622,f17799]) ).

fof(f17801,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1622,f17800]) ).

fof(f17802,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(b),compose(compose(g,a),compose(b,compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(g,a),b),compose(h,compose(a,b)))) = compose(compose(compose(g,a),b),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1583,f17713]) ).

fof(f17803,plain,
    ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,compose(h,compose(a,b)))),compose(compose(compose(g,a),b),compose(h,compose(a,b)))) = compose(compose(compose(g,a),b),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17802]) ).

fof(f17804,plain,
    ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),b),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f446,f17803]) ).

fof(f17805,plain,
    ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f446,f17804]) ).

fof(f17812,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(g),domain(domain(a)),compose(g,compose(domain(a),compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))),compose(compose(g,domain(a)),compose(h,compose(a,b)))) = compose(compose(g,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f17715]) ).

fof(f17813,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(domain(a)),compose(g,compose(domain(a),compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))),compose(compose(g,domain(a)),compose(h,compose(a,b)))) = compose(compose(g,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f316,f17812]) ).

fof(f17814,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(a),compose(g,compose(domain(a),compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))),compose(compose(g,domain(a)),compose(h,compose(a,b)))) = compose(compose(g,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f17813]) ).

fof(f17815,plain,
    ifeq(domain(a),domain(h),compose(g,compose(domain(a),compose(h,compose(a,b)))),compose(compose(g,domain(a)),compose(h,compose(a,b)))) = compose(compose(g,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17814]) ).

fof(f17816,plain,
    ifeq(domain(a),domain(h),compose(g,compose(domain(a),compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(compose(g,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f334,f17815]) ).

fof(f17817,plain,
    ifeq(domain(a),domain(h),compose(g,compose(domain(a),compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f334,f17816]) ).

fof(f17818,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(h),domain(domain(a)),compose(h,compose(domain(a),compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))),compose(compose(h,domain(a)),compose(h,compose(a,b)))) = compose(compose(h,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f17716]) ).

fof(f17819,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(domain(a)),compose(h,compose(domain(a),compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))),compose(compose(h,domain(a)),compose(h,compose(a,b)))) = compose(compose(h,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f147,f17818]) ).

fof(f17820,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(a),compose(h,compose(domain(a),compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))),compose(compose(h,domain(a)),compose(h,compose(a,b)))) = compose(compose(h,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f17819]) ).

fof(f17821,plain,
    ifeq(domain(a),domain(h),compose(h,compose(domain(a),compose(h,compose(a,b)))),compose(compose(h,domain(a)),compose(h,compose(a,b)))) = compose(compose(h,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17820]) ).

fof(f17822,plain,
    ifeq(domain(a),domain(h),compose(h,compose(domain(a),compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(compose(h,domain(a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f271,f17821]) ).

fof(f17823,plain,
    ifeq(domain(a),domain(h),compose(h,compose(domain(a),compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f271,f17822]) ).

fof(f17842,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(domain(h)),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1583,f17720]) ).

fof(f17843,plain,
    ifeq(domain(b),domain(h),ifeq(domain(h),domain(compose(g,a)),compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f17842]) ).

fof(f17844,plain,
    ifeq(domain(b),domain(h),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f2123,f17843]) ).

fof(f17845,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17844]) ).

fof(f17846,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f2177,f17845]) ).

fof(f17847,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f2177,f17846]) ).

fof(f17848,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f17721]) ).

fof(f17849,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(h),domain(compose(h,compose(a,b))),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f17848]) ).

fof(f17850,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f17849]) ).

fof(f17851,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17850]) ).

fof(f17852,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f8322,f17851]) ).

fof(f17853,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f8322,f17852]) ).

fof(f17854,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(domain(h)),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1465,f17722]) ).

fof(f17855,plain,
    ifeq(domain(b),domain(h),ifeq(domain(h),domain(compose(h,a)),compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f17854]) ).

fof(f17856,plain,
    ifeq(domain(b),domain(h),ifeq(domain(h),domain(h),compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f17855]) ).

fof(f17857,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f17856]) ).

fof(f17858,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(domain(h),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1957,f17857]) ).

fof(f17859,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1957,f17858]) ).

fof(f17982,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(h,compose(a,b)))),codomain(compose(h,compose(a,b)))) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f478,f470]) ).

fof(f17983,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(h,compose(a,b)))),codomain(b)) = codomain(compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1016,f17982]) ).

fof(f17984,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),codomain(compose(X0,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f1016,f17983]) ).

fof(f18002,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),X0)),domain(g)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f1016,f484]) ).

fof(f18003,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),X0)),domain(h)) = domain(g),
    inference(forward_demodulation,[status(thm)],[f478,f18002]) ).

fof(f18004,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),domain(compose(compose(h,compose(a,b)),X0)),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f478,f18003]) ).

fof(f18071,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),X0,ifeq(compose(g,b),X0,g,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f500]) ).

fof(f18072,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(g,b),X0,g,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f500]) ).

fof(f18073,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(g,b),X0,g,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f500]) ).

fof(f18074,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(g,b),X0,g,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f500]) ).

fof(f18075,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(g,b),X0,g,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f500]) ).

fof(f18076,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(g,b),X0,g,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f500]) ).

fof(f18077,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(g,b),X1,g,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f500]) ).

fof(f18088,plain,
    ! [X0] : ifeq(compose(compose(g,a),b),X0,ifeq(compose(g,b),X0,g,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f18071]) ).

fof(f18089,plain,
    ! [X0] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(g,b),X0,g,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f18088]) ).

fof(f18090,plain,
    ! [X0] : ifeq(compose(compose(h,a),b),X0,ifeq(compose(g,b),X0,g,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f18072]) ).

fof(f18226,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),X0,ifeq(compose(h,b),X0,h,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f501]) ).

fof(f18227,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(h,b),X0,h,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f501]) ).

fof(f18228,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(h,b),X0,h,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f501]) ).

fof(f18229,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(h,b),X0,h,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f501]) ).

fof(f18230,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(h,b),X0,h,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f501]) ).

fof(f18231,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(h,b),X0,h,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f501]) ).

fof(f18232,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(h,b),X1,h,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f501]) ).

fof(f18243,plain,
    ! [X0] : ifeq(compose(compose(g,a),b),X0,ifeq(compose(h,b),X0,h,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f18226]) ).

fof(f18244,plain,
    ! [X0] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,b),X0,h,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f18243]) ).

fof(f18245,plain,
    ! [X0] : ifeq(compose(compose(h,a),b),X0,ifeq(compose(h,b),X0,h,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f18227]) ).

fof(f18269,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f488]) ).

fof(f18270,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f488]) ).

fof(f18271,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f488]) ).

fof(f18272,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f488]) ).

fof(f18273,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f488]) ).

fof(f18274,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f488]) ).

fof(f18275,plain,
    ! [X0,X1,X2] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),X2,ifeq(compose(codomain(X0),b),X2,codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f488]) ).

fof(f18327,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f18269]) ).

fof(f18328,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f18327]) ).

fof(f18329,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),b),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f18270]) ).

fof(f18471,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(compose(g,a),b),X0,compose(g,a),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1583,f491]) ).

fof(f18472,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1465,f491]) ).

fof(f18473,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1016,f491]) ).

fof(f18474,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),g),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f975,f491]) ).

fof(f18484,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),g),g),g),g) = g,
    inference(forward_demodulation,[status(thm)],[f446,f18471]) ).

fof(f18575,plain,
    ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(compose(h,a),b))),compose(a,compose(compose(h,a),b))) = compose(a,compose(compose(h,a),b)),
    inference(paramodulation,[status(thm)],[f13578,f2337]) ).

fof(f18576,plain,
    ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(g,a))),compose(a,compose(g,a))) = compose(a,compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2337]) ).

fof(f18577,plain,
    ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(h,a))),compose(a,compose(h,a))) = compose(a,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2337]) ).

fof(f18579,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)],[f261,f2337]) ).

fof(f18580,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)],[f35,f2337]) ).

fof(f18581,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)],[f18,f2337]) ).

fof(f18605,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(compose(g,a),b),X0,compose(g,a),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1583,f492]) ).

fof(f18606,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1465,f492]) ).

fof(f18607,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1016,f492]) ).

fof(f18608,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),h),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f975,f492]) ).

fof(f18618,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),h),h),h),h) = h,
    inference(forward_demodulation,[status(thm)],[f446,f18605]) ).

fof(f18624,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(compose(g,a),b),X1,compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1583,f493]) ).

fof(f18625,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(compose(h,a),b),X1,compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1465,f493]) ).

fof(f18626,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(compose(h,compose(a,b)),b),X1,compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1016,f493]) ).

fof(f18627,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(compose(a,b),b),X1,compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f975,f493]) ).

fof(f18697,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f446,f18624]) ).

fof(f19086,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(compose(h,a),b))),compose(h,compose(compose(h,a),b))) = compose(h,compose(compose(h,a),b)),
    inference(paramodulation,[status(thm)],[f13578,f7990]) ).

fof(f19087,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(g,a))),compose(h,compose(g,a))) = compose(h,compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f7990]) ).

fof(f19088,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(h,a))),compose(h,compose(h,a))) = compose(h,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f7990]) ).

fof(f19091,plain,
    ! [X0] : ifeq(domain(a),domain(X0),compose(domain(h),compose(h,domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
    inference(paramodulation,[status(thm)],[f35,f7990]) ).

fof(f19092,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),compose(domain(h),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
    inference(paramodulation,[status(thm)],[f18,f7990]) ).

fof(f19183,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,compose(a,b)),X1,compose(g,a),X0),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f1583,f576]) ).

fof(f19185,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f19183]) ).

fof(f19186,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f19183]) ).

fof(f19187,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f19183]) ).

fof(f19188,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f19183]) ).

fof(f19198,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f19185]) ).

fof(f19199,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f19198]) ).

fof(f19200,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f19186]) ).

fof(f19206,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f1583,f577]) ).

fof(f19207,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f19206]) ).

fof(f19210,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1465,f19207]) ).

fof(f19211,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1016,f19207]) ).

fof(f19212,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f975,f19207]) ).

fof(f19227,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(b),compose(compose(g,a),compose(b,X0)),compose(compose(h,compose(a,b)),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f1583,f594]) ).

fof(f19228,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(g,a),compose(b,X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f16,f19227]) ).

fof(f19229,plain,
    ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
    inference(paramodulation,[status(thm)],[f478,f19228]) ).

fof(f19231,plain,
    ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f19228]) ).

fof(f19232,plain,
    ifeq(codomain(b),domain(h),compose(compose(g,a),compose(b,compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f19228]) ).

fof(f19254,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(compose(g,a)),domain(b),codomain(compose(g,a)),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f10325]) ).

fof(f19308,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),codomain(compose(g,a)),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f19254]) ).

fof(f19309,plain,
    ifeq(domain(b),domain(a),codomain(compose(g,a)),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f19308]) ).

fof(f19310,plain,
    ifeq(domain(b),domain(a),domain(b),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f19309]) ).

fof(f19311,plain,
    ifeq(domain(b),domain(a),domain(b),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f19310]) ).

fof(f19312,plain,
    ifeq(domain(b),domain(a),domain(b),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f19311]) ).

fof(f19560,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(compose(g,a)),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(g,a)),b)),compose(compose(X0,compose(g,a)),b)) = compose(compose(X0,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f1583,f580]) ).

fof(f19561,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(g,a)),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(g,a)),b)) = compose(compose(X0,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f19560]) ).

fof(f19562,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(g,a)),b)) = compose(compose(X0,compose(g,a)),b),
    inference(forward_demodulation,[status(thm)],[f2123,f19561]) ).

fof(f19564,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(g,a)),b)) = compose(compose(compose(g,a),compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f1583,f19562]) ).

fof(f19565,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),compose(g,a)),b)) = compose(compose(compose(h,a),compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f1465,f19562]) ).

fof(f19566,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),b)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f1016,f19562]) ).

fof(f19567,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(g,a)),b)) = compose(compose(compose(a,b),compose(g,a)),b),
    inference(paramodulation,[status(thm)],[f975,f19562]) ).

fof(f19858,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X1,ifeq(compose(X0,b),X1,X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f975,f599]) ).

fof(f19861,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f19858]) ).

fof(f19862,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f19858]) ).

fof(f19863,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f19858]) ).

fof(f19878,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(compose(h,compose(a,b)),b),X1,compose(h,compose(a,b)),X0),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f975,f600]) ).

fof(f19881,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f19878]) ).

fof(f19883,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f19878]) ).

fof(f19895,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),b),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f19881]) ).

fof(f19961,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X1,ifeq(compose(X0,a),X1,X0,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f975,f601]) ).

fof(f19963,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f19961]) ).

fof(f19964,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f19961]) ).

fof(f19965,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f19961]) ).

fof(f19966,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f19961]) ).

fof(f19979,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,a),X1,ifeq(compose(compose(h,compose(a,b)),a),X1,compose(h,compose(a,b)),X0),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f975,f602]) ).

fof(f19981,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f19979]) ).

fof(f19982,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f19979]) ).

fof(f19984,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f19979]) ).

fof(f19993,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f19981]) ).

fof(f19994,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f19982]) ).

fof(f19997,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,X1)),compose(compose(compose(h,compose(a,b)),X0),X1)),compose(compose(compose(h,compose(a,b)),X0),X1)) = compose(compose(compose(h,compose(a,b)),X0),X1),
    inference(forward_demodulation,[status(thm)],[f975,f603]) ).

fof(f19999,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(compose(g,a)),compose(compose(h,compose(a,b)),compose(compose(g,a),X0)),compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)),compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f19997]) ).

fof(f20000,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(compose(h,a),X0)),compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)),compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f19997]) ).

fof(f20008,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,g)),compose(compose(compose(h,compose(a,b)),X0),g)),compose(compose(compose(h,compose(a,b)),X0),g)) = compose(compose(compose(h,compose(a,b)),X0),g),
    inference(paramodulation,[status(thm)],[f478,f19997]) ).

fof(f20010,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,compose(g,a))),compose(compose(compose(h,compose(a,b)),X0),compose(g,a))),compose(compose(compose(h,compose(a,b)),X0),compose(g,a))) = compose(compose(compose(h,compose(a,b)),X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f19997]) ).

fof(f20011,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(X0,compose(h,a))),compose(compose(compose(h,compose(a,b)),X0),compose(h,a))),compose(compose(compose(h,compose(a,b)),X0),compose(h,a))) = compose(compose(compose(h,compose(a,b)),X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f19997]) ).

fof(f20025,plain,
    ifeq(codomain(compose(h,compose(a,b))),domain(codomain(b)),ifeq(codomain(b),domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f1103,f19997]) ).

fof(f20026,plain,
    ifeq(codomain(compose(h,a)),domain(domain(b)),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1534,f19997]) ).

fof(f20027,plain,
    ifeq(codomain(compose(a,b)),domain(codomain(b)),ifeq(codomain(b),domain(compose(a,b)),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b)),
    inference(paramodulation,[status(thm)],[f1043,f19997]) ).

fof(f20028,plain,
    ifeq(codomain(compose(g,a)),domain(domain(b)),ifeq(codomain(b),domain(compose(g,a)),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b)),
    inference(paramodulation,[status(thm)],[f1622,f19997]) ).

fof(f20031,plain,
    ifeq(codomain(g),domain(domain(a)),ifeq(codomain(b),domain(g),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),g),domain(a))),compose(compose(compose(h,compose(a,b)),g),domain(a))) = compose(compose(compose(h,compose(a,b)),g),domain(a)),
    inference(paramodulation,[status(thm)],[f334,f19997]) ).

fof(f20032,plain,
    ifeq(codomain(h),domain(domain(a)),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),h),compose(compose(compose(h,compose(a,b)),h),domain(a))),compose(compose(compose(h,compose(a,b)),h),domain(a))) = compose(compose(compose(h,compose(a,b)),h),domain(a)),
    inference(paramodulation,[status(thm)],[f271,f19997]) ).

fof(f20036,plain,
    ifeq(codomain(domain(h)),domain(compose(g,a)),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2177,f19997]) ).

fof(f20037,plain,
    ifeq(codomain(domain(h)),domain(compose(h,compose(a,b))),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f8322,f19997]) ).

fof(f20038,plain,
    ifeq(codomain(domain(h)),domain(compose(h,a)),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1957,f19997]) ).

fof(f20039,plain,
    ifeq(codomain(domain(h)),domain(g),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),domain(h)),g)),compose(compose(compose(h,compose(a,b)),domain(h)),g)) = compose(compose(compose(h,compose(a,b)),domain(h)),g),
    inference(paramodulation,[status(thm)],[f516,f19997]) ).

fof(f20051,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),X0)),compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)),compose(compose(compose(h,compose(a,b)),compose(g,a)),X0)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f19999]) ).

fof(f20052,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),X0)),compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)),compose(compose(compose(h,compose(a,b)),compose(h,a)),X0)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f20000]) ).

fof(f20070,plain,
    ifeq(codomain(b),domain(codomain(b)),ifeq(codomain(b),domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f1016,f20025]) ).

fof(f20071,plain,
    ifeq(codomain(b),codomain(b),ifeq(codomain(b),domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f18,f20070]) ).

fof(f20072,plain,
    ifeq(codomain(b),domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f20071]) ).

fof(f20073,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f506,f20072]) ).

fof(f20074,plain,
    ifeq(domain(b),domain(domain(b)),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f20026]) ).

fof(f20075,plain,
    ifeq(domain(b),domain(b),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f20074]) ).

fof(f20076,plain,
    ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f20075]) ).

fof(f20077,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1908,f20076]) ).

fof(f20078,plain,
    ifeq(codomain(b),domain(codomain(b)),ifeq(codomain(b),domain(compose(a,b)),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f975,f20027]) ).

fof(f20079,plain,
    ifeq(codomain(b),codomain(b),ifeq(codomain(b),domain(compose(a,b)),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f18,f20078]) ).

fof(f20080,plain,
    ifeq(codomain(b),domain(compose(a,b)),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f20079]) ).

fof(f20081,plain,
    ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(b)),
    inference(forward_demodulation,[status(thm)],[f261,f20080]) ).

fof(f20082,plain,
    ifeq(domain(b),domain(domain(b)),ifeq(codomain(b),domain(compose(g,a)),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f20028]) ).

fof(f20083,plain,
    ifeq(domain(b),domain(b),ifeq(codomain(b),domain(compose(g,a)),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f35,f20082]) ).

fof(f20084,plain,
    ifeq(codomain(b),domain(compose(g,a)),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f16,f20083]) ).

fof(f20085,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f2123,f20084]) ).

fof(f20093,plain,
    ifeq(domain(a),domain(domain(a)),ifeq(codomain(b),domain(g),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),g),domain(a))),compose(compose(compose(h,compose(a,b)),g),domain(a))) = compose(compose(compose(h,compose(a,b)),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f316,f20031]) ).

fof(f20094,plain,
    ifeq(domain(a),domain(a),ifeq(codomain(b),domain(g),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),g),domain(a))),compose(compose(compose(h,compose(a,b)),g),domain(a))) = compose(compose(compose(h,compose(a,b)),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f20093]) ).

fof(f20095,plain,
    ifeq(codomain(b),domain(g),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),g),domain(a))) = compose(compose(compose(h,compose(a,b)),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f20094]) ).

fof(f20096,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),g),domain(a))) = compose(compose(compose(h,compose(a,b)),g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f478,f20095]) ).

fof(f20097,plain,
    ifeq(domain(a),domain(domain(a)),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),h),compose(compose(compose(h,compose(a,b)),h),domain(a))),compose(compose(compose(h,compose(a,b)),h),domain(a))) = compose(compose(compose(h,compose(a,b)),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f147,f20032]) ).

fof(f20098,plain,
    ifeq(domain(a),domain(a),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),h),compose(compose(compose(h,compose(a,b)),h),domain(a))),compose(compose(compose(h,compose(a,b)),h),domain(a))) = compose(compose(compose(h,compose(a,b)),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f35,f20097]) ).

fof(f20099,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),h),compose(compose(compose(h,compose(a,b)),h),domain(a))) = compose(compose(compose(h,compose(a,b)),h),domain(a)),
    inference(forward_demodulation,[status(thm)],[f16,f20098]) ).

fof(f20111,plain,
    ifeq(domain(h),domain(compose(g,a)),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f17,f20036]) ).

fof(f20112,plain,
    ifeq(domain(h),domain(h),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f20111]) ).

fof(f20113,plain,
    ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f20112]) ).

fof(f20114,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f35,f20113]) ).

fof(f20115,plain,
    ifeq(domain(h),domain(compose(h,compose(a,b))),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f20037]) ).

fof(f20116,plain,
    ifeq(domain(h),domain(h),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f506,f20115]) ).

fof(f20117,plain,
    ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f20116]) ).

fof(f20118,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f35,f20117]) ).

fof(f20119,plain,
    ifeq(domain(h),domain(compose(h,a)),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f17,f20038]) ).

fof(f20120,plain,
    ifeq(domain(h),domain(h),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f20119]) ).

fof(f20121,plain,
    ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f16,f20120]) ).

fof(f20122,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f35,f20121]) ).

fof(f20123,plain,
    ifeq(domain(h),domain(g),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),domain(h)),g)),compose(compose(compose(h,compose(a,b)),domain(h)),g)) = compose(compose(compose(h,compose(a,b)),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f17,f20039]) ).

fof(f20124,plain,
    ifeq(domain(h),domain(h),ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),domain(h)),g)),compose(compose(compose(h,compose(a,b)),domain(h)),g)) = compose(compose(compose(h,compose(a,b)),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f478,f20123]) ).

fof(f20125,plain,
    ifeq(codomain(b),domain(domain(h)),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),domain(h)),g)) = compose(compose(compose(h,compose(a,b)),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f16,f20124]) ).

fof(f20126,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),g),compose(compose(compose(h,compose(a,b)),domain(h)),g)) = compose(compose(compose(h,compose(a,b)),domain(h)),g),
    inference(forward_demodulation,[status(thm)],[f35,f20125]) ).

fof(f20588,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f975,f655]) ).

fof(f21127,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(compose(h,a),b),b),b,compose(compose(h,a),b),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f9281,f11002]) ).

fof(f21128,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),b,compose(g,a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1583,f11002]) ).

fof(f21129,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),b,compose(h,a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1465,f11002]) ).

fof(f21131,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),b),b,compose(a,b),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f975,f11002]) ).

fof(f21134,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),b,codomain(X0),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f36,f11002]) ).

fof(f21135,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),b,a,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f24,f11002]) ).

fof(f21136,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),b,domain(X0),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f17,f11002]) ).

fof(f21141,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),b,compose(g,a),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f446,f21128]) ).

fof(f21149,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(h,compose(a,b)))),codomain(b)) = codomain(compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f975,f993]) ).

fof(f21150,plain,
    ifeq(domain(b),domain(h),codomain(compose(a,compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f975,f21149]) ).

fof(f21151,plain,
    ifeq(codomain(b),domain(a),ifeq(b,compose(compose(compose(h,a),b),b),compose(compose(h,a),b),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f9281,f11248]) ).

fof(f21152,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(compose(g,a),b),compose(g,a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1583,f11248]) ).

fof(f21153,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(compose(h,a),b),compose(h,a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1465,f11248]) ).

fof(f21155,plain,
    ifeq(codomain(b),domain(a),ifeq(b,compose(compose(a,b),b),compose(a,b),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f975,f11248]) ).

fof(f21158,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(b,compose(codomain(X0),b),codomain(X0),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f36,f11248]) ).

fof(f21159,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(a,b),a,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f24,f11248]) ).

fof(f21160,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(b,compose(domain(X0),b),domain(X0),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f17,f11248]) ).

fof(f21165,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(h,compose(a,b)),compose(g,a),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f446,f21152]) ).

fof(f22220,plain,
    ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,b)),compose(compose(compose(g,a),a),b)) = compose(compose(compose(g,a),a),b),
    inference(paramodulation,[status(thm)],[f1583,f2268]) ).

fof(f22221,plain,
    ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,b)),compose(compose(compose(h,a),a),b)) = compose(compose(compose(h,a),a),b),
    inference(paramodulation,[status(thm)],[f1465,f2268]) ).

fof(f22222,plain,
    ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(compose(h,compose(a,b)),a),b)) = compose(compose(compose(h,compose(a,b)),a),b),
    inference(paramodulation,[status(thm)],[f1016,f2268]) ).

fof(f22223,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)],[f975,f2268]) ).

fof(f22225,plain,
    ifeq(domain(a),domain(a),compose(h,compose(a,b)),compose(compose(h,a),b)) = compose(compose(h,a),b),
    inference(paramodulation,[status(thm)],[f147,f2268]) ).

fof(f22226,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)],[f36,f2268]) ).

fof(f22227,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,f2268]) ).

fof(f22228,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)],[f17,f2268]) ).

fof(f22238,plain,
    compose(h,compose(a,b)) = compose(compose(h,a),b),
    inference(forward_demodulation,[status(thm)],[f16,f22225]) ).

fof(f22258,plain,
    ifeq(compose(h,compose(a,b)),compose(h,b),h,compose(h,a)) = compose(h,a),
    inference(backward_demodulation,[status(thm)],[f22238,f11633]) ).

fof(f22259,plain,
    ifeq(compose(h,compose(a,b)),compose(g,b),g,compose(h,a)) = compose(h,a),
    inference(backward_demodulation,[status(thm)],[f22238,f11602]) ).

fof(f22260,plain,
    ifeq(compose(h,b),compose(h,compose(a,b)),h,compose(h,a)) = compose(h,a),
    inference(backward_demodulation,[status(thm)],[f22238,f11557]) ).

fof(f22261,plain,
    ifeq(compose(g,b),compose(h,compose(a,b)),g,compose(h,a)) = compose(h,a),
    inference(backward_demodulation,[status(thm)],[f22238,f11514]) ).

fof(f22309,plain,
    ifeq(codomain(compose(h,a)),domain(b),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),b)),compose(compose(compose(h,compose(a,b)),compose(h,a)),b)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f19997]) ).

fof(f22310,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(compose(h,a)),domain(b),compose(compose(h,a),compose(b,compose(h,compose(a,b)))),compose(compose(compose(h,a),b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),b),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f22238,f17676]) ).

fof(f22312,plain,
    ifeq(codomain(compose(h,a)),domain(b),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,a)),b)),compose(compose(g,compose(h,a)),b)) = compose(compose(g,compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f325]) ).

fof(f22313,plain,
    ifeq(codomain(compose(h,a)),domain(b),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,a)),b)),compose(compose(h,compose(h,a)),b)) = compose(compose(h,compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f262]) ).

fof(f22314,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(b),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,a)),b)),compose(compose(codomain(X0),compose(h,a)),b)) = compose(compose(codomain(X0),compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f161]) ).

fof(f22315,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(h,a)),domain(b),compose(compose(h,a),compose(b,domain(X0))),compose(compose(compose(h,a),b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(h,a),b),domain(X0)),
    inference(paramodulation,[status(thm)],[f22238,f159]) ).

fof(f22331,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(b),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,a)),b)),compose(compose(domain(X0),compose(h,a)),b)) = compose(compose(domain(X0),compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f163]) ).

fof(f22332,plain,
    ifeq(codomain(compose(h,a)),domain(b),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,a)),b)),compose(compose(a,compose(h,a)),b)) = compose(compose(a,compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f162]) ).

fof(f22333,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(compose(h,a)),domain(b),compose(compose(h,a),compose(b,codomain(X0))),compose(compose(compose(h,a),b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),b),codomain(X0)),
    inference(paramodulation,[status(thm)],[f22238,f160]) ).

fof(f22335,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(compose(h,a)),domain(b),compose(compose(h,a),compose(b,compose(a,b))),compose(compose(compose(h,a),b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),b),compose(a,b)),
    inference(paramodulation,[status(thm)],[f22238,f2966]) ).

fof(f22337,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(compose(h,a)),domain(b),compose(compose(h,a),compose(b,X0)),compose(compose(compose(h,a),b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,a),b),X0),
    inference(paramodulation,[status(thm)],[f22238,f23]) ).

fof(f22339,plain,
    ! [X0] : ifeq(codomain(compose(h,a)),domain(b),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,a)),b)),compose(compose(X0,compose(h,a)),b)) = compose(compose(X0,compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f23]) ).

fof(f22409,plain,
    ifeq(domain(b),domain(b),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),b)),compose(compose(compose(h,compose(a,b)),compose(h,a)),b)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f22309]) ).

fof(f22410,plain,
    ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),b)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f22409]) ).

fof(f22411,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),b)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f22410]) ).

fof(f22412,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(b),compose(compose(h,a),compose(b,compose(h,compose(a,b)))),compose(compose(compose(h,a),b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),b),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1465,f22310]) ).

fof(f22413,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),b),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f22412]) ).

fof(f22414,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f22238,f22413]) ).

fof(f22419,plain,
    ifeq(domain(b),domain(b),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,a)),b)),compose(compose(g,compose(h,a)),b)) = compose(compose(g,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f22312]) ).

fof(f22420,plain,
    ifeq(domain(a),domain(compose(h,a)),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,a)),b)) = compose(compose(g,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f22419]) ).

fof(f22421,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,compose(h,a)),b)) = compose(compose(g,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f22420]) ).

fof(f22422,plain,
    ifeq(domain(b),domain(b),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,a)),b)),compose(compose(h,compose(h,a)),b)) = compose(compose(h,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f22313]) ).

fof(f22423,plain,
    ifeq(domain(a),domain(compose(h,a)),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,a)),b)) = compose(compose(h,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f22422]) ).

fof(f22424,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,compose(h,a)),b)) = compose(compose(h,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f22423]) ).

fof(f22425,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,a)),b)),compose(compose(codomain(X0),compose(h,a)),b)) = compose(compose(codomain(X0),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f22314]) ).

fof(f22426,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,a)),b)) = compose(compose(codomain(X0),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f22425]) ).

fof(f22427,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),compose(h,a)),b)) = compose(compose(codomain(X0),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f22426]) ).

fof(f22428,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(b),compose(compose(h,a),compose(b,domain(X0))),compose(compose(compose(h,a),b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(h,a),b),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1465,f22315]) ).

fof(f22429,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,a),compose(b,domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(h,a),b),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f22428]) ).

fof(f22430,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,a),compose(b,domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f22238,f22429]) ).

fof(f22521,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,a)),b)),compose(compose(domain(X0),compose(h,a)),b)) = compose(compose(domain(X0),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f22331]) ).

fof(f22522,plain,
    ! [X0] : ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,a)),b)) = compose(compose(domain(X0),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f22521]) ).

fof(f22523,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),compose(h,a)),b)) = compose(compose(domain(X0),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f22522]) ).

fof(f22524,plain,
    ifeq(domain(b),domain(b),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,a)),b)),compose(compose(a,compose(h,a)),b)) = compose(compose(a,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f22332]) ).

fof(f22525,plain,
    ifeq(domain(b),domain(compose(h,a)),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,a)),b)) = compose(compose(a,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f22524]) ).

fof(f22526,plain,
    ifeq(domain(b),domain(h),compose(a,compose(h,compose(a,b))),compose(compose(a,compose(h,a)),b)) = compose(compose(a,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f22525]) ).

fof(f22527,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(b),compose(compose(h,a),compose(b,codomain(X0))),compose(compose(compose(h,a),b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),b),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1465,f22333]) ).

fof(f22528,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(h,a),compose(b,codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),b),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f22527]) ).

fof(f22529,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(compose(h,a),compose(b,codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f22238,f22528]) ).

fof(f22534,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(b),domain(b),compose(compose(h,a),compose(b,compose(a,b))),compose(compose(compose(h,a),b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),b),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1465,f22335]) ).

fof(f22535,plain,
    ifeq(codomain(b),domain(a),compose(compose(h,a),compose(b,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),b),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f22534]) ).

fof(f22536,plain,
    ifeq(codomain(b),domain(a),compose(compose(h,a),compose(b,compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f22238,f22535]) ).

fof(f22541,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(b),compose(compose(h,a),compose(b,X0)),compose(compose(compose(h,a),b),X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,a),b),X0),
    inference(forward_demodulation,[status(thm)],[f1465,f22337]) ).

fof(f22542,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,a),compose(b,X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(compose(h,a),b),X0),
    inference(forward_demodulation,[status(thm)],[f16,f22541]) ).

fof(f22543,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(compose(h,a),compose(b,X0)),compose(compose(h,compose(a,b)),X0)) = compose(compose(h,compose(a,b)),X0),
    inference(forward_demodulation,[status(thm)],[f22238,f22542]) ).

fof(f22548,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,a)),b)),compose(compose(X0,compose(h,a)),b)) = compose(compose(X0,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f22339]) ).

fof(f22549,plain,
    ! [X0] : ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,a)),b)) = compose(compose(X0,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f22548]) ).

fof(f22550,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,compose(h,compose(a,b))),compose(compose(X0,compose(h,a)),b)) = compose(compose(X0,compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f22549]) ).

fof(f22556,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,compose(h,compose(a,b)))),compose(compose(compose(g,a),a),compose(h,compose(a,b)))),compose(compose(compose(g,a),a),compose(h,compose(a,b)))) = compose(compose(compose(g,a),a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f2272]) ).

fof(f22557,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,compose(h,compose(a,b)))),compose(compose(compose(h,a),a),compose(h,compose(a,b)))),compose(compose(compose(h,a),a),compose(h,compose(a,b)))) = compose(compose(compose(h,a),a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f2272]) ).

fof(f22558,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f2272]) ).

fof(f22559,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(h,compose(a,b)))),compose(compose(compose(a,b),a),compose(h,compose(a,b)))),compose(compose(compose(a,b),a),compose(h,compose(a,b)))) = compose(compose(compose(a,b),a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f2272]) ).

fof(f22560,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(a),compose(g,compose(a,compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f316,f2272]) ).

fof(f22561,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(a),compose(h,compose(a,compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f147,f2272]) ).

fof(f22562,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(h,compose(a,b)))),compose(compose(codomain(X0),a),compose(h,compose(a,b)))),compose(compose(codomain(X0),a),compose(h,compose(a,b)))) = compose(compose(codomain(X0),a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f36,f2272]) ).

fof(f22563,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(a,compose(h,compose(a,b)))),compose(compose(a,a),compose(h,compose(a,b)))),compose(compose(a,a),compose(h,compose(a,b)))) = compose(compose(a,a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f24,f2272]) ).

fof(f22564,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(h,compose(a,b)))),compose(compose(domain(X0),a),compose(h,compose(a,b)))),compose(compose(domain(X0),a),compose(h,compose(a,b)))) = compose(compose(domain(X0),a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f17,f2272]) ).

fof(f22565,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(a,compose(h,compose(a,b))))),domain(a),compose(a,compose(h,compose(a,b))),compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b)))),compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b)))) = compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f19,f2272]) ).

fof(f22568,plain,
    ifeq(domain(b),domain(h),compose(g,compose(a,compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f22560]) ).

fof(f22569,plain,
    ifeq(domain(b),domain(h),compose(h,compose(a,compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f22561]) ).

fof(f22570,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(a,compose(h,compose(a,b)))),domain(a),compose(a,compose(h,compose(a,b))),compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b)))),compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b)))) = compose(compose(domain(compose(a,compose(h,compose(a,b)))),a),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f22565]) ).

fof(f22584,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,compose(a,b))),compose(compose(compose(g,a),a),compose(a,b))),compose(compose(compose(g,a),a),compose(a,b))) = compose(compose(compose(g,a),a),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2273]) ).

fof(f22585,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,compose(a,b))),compose(compose(compose(h,a),a),compose(a,b))),compose(compose(compose(h,a),a),compose(a,b))) = compose(compose(compose(h,a),a),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2273]) ).

fof(f22586,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,compose(a,b))),compose(compose(compose(h,compose(a,b)),a),compose(a,b))),compose(compose(compose(h,compose(a,b)),a),compose(a,b))) = compose(compose(compose(h,compose(a,b)),a),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f2273]) ).

fof(f22587,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)],[f975,f2273]) ).

fof(f22588,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),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)],[f316,f2273]) ).

fof(f22589,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(a),compose(h,compose(a,compose(a,b))),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
    inference(paramodulation,[status(thm)],[f147,f2273]) ).

fof(f22590,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)],[f36,f2273]) ).

fof(f22591,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)],[f24,f2273]) ).

fof(f22592,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)],[f17,f2273]) ).

fof(f22593,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(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)],[f19,f2273]) ).

fof(f22596,plain,
    ifeq(domain(b),domain(a),compose(g,compose(a,compose(a,b))),compose(compose(g,a),compose(a,b))) = compose(compose(g,a),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f22588]) ).

fof(f22597,plain,
    ifeq(domain(b),domain(a),compose(h,compose(a,compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f22589]) ).

fof(f22598,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(forward_demodulation,[status(thm)],[f17,f22593]) ).

fof(f22634,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,domain(X0))),compose(compose(compose(g,a),a),domain(X0))),compose(compose(compose(g,a),a),domain(X0))) = compose(compose(compose(g,a),a),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f2274]) ).

fof(f22635,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,domain(X0))),compose(compose(compose(h,a),a),domain(X0))),compose(compose(compose(h,a),a),domain(X0))) = compose(compose(compose(h,a),a),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f2274]) ).

fof(f22636,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,domain(X0))),compose(compose(compose(h,compose(a,b)),a),domain(X0))),compose(compose(compose(h,compose(a,b)),a),domain(X0))) = compose(compose(compose(h,compose(a,b)),a),domain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f2274]) ).

fof(f22637,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)],[f975,f2274]) ).

fof(f22638,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),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)],[f316,f2274]) ).

fof(f22639,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(a),compose(h,compose(a,domain(X0))),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
    inference(paramodulation,[status(thm)],[f147,f2274]) ).

fof(f22640,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)],[f36,f2274]) ).

fof(f22641,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,f2274]) ).

fof(f22642,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)],[f17,f2274]) ).

fof(f22643,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)],[f19,f2274]) ).

fof(f22702,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(g,compose(a,domain(X0))),compose(compose(g,a),domain(X0))) = compose(compose(g,a),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f22638]) ).

fof(f22703,plain,
    ! [X0] : ifeq(domain(b),domain(X0),compose(h,compose(a,domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f22639]) ).

fof(f22704,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)],[f17,f22643]) ).

fof(f22814,plain,
    ifeq(domain(b),domain(b),ifeq(a,compose(codomain(compose(g,a)),a),domain(a),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f10368]) ).

fof(f22850,plain,
    ifeq(a,compose(codomain(compose(g,a)),a),domain(a),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f22814]) ).

fof(f22851,plain,
    ifeq(a,compose(domain(b),a),domain(a),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f22850]) ).

fof(f22852,plain,
    ifeq(a,compose(domain(b),a),domain(a),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f22851]) ).

fof(f22853,plain,
    ifeq(a,compose(domain(b),a),domain(a),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f22852]) ).

fof(f23021,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,codomain(X0))),compose(compose(compose(g,a),a),codomain(X0))),compose(compose(compose(g,a),a),codomain(X0))) = compose(compose(compose(g,a),a),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f2275]) ).

fof(f23022,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,codomain(X0))),compose(compose(compose(h,a),a),codomain(X0))),compose(compose(compose(h,a),a),codomain(X0))) = compose(compose(compose(h,a),a),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f2275]) ).

fof(f23023,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,codomain(X0))),compose(compose(compose(h,compose(a,b)),a),codomain(X0))),compose(compose(compose(h,compose(a,b)),a),codomain(X0))) = compose(compose(compose(h,compose(a,b)),a),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f2275]) ).

fof(f23024,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)],[f975,f2275]) ).

fof(f23025,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),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)],[f316,f2275]) ).

fof(f23026,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(a),compose(h,compose(a,codomain(X0))),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
    inference(paramodulation,[status(thm)],[f147,f2275]) ).

fof(f23027,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)],[f36,f2275]) ).

fof(f23028,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,f2275]) ).

fof(f23029,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)],[f17,f2275]) ).

fof(f23030,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)],[f19,f2275]) ).

fof(f23099,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(g,compose(a,codomain(X0))),compose(compose(g,a),codomain(X0))) = compose(compose(g,a),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f23025]) ).

fof(f23100,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),compose(h,compose(a,codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f23026]) ).

fof(f23101,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)],[f17,f23030]) ).

fof(f23230,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,g)),compose(compose(compose(h,compose(a,b)),a),g)),compose(compose(compose(h,compose(a,b)),a),g)) = compose(compose(compose(h,compose(a,b)),a),g),
    inference(paramodulation,[status(thm)],[f478,f2278]) ).

fof(f23231,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,compose(g,a))),compose(compose(compose(h,compose(a,b)),a),compose(g,a))),compose(compose(compose(h,compose(a,b)),a),compose(g,a))) = compose(compose(compose(h,compose(a,b)),a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2278]) ).

fof(f23232,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,compose(h,a))),compose(compose(compose(h,compose(a,b)),a),compose(h,a))),compose(compose(compose(h,compose(a,b)),a),compose(h,a))) = compose(compose(compose(h,compose(a,b)),a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2278]) ).

fof(f23239,plain,
    ifeq(domain(b),domain(codomain(compose(compose(h,compose(a,b)),a))),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,codomain(compose(compose(h,compose(a,b)),a)))),compose(compose(h,compose(a,b)),a)),compose(compose(compose(h,compose(a,b)),a),codomain(compose(compose(h,compose(a,b)),a)))) = compose(compose(compose(h,compose(a,b)),a),codomain(compose(compose(h,compose(a,b)),a))),
    inference(paramodulation,[status(thm)],[f20,f2278]) ).

fof(f23249,plain,
    ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),a)),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,codomain(compose(compose(h,compose(a,b)),a)))),compose(compose(h,compose(a,b)),a)),compose(compose(compose(h,compose(a,b)),a),codomain(compose(compose(h,compose(a,b)),a)))) = compose(compose(compose(h,compose(a,b)),a),codomain(compose(compose(h,compose(a,b)),a))),
    inference(forward_demodulation,[status(thm)],[f18,f23239]) ).

fof(f23250,plain,
    ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),a)),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,codomain(compose(compose(h,compose(a,b)),a)))),compose(compose(h,compose(a,b)),a)),compose(compose(h,compose(a,b)),a)) = compose(compose(compose(h,compose(a,b)),a),codomain(compose(compose(h,compose(a,b)),a))),
    inference(forward_demodulation,[status(thm)],[f20,f23249]) ).

fof(f23251,plain,
    ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),a)),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(a,codomain(compose(compose(h,compose(a,b)),a)))),compose(compose(h,compose(a,b)),a)),compose(compose(h,compose(a,b)),a)) = compose(compose(h,compose(a,b)),a),
    inference(forward_demodulation,[status(thm)],[f20,f23250]) ).

fof(f23405,plain,
    ifeq(domain(b),domain(b),ifeq(compose(codomain(compose(g,a)),a),a,domain(a),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f10419]) ).

fof(f23441,plain,
    ifeq(compose(codomain(compose(g,a)),a),a,domain(a),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f23405]) ).

fof(f23442,plain,
    ifeq(compose(domain(b),a),a,domain(a),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f23441]) ).

fof(f23443,plain,
    ifeq(compose(domain(b),a),a,domain(a),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f23442]) ).

fof(f23444,plain,
    ifeq(compose(domain(b),a),a,domain(a),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f23443]) ).

fof(f23601,plain,
    ifeq(domain(b),domain(h),compose(g,compose(a,g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
    inference(paramodulation,[status(thm)],[f478,f2301]) ).

fof(f23602,plain,
    ifeq(domain(b),domain(h),compose(g,compose(a,compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2301]) ).

fof(f23603,plain,
    ifeq(domain(b),domain(h),compose(g,compose(a,compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2301]) ).

fof(f23635,plain,
    ifeq(domain(b),domain(h),compose(h,compose(a,g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
    inference(paramodulation,[status(thm)],[f478,f2302]) ).

fof(f23636,plain,
    ifeq(domain(b),domain(h),compose(h,compose(a,compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2302]) ).

fof(f23637,plain,
    ifeq(domain(b),domain(h),compose(h,compose(a,compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2302]) ).

fof(f23814,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,g)),compose(compose(codomain(X0),a),g)),compose(compose(codomain(X0),a),g)) = compose(compose(codomain(X0),a),g),
    inference(paramodulation,[status(thm)],[f478,f2282]) ).

fof(f23815,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(g,a))),compose(compose(codomain(X0),a),compose(g,a))),compose(compose(codomain(X0),a),compose(g,a))) = compose(compose(codomain(X0),a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2282]) ).

fof(f23816,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(a,compose(h,a))),compose(compose(codomain(X0),a),compose(h,a))),compose(compose(codomain(X0),a),compose(h,a))) = compose(compose(codomain(X0),a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2282]) ).

fof(f23841,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)],[f20,f2282]) ).

fof(f23949,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)],[f18,f23841]) ).

fof(f23950,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)],[f20,f23949]) ).

fof(f23951,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)],[f20,f23950]) ).

fof(f24377,plain,
    ifeq(domain(a),domain(a),ifeq(compose(codomain(g),b),compose(a,b),codomain(g),a),a) = a,
    inference(paramodulation,[status(thm)],[f316,f17117]) ).

fof(f24410,plain,
    ifeq(compose(codomain(g),b),compose(a,b),codomain(g),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f24377]) ).

fof(f24411,plain,
    ifeq(compose(domain(a),b),compose(a,b),codomain(g),a) = a,
    inference(forward_demodulation,[status(thm)],[f316,f24410]) ).

fof(f24412,plain,
    ifeq(compose(domain(a),b),compose(a,b),domain(a),a) = a,
    inference(forward_demodulation,[status(thm)],[f316,f24411]) ).

fof(f24488,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(a,g)),compose(compose(a,a),g)),compose(compose(a,a),g)) = compose(compose(a,a),g),
    inference(paramodulation,[status(thm)],[f478,f2283]) ).

fof(f24489,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(a,compose(g,a))),compose(compose(a,a),compose(g,a))),compose(compose(a,a),compose(g,a))) = compose(compose(a,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2283]) ).

fof(f24490,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(a,compose(h,a))),compose(compose(a,a),compose(h,a))),compose(compose(a,a),compose(h,a))) = compose(compose(a,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2283]) ).

fof(f24497,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)],[f20,f2283]) ).

fof(f24507,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)],[f18,f24497]) ).

fof(f24508,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)],[f20,f24507]) ).

fof(f24509,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)],[f20,f24508]) ).

fof(f24584,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,g)),compose(compose(domain(X0),a),g)),compose(compose(domain(X0),a),g)) = compose(compose(domain(X0),a),g),
    inference(paramodulation,[status(thm)],[f478,f2284]) ).

fof(f24585,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(g,a))),compose(compose(domain(X0),a),compose(g,a))),compose(compose(domain(X0),a),compose(g,a))) = compose(compose(domain(X0),a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2284]) ).

fof(f24586,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(a,compose(h,a))),compose(compose(domain(X0),a),compose(h,a))),compose(compose(domain(X0),a),compose(h,a))) = compose(compose(domain(X0),a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2284]) ).

fof(f24610,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)],[f20,f2284]) ).

fof(f24700,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)],[f18,f24610]) ).

fof(f24701,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)],[f20,f24700]) ).

fof(f24702,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)],[f20,f24701]) ).

fof(f24776,plain,
    ifeq(domain(a),domain(a),ifeq(compose(a,b),compose(codomain(g),b),codomain(g),a),a) = a,
    inference(paramodulation,[status(thm)],[f316,f17142]) ).

fof(f24809,plain,
    ifeq(compose(a,b),compose(codomain(g),b),codomain(g),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f24776]) ).

fof(f24810,plain,
    ifeq(compose(a,b),compose(domain(a),b),codomain(g),a) = a,
    inference(forward_demodulation,[status(thm)],[f316,f24809]) ).

fof(f24811,plain,
    ifeq(compose(a,b),compose(domain(a),b),domain(a),a) = a,
    inference(forward_demodulation,[status(thm)],[f316,f24810]) ).

fof(f24875,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(a,g)),domain(a),compose(a,g),compose(compose(domain(compose(a,g)),a),g)),compose(compose(domain(compose(a,g)),a),g)) = compose(compose(domain(compose(a,g)),a),g),
    inference(paramodulation,[status(thm)],[f478,f2309]) ).

fof(f24876,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(a,compose(g,a))),domain(a),compose(a,compose(g,a)),compose(compose(domain(compose(a,compose(g,a))),a),compose(g,a))),compose(compose(domain(compose(a,compose(g,a))),a),compose(g,a))) = compose(compose(domain(compose(a,compose(g,a))),a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2309]) ).

fof(f24877,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(a,compose(h,a))),domain(a),compose(a,compose(h,a)),compose(compose(domain(compose(a,compose(h,a))),a),compose(h,a))),compose(compose(domain(compose(a,compose(h,a))),a),compose(h,a))) = compose(compose(domain(compose(a,compose(h,a))),a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2309]) ).

fof(f25040,plain,
    ifeq(domain(b),codomain(compose(compose(g,a),a)),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,codomain(compose(compose(g,a),a)))),compose(compose(g,a),a)),compose(compose(g,a),a)) = compose(compose(g,a),a),
    inference(paramodulation,[status(thm)],[f1583,f2333]) ).

fof(f25041,plain,
    ifeq(domain(b),codomain(compose(compose(h,a),a)),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,codomain(compose(compose(h,a),a)))),compose(compose(h,a),a)),compose(compose(h,a),a)) = compose(compose(h,a),a),
    inference(paramodulation,[status(thm)],[f1465,f2333]) ).

fof(f25043,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)],[f975,f2333]) ).

fof(f25179,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(X0)),compose(h,compose(a,b)))),compose(compose(compose(g,a),domain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f2647]) ).

fof(f25180,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(X0)),compose(h,compose(a,b)))),compose(compose(compose(h,a),domain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f2647]) ).

fof(f25181,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f2647]) ).

fof(f25182,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(compose(a,b),domain(X0)),compose(h,compose(a,b)))),compose(compose(compose(a,b),domain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f2647]) ).

fof(f25183,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(g,domain(X0)),compose(h,compose(a,b)))),compose(compose(g,domain(X0)),compose(h,compose(a,b)))) = compose(compose(g,domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f316,f2647]) ).

fof(f25184,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(h,domain(X0)),compose(h,compose(a,b)))),compose(compose(h,domain(X0)),compose(h,compose(a,b)))) = compose(compose(h,domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f147,f2647]) ).

fof(f25185,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(codomain(X1),domain(X0)),compose(h,compose(a,b)))),compose(compose(codomain(X1),domain(X0)),compose(h,compose(a,b)))) = compose(compose(codomain(X1),domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f36,f2647]) ).

fof(f25186,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(h,compose(a,b)))),compose(compose(a,domain(X0)),compose(h,compose(a,b)))),compose(compose(a,domain(X0)),compose(h,compose(a,b)))) = compose(compose(a,domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f24,f2647]) ).

fof(f25187,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(domain(X1),domain(X0)),compose(h,compose(a,b)))),compose(compose(domain(X1),domain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(X1),domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f17,f2647]) ).

fof(f25195,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(codomain(domain(compose(domain(X0),compose(h,compose(a,b))))),domain(X0),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b)))),compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f19,f2647]) ).

fof(f25311,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b)))),compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(compose(domain(X0),compose(h,compose(a,b)))),domain(X0)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f25195]) ).

fof(f25496,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),compose(a,b))),compose(compose(compose(g,a),domain(X0)),compose(a,b))),compose(compose(compose(g,a),domain(X0)),compose(a,b))) = compose(compose(compose(g,a),domain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2648]) ).

fof(f25497,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),compose(a,b))),compose(compose(compose(h,a),domain(X0)),compose(a,b))),compose(compose(compose(h,a),domain(X0)),compose(a,b))) = compose(compose(compose(h,a),domain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2648]) ).

fof(f25498,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(a,b))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),domain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f2648]) ).

fof(f25499,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)],[f975,f2648]) ).

fof(f25500,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),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)],[f316,f2648]) ).

fof(f25501,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),compose(a,b))),compose(compose(h,domain(X0)),compose(a,b))),compose(compose(h,domain(X0)),compose(a,b))) = compose(compose(h,domain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f147,f2648]) ).

fof(f25502,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)],[f36,f2648]) ).

fof(f25503,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)],[f24,f2648]) ).

fof(f25504,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)],[f17,f2648]) ).

fof(f25512,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(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)],[f19,f2648]) ).

fof(f25622,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(forward_demodulation,[status(thm)],[f17,f25512]) ).

fof(f25808,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),domain(X1))),compose(compose(compose(g,a),domain(X0)),domain(X1))),compose(compose(compose(g,a),domain(X0)),domain(X1))) = compose(compose(compose(g,a),domain(X0)),domain(X1)),
    inference(paramodulation,[status(thm)],[f1583,f2649]) ).

fof(f25809,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),domain(X1))),compose(compose(compose(h,a),domain(X0)),domain(X1))),compose(compose(compose(h,a),domain(X0)),domain(X1))) = compose(compose(compose(h,a),domain(X0)),domain(X1)),
    inference(paramodulation,[status(thm)],[f1465,f2649]) ).

fof(f25810,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),domain(X1))),compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X1))),compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X1))) = compose(compose(compose(h,compose(a,b)),domain(X0)),domain(X1)),
    inference(paramodulation,[status(thm)],[f1016,f2649]) ).

fof(f25811,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)],[f975,f2649]) ).

fof(f25812,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(a),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)],[f316,f2649]) ).

fof(f25813,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),domain(X1))),compose(compose(h,domain(X0)),domain(X1))),compose(compose(h,domain(X0)),domain(X1))) = compose(compose(h,domain(X0)),domain(X1)),
    inference(paramodulation,[status(thm)],[f147,f2649]) ).

fof(f25814,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)],[f36,f2649]) ).

fof(f25815,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,f2649]) ).

fof(f25816,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)],[f17,f2649]) ).

fof(f25824,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)],[f19,f2649]) ).

fof(f25983,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)],[f17,f25824]) ).

fof(f26593,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),codomain(X1))),compose(compose(compose(g,a),domain(X0)),codomain(X1))),compose(compose(compose(g,a),domain(X0)),codomain(X1))) = compose(compose(compose(g,a),domain(X0)),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1583,f2650]) ).

fof(f26594,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),codomain(X1))),compose(compose(compose(h,a),domain(X0)),codomain(X1))),compose(compose(compose(h,a),domain(X0)),codomain(X1))) = compose(compose(compose(h,a),domain(X0)),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1465,f2650]) ).

fof(f26595,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),codomain(X1))),compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(X1))),compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(X1))) = compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1016,f2650]) ).

fof(f26596,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)],[f975,f2650]) ).

fof(f26597,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(domain(a),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)],[f316,f2650]) ).

fof(f26598,plain,
    ! [X0,X1] : ifeq(domain(X0),codomain(X1),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(X1))),compose(compose(h,domain(X0)),codomain(X1))),compose(compose(h,domain(X0)),codomain(X1))) = compose(compose(h,domain(X0)),codomain(X1)),
    inference(paramodulation,[status(thm)],[f147,f2650]) ).

fof(f26599,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)],[f36,f2650]) ).

fof(f26600,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,f2650]) ).

fof(f26601,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)],[f17,f2650]) ).

fof(f26609,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)],[f19,f2650]) ).

fof(f26782,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)],[f17,f26609]) ).

fof(f27143,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),g)),compose(compose(compose(h,compose(a,b)),domain(X0)),g)),compose(compose(compose(h,compose(a,b)),domain(X0)),g)) = compose(compose(compose(h,compose(a,b)),domain(X0)),g),
    inference(paramodulation,[status(thm)],[f478,f2653]) ).

fof(f27144,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),compose(g,a))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(g,a))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2653]) ).

fof(f27145,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),compose(h,a))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,a))),compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2653]) ).

fof(f27172,plain,
    ! [X0] : ifeq(domain(X0),domain(codomain(compose(compose(h,compose(a,b)),domain(X0)))),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(compose(compose(h,compose(a,b)),domain(X0))))) = compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(compose(compose(h,compose(a,b)),domain(X0)))),
    inference(paramodulation,[status(thm)],[f20,f2653]) ).

fof(f27313,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(compose(compose(h,compose(a,b)),domain(X0))))) = compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(compose(compose(h,compose(a,b)),domain(X0)))),
    inference(forward_demodulation,[status(thm)],[f18,f27172]) ).

fof(f27314,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),domain(X0)),codomain(compose(compose(h,compose(a,b)),domain(X0)))),
    inference(forward_demodulation,[status(thm)],[f20,f27313]) ).

fof(f27315,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))),ifeq(codomain(b),domain(X0),compose(compose(h,compose(a,b)),compose(domain(X0),codomain(compose(compose(h,compose(a,b)),domain(X0))))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f20,f27314]) ).

fof(f27398,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(a),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)],[f478,f2655]) ).

fof(f27399,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),compose(g,a))),compose(compose(g,domain(X0)),compose(g,a))),compose(compose(g,domain(X0)),compose(g,a))) = compose(compose(g,domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2655]) ).

fof(f27400,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),compose(h,a))),compose(compose(g,domain(X0)),compose(h,a))),compose(compose(g,domain(X0)),compose(h,a))) = compose(compose(g,domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2655]) ).

fof(f27428,plain,
    ! [X0] : ifeq(domain(X0),domain(codomain(compose(g,domain(X0)))),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),codomain(compose(g,domain(X0))))),compose(g,domain(X0))),compose(compose(g,domain(X0)),codomain(compose(g,domain(X0))))) = compose(compose(g,domain(X0)),codomain(compose(g,domain(X0)))),
    inference(paramodulation,[status(thm)],[f20,f2655]) ).

fof(f27582,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(g,domain(X0))),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),codomain(compose(g,domain(X0))))),compose(g,domain(X0))),compose(compose(g,domain(X0)),codomain(compose(g,domain(X0))))) = compose(compose(g,domain(X0)),codomain(compose(g,domain(X0)))),
    inference(forward_demodulation,[status(thm)],[f18,f27428]) ).

fof(f27583,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(g,domain(X0))),ifeq(domain(a),domain(X0),compose(g,compose(domain(X0),codomain(compose(g,domain(X0))))),compose(g,domain(X0))),compose(g,domain(X0))) = compose(compose(g,domain(X0)),codomain(compose(g,domain(X0)))),
    inference(forward_demodulation,[status(thm)],[f20,f27582]) ).

fof(f27584,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(g,domain(X0))),ifeq(domain(a),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(forward_demodulation,[status(thm)],[f20,f27583]) ).

fof(f27680,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),g)),compose(compose(h,domain(X0)),g)),compose(compose(h,domain(X0)),g)) = compose(compose(h,domain(X0)),g),
    inference(paramodulation,[status(thm)],[f478,f2656]) ).

fof(f27681,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),compose(g,a))),compose(compose(h,domain(X0)),compose(g,a))),compose(compose(h,domain(X0)),compose(g,a))) = compose(compose(h,domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2656]) ).

fof(f27682,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),compose(h,a))),compose(compose(h,domain(X0)),compose(h,a))),compose(compose(h,domain(X0)),compose(h,a))) = compose(compose(h,domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2656]) ).

fof(f27710,plain,
    ! [X0] : ifeq(domain(X0),domain(codomain(compose(h,domain(X0)))),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(compose(h,domain(X0))))),compose(h,domain(X0))),compose(compose(h,domain(X0)),codomain(compose(h,domain(X0))))) = compose(compose(h,domain(X0)),codomain(compose(h,domain(X0)))),
    inference(paramodulation,[status(thm)],[f20,f2656]) ).

fof(f27862,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(h,domain(X0))),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(compose(h,domain(X0))))),compose(h,domain(X0))),compose(compose(h,domain(X0)),codomain(compose(h,domain(X0))))) = compose(compose(h,domain(X0)),codomain(compose(h,domain(X0)))),
    inference(forward_demodulation,[status(thm)],[f18,f27710]) ).

fof(f27863,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(h,domain(X0))),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(compose(h,domain(X0))))),compose(h,domain(X0))),compose(h,domain(X0))) = compose(compose(h,domain(X0)),codomain(compose(h,domain(X0)))),
    inference(forward_demodulation,[status(thm)],[f20,f27862]) ).

fof(f27864,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(h,domain(X0))),ifeq(domain(a),domain(X0),compose(h,compose(domain(X0),codomain(compose(h,domain(X0))))),compose(h,domain(X0))),compose(h,domain(X0))) = compose(h,domain(X0)),
    inference(forward_demodulation,[status(thm)],[f20,f27863]) ).

fof(f27957,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),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)],[f478,f2657]) ).

fof(f27958,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(g,a))),compose(compose(codomain(X1),domain(X0)),compose(g,a))),compose(compose(codomain(X1),domain(X0)),compose(g,a))) = compose(compose(codomain(X1),domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2657]) ).

fof(f27959,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(codomain(X1),domain(X0),compose(codomain(X1),compose(domain(X0),compose(h,a))),compose(compose(codomain(X1),domain(X0)),compose(h,a))),compose(compose(codomain(X1),domain(X0)),compose(h,a))) = compose(compose(codomain(X1),domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2657]) ).

fof(f28004,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)],[f20,f2657]) ).

fof(f28235,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)],[f18,f28004]) ).

fof(f28236,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)],[f20,f28235]) ).

fof(f28237,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)],[f20,f28236]) ).

fof(f28392,plain,
    ! [X0] : ifeq(domain(X0),domain(h),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)],[f478,f2658]) ).

fof(f28393,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(g,a))),compose(compose(a,domain(X0)),compose(g,a))),compose(compose(a,domain(X0)),compose(g,a))) = compose(compose(a,domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2658]) ).

fof(f28394,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(a,compose(domain(X0),compose(h,a))),compose(compose(a,domain(X0)),compose(h,a))),compose(compose(a,domain(X0)),compose(h,a))) = compose(compose(a,domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2658]) ).

fof(f28422,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)],[f20,f2658]) ).

fof(f28567,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)],[f18,f28422]) ).

fof(f28568,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)],[f20,f28567]) ).

fof(f28569,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)],[f20,f28568]) ).

fof(f28657,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),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)],[f478,f2659]) ).

fof(f28658,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(g,a))),compose(compose(domain(X1),domain(X0)),compose(g,a))),compose(compose(domain(X1),domain(X0)),compose(g,a))) = compose(compose(domain(X1),domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2659]) ).

fof(f28659,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(h),ifeq(domain(X1),domain(X0),compose(domain(X1),compose(domain(X0),compose(h,a))),compose(compose(domain(X1),domain(X0)),compose(h,a))),compose(compose(domain(X1),domain(X0)),compose(h,a))) = compose(compose(domain(X1),domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2659]) ).

fof(f28702,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)],[f20,f2659]) ).

fof(f28919,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)],[f18,f28702]) ).

fof(f28920,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)],[f20,f28919]) ).

fof(f28921,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)],[f20,f28920]) ).

fof(f29077,plain,
    ! [X0] : ifeq(domain(X0),domain(h),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(paramodulation,[status(thm)],[f478,f2784]) ).

fof(f29078,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(compose(domain(X0),compose(g,a))),domain(X0),compose(domain(X0),compose(g,a)),compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a))),compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a))) = compose(compose(domain(compose(domain(X0),compose(g,a))),domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2784]) ).

fof(f29079,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(compose(domain(X0),compose(h,a))),domain(X0),compose(domain(X0),compose(h,a)),compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a))),compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a))) = compose(compose(domain(compose(domain(X0),compose(h,a))),domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2784]) ).

fof(f29965,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(compose(g,a),domain(X0))),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),codomain(compose(compose(g,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)],[f1583,f2838]) ).

fof(f29966,plain,
    ! [X0] : ifeq(domain(X0),codomain(compose(compose(h,a),domain(X0))),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),codomain(compose(compose(h,a),domain(X0))))),compose(compose(h,a),domain(X0))),compose(compose(h,a),domain(X0))) = compose(compose(h,a),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f2838]) ).

fof(f29968,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)],[f975,f2838]) ).

fof(f30567,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f3030]) ).

fof(f30568,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f3030]) ).

fof(f30569,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f3030]) ).

fof(f30570,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f3030]) ).

fof(f30571,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(g,compose(h,compose(a,b))),compose(a,b))),compose(compose(g,compose(h,compose(a,b))),compose(a,b))) = compose(compose(g,compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f316,f3030]) ).

fof(f30572,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(h,compose(a,b))),compose(a,b))),compose(compose(h,compose(h,compose(a,b))),compose(a,b))) = compose(compose(h,compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f147,f3030]) ).

fof(f30573,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f36,f3030]) ).

fof(f30574,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(a,compose(h,compose(a,b))),compose(a,b))),compose(compose(a,compose(h,compose(a,b))),compose(a,b))) = compose(compose(a,compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f24,f3030]) ).

fof(f30575,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f17,f3030]) ).

fof(f30576,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(domain(compose(compose(h,compose(a,b)),compose(a,b)))),domain(h),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b)),
    inference(paramodulation,[status(thm)],[f19,f3030]) ).

fof(f30581,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(compose(compose(h,compose(a,b)),compose(a,b))),domain(h),compose(compose(h,compose(a,b)),compose(a,b)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(a,b))),compose(h,compose(a,b))),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f17,f30576]) ).

fof(f30606,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),h),compose(a,b))) = compose(compose(compose(g,a),h),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f3035]) ).

fof(f30607,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),h),compose(a,b))) = compose(compose(compose(h,a),h),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f3035]) ).

fof(f30608,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(compose(h,compose(a,b)),h),compose(a,b))) = compose(compose(compose(h,compose(a,b)),h),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f3035]) ).

fof(f30609,plain,
    ifeq(codomain(b),domain(h),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)),
    inference(paramodulation,[status(thm)],[f975,f3035]) ).

fof(f30610,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(g,h),compose(a,b))) = compose(compose(g,h),compose(a,b)),
    inference(paramodulation,[status(thm)],[f316,f3035]) ).

fof(f30611,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(h,h),compose(a,b))) = compose(compose(h,h),compose(a,b)),
    inference(paramodulation,[status(thm)],[f147,f3035]) ).

fof(f30612,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(codomain(X0),h),compose(a,b))) = compose(compose(codomain(X0),h),compose(a,b)),
    inference(paramodulation,[status(thm)],[f36,f3035]) ).

fof(f30613,plain,
    ifeq(domain(b),domain(h),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)],[f24,f3035]) ).

fof(f30614,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(a,b))),compose(compose(domain(X0),h),compose(a,b))) = compose(compose(domain(X0),h),compose(a,b)),
    inference(paramodulation,[status(thm)],[f17,f3035]) ).

fof(f30650,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),compose(a,b))),compose(compose(compose(g,a),codomain(X0)),compose(a,b))),compose(compose(compose(g,a),codomain(X0)),compose(a,b))) = compose(compose(compose(g,a),codomain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f3036]) ).

fof(f30651,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),compose(a,b))),compose(compose(compose(h,a),codomain(X0)),compose(a,b))),compose(compose(compose(h,a),codomain(X0)),compose(a,b))) = compose(compose(compose(h,a),codomain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f3036]) ).

fof(f30652,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),compose(a,b))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(a,b))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f3036]) ).

fof(f30653,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)],[f975,f3036]) ).

fof(f30654,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),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)],[f316,f3036]) ).

fof(f30655,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),compose(a,b))),compose(compose(h,codomain(X0)),compose(a,b))),compose(compose(h,codomain(X0)),compose(a,b))) = compose(compose(h,codomain(X0)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f147,f3036]) ).

fof(f30656,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)],[f36,f3036]) ).

fof(f30657,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)],[f24,f3036]) ).

fof(f30658,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)],[f17,f3036]) ).

fof(f30668,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(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)],[f19,f3036]) ).

fof(f30802,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(forward_demodulation,[status(thm)],[f17,f30668]) ).

fof(f30983,plain,
    ifeq(domain(b),domain(b),ifeq(compose(g,a),compose(codomain(compose(g,a)),a),g,codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f11403]) ).

fof(f31019,plain,
    ifeq(compose(g,a),compose(codomain(compose(g,a)),a),g,codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f30983]) ).

fof(f31020,plain,
    ifeq(compose(g,a),compose(domain(b),a),g,codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f31019]) ).

fof(f31021,plain,
    ifeq(compose(g,a),compose(domain(b),a),g,domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f31020]) ).

fof(f31022,plain,
    ifeq(compose(g,a),compose(domain(b),a),g,domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f31021]) ).

fof(f31340,plain,
    ifeq(domain(b),domain(b),ifeq(compose(h,a),compose(codomain(compose(g,a)),a),h,codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f11427]) ).

fof(f31376,plain,
    ifeq(compose(h,a),compose(codomain(compose(g,a)),a),h,codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f31340]) ).

fof(f31377,plain,
    ifeq(compose(h,a),compose(domain(b),a),h,codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f31376]) ).

fof(f31378,plain,
    ifeq(compose(h,a),compose(domain(b),a),h,domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f31377]) ).

fof(f31379,plain,
    ifeq(compose(h,a),compose(domain(b),a),h,domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f31378]) ).

fof(f31549,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(compose(g,a)),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2978]) ).

fof(f31550,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2978]) ).

fof(f31552,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(compose(a,b)),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f2978]) ).

fof(f31572,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f31549]) ).

fof(f31573,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f31550]) ).

fof(f31575,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f261,f31552]) ).

fof(f31628,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(compose(g,a),compose(a,b))),compose(compose(g,compose(g,a)),compose(a,b))),compose(compose(g,compose(g,a)),compose(a,b))) = compose(compose(g,compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2980]) ).

fof(f31629,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),compose(a,b))),compose(compose(g,compose(h,a)),compose(a,b))),compose(compose(g,compose(h,a)),compose(a,b))) = compose(compose(g,compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2980]) ).

fof(f31654,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(a,b))),compose(compose(g,compose(g,a)),compose(a,b))),compose(compose(g,compose(g,a)),compose(a,b))) = compose(compose(g,compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f31628]) ).

fof(f31655,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(a,b))),compose(compose(g,compose(h,a)),compose(a,b))),compose(compose(g,compose(h,a)),compose(a,b))) = compose(compose(g,compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f31629]) ).

fof(f31885,plain,
    ifeq(domain(b),domain(b),ifeq(compose(codomain(compose(g,a)),a),compose(g,a),g,codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f11452]) ).

fof(f31921,plain,
    ifeq(compose(codomain(compose(g,a)),a),compose(g,a),g,codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f31885]) ).

fof(f31922,plain,
    ifeq(compose(domain(b),a),compose(g,a),g,codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f31921]) ).

fof(f31923,plain,
    ifeq(compose(domain(b),a),compose(g,a),g,domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f31922]) ).

fof(f31924,plain,
    ifeq(compose(domain(b),a),compose(g,a),g,domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f31923]) ).

fof(f32082,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(compose(g,a),compose(a,b))),compose(compose(h,compose(g,a)),compose(a,b))),compose(compose(h,compose(g,a)),compose(a,b))) = compose(compose(h,compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2981]) ).

fof(f32083,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),compose(a,b))),compose(compose(h,compose(h,a)),compose(a,b))),compose(compose(h,compose(h,a)),compose(a,b))) = compose(compose(h,compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2981]) ).

fof(f32085,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(compose(a,b)),compose(h,compose(compose(a,b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f2981]) ).

fof(f32106,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(a,b))),compose(compose(h,compose(g,a)),compose(a,b))),compose(compose(h,compose(g,a)),compose(a,b))) = compose(compose(h,compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f32082]) ).

fof(f32107,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(a,b))),compose(compose(h,compose(h,a)),compose(a,b))),compose(compose(h,compose(h,a)),compose(a,b))) = compose(compose(h,compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f32083]) ).

fof(f32109,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(a),compose(h,compose(compose(a,b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f261,f32085]) ).

fof(f32110,plain,
    ifeq(codomain(b),domain(a),compose(h,compose(compose(a,b),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f16,f32109]) ).

fof(f32166,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(compose(g,a),compose(a,b))),compose(compose(codomain(X0),compose(g,a)),compose(a,b))),compose(compose(codomain(X0),compose(g,a)),compose(a,b))) = compose(compose(codomain(X0),compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2982]) ).

fof(f32167,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(compose(h,a),compose(a,b))),compose(compose(codomain(X0),compose(h,a)),compose(a,b))),compose(compose(codomain(X0),compose(h,a)),compose(a,b))) = compose(compose(codomain(X0),compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2982]) ).

fof(f32169,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(compose(a,b)),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)],[f975,f2982]) ).

fof(f32225,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(a,b))),compose(compose(codomain(X0),compose(g,a)),compose(a,b))),compose(compose(codomain(X0),compose(g,a)),compose(a,b))) = compose(compose(codomain(X0),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f32166]) ).

fof(f32226,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(a,b))),compose(compose(codomain(X0),compose(h,a)),compose(a,b))),compose(compose(codomain(X0),compose(h,a)),compose(a,b))) = compose(compose(codomain(X0),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f32167]) ).

fof(f32228,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(forward_demodulation,[status(thm)],[f261,f32169]) ).

fof(f32573,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(compose(g,a),compose(a,b))),compose(compose(a,compose(g,a)),compose(a,b))),compose(compose(a,compose(g,a)),compose(a,b))) = compose(compose(a,compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2983]) ).

fof(f32574,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),compose(a,b))),compose(compose(a,compose(h,a)),compose(a,b))),compose(compose(a,compose(h,a)),compose(a,b))) = compose(compose(a,compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2983]) ).

fof(f32576,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(b),domain(compose(a,b)),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)],[f975,f2983]) ).

fof(f32582,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)],[f16,f2983]) ).

fof(f32597,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(a,b))),compose(compose(a,compose(g,a)),compose(a,b))),compose(compose(a,compose(g,a)),compose(a,b))) = compose(compose(a,compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f32573]) ).

fof(f32598,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(a,b))),compose(compose(a,compose(h,a)),compose(a,b))),compose(compose(a,compose(h,a)),compose(a,b))) = compose(compose(a,compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f32574]) ).

fof(f32600,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(forward_demodulation,[status(thm)],[f261,f32576]) ).

fof(f32650,plain,
    ifeq(domain(b),domain(b),ifeq(compose(codomain(compose(g,a)),a),compose(h,a),h,codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f11478]) ).

fof(f32686,plain,
    ifeq(compose(codomain(compose(g,a)),a),compose(h,a),h,codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f32650]) ).

fof(f32687,plain,
    ifeq(compose(domain(b),a),compose(h,a),h,codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f32686]) ).

fof(f32688,plain,
    ifeq(compose(domain(b),a),compose(h,a),h,domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f32687]) ).

fof(f32689,plain,
    ifeq(compose(domain(b),a),compose(h,a),h,domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f32688]) ).

fof(f32847,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(compose(g,a),compose(a,b))),compose(compose(domain(X0),compose(g,a)),compose(a,b))),compose(compose(domain(X0),compose(g,a)),compose(a,b))) = compose(compose(domain(X0),compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f2984]) ).

fof(f32848,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(compose(h,a),compose(a,b))),compose(compose(domain(X0),compose(h,a)),compose(a,b))),compose(compose(domain(X0),compose(h,a)),compose(a,b))) = compose(compose(domain(X0),compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2984]) ).

fof(f32850,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(compose(a,b)),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)],[f975,f2984]) ).

fof(f32913,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(a,b))),compose(compose(domain(X0),compose(g,a)),compose(a,b))),compose(compose(domain(X0),compose(g,a)),compose(a,b))) = compose(compose(domain(X0),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f32847]) ).

fof(f32914,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(a,b))),compose(compose(domain(X0),compose(h,a)),compose(a,b))),compose(compose(domain(X0),compose(h,a)),compose(a,b))) = compose(compose(domain(X0),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f32848]) ).

fof(f32916,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(forward_demodulation,[status(thm)],[f261,f32850]) ).

fof(f33971,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(a,b))),compose(compose(compose(g,a),compose(a,b)),compose(a,b))),compose(compose(compose(g,a),compose(a,b)),compose(a,b))) = compose(compose(compose(g,a),compose(a,b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f3044]) ).

fof(f33972,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(a,b))),compose(compose(compose(h,a),compose(a,b)),compose(a,b))),compose(compose(compose(h,a),compose(a,b)),compose(a,b))) = compose(compose(compose(h,a),compose(a,b)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f3044]) ).

fof(f33974,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(paramodulation,[status(thm)],[f975,f3044]) ).

fof(f33980,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(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)],[f19,f3044]) ).

fof(f33991,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(forward_demodulation,[status(thm)],[f17,f33980]) ).

fof(f35063,plain,
    ifeq(domain(b),domain(a),ifeq(domain(compose(compose(g,a),compose(a,b))),domain(compose(g,a)),compose(compose(g,a),compose(a,b)),compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b))),compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b))) = compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f3047]) ).

fof(f35064,plain,
    ifeq(domain(b),domain(a),ifeq(domain(compose(compose(h,a),compose(a,b))),domain(compose(h,a)),compose(compose(h,a),compose(a,b)),compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b))),compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b))) = compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f3047]) ).

fof(f35094,plain,
    ifeq(domain(b),domain(a),ifeq(domain(compose(compose(g,a),compose(a,b))),domain(h),compose(compose(g,a),compose(a,b)),compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b))),compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b))) = compose(compose(domain(compose(compose(g,a),compose(a,b))),compose(g,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f2123,f35063]) ).

fof(f35095,plain,
    ifeq(domain(b),domain(a),ifeq(domain(compose(compose(h,a),compose(a,b))),domain(h),compose(compose(h,a),compose(a,b)),compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b))),compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b))) = compose(compose(domain(compose(compose(h,a),compose(a,b))),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f35064]) ).

fof(f35264,plain,
    ifeq(domain(a),domain(a),ifeq(compose(codomain(g),b),b,codomain(g),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f316,f21134]) ).

fof(f35299,plain,
    ifeq(compose(codomain(g),b),b,codomain(g),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f35264]) ).

fof(f35300,plain,
    ifeq(compose(domain(a),b),b,codomain(g),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f316,f35299]) ).

fof(f35301,plain,
    ifeq(compose(domain(a),b),b,domain(a),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f316,f35300]) ).

fof(f35461,plain,
    ifeq(domain(a),domain(a),ifeq(b,compose(codomain(g),b),codomain(g),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f316,f21158]) ).

fof(f35496,plain,
    ifeq(b,compose(codomain(g),b),codomain(g),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f35461]) ).

fof(f35497,plain,
    ifeq(b,compose(domain(a),b),codomain(g),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f316,f35496]) ).

fof(f35498,plain,
    ifeq(b,compose(domain(a),b),domain(a),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f316,f35497]) ).

fof(f36115,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),h),compose(compose(compose(g,a),h),domain(a))) = compose(compose(compose(g,a),h),domain(a)),
    inference(paramodulation,[status(thm)],[f1583,f297]) ).

fof(f36116,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),h),compose(compose(compose(h,a),h),domain(a))) = compose(compose(compose(h,a),h),domain(a)),
    inference(paramodulation,[status(thm)],[f1465,f297]) ).

fof(f36118,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),h),compose(compose(compose(a,b),h),domain(a))) = compose(compose(compose(a,b),h),domain(a)),
    inference(paramodulation,[status(thm)],[f975,f297]) ).

fof(f36133,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(X0,g),compose(compose(X0,g),domain(a))) = compose(compose(X0,g),domain(a)),
    inference(forward_demodulation,[status(thm)],[f478,f360]) ).

fof(f36134,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),g),compose(compose(compose(g,a),g),domain(a))) = compose(compose(compose(g,a),g),domain(a)),
    inference(paramodulation,[status(thm)],[f1583,f36133]) ).

fof(f36135,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),g),compose(compose(compose(h,a),g),domain(a))) = compose(compose(compose(h,a),g),domain(a)),
    inference(paramodulation,[status(thm)],[f1465,f36133]) ).

fof(f36137,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),g),compose(compose(compose(a,b),g),domain(a))) = compose(compose(compose(a,b),g),domain(a)),
    inference(paramodulation,[status(thm)],[f975,f36133]) ).

fof(f36163,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),g),compose(compose(compose(g,a),domain(h)),g)) = compose(compose(compose(g,a),domain(h)),g),
    inference(paramodulation,[status(thm)],[f1583,f547]) ).

fof(f36164,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),g),compose(compose(compose(h,a),domain(h)),g)) = compose(compose(compose(h,a),domain(h)),g),
    inference(paramodulation,[status(thm)],[f1465,f547]) ).

fof(f36166,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),g),compose(compose(compose(a,b),domain(h)),g)) = compose(compose(compose(a,b),domain(h)),g),
    inference(paramodulation,[status(thm)],[f975,f547]) ).

fof(f36721,plain,
    ifeq(codomain(b),domain(h),compose(a,compose(b,g)),compose(compose(a,b),g)) = compose(compose(a,b),g),
    inference(paramodulation,[status(thm)],[f478,f4171]) ).

fof(f36722,plain,
    ifeq(codomain(b),domain(h),compose(a,compose(b,compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4171]) ).

fof(f36723,plain,
    ifeq(codomain(b),domain(h),compose(a,compose(b,compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4171]) ).

fof(f36724,plain,
    ifeq(codomain(b),domain(h),compose(a,compose(b,compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4171]) ).

fof(f36726,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)],[f35,f4171]) ).

fof(f36727,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)],[f18,f4171]) ).

fof(f37477,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3697]) ).

fof(f37478,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3697]) ).

fof(f37479,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f3697]) ).

fof(f37480,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0))) = compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f975,f3697]) ).

fof(f37481,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(g,compose(h,compose(a,b))),codomain(X0))),compose(compose(g,compose(h,compose(a,b))),codomain(X0))) = compose(compose(g,compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f316,f3697]) ).

fof(f37482,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(h,compose(a,b))),codomain(X0))),compose(compose(h,compose(h,compose(a,b))),codomain(X0))) = compose(compose(h,compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f147,f3697]) ).

fof(f37483,plain,
    ! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0))) = compose(compose(codomain(X1),compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f36,f3697]) ).

fof(f37484,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(a,compose(h,compose(a,b))),codomain(X0))),compose(compose(a,compose(h,compose(a,b))),codomain(X0))) = compose(compose(a,compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f24,f3697]) ).

fof(f37485,plain,
    ! [X0,X1] : ifeq(codomain(b),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0))) = compose(compose(domain(X1),compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f17,f3697]) ).

fof(f37486,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(domain(compose(compose(h,compose(a,b)),codomain(X0)))),domain(h),compose(compose(h,compose(a,b)),codomain(X0)),compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0))),compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0))) = compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0)),
    inference(paramodulation,[status(thm)],[f19,f3697]) ).

fof(f37561,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(compose(compose(h,compose(a,b)),codomain(X0))),domain(h),compose(compose(h,compose(a,b)),codomain(X0)),compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0))),compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0))) = compose(compose(domain(compose(compose(h,compose(a,b)),codomain(X0))),compose(h,compose(a,b))),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f17,f37486]) ).

fof(f37708,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10538]) ).

fof(f37709,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10538]) ).

fof(f37710,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10538]) ).

fof(f37711,plain,
    ! [X0] : ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10538]) ).

fof(f37712,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(domain(a),b),X0,domain(a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10538]) ).

fof(f37713,plain,
    ! [X0] : ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(domain(a),b),X0,domain(a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10538]) ).

fof(f37714,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(domain(a),b),X1,domain(a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10538]) ).

fof(f37715,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(compose(a,b),X0,ifeq(compose(domain(a),b),X0,domain(a),a),a),a) = a,
    inference(paramodulation,[status(thm)],[f24,f10538]) ).

fof(f37716,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(domain(a),b),X1,domain(a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10538]) ).

fof(f37717,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(domain(a),b),compose(X0,b),domain(a),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f16,f10538]) ).

fof(f37720,plain,
    ! [X0] : ifeq(codomain(domain(b)),domain(b),ifeq(b,X0,ifeq(compose(domain(a),b),X0,domain(a),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f19,f10538]) ).

fof(f37723,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(domain(a),b),domain(a),X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f16,f10538]) ).

fof(f37726,plain,
    ! [X0] : ifeq(compose(compose(g,a),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f37708]) ).

fof(f37727,plain,
    ! [X0] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f37726]) ).

fof(f37728,plain,
    ! [X0] : ifeq(compose(compose(h,a),b),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f37709]) ).

fof(f37729,plain,
    ! [X0] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(domain(a),b),X0,domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f37728]) ).

fof(f37730,plain,
    ! [X0] : ifeq(compose(a,b),X0,ifeq(compose(domain(a),b),X0,domain(a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f16,f37715]) ).

fof(f37735,plain,
    ! [X0] : ifeq(domain(b),domain(b),ifeq(b,X0,ifeq(compose(domain(a),b),X0,domain(a),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f17,f37720]) ).

fof(f37736,plain,
    ! [X0] : ifeq(b,X0,ifeq(compose(domain(a),b),X0,domain(a),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f16,f37735]) ).

fof(f37752,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,codomain(X0))),compose(compose(compose(g,a),g),codomain(X0))),compose(compose(compose(g,a),g),codomain(X0))) = compose(compose(compose(g,a),g),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3699]) ).

fof(f37753,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,codomain(X0))),compose(compose(compose(h,a),g),codomain(X0))),compose(compose(compose(h,a),g),codomain(X0))) = compose(compose(compose(h,a),g),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3699]) ).

fof(f37754,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,codomain(X0))),compose(compose(compose(h,compose(a,b)),g),codomain(X0))),compose(compose(compose(h,compose(a,b)),g),codomain(X0))) = compose(compose(compose(h,compose(a,b)),g),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f3699]) ).

fof(f37755,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(b),domain(h),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)],[f975,f3699]) ).

fof(f37756,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(h),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)],[f316,f3699]) ).

fof(f37757,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(g,codomain(X0))),compose(compose(h,g),codomain(X0))),compose(compose(h,g),codomain(X0))) = compose(compose(h,g),codomain(X0)),
    inference(paramodulation,[status(thm)],[f147,f3699]) ).

fof(f37758,plain,
    ! [X0,X1] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(h),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)],[f36,f3699]) ).

fof(f37759,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(g,codomain(X0))),compose(compose(a,g),codomain(X0))),compose(compose(a,g),codomain(X0))) = compose(compose(a,g),codomain(X0)),
    inference(paramodulation,[status(thm)],[f24,f3699]) ).

fof(f37760,plain,
    ! [X0,X1] : ifeq(domain(a),codomain(X0),ifeq(domain(X1),domain(h),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)],[f17,f3699]) ).

fof(f37761,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(domain(compose(g,codomain(X0)))),domain(h),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)],[f19,f3699]) ).

fof(f37833,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(compose(g,codomain(X0))),domain(h),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)],[f17,f37761]) ).

fof(f37989,plain,
    ifeq(domain(b),domain(b),ifeq(compose(domain(a),b),compose(compose(g,a),b),domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f37717]) ).

fof(f37990,plain,
    ifeq(domain(b),domain(b),ifeq(compose(domain(a),b),compose(compose(h,a),b),domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f37717]) ).

fof(f37991,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(domain(a),b),compose(compose(h,compose(a,b)),b),domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f37717]) ).

fof(f37992,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(domain(a),b),compose(compose(a,b),b),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f37717]) ).

fof(f37993,plain,
    ifeq(domain(a),domain(b),ifeq(compose(domain(a),b),compose(g,b),domain(a),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f37717]) ).

fof(f37994,plain,
    ifeq(domain(a),domain(b),ifeq(compose(domain(a),b),compose(h,b),domain(a),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f37717]) ).

fof(f37995,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(domain(a),b),compose(codomain(X0),b),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f37717]) ).

fof(f37997,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(domain(a),b),compose(domain(X0),b),domain(a),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f37717]) ).

fof(f38005,plain,
    ifeq(compose(domain(a),b),compose(compose(g,a),b),domain(a),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f37989]) ).

fof(f38006,plain,
    ifeq(compose(domain(a),b),compose(h,compose(a,b)),domain(a),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f38005]) ).

fof(f38007,plain,
    ifeq(compose(domain(a),b),compose(compose(h,a),b),domain(a),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f37990]) ).

fof(f38008,plain,
    ifeq(compose(domain(a),b),compose(h,compose(a,b)),domain(a),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f38007]) ).

fof(f38021,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(domain(a),b),domain(a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f37723]) ).

fof(f38022,plain,
    ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(domain(a),b),domain(a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f37723]) ).

fof(f38023,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(domain(a),b),domain(a),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f37723]) ).

fof(f38024,plain,
    ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(domain(a),b),domain(a),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f37723]) ).

fof(f38025,plain,
    ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(domain(a),b),domain(a),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f37723]) ).

fof(f38026,plain,
    ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(domain(a),b),domain(a),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f37723]) ).

fof(f38027,plain,
    ! [X0] : ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(domain(a),b),domain(a),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f37723]) ).

fof(f38029,plain,
    ! [X0] : ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(domain(a),b),domain(a),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f37723]) ).

fof(f38038,plain,
    ifeq(compose(compose(g,a),b),compose(domain(a),b),domain(a),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f38021]) ).

fof(f38039,plain,
    ifeq(compose(h,compose(a,b)),compose(domain(a),b),domain(a),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f38038]) ).

fof(f38040,plain,
    ifeq(compose(compose(h,a),b),compose(domain(a),b),domain(a),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f38022]) ).

fof(f38041,plain,
    ifeq(compose(h,compose(a,b)),compose(domain(a),b),domain(a),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f38040]) ).

fof(f38068,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,codomain(X0))),compose(compose(compose(g,a),h),codomain(X0))),compose(compose(compose(g,a),h),codomain(X0))) = compose(compose(compose(g,a),h),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3596]) ).

fof(f38069,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,codomain(X0))),compose(compose(compose(h,a),h),codomain(X0))),compose(compose(compose(h,a),h),codomain(X0))) = compose(compose(compose(h,a),h),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3596]) ).

fof(f38070,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,codomain(X0))),compose(compose(compose(h,compose(a,b)),h),codomain(X0))),compose(compose(compose(h,compose(a,b)),h),codomain(X0))) = compose(compose(compose(h,compose(a,b)),h),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f3596]) ).

fof(f38071,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(b),domain(h),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)],[f975,f3596]) ).

fof(f38072,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(h),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)],[f316,f3596]) ).

fof(f38073,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(h,codomain(X0))),compose(compose(h,h),codomain(X0))),compose(compose(h,h),codomain(X0))) = compose(compose(h,h),codomain(X0)),
    inference(paramodulation,[status(thm)],[f147,f3596]) ).

fof(f38074,plain,
    ! [X0,X1] : ifeq(domain(a),codomain(X0),ifeq(codomain(X1),domain(h),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)],[f36,f3596]) ).

fof(f38075,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(h,codomain(X0))),compose(compose(a,h),codomain(X0))),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0)),
    inference(paramodulation,[status(thm)],[f24,f3596]) ).

fof(f38076,plain,
    ! [X0,X1] : ifeq(domain(a),codomain(X0),ifeq(domain(X1),domain(h),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)],[f17,f3596]) ).

fof(f38077,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(codomain(domain(compose(h,codomain(X0)))),domain(h),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)],[f19,f3596]) ).

fof(f38145,plain,
    ! [X0] : ifeq(domain(a),codomain(X0),ifeq(domain(compose(h,codomain(X0))),domain(h),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)],[f17,f38077]) ).

fof(f38271,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(b,compose(compose(g,a),b),domain(b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10998]) ).

fof(f38272,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(b,compose(compose(h,a),b),domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10998]) ).

fof(f38273,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(b,compose(compose(h,compose(a,b)),b),domain(b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10998]) ).

fof(f38274,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(b,compose(compose(a,b),b),domain(b),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10998]) ).

fof(f38275,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(b,compose(g,b),domain(b),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10998]) ).

fof(f38276,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(b,compose(h,b),domain(b),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10998]) ).

fof(f38277,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(b,compose(codomain(X0),b),domain(b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10998]) ).

fof(f38279,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(b,compose(domain(X0),b),domain(b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10998]) ).

fof(f38283,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(compose(g,a),b),domain(b),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f38271]) ).

fof(f38284,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(h,compose(a,b)),domain(b),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f38283]) ).

fof(f38285,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(compose(h,a),b),domain(b),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f38272]) ).

fof(f38286,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(h,compose(a,b)),domain(b),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f38285]) ).

fof(f38295,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),b,domain(b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f11330]) ).

fof(f38296,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),b,domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f11330]) ).

fof(f38297,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),b,domain(b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f11330]) ).

fof(f38298,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),b,domain(b),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f11330]) ).

fof(f38299,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),b,domain(b),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f11330]) ).

fof(f38300,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),b,domain(b),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f11330]) ).

fof(f38301,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),b,domain(b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f11330]) ).

fof(f38303,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),b,domain(b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f11330]) ).

fof(f38307,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),b,domain(b),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f38295]) ).

fof(f38308,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),b,domain(b),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f38307]) ).

fof(f38309,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),b,domain(b),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f38296]) ).

fof(f38310,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),b,domain(b),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f38309]) ).

fof(f38339,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),codomain(X1))),compose(compose(compose(g,a),codomain(X0)),codomain(X1))),compose(compose(compose(g,a),codomain(X0)),codomain(X1))) = compose(compose(compose(g,a),codomain(X0)),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1583,f3700]) ).

fof(f38340,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),codomain(X1))),compose(compose(compose(h,a),codomain(X0)),codomain(X1))),compose(compose(compose(h,a),codomain(X0)),codomain(X1))) = compose(compose(compose(h,a),codomain(X0)),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1465,f3700]) ).

fof(f38341,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),codomain(X1))),compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X1))),compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X1))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(X1)),
    inference(paramodulation,[status(thm)],[f1016,f3700]) ).

fof(f38342,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)],[f975,f3700]) ).

fof(f38343,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(a),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)],[f316,f3700]) ).

fof(f38344,plain,
    ! [X0,X1] : ifeq(codomain(X0),codomain(X1),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(X1))),compose(compose(h,codomain(X0)),codomain(X1))),compose(compose(h,codomain(X0)),codomain(X1))) = compose(compose(h,codomain(X0)),codomain(X1)),
    inference(paramodulation,[status(thm)],[f147,f3700]) ).

fof(f38345,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)],[f36,f3700]) ).

fof(f38346,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,f3700]) ).

fof(f38347,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)],[f17,f3700]) ).

fof(f38357,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)],[f19,f3700]) ).

fof(f38556,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)],[f17,f38357]) ).

fof(f39239,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(compose(g,a)),compose(compose(h,compose(a,b)),compose(compose(g,a),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3611]) ).

fof(f39240,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3611]) ).

fof(f39242,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(compose(a,b)),compose(compose(h,compose(a,b)),compose(compose(a,b),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f975,f3611]) ).

fof(f39304,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f39239]) ).

fof(f39305,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f39240]) ).

fof(f39307,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f261,f39242]) ).

fof(f39508,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),h),a)) = compose(compose(compose(g,a),h),a),
    inference(paramodulation,[status(thm)],[f1583,f15913]) ).

fof(f39509,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),h),a)) = compose(compose(compose(h,a),h),a),
    inference(paramodulation,[status(thm)],[f1465,f15913]) ).

fof(f39510,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(compose(h,compose(a,b)),h),a)) = compose(compose(compose(h,compose(a,b)),h),a),
    inference(paramodulation,[status(thm)],[f1016,f15913]) ).

fof(f39511,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),h),a)) = compose(compose(compose(a,b),h),a),
    inference(paramodulation,[status(thm)],[f975,f15913]) ).

fof(f39512,plain,
    ifeq(domain(a),domain(h),compose(g,compose(h,a)),compose(compose(g,h),a)) = compose(compose(g,h),a),
    inference(paramodulation,[status(thm)],[f316,f15913]) ).

fof(f39513,plain,
    ifeq(domain(a),domain(h),compose(h,compose(h,a)),compose(compose(h,h),a)) = compose(compose(h,h),a),
    inference(paramodulation,[status(thm)],[f147,f15913]) ).

fof(f39514,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,a)),compose(compose(codomain(X0),h),a)) = compose(compose(codomain(X0),h),a),
    inference(paramodulation,[status(thm)],[f36,f15913]) ).

fof(f39515,plain,
    ifeq(domain(b),domain(h),compose(a,compose(h,a)),compose(compose(a,h),a)) = compose(compose(a,h),a),
    inference(paramodulation,[status(thm)],[f24,f15913]) ).

fof(f39516,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,a)),compose(compose(domain(X0),h),a)) = compose(compose(domain(X0),h),a),
    inference(paramodulation,[status(thm)],[f17,f15913]) ).

fof(f39533,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(compose(g,a),codomain(X0))),compose(compose(g,compose(g,a)),codomain(X0))),compose(compose(g,compose(g,a)),codomain(X0))) = compose(compose(g,compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3613]) ).

fof(f39534,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),codomain(X0))),compose(compose(g,compose(h,a)),codomain(X0))),compose(compose(g,compose(h,a)),codomain(X0))) = compose(compose(g,compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3613]) ).

fof(f39601,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),codomain(X0))),compose(compose(g,compose(g,a)),codomain(X0))),compose(compose(g,compose(g,a)),codomain(X0))) = compose(compose(g,compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f39533]) ).

fof(f39602,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),codomain(X0))),compose(compose(g,compose(h,a)),codomain(X0))),compose(compose(g,compose(h,a)),codomain(X0))) = compose(compose(g,compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f39534]) ).

fof(f39822,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),g),a)) = compose(compose(compose(g,a),g),a),
    inference(paramodulation,[status(thm)],[f1583,f16195]) ).

fof(f39823,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),g),a)) = compose(compose(compose(h,a),g),a),
    inference(paramodulation,[status(thm)],[f1465,f16195]) ).

fof(f39824,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(compose(h,compose(a,b)),g),a)) = compose(compose(compose(h,compose(a,b)),g),a),
    inference(paramodulation,[status(thm)],[f1016,f16195]) ).

fof(f39825,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),g),a)) = compose(compose(compose(a,b),g),a),
    inference(paramodulation,[status(thm)],[f975,f16195]) ).

fof(f39826,plain,
    ifeq(domain(a),domain(h),compose(g,compose(g,a)),compose(compose(g,g),a)) = compose(compose(g,g),a),
    inference(paramodulation,[status(thm)],[f316,f16195]) ).

fof(f39827,plain,
    ifeq(domain(a),domain(h),compose(h,compose(g,a)),compose(compose(h,g),a)) = compose(compose(h,g),a),
    inference(paramodulation,[status(thm)],[f147,f16195]) ).

fof(f39828,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,a)),compose(compose(codomain(X0),g),a)) = compose(compose(codomain(X0),g),a),
    inference(paramodulation,[status(thm)],[f36,f16195]) ).

fof(f39829,plain,
    ifeq(domain(b),domain(h),compose(a,compose(g,a)),compose(compose(a,g),a)) = compose(compose(a,g),a),
    inference(paramodulation,[status(thm)],[f24,f16195]) ).

fof(f39830,plain,
    ! [X0] : ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,a)),compose(compose(domain(X0),g),a)) = compose(compose(domain(X0),g),a),
    inference(paramodulation,[status(thm)],[f17,f16195]) ).

fof(f39851,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(compose(g,a),codomain(X0))),compose(compose(h,compose(g,a)),codomain(X0))),compose(compose(h,compose(g,a)),codomain(X0))) = compose(compose(h,compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3614]) ).

fof(f39852,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),codomain(X0))),compose(compose(h,compose(h,a)),codomain(X0))),compose(compose(h,compose(h,a)),codomain(X0))) = compose(compose(h,compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3614]) ).

fof(f39854,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(compose(a,b)),compose(h,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f975,f3614]) ).

fof(f39919,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),codomain(X0))),compose(compose(h,compose(g,a)),codomain(X0))),compose(compose(h,compose(g,a)),codomain(X0))) = compose(compose(h,compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f39851]) ).

fof(f39920,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),codomain(X0))),compose(compose(h,compose(h,a)),codomain(X0))),compose(compose(h,compose(h,a)),codomain(X0))) = compose(compose(h,compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f39852]) ).

fof(f39922,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(a),domain(a),compose(h,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f261,f39854]) ).

fof(f39923,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),compose(h,compose(compose(a,b),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f39922]) ).

fof(f40136,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(compose(g,a)),compose(codomain(X1),compose(compose(g,a),codomain(X0))),compose(compose(codomain(X1),compose(g,a)),codomain(X0))),compose(compose(codomain(X1),compose(g,a)),codomain(X0))) = compose(compose(codomain(X1),compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3615]) ).

fof(f40137,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(compose(h,a)),compose(codomain(X1),compose(compose(h,a),codomain(X0))),compose(compose(codomain(X1),compose(h,a)),codomain(X0))),compose(compose(codomain(X1),compose(h,a)),codomain(X0))) = compose(compose(codomain(X1),compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3615]) ).

fof(f40139,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)],[f975,f3615]) ).

fof(f40237,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(g,a),codomain(X0))),compose(compose(codomain(X1),compose(g,a)),codomain(X0))),compose(compose(codomain(X1),compose(g,a)),codomain(X0))) = compose(compose(codomain(X1),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f40136]) ).

fof(f40238,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,a),codomain(X0))),compose(compose(codomain(X1),compose(h,a)),codomain(X0))),compose(compose(codomain(X1),compose(h,a)),codomain(X0))) = compose(compose(codomain(X1),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f40137]) ).

fof(f40240,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)],[f261,f40139]) ).

fof(f40583,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(compose(g,a),codomain(X0))),compose(compose(a,compose(g,a)),codomain(X0))),compose(compose(a,compose(g,a)),codomain(X0))) = compose(compose(a,compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3616]) ).

fof(f40584,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),codomain(X0))),compose(compose(a,compose(h,a)),codomain(X0))),compose(compose(a,compose(h,a)),codomain(X0))) = compose(compose(a,compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3616]) ).

fof(f40586,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)],[f975,f3616]) ).

fof(f40651,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),codomain(X0))),compose(compose(a,compose(g,a)),codomain(X0))),compose(compose(a,compose(g,a)),codomain(X0))) = compose(compose(a,compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f40583]) ).

fof(f40652,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),codomain(X0))),compose(compose(a,compose(h,a)),codomain(X0))),compose(compose(a,compose(h,a)),codomain(X0))) = compose(compose(a,compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f40584]) ).

fof(f40654,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)],[f261,f40586]) ).

fof(f41319,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(domain(X1),domain(compose(g,a)),compose(domain(X1),compose(compose(g,a),codomain(X0))),compose(compose(domain(X1),compose(g,a)),codomain(X0))),compose(compose(domain(X1),compose(g,a)),codomain(X0))) = compose(compose(domain(X1),compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3617]) ).

fof(f41320,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(domain(X1),domain(compose(h,a)),compose(domain(X1),compose(compose(h,a),codomain(X0))),compose(compose(domain(X1),compose(h,a)),codomain(X0))),compose(compose(domain(X1),compose(h,a)),codomain(X0))) = compose(compose(domain(X1),compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3617]) ).

fof(f41322,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)],[f975,f3617]) ).

fof(f41426,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(g,a),codomain(X0))),compose(compose(domain(X1),compose(g,a)),codomain(X0))),compose(compose(domain(X1),compose(g,a)),codomain(X0))) = compose(compose(domain(X1),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f41319]) ).

fof(f41427,plain,
    ! [X0,X1] : ifeq(domain(b),codomain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,a),codomain(X0))),compose(compose(domain(X1),compose(h,a)),codomain(X0))),compose(compose(domain(X1),compose(h,a)),codomain(X0))) = compose(compose(domain(X1),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f41320]) ).

fof(f41429,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)],[f261,f41322]) ).

fof(f41801,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),codomain(X0))),compose(compose(compose(g,a),compose(a,b)),codomain(X0))),compose(compose(compose(g,a),compose(a,b)),codomain(X0))) = compose(compose(compose(g,a),compose(a,b)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3742]) ).

fof(f41802,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),codomain(X0))),compose(compose(compose(h,a),compose(a,b)),codomain(X0))),compose(compose(compose(h,a),compose(a,b)),codomain(X0))) = compose(compose(compose(h,a),compose(a,b)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3742]) ).

fof(f41804,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)],[f975,f3742]) ).

fof(f41810,plain,
    ! [X0] : ifeq(codomain(b),codomain(X0),ifeq(codomain(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(paramodulation,[status(thm)],[f19,f3742]) ).

fof(f41893,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)],[f17,f41810]) ).

fof(f42053,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(compose(compose(g,a),codomain(X0))),domain(compose(g,a)),compose(compose(g,a),codomain(X0)),compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0))),compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0))) = compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3745]) ).

fof(f42054,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(compose(compose(h,a),codomain(X0))),domain(compose(h,a)),compose(compose(h,a),codomain(X0)),compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0))),compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0))) = compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3745]) ).

fof(f42158,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(compose(compose(g,a),codomain(X0))),domain(h),compose(compose(g,a),codomain(X0)),compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0))),compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0))) = compose(compose(domain(compose(compose(g,a),codomain(X0))),compose(g,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f42053]) ).

fof(f42159,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(compose(compose(h,a),codomain(X0))),domain(h),compose(compose(h,a),codomain(X0)),compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0))),compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0))) = compose(compose(domain(compose(compose(h,a),codomain(X0))),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f42054]) ).

fof(f44375,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),g)),compose(compose(a,compose(h,compose(a,b))),g)),compose(compose(a,compose(h,compose(a,b))),g)) = compose(compose(a,compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f478,f4205]) ).

fof(f44376,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(a,compose(h,compose(a,b))),compose(g,a))),compose(compose(a,compose(h,compose(a,b))),compose(g,a))) = compose(compose(a,compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4205]) ).

fof(f44377,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(a,compose(h,compose(a,b))),compose(h,a))),compose(compose(a,compose(h,compose(a,b))),compose(h,a))) = compose(compose(a,compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4205]) ).

fof(f44378,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(a,compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4205]) ).

fof(f44380,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(a,compose(h,compose(a,b))),domain(X0))),compose(compose(a,compose(h,compose(a,b))),domain(X0))) = compose(compose(a,compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f35,f4205]) ).

fof(f44384,plain,
    ifeq(codomain(b),domain(codomain(compose(a,compose(h,compose(a,b))))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(compose(a,compose(h,compose(a,b)))))),compose(a,compose(h,compose(a,b)))),compose(compose(a,compose(h,compose(a,b))),codomain(compose(a,compose(h,compose(a,b)))))) = compose(compose(a,compose(h,compose(a,b))),codomain(compose(a,compose(h,compose(a,b))))),
    inference(paramodulation,[status(thm)],[f20,f4205]) ).

fof(f44393,plain,
    ifeq(codomain(b),codomain(compose(a,compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(compose(a,compose(h,compose(a,b)))))),compose(a,compose(h,compose(a,b)))),compose(compose(a,compose(h,compose(a,b))),codomain(compose(a,compose(h,compose(a,b)))))) = compose(compose(a,compose(h,compose(a,b))),codomain(compose(a,compose(h,compose(a,b))))),
    inference(forward_demodulation,[status(thm)],[f18,f44384]) ).

fof(f44394,plain,
    ifeq(codomain(b),codomain(compose(a,compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(compose(a,compose(h,compose(a,b)))))),compose(a,compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(compose(a,compose(h,compose(a,b))),codomain(compose(a,compose(h,compose(a,b))))),
    inference(forward_demodulation,[status(thm)],[f20,f44393]) ).

fof(f44395,plain,
    ifeq(codomain(b),codomain(compose(a,compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,compose(a,b)),codomain(compose(a,compose(h,compose(a,b)))))),compose(a,compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f20,f44394]) ).

fof(f44400,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,g)),compose(compose(a,g),g)),compose(compose(a,g),g)) = compose(compose(a,g),g),
    inference(paramodulation,[status(thm)],[f478,f4207]) ).

fof(f44401,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,compose(g,a))),compose(compose(a,g),compose(g,a))),compose(compose(a,g),compose(g,a))) = compose(compose(a,g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4207]) ).

fof(f44402,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,compose(h,a))),compose(compose(a,g),compose(h,a))),compose(compose(a,g),compose(h,a))) = compose(compose(a,g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4207]) ).

fof(f44403,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(g,compose(h,compose(a,b)))),compose(compose(a,g),compose(h,compose(a,b)))),compose(compose(a,g),compose(h,compose(a,b)))) = compose(compose(a,g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4207]) ).

fof(f44405,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(g,domain(X0))),compose(compose(a,g),domain(X0))),compose(compose(a,g),domain(X0))) = compose(compose(a,g),domain(X0)),
    inference(paramodulation,[status(thm)],[f35,f4207]) ).

fof(f44410,plain,
    ifeq(domain(a),domain(codomain(compose(a,g))),ifeq(domain(b),domain(h),compose(a,compose(g,codomain(compose(a,g)))),compose(a,g)),compose(compose(a,g),codomain(compose(a,g)))) = compose(compose(a,g),codomain(compose(a,g))),
    inference(paramodulation,[status(thm)],[f20,f4207]) ).

fof(f44424,plain,
    ifeq(domain(a),codomain(compose(a,g)),ifeq(domain(b),domain(h),compose(a,compose(g,codomain(compose(a,g)))),compose(a,g)),compose(compose(a,g),codomain(compose(a,g)))) = compose(compose(a,g),codomain(compose(a,g))),
    inference(forward_demodulation,[status(thm)],[f18,f44410]) ).

fof(f44425,plain,
    ifeq(domain(a),codomain(compose(a,g)),ifeq(domain(b),domain(h),compose(a,compose(g,codomain(compose(a,g)))),compose(a,g)),compose(a,g)) = compose(compose(a,g),codomain(compose(a,g))),
    inference(forward_demodulation,[status(thm)],[f20,f44424]) ).

fof(f44426,plain,
    ifeq(domain(a),codomain(compose(a,g)),ifeq(domain(b),domain(h),compose(a,compose(g,codomain(compose(a,g)))),compose(a,g)),compose(a,g)) = compose(a,g),
    inference(forward_demodulation,[status(thm)],[f20,f44425]) ).

fof(f44431,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(h,g)),compose(compose(a,h),g)),compose(compose(a,h),g)) = compose(compose(a,h),g),
    inference(paramodulation,[status(thm)],[f478,f4160]) ).

fof(f44432,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(h,compose(g,a))),compose(compose(a,h),compose(g,a))),compose(compose(a,h),compose(g,a))) = compose(compose(a,h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4160]) ).

fof(f44433,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(h,compose(h,a))),compose(compose(a,h),compose(h,a))),compose(compose(a,h),compose(h,a))) = compose(compose(a,h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4160]) ).

fof(f44434,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(a,compose(h,compose(h,compose(a,b)))),compose(compose(a,h),compose(h,compose(a,b)))),compose(compose(a,h),compose(h,compose(a,b)))) = compose(compose(a,h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4160]) ).

fof(f44436,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(h,domain(X0))),compose(compose(a,h),domain(X0))),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0)),
    inference(paramodulation,[status(thm)],[f35,f4160]) ).

fof(f44440,plain,
    ifeq(domain(a),domain(codomain(compose(a,h))),ifeq(domain(b),domain(h),compose(a,compose(h,codomain(compose(a,h)))),compose(a,h)),compose(compose(a,h),codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h))),
    inference(paramodulation,[status(thm)],[f20,f4160]) ).

fof(f44449,plain,
    ifeq(domain(a),codomain(compose(a,h)),ifeq(domain(b),domain(h),compose(a,compose(h,codomain(compose(a,h)))),compose(a,h)),compose(compose(a,h),codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h))),
    inference(forward_demodulation,[status(thm)],[f18,f44440]) ).

fof(f44450,plain,
    ifeq(domain(a),codomain(compose(a,h)),ifeq(domain(b),domain(h),compose(a,compose(h,codomain(compose(a,h)))),compose(a,h)),compose(a,h)) = compose(compose(a,h),codomain(compose(a,h))),
    inference(forward_demodulation,[status(thm)],[f20,f44449]) ).

fof(f44451,plain,
    ifeq(domain(a),codomain(compose(a,h)),ifeq(domain(b),domain(h),compose(a,compose(h,codomain(compose(a,h)))),compose(a,h)),compose(a,h)) = compose(a,h),
    inference(forward_demodulation,[status(thm)],[f20,f44450]) ).

fof(f44464,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),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)],[f478,f4208]) ).

fof(f44465,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(g,a))),compose(compose(a,codomain(X0)),compose(g,a))),compose(compose(a,codomain(X0)),compose(g,a))) = compose(compose(a,codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4208]) ).

fof(f44466,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(h,a))),compose(compose(a,codomain(X0)),compose(h,a))),compose(compose(a,codomain(X0)),compose(h,a))) = compose(compose(a,codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4208]) ).

fof(f44467,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(a,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(a,codomain(X0)),compose(h,compose(a,b)))),compose(compose(a,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(a,codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4208]) ).

fof(f44469,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)],[f35,f4208]) ).

fof(f44491,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)],[f20,f4208]) ).

fof(f44667,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)],[f18,f44491]) ).

fof(f44668,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)],[f20,f44667]) ).

fof(f44669,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)],[f20,f44668]) ).

fof(f44798,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(a,compose(g,a)),compose(h,compose(a,b)))),compose(compose(a,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(a,compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f4167]) ).

fof(f44799,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(a,compose(h,a)),compose(h,compose(a,b)))),compose(compose(a,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(a,compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f4167]) ).

fof(f44801,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(compose(a,b)),compose(a,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(a,compose(a,b)),compose(h,compose(a,b)))),compose(compose(a,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f4167]) ).

fof(f44821,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(a,compose(g,a)),compose(h,compose(a,b)))),compose(compose(a,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(a,compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f2123,f44798]) ).

fof(f44822,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(a,compose(h,a)),compose(h,compose(a,b)))),compose(compose(a,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(a,compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f44799]) ).

fof(f44824,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(a,compose(a,b)),compose(h,compose(a,b)))),compose(compose(a,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(a,compose(a,b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f261,f44801]) ).

fof(f44875,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,a),compose(compose(g,a),a),a,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f9714]) ).

fof(f44876,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,a),compose(compose(h,a),a),a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f9714]) ).

fof(f44877,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(a,a),compose(compose(h,compose(a,b)),a),a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f9714]) ).

fof(f44878,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(a,a),compose(compose(a,b),a),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f9714]) ).

fof(f44879,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,a),compose(g,a),a,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f9714]) ).

fof(f44880,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,a),compose(h,a),a,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f9714]) ).

fof(f44881,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(a,a),compose(codomain(X0),a),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f9714]) ).

fof(f44883,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(a,a),compose(domain(X0),a),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f9714]) ).

fof(f44885,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(compose(a,a),a,a,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f9714]) ).

fof(f44886,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(compose(g,a),a),a,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f44875]) ).

fof(f44887,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(compose(h,a),a),a,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f44876]) ).

fof(f44892,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,a),a,a,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f44885]) ).

fof(f44894,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),compose(a,a),a,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f9716]) ).

fof(f44895,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),compose(a,a),a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f9716]) ).

fof(f44896,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(a,a),a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f9716]) ).

fof(f44897,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(a,a),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f9716]) ).

fof(f44898,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(a,a),a,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f9716]) ).

fof(f44899,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(a,a),a,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f9716]) ).

fof(f44900,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(a,a),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f9716]) ).

fof(f44902,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(a,a),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f9716]) ).

fof(f44904,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(a,compose(a,a),a,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f9716]) ).

fof(f44906,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(a,a),a,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f44894]) ).

fof(f44907,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(a,a),a,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f44895]) ).

fof(f44912,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(a,a),a,domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f44904]) ).

fof(f44913,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(compose(g,a),domain(X0))),compose(compose(a,compose(g,a)),domain(X0))),compose(compose(a,compose(g,a)),domain(X0))) = compose(compose(a,compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f4169]) ).

fof(f44914,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),domain(X0))),compose(compose(a,compose(h,a)),domain(X0))),compose(compose(a,compose(h,a)),domain(X0))) = compose(compose(a,compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f4169]) ).

fof(f44916,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)],[f975,f4169]) ).

fof(f44969,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),domain(X0))),compose(compose(a,compose(g,a)),domain(X0))),compose(compose(a,compose(g,a)),domain(X0))) = compose(compose(a,compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f44913]) ).

fof(f44970,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),domain(X0))),compose(compose(a,compose(h,a)),domain(X0))),compose(compose(a,compose(h,a)),domain(X0))) = compose(compose(a,compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f44914]) ).

fof(f44972,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)],[f261,f44916]) ).

fof(f45143,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,b),compose(compose(g,a),b),a,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10526]) ).

fof(f45144,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(a,b),compose(compose(h,a),b),a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10526]) ).

fof(f45145,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(a,b),compose(compose(h,compose(a,b)),b),a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10526]) ).

fof(f45146,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(a,b),compose(compose(a,b),b),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10526]) ).

fof(f45147,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,b),compose(g,b),a,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10526]) ).

fof(f45148,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(a,b),compose(h,b),a,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10526]) ).

fof(f45149,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(a,b),compose(codomain(X0),b),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10526]) ).

fof(f45151,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(a,b),compose(domain(X0),b),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10526]) ).

fof(f45156,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(compose(g,a),b),a,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f45143]) ).

fof(f45157,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(h,compose(a,b)),a,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f45156]) ).

fof(f45158,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(compose(h,a),b),a,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f45144]) ).

fof(f45159,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(h,compose(a,b)),a,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f45158]) ).

fof(f45171,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(a,b),a,compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10529]) ).

fof(f45172,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(a,b),a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10529]) ).

fof(f45173,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(a,b),a,compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10529]) ).

fof(f45174,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(a,b),a,compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10529]) ).

fof(f45175,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(a,b),a,g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10529]) ).

fof(f45176,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(a,b),a,h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10529]) ).

fof(f45177,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(a,b),a,codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f36,f10529]) ).

fof(f45179,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(a,b),a,domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f17,f10529]) ).

fof(f45185,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),compose(a,b),a,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f45171]) ).

fof(f45186,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(a,b),a,compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f45185]) ).

fof(f45187,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),compose(a,b),a,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f45172]) ).

fof(f45188,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(a,b),a,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f45187]) ).

fof(f45199,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(h,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f13561]) ).

fof(f45202,plain,
    ifeq(codomain(b),domain(h),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(paramodulation,[status(thm)],[f478,f4214]) ).

fof(f45203,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(g,a))),compose(compose(a,compose(a,b)),compose(g,a))),compose(compose(a,compose(a,b)),compose(g,a))) = compose(compose(a,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4214]) ).

fof(f45204,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(a,compose(compose(a,b),compose(h,a))),compose(compose(a,compose(a,b)),compose(h,a))),compose(compose(a,compose(a,b)),compose(h,a))) = compose(compose(a,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4214]) ).

fof(f45211,plain,
    ifeq(codomain(b),domain(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(compose(a,compose(a,b)),codomain(compose(a,compose(a,b))))) = compose(compose(a,compose(a,b)),codomain(compose(a,compose(a,b)))),
    inference(paramodulation,[status(thm)],[f20,f4214]) ).

fof(f45220,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(compose(a,compose(a,b)),codomain(compose(a,compose(a,b))))) = compose(compose(a,compose(a,b)),codomain(compose(a,compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f18,f45211]) ).

fof(f45221,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(compose(a,compose(a,b)),codomain(compose(a,compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f20,f45220]) ).

fof(f45222,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)],[f20,f45221]) ).

fof(f45232,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(g,a))),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f14928]) ).

fof(f45233,plain,
    ifeq(domain(b),domain(h),domain(compose(compose(g,a),compose(h,compose(a,b)))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f22238,f14947]) ).

fof(f45695,plain,
    ifeq(domain(b),codomain(compose(a,compose(g,a))),ifeq(domain(b),domain(compose(g,a)),compose(a,compose(compose(g,a),codomain(compose(a,compose(g,a))))),compose(a,compose(g,a))),compose(a,compose(g,a))) = compose(a,compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f4281]) ).

fof(f45696,plain,
    ifeq(domain(b),codomain(compose(a,compose(h,a))),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),codomain(compose(a,compose(h,a))))),compose(a,compose(h,a))),compose(a,compose(h,a))) = compose(a,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f4281]) ).

fof(f45722,plain,
    ifeq(domain(b),codomain(compose(a,compose(g,a))),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),codomain(compose(a,compose(g,a))))),compose(a,compose(g,a))),compose(a,compose(g,a))) = compose(a,compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f45695]) ).

fof(f45723,plain,
    ifeq(domain(b),codomain(compose(a,compose(h,a))),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),codomain(compose(a,compose(h,a))))),compose(a,compose(h,a))),compose(a,compose(h,a))) = compose(a,compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f45696]) ).

fof(f45912,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(domain(X0),a),compose(compose(g,a),a),domain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f9739]) ).

fof(f45913,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(domain(X0),a),compose(compose(h,a),a),domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f9739]) ).

fof(f45914,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(domain(X0),a),compose(compose(h,compose(a,b)),a),domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f9739]) ).

fof(f45915,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(domain(X0),a),compose(compose(a,b),a),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f9739]) ).

fof(f45916,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),a),compose(g,a),domain(X0),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f9739]) ).

fof(f45917,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),a),compose(h,a),domain(X0),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f9739]) ).

fof(f45918,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(domain(X0),a),compose(codomain(X1),a),domain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f9739]) ).

fof(f45920,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X0),a),compose(domain(X1),a),domain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f9739]) ).

fof(f45930,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(compose(domain(X0),a),a,domain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f9739]) ).

fof(f45956,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),a),compose(compose(g,a),a),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f45912]) ).

fof(f45957,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),a),compose(compose(h,a),a),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f45913]) ).

fof(f45977,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),a),a,domain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f45930]) ).

fof(f46004,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),compose(domain(X0),a),domain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f9741]) ).

fof(f46005,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),compose(domain(X0),a),domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f9741]) ).

fof(f46006,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(domain(X0),a),domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f9741]) ).

fof(f46007,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(domain(X0),a),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f9741]) ).

fof(f46008,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(domain(X0),a),domain(X0),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f9741]) ).

fof(f46009,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(domain(X0),a),domain(X0),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f9741]) ).

fof(f46010,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),compose(domain(X0),a),domain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f9741]) ).

fof(f46012,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),compose(domain(X0),a),domain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f9741]) ).

fof(f46014,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(a,compose(domain(X0),a),domain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f9741]) ).

fof(f46049,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(compose(g,a),a),compose(domain(X0),a),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f46004]) ).

fof(f46050,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(compose(h,a),a),compose(domain(X0),a),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f46005]) ).

fof(f46053,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(domain(X0),a),domain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f46014]) ).

fof(f46183,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),g)),compose(compose(domain(X0),compose(h,compose(a,b))),g)),compose(compose(domain(X0),compose(h,compose(a,b))),g)) = compose(compose(domain(X0),compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f478,f4671]) ).

fof(f46184,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4671]) ).

fof(f46185,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4671]) ).

fof(f46186,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4671]) ).

fof(f46188,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0))),compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(X1),compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f35,f4671]) ).

fof(f46208,plain,
    ! [X0] : ifeq(codomain(b),domain(codomain(compose(domain(X0),compose(h,compose(a,b))))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),codomain(compose(domain(X0),compose(h,compose(a,b)))))),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(compose(domain(X0),compose(h,compose(a,b)))))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(compose(domain(X0),compose(h,compose(a,b))))),
    inference(paramodulation,[status(thm)],[f20,f4671]) ).

fof(f46305,plain,
    ! [X0] : ifeq(codomain(b),codomain(compose(domain(X0),compose(h,compose(a,b)))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),codomain(compose(domain(X0),compose(h,compose(a,b)))))),compose(domain(X0),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,compose(a,b))),codomain(compose(domain(X0),compose(h,compose(a,b)))))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(compose(domain(X0),compose(h,compose(a,b))))),
    inference(forward_demodulation,[status(thm)],[f18,f46208]) ).

fof(f46306,plain,
    ! [X0] : ifeq(codomain(b),codomain(compose(domain(X0),compose(h,compose(a,b)))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),codomain(compose(domain(X0),compose(h,compose(a,b)))))),compose(domain(X0),compose(h,compose(a,b)))),compose(domain(X0),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(h,compose(a,b))),codomain(compose(domain(X0),compose(h,compose(a,b))))),
    inference(forward_demodulation,[status(thm)],[f20,f46305]) ).

fof(f46307,plain,
    ! [X0] : ifeq(codomain(b),codomain(compose(domain(X0),compose(h,compose(a,b)))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,compose(a,b)),codomain(compose(domain(X0),compose(h,compose(a,b)))))),compose(domain(X0),compose(h,compose(a,b)))),compose(domain(X0),compose(h,compose(a,b)))) = compose(domain(X0),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f20,f46306]) ).

fof(f46407,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(codomain(X0),a),compose(compose(g,a),a),codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10270]) ).

fof(f46408,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(codomain(X0),a),compose(compose(h,a),a),codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10270]) ).

fof(f46409,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(codomain(X0),a),compose(compose(h,compose(a,b)),a),codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10270]) ).

fof(f46410,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(codomain(X0),a),compose(compose(a,b),a),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10270]) ).

fof(f46411,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),a),compose(g,a),codomain(X0),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10270]) ).

fof(f46412,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),a),compose(h,a),codomain(X0),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10270]) ).

fof(f46413,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X0),a),compose(codomain(X1),a),codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f10270]) ).

fof(f46415,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(codomain(X0),a),compose(domain(X1),a),codomain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f10270]) ).

fof(f46426,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(compose(codomain(X0),a),a,codomain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f10270]) ).

fof(f46458,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),a),compose(compose(g,a),a),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f46407]) ).

fof(f46459,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),a),compose(compose(h,a),a),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f46408]) ).

fof(f46484,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),a),a,codomain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f46426]) ).

fof(f46517,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),compose(codomain(X0),a),codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10387]) ).

fof(f46518,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),compose(codomain(X0),a),codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10387]) ).

fof(f46519,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(codomain(X0),a),codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10387]) ).

fof(f46520,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(codomain(X0),a),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10387]) ).

fof(f46521,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(codomain(X0),a),codomain(X0),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10387]) ).

fof(f46522,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(codomain(X0),a),codomain(X0),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10387]) ).

fof(f46523,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),a),compose(codomain(X0),a),codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f10387]) ).

fof(f46525,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),a),compose(codomain(X0),a),codomain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f10387]) ).

fof(f46527,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(domain(a)),domain(b),ifeq(a,compose(codomain(X0),a),codomain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f19,f10387]) ).

fof(f46569,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),a),compose(codomain(X0),a),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f46517]) ).

fof(f46570,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),a),compose(codomain(X0),a),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f46518]) ).

fof(f46573,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(codomain(X0),a),codomain(X0),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(forward_demodulation,[status(thm)],[f17,f46527]) ).

fof(f46693,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),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)],[f478,f4673]) ).

fof(f46694,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,compose(g,a))),compose(compose(domain(X0),g),compose(g,a))),compose(compose(domain(X0),g),compose(g,a))) = compose(compose(domain(X0),g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4673]) ).

fof(f46695,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,compose(h,a))),compose(compose(domain(X0),g),compose(h,a))),compose(compose(domain(X0),g),compose(h,a))) = compose(compose(domain(X0),g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4673]) ).

fof(f46696,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(g,compose(h,compose(a,b)))),compose(compose(domain(X0),g),compose(h,compose(a,b)))),compose(compose(domain(X0),g),compose(h,compose(a,b)))) = compose(compose(domain(X0),g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4673]) ).

fof(f46698,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(h),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)],[f35,f4673]) ).

fof(f46720,plain,
    ! [X0] : ifeq(domain(a),domain(codomain(compose(domain(X0),g))),ifeq(domain(X0),domain(h),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)],[f20,f4673]) ).

fof(f46824,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(domain(X0),g)),ifeq(domain(X0),domain(h),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)],[f18,f46720]) ).

fof(f46825,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(domain(X0),g)),ifeq(domain(X0),domain(h),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)],[f20,f46824]) ).

fof(f46826,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(domain(X0),g)),ifeq(domain(X0),domain(h),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)],[f20,f46825]) ).

fof(f46927,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(domain(X0),b),compose(compose(g,a),b),domain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10556]) ).

fof(f46928,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(domain(X0),b),compose(compose(h,a),b),domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10556]) ).

fof(f46929,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(domain(X0),b),compose(compose(h,compose(a,b)),b),domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10556]) ).

fof(f46930,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(domain(X0),b),compose(compose(a,b),b),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10556]) ).

fof(f46931,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),b),compose(g,b),domain(X0),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10556]) ).

fof(f46932,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(domain(X0),b),compose(h,b),domain(X0),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10556]) ).

fof(f46933,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(domain(X0),b),compose(codomain(X1),b),domain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f10556]) ).

fof(f46935,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X0),b),compose(domain(X1),b),domain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f10556]) ).

fof(f46972,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),compose(compose(g,a),b),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f46927]) ).

fof(f46973,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),compose(h,compose(a,b)),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f46972]) ).

fof(f46974,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),compose(compose(h,a),b),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f46928]) ).

fof(f46975,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),b),compose(h,compose(a,b)),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f46974]) ).

fof(f47027,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(domain(X0),b),domain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10559]) ).

fof(f47028,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(domain(X0),b),domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10559]) ).

fof(f47029,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(domain(X0),b),domain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10559]) ).

fof(f47030,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(domain(X0),b),domain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10559]) ).

fof(f47031,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(domain(X0),b),domain(X0),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10559]) ).

fof(f47032,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(domain(X0),b),domain(X0),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10559]) ).

fof(f47033,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),compose(domain(X0),b),domain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f10559]) ).

fof(f47035,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),compose(domain(X0),b),domain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f10559]) ).

fof(f47073,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(compose(g,a),b),compose(domain(X0),b),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f47027]) ).

fof(f47074,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(domain(X0),b),domain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f47073]) ).

fof(f47075,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(compose(h,a),b),compose(domain(X0),b),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f47028]) ).

fof(f47076,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(domain(X0),b),domain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f47075]) ).

fof(f47213,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),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)],[f478,f4586]) ).

fof(f47214,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(g,a))),compose(compose(domain(X0),h),compose(g,a))),compose(compose(domain(X0),h),compose(g,a))) = compose(compose(domain(X0),h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4586]) ).

fof(f47215,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(h,a))),compose(compose(domain(X0),h),compose(h,a))),compose(compose(domain(X0),h),compose(h,a))) = compose(compose(domain(X0),h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4586]) ).

fof(f47216,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(h,compose(h,compose(a,b)))),compose(compose(domain(X0),h),compose(h,compose(a,b)))),compose(compose(domain(X0),h),compose(h,compose(a,b)))) = compose(compose(domain(X0),h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4586]) ).

fof(f47218,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(domain(X1),domain(h),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)],[f35,f4586]) ).

fof(f47240,plain,
    ! [X0] : ifeq(domain(a),domain(codomain(compose(domain(X0),h))),ifeq(domain(X0),domain(h),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)],[f20,f4586]) ).

fof(f47344,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(domain(X0),h)),ifeq(domain(X0),domain(h),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)],[f18,f47240]) ).

fof(f47345,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(domain(X0),h)),ifeq(domain(X0),domain(h),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)],[f20,f47344]) ).

fof(f47346,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(domain(X0),h)),ifeq(domain(X0),domain(h),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)],[f20,f47345]) ).

fof(f47440,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(codomain(X0),b),compose(compose(g,a),b),codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f10972]) ).

fof(f47441,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(codomain(X0),b),compose(compose(h,a),b),codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f10972]) ).

fof(f47442,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(codomain(X0),b),compose(compose(h,compose(a,b)),b),codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f10972]) ).

fof(f47443,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(codomain(X0),b),compose(compose(a,b),b),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10972]) ).

fof(f47444,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),b),compose(g,b),codomain(X0),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f10972]) ).

fof(f47445,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(codomain(X0),b),compose(h,b),codomain(X0),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f10972]) ).

fof(f47446,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X0),b),compose(codomain(X1),b),codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f10972]) ).

fof(f47448,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(codomain(X0),b),compose(domain(X1),b),codomain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f10972]) ).

fof(f47494,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),compose(compose(g,a),b),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f47440]) ).

fof(f47495,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),compose(h,compose(a,b)),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f47494]) ).

fof(f47496,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),compose(compose(h,a),b),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f47441]) ).

fof(f47497,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),b),compose(h,compose(a,b)),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f47496]) ).

fof(f47559,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),b),compose(codomain(X0),b),codomain(X0),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f11299]) ).

fof(f47560,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),compose(codomain(X0),b),codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f11299]) ).

fof(f47561,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(codomain(X0),b),codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f11299]) ).

fof(f47562,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(codomain(X0),b),codomain(X0),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f11299]) ).

fof(f47563,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(codomain(X0),b),codomain(X0),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f316,f11299]) ).

fof(f47564,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(codomain(X0),b),codomain(X0),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f147,f11299]) ).

fof(f47565,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(codomain(X1),domain(b),ifeq(compose(codomain(X1),b),compose(codomain(X0),b),codomain(X0),codomain(X1)),codomain(X1)),codomain(X1)) = codomain(X1),
    inference(paramodulation,[status(thm)],[f36,f11299]) ).

fof(f47567,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(domain(X1),domain(b),ifeq(compose(domain(X1),b),compose(codomain(X0),b),codomain(X0),domain(X1)),domain(X1)),domain(X1)) = domain(X1),
    inference(paramodulation,[status(thm)],[f17,f11299]) ).

fof(f47614,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(g,a),b),compose(codomain(X0),b),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f47559]) ).

fof(f47615,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(codomain(X0),b),codomain(X0),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f446,f47614]) ).

fof(f47616,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(compose(h,a),b),compose(codomain(X0),b),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f47560]) ).

fof(f47617,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(codomain(X0),b),codomain(X0),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f47616]) ).

fof(f47678,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),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)],[f478,f4674]) ).

fof(f47679,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(g,a))),compose(compose(domain(X1),codomain(X0)),compose(g,a))),compose(compose(domain(X1),codomain(X0)),compose(g,a))) = compose(compose(domain(X1),codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4674]) ).

fof(f47680,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(h,a))),compose(compose(domain(X1),codomain(X0)),compose(h,a))),compose(compose(domain(X1),codomain(X0)),compose(h,a))) = compose(compose(domain(X1),codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4674]) ).

fof(f47681,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(domain(X1),codomain(X0),compose(domain(X1),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(domain(X1),codomain(X0)),compose(h,compose(a,b)))),compose(compose(domain(X1),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(X1),codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f4674]) ).

fof(f47683,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)],[f35,f4674]) ).

fof(f47720,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)],[f20,f4674]) ).

fof(f47956,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)],[f18,f47720]) ).

fof(f47957,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)],[f20,f47956]) ).

fof(f47958,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)],[f20,f47957]) ).

fof(f48820,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f4593]) ).

fof(f48821,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f4593]) ).

fof(f48823,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(compose(a,b)),compose(domain(X0),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f4593]) ).

fof(f48884,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f2123,f48820]) ).

fof(f48885,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f48821]) ).

fof(f48887,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(domain(X0),compose(a,b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f261,f48823]) ).

fof(f49093,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(compose(g,a)),compose(domain(X1),compose(compose(g,a),domain(X0))),compose(compose(domain(X1),compose(g,a)),domain(X0))),compose(compose(domain(X1),compose(g,a)),domain(X0))) = compose(compose(domain(X1),compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f4595]) ).

fof(f49094,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(compose(h,a)),compose(domain(X1),compose(compose(h,a),domain(X0))),compose(compose(domain(X1),compose(h,a)),domain(X0))),compose(compose(domain(X1),compose(h,a)),domain(X0))) = compose(compose(domain(X1),compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f4595]) ).

fof(f49096,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)],[f975,f4595]) ).

fof(f49190,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(g,a),domain(X0))),compose(compose(domain(X1),compose(g,a)),domain(X0))),compose(compose(domain(X1),compose(g,a)),domain(X0))) = compose(compose(domain(X1),compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f49093]) ).

fof(f49191,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(domain(X1),domain(h),compose(domain(X1),compose(compose(h,a),domain(X0))),compose(compose(domain(X1),compose(h,a)),domain(X0))),compose(compose(domain(X1),compose(h,a)),domain(X0))) = compose(compose(domain(X1),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f49094]) ).

fof(f49193,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)],[f261,f49096]) ).

fof(f49527,plain,
    ! [X0] : ifeq(compose(domain(b),a),X0,ifeq(a,X0,domain(a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f10035]) ).

fof(f50698,plain,
    ! [X0] : ifeq(codomain(b),domain(h),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(paramodulation,[status(thm)],[f478,f4710]) ).

fof(f50699,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(g,a))),compose(compose(domain(X0),compose(a,b)),compose(g,a))),compose(compose(domain(X0),compose(a,b)),compose(g,a))) = compose(compose(domain(X0),compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4710]) ).

fof(f50700,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(domain(X0),domain(a),compose(domain(X0),compose(compose(a,b),compose(h,a))),compose(compose(domain(X0),compose(a,b)),compose(h,a))),compose(compose(domain(X0),compose(a,b)),compose(h,a))) = compose(compose(domain(X0),compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4710]) ).

fof(f50723,plain,
    ! [X0] : ifeq(codomain(b),domain(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(compose(domain(X0),compose(a,b)),codomain(compose(domain(X0),compose(a,b))))) = compose(compose(domain(X0),compose(a,b)),codomain(compose(domain(X0),compose(a,b)))),
    inference(paramodulation,[status(thm)],[f20,f4710]) ).

fof(f50808,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(compose(domain(X0),compose(a,b)),codomain(compose(domain(X0),compose(a,b))))) = compose(compose(domain(X0),compose(a,b)),codomain(compose(domain(X0),compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f18,f50723]) ).

fof(f50809,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(compose(domain(X0),compose(a,b)),codomain(compose(domain(X0),compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f20,f50808]) ).

fof(f50810,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)],[f20,f50809]) ).

fof(f51071,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(a,b),compose(h,a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f17112]) ).

fof(f51072,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,b),compose(h,compose(a,b)),compose(h,a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f17137]) ).

fof(f52143,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(domain(X0),compose(g,a))),ifeq(domain(X0),domain(compose(g,a)),compose(domain(X0),compose(compose(g,a),codomain(compose(domain(X0),compose(g,a))))),compose(domain(X0),compose(g,a))),compose(domain(X0),compose(g,a))) = compose(domain(X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f4811]) ).

fof(f52144,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(domain(X0),compose(h,a))),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(compose(h,a),codomain(compose(domain(X0),compose(h,a))))),compose(domain(X0),compose(h,a))),compose(domain(X0),compose(h,a))) = compose(domain(X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f4811]) ).

fof(f52234,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(domain(X0),compose(g,a))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),codomain(compose(domain(X0),compose(g,a))))),compose(domain(X0),compose(g,a))),compose(domain(X0),compose(g,a))) = compose(domain(X0),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f52143]) ).

fof(f52235,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(domain(X0),compose(h,a))),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),codomain(compose(domain(X0),compose(h,a))))),compose(domain(X0),compose(h,a))),compose(domain(X0),compose(h,a))) = compose(domain(X0),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f52144]) ).

fof(f52702,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f5145]) ).

fof(f52703,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f5145]) ).

fof(f52704,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f5145]) ).

fof(f52705,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f5145]) ).

fof(f52707,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(a),compose(h,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f147,f5145]) ).

fof(f52708,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(a,b)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f36,f5145]) ).

fof(f52711,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(domain(compose(compose(a,b),compose(h,compose(a,b))))),domain(a),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f19,f5145]) ).

fof(f52721,plain,
    ifeq(codomain(b),domain(h),compose(h,compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f16,f52707]) ).

fof(f52722,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(a,b),compose(h,compose(a,b)))),domain(a),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(a,b),compose(h,compose(a,b)))),compose(a,b)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f52711]) ).

fof(f52755,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),domain(X0))),compose(compose(compose(g,a),compose(a,b)),domain(X0))),compose(compose(compose(g,a),compose(a,b)),domain(X0))) = compose(compose(compose(g,a),compose(a,b)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f5147]) ).

fof(f52756,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),domain(X0))),compose(compose(compose(h,a),compose(a,b)),domain(X0))),compose(compose(compose(h,a),compose(a,b)),domain(X0))) = compose(compose(compose(h,a),compose(a,b)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f5147]) ).

fof(f52757,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(a,b)),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f5147]) ).

fof(f52758,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)],[f975,f5147]) ).

fof(f52760,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(a),compose(h,compose(compose(a,b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
    inference(paramodulation,[status(thm)],[f147,f5147]) ).

fof(f52761,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)],[f36,f5147]) ).

fof(f52764,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(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(paramodulation,[status(thm)],[f19,f5147]) ).

fof(f52823,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),compose(h,compose(compose(a,b),domain(X0))),compose(compose(h,compose(a,b)),domain(X0))) = compose(compose(h,compose(a,b)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f52760]) ).

fof(f52824,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)],[f17,f52764]) ).

fof(f52934,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),g)),compose(compose(compose(h,compose(a,b)),compose(a,b)),g)),compose(compose(compose(h,compose(a,b)),compose(a,b)),g)) = compose(compose(compose(h,compose(a,b)),compose(a,b)),g),
    inference(paramodulation,[status(thm)],[f478,f5151]) ).

fof(f52935,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5151]) ).

fof(f52936,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5151]) ).

fof(f52943,plain,
    ifeq(codomain(b),domain(codomain(compose(compose(h,compose(a,b)),compose(a,b)))),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),codomain(compose(compose(h,compose(a,b)),compose(a,b))))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(compose(compose(h,compose(a,b)),compose(a,b))))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(compose(compose(h,compose(a,b)),compose(a,b)))),
    inference(paramodulation,[status(thm)],[f20,f5151]) ).

fof(f52952,plain,
    ifeq(codomain(b),codomain(compose(compose(h,compose(a,b)),compose(a,b))),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),codomain(compose(compose(h,compose(a,b)),compose(a,b))))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(compose(compose(h,compose(a,b)),compose(a,b))))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(compose(compose(h,compose(a,b)),compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f18,f52943]) ).

fof(f52953,plain,
    ifeq(codomain(b),codomain(compose(compose(h,compose(a,b)),compose(a,b))),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),codomain(compose(compose(h,compose(a,b)),compose(a,b))))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(compose(h,compose(a,b)),compose(a,b)),codomain(compose(compose(h,compose(a,b)),compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f20,f52952]) ).

fof(f52954,plain,
    ifeq(codomain(b),codomain(compose(compose(h,compose(a,b)),compose(a,b))),ifeq(codomain(b),domain(a),compose(compose(h,compose(a,b)),compose(compose(a,b),codomain(compose(compose(h,compose(a,b)),compose(a,b))))),compose(compose(h,compose(a,b)),compose(a,b))),compose(compose(h,compose(a,b)),compose(a,b))) = compose(compose(h,compose(a,b)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f20,f52953]) ).

fof(f52958,plain,
    ifeq(codomain(b),domain(h),compose(h,compose(compose(a,b),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
    inference(paramodulation,[status(thm)],[f478,f5172]) ).

fof(f52959,plain,
    ifeq(codomain(b),domain(h),compose(h,compose(compose(a,b),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5172]) ).

fof(f52960,plain,
    ifeq(codomain(b),domain(h),compose(h,compose(compose(a,b),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5172]) ).

fof(f52983,plain,
    ! [X0] : ifeq(codomain(b),domain(h),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(paramodulation,[status(thm)],[f478,f5155]) ).

fof(f52984,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(g,a))),compose(compose(codomain(X0),compose(a,b)),compose(g,a))),compose(compose(codomain(X0),compose(a,b)),compose(g,a))) = compose(compose(codomain(X0),compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5155]) ).

fof(f52985,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(a),compose(codomain(X0),compose(compose(a,b),compose(h,a))),compose(compose(codomain(X0),compose(a,b)),compose(h,a))),compose(compose(codomain(X0),compose(a,b)),compose(h,a))) = compose(compose(codomain(X0),compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5155]) ).

fof(f53010,plain,
    ! [X0] : ifeq(codomain(b),domain(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(compose(codomain(X0),compose(a,b)),codomain(compose(codomain(X0),compose(a,b))))) = compose(compose(codomain(X0),compose(a,b)),codomain(compose(codomain(X0),compose(a,b)))),
    inference(paramodulation,[status(thm)],[f20,f5155]) ).

fof(f53117,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(compose(codomain(X0),compose(a,b)),codomain(compose(codomain(X0),compose(a,b))))) = compose(compose(codomain(X0),compose(a,b)),codomain(compose(codomain(X0),compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f18,f53010]) ).

fof(f53118,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(compose(codomain(X0),compose(a,b)),codomain(compose(codomain(X0),compose(a,b)))),
    inference(forward_demodulation,[status(thm)],[f20,f53117]) ).

fof(f53119,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)],[f20,f53118]) ).

fof(f53205,plain,
    ifeq(codomain(b),domain(h),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(paramodulation,[status(thm)],[f478,f5173]) ).

fof(f53206,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(a,b),compose(g,a))),domain(a),compose(compose(a,b),compose(g,a)),compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a))),compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a))) = compose(compose(domain(compose(compose(a,b),compose(g,a))),compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5173]) ).

fof(f53207,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(a,b),compose(h,a))),domain(a),compose(compose(a,b),compose(h,a)),compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a))),compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a))) = compose(compose(domain(compose(compose(a,b),compose(h,a))),compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5173]) ).

fof(f53284,plain,
    ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,b)),compose(compose(compose(g,a),compose(a,b)),codomain(b))) = compose(compose(compose(g,a),compose(a,b)),codomain(b)),
    inference(paramodulation,[status(thm)],[f1583,f5180]) ).

fof(f53285,plain,
    ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,b)),compose(compose(compose(h,a),compose(a,b)),codomain(b))) = compose(compose(compose(h,a),compose(a,b)),codomain(b)),
    inference(paramodulation,[status(thm)],[f1465,f5180]) ).

fof(f53287,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(paramodulation,[status(thm)],[f975,f5180]) ).

fof(f53333,plain,
    ifeq(codomain(b),codomain(compose(compose(g,a),compose(a,b))),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),codomain(compose(compose(g,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)],[f1583,f5183]) ).

fof(f53334,plain,
    ifeq(codomain(b),codomain(compose(compose(h,a),compose(a,b))),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),codomain(compose(compose(h,a),compose(a,b))))),compose(compose(h,a),compose(a,b))),compose(compose(h,a),compose(a,b))) = compose(compose(h,a),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f5183]) ).

fof(f53336,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)],[f975,f5183]) ).

fof(f53474,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(compose(g,a),codomain(X0)),compose(h,compose(a,b)))),compose(compose(compose(g,a),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f5674]) ).

fof(f53475,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(compose(h,a),codomain(X0)),compose(h,compose(a,b)))),compose(compose(compose(h,a),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f5674]) ).

fof(f53476,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f5674]) ).

fof(f53477,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(X0)),compose(h,compose(a,b)))),compose(compose(compose(a,b),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f5674]) ).

fof(f53478,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(g,codomain(X0)),compose(h,compose(a,b)))),compose(compose(g,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(g,codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f316,f5674]) ).

fof(f53479,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(h,codomain(X0)),compose(h,compose(a,b)))),compose(compose(h,codomain(X0)),compose(h,compose(a,b)))) = compose(compose(h,codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f147,f5674]) ).

fof(f53480,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(h,compose(a,b)))),compose(compose(codomain(X1),codomain(X0)),compose(h,compose(a,b)))),compose(compose(codomain(X1),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(codomain(X1),codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f36,f5674]) ).

fof(f53492,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(domain(compose(codomain(X0),compose(h,compose(a,b))))),codomain(X0),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b)))),compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f19,f5674]) ).

fof(f53622,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0),compose(codomain(X0),compose(h,compose(a,b))),compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b)))),compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b)))) = compose(compose(domain(compose(codomain(X0),compose(h,compose(a,b)))),codomain(X0)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f17,f53492]) ).

fof(f53795,plain,
    ifeq(domain(b),domain(h),compose(domain(compose(g,a)),compose(compose(g,a),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f7995]) ).

fof(f53796,plain,
    ifeq(domain(b),domain(h),compose(domain(compose(h,a)),compose(compose(h,a),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f7995]) ).

fof(f53797,plain,
    ifeq(codomain(b),domain(h),compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1016,f7995]) ).

fof(f53815,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f53795]) ).

fof(f53816,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f53796]) ).

fof(f53817,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f506,f53797]) ).

fof(f53844,plain,
    ifeq(domain(b),domain(h),compose(domain(compose(g,a)),compose(compose(g,a),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1583,f7996]) ).

fof(f53845,plain,
    ifeq(domain(b),domain(h),compose(domain(compose(h,a)),compose(compose(h,a),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f7996]) ).

fof(f53846,plain,
    ifeq(codomain(b),domain(h),compose(domain(compose(h,compose(a,b))),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1016,f7996]) ).

fof(f53864,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(g,a),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f53844]) ).

fof(f53865,plain,
    ifeq(domain(b),domain(h),compose(domain(h),compose(compose(h,a),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f53845]) ).

fof(f53866,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f506,f53846]) ).

fof(f53893,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(codomain(compose(g,a)),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f8202]) ).

fof(f53894,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(codomain(compose(h,a)),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f8202]) ).

fof(f53895,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1016,f8202]) ).

fof(f53896,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(compose(a,b)),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
    inference(paramodulation,[status(thm)],[f975,f8202]) ).

fof(f53913,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f53893]) ).

fof(f53914,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f53894]) ).

fof(f53915,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1016,f53895]) ).

fof(f53916,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f975,f53896]) ).

fof(f53941,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(codomain(compose(g,a)),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1583,f8203]) ).

fof(f53942,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(codomain(compose(h,a)),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f8203]) ).

fof(f53943,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(compose(h,compose(a,b))),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1016,f8203]) ).

fof(f53944,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(compose(a,b)),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
    inference(paramodulation,[status(thm)],[f975,f8203]) ).

fof(f53961,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(domain(b),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f53941]) ).

fof(f53962,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(domain(b),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1465,f53942]) ).

fof(f53963,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1016,f53943]) ).

fof(f53964,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(codomain(b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f975,f53944]) ).

fof(f53989,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),a),compose(g,a),compose(g,a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1583,f10278]) ).

fof(f53990,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),a),compose(g,a),compose(h,a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1465,f10278]) ).

fof(f53991,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(g,a),compose(h,compose(a,b)),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1016,f10278]) ).

fof(f53992,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),a),compose(g,a),compose(a,b),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f975,f10278]) ).

fof(f54009,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),a),compose(h,a),compose(g,a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1583,f10279]) ).

fof(f54010,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),a),compose(h,a),compose(h,a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1465,f10279]) ).

fof(f54011,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(h,a),compose(h,compose(a,b)),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1016,f10279]) ).

fof(f54012,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),a),compose(h,a),compose(a,b),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f975,f10279]) ).

fof(f54030,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(compose(g,a),a),compose(g,a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1583,f10395]) ).

fof(f54031,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(compose(h,a),a),compose(h,a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1465,f10395]) ).

fof(f54032,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1016,f10395]) ).

fof(f54033,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,a),compose(compose(a,b),a),compose(a,b),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f975,f10395]) ).

fof(f54068,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),domain(X1))),compose(compose(compose(g,a),codomain(X0)),domain(X1))),compose(compose(compose(g,a),codomain(X0)),domain(X1))) = compose(compose(compose(g,a),codomain(X0)),domain(X1)),
    inference(paramodulation,[status(thm)],[f1583,f5676]) ).

fof(f54069,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),domain(X1))),compose(compose(compose(h,a),codomain(X0)),domain(X1))),compose(compose(compose(h,a),codomain(X0)),domain(X1))) = compose(compose(compose(h,a),codomain(X0)),domain(X1)),
    inference(paramodulation,[status(thm)],[f1465,f5676]) ).

fof(f54070,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),domain(X1))),compose(compose(compose(h,compose(a,b)),codomain(X0)),domain(X1))),compose(compose(compose(h,compose(a,b)),codomain(X0)),domain(X1))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),domain(X1)),
    inference(paramodulation,[status(thm)],[f1016,f5676]) ).

fof(f54071,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)],[f975,f5676]) ).

fof(f54072,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),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)],[f316,f5676]) ).

fof(f54073,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(X1),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),domain(X1))),compose(compose(h,codomain(X0)),domain(X1))),compose(compose(h,codomain(X0)),domain(X1))) = compose(compose(h,codomain(X0)),domain(X1)),
    inference(paramodulation,[status(thm)],[f147,f5676]) ).

fof(f54074,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)],[f36,f5676]) ).

fof(f54086,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)],[f19,f5676]) ).

fof(f54265,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)],[f17,f54086]) ).

fof(f54523,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(compose(g,a),a),compose(g,a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1583,f10396]) ).

fof(f54524,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(compose(h,a),a),compose(h,a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1465,f10396]) ).

fof(f54525,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1016,f10396]) ).

fof(f54526,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,a),compose(compose(a,b),a),compose(a,b),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f975,f10396]) ).

fof(f54544,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),b),compose(g,b),compose(g,a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1583,f10980]) ).

fof(f54545,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),b),compose(g,b),compose(h,a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1465,f10980]) ).

fof(f54546,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(g,b),compose(h,compose(a,b)),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1016,f10980]) ).

fof(f54547,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),b),compose(g,b),compose(a,b),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f975,f10980]) ).

fof(f54559,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,compose(a,b)),compose(g,b),compose(g,a),g),g),g) = g,
    inference(forward_demodulation,[status(thm)],[f446,f54544]) ).

fof(f54560,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,compose(a,b)),compose(g,b),compose(h,a),g),g),g) = g,
    inference(forward_demodulation,[status(thm)],[f22238,f54545]) ).

fof(f54571,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),b),compose(h,b),compose(g,a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1583,f10981]) ).

fof(f54572,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),b),compose(h,b),compose(h,a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1465,f10981]) ).

fof(f54573,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(h,b),compose(h,compose(a,b)),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1016,f10981]) ).

fof(f54574,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),b),compose(h,b),compose(a,b),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f975,f10981]) ).

fof(f54586,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,compose(a,b)),compose(h,b),compose(g,a),h),h),h) = h,
    inference(forward_demodulation,[status(thm)],[f446,f54571]) ).

fof(f54587,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,compose(a,b)),compose(h,b),compose(h,a),h),h),h) = h,
    inference(forward_demodulation,[status(thm)],[f22238,f54572]) ).

fof(f54599,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(compose(g,a),b),compose(g,a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1583,f11307]) ).

fof(f54600,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(compose(h,a),b),compose(h,a),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1465,f11307]) ).

fof(f54601,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f1016,f11307]) ).

fof(f54602,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(compose(a,b),b),compose(a,b),g),g),g) = g,
    inference(paramodulation,[status(thm)],[f975,f11307]) ).

fof(f54615,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(h,compose(a,b)),compose(g,a),g),g),g) = g,
    inference(forward_demodulation,[status(thm)],[f446,f54599]) ).

fof(f54616,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),compose(h,compose(a,b)),compose(h,a),g),g),g) = g,
    inference(forward_demodulation,[status(thm)],[f22238,f54600]) ).

fof(f54628,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(compose(g,a),b),compose(g,a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1583,f11308]) ).

fof(f54629,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(compose(h,a),b),compose(h,a),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1465,f11308]) ).

fof(f54630,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f1016,f11308]) ).

fof(f54631,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(compose(a,b),b),compose(a,b),h),h),h) = h,
    inference(paramodulation,[status(thm)],[f975,f11308]) ).

fof(f54644,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(h,compose(a,b)),compose(g,a),h),h),h) = h,
    inference(forward_demodulation,[status(thm)],[f446,f54628]) ).

fof(f54645,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),compose(h,compose(a,b)),compose(h,a),h),h),h) = h,
    inference(forward_demodulation,[status(thm)],[f22238,f54629]) ).

fof(f54665,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),g)),compose(compose(compose(h,compose(a,b)),codomain(X0)),g)),compose(compose(compose(h,compose(a,b)),codomain(X0)),g)) = compose(compose(compose(h,compose(a,b)),codomain(X0)),g),
    inference(paramodulation,[status(thm)],[f478,f5681]) ).

fof(f54666,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),compose(g,a))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(g,a))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5681]) ).

fof(f54667,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),compose(h,a))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,a))),compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5681]) ).

fof(f54693,plain,
    ! [X0] : ifeq(codomain(X0),domain(codomain(compose(compose(h,compose(a,b)),codomain(X0)))),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(compose(compose(h,compose(a,b)),codomain(X0))))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(compose(compose(h,compose(a,b)),codomain(X0)))),
    inference(paramodulation,[status(thm)],[f20,f5681]) ).

fof(f54867,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(compose(compose(h,compose(a,b)),codomain(X0))))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(compose(compose(h,compose(a,b)),codomain(X0)))),
    inference(forward_demodulation,[status(thm)],[f18,f54693]) ).

fof(f54868,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(compose(h,compose(a,b)),codomain(X0)),codomain(compose(compose(h,compose(a,b)),codomain(X0)))),
    inference(forward_demodulation,[status(thm)],[f20,f54867]) ).

fof(f54869,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))),ifeq(codomain(b),codomain(X0),compose(compose(h,compose(a,b)),compose(codomain(X0),codomain(compose(compose(h,compose(a,b)),codomain(X0))))),compose(compose(h,compose(a,b)),codomain(X0))),compose(compose(h,compose(a,b)),codomain(X0))) = compose(compose(h,compose(a,b)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f20,f54868]) ).

fof(f54995,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),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)],[f478,f5683]) ).

fof(f54996,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),compose(g,a))),compose(compose(g,codomain(X0)),compose(g,a))),compose(compose(g,codomain(X0)),compose(g,a))) = compose(compose(g,codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5683]) ).

fof(f54997,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),compose(h,a))),compose(compose(g,codomain(X0)),compose(h,a))),compose(compose(g,codomain(X0)),compose(h,a))) = compose(compose(g,codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5683]) ).

fof(f55022,plain,
    ! [X0] : ifeq(codomain(X0),domain(codomain(compose(g,codomain(X0)))),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),codomain(compose(g,codomain(X0))))),compose(g,codomain(X0))),compose(compose(g,codomain(X0)),codomain(compose(g,codomain(X0))))) = compose(compose(g,codomain(X0)),codomain(compose(g,codomain(X0)))),
    inference(paramodulation,[status(thm)],[f20,f5683]) ).

fof(f55192,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(g,codomain(X0))),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),codomain(compose(g,codomain(X0))))),compose(g,codomain(X0))),compose(compose(g,codomain(X0)),codomain(compose(g,codomain(X0))))) = compose(compose(g,codomain(X0)),codomain(compose(g,codomain(X0)))),
    inference(forward_demodulation,[status(thm)],[f18,f55022]) ).

fof(f55193,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(g,codomain(X0))),ifeq(domain(a),codomain(X0),compose(g,compose(codomain(X0),codomain(compose(g,codomain(X0))))),compose(g,codomain(X0))),compose(g,codomain(X0))) = compose(compose(g,codomain(X0)),codomain(compose(g,codomain(X0)))),
    inference(forward_demodulation,[status(thm)],[f20,f55192]) ).

fof(f55194,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(g,codomain(X0))),ifeq(domain(a),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(forward_demodulation,[status(thm)],[f20,f55193]) ).

fof(f55315,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),g)),compose(compose(h,codomain(X0)),g)),compose(compose(h,codomain(X0)),g)) = compose(compose(h,codomain(X0)),g),
    inference(paramodulation,[status(thm)],[f478,f5684]) ).

fof(f55316,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),compose(g,a))),compose(compose(h,codomain(X0)),compose(g,a))),compose(compose(h,codomain(X0)),compose(g,a))) = compose(compose(h,codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5684]) ).

fof(f55317,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),compose(h,a))),compose(compose(h,codomain(X0)),compose(h,a))),compose(compose(h,codomain(X0)),compose(h,a))) = compose(compose(h,codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5684]) ).

fof(f55342,plain,
    ! [X0] : ifeq(codomain(X0),domain(codomain(compose(h,codomain(X0)))),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(compose(h,codomain(X0))))),compose(h,codomain(X0))),compose(compose(h,codomain(X0)),codomain(compose(h,codomain(X0))))) = compose(compose(h,codomain(X0)),codomain(compose(h,codomain(X0)))),
    inference(paramodulation,[status(thm)],[f20,f5684]) ).

fof(f55512,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(h,codomain(X0))),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(compose(h,codomain(X0))))),compose(h,codomain(X0))),compose(compose(h,codomain(X0)),codomain(compose(h,codomain(X0))))) = compose(compose(h,codomain(X0)),codomain(compose(h,codomain(X0)))),
    inference(forward_demodulation,[status(thm)],[f18,f55342]) ).

fof(f55513,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(h,codomain(X0))),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(compose(h,codomain(X0))))),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(compose(h,codomain(X0)),codomain(compose(h,codomain(X0)))),
    inference(forward_demodulation,[status(thm)],[f20,f55512]) ).

fof(f55514,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(h,codomain(X0))),ifeq(domain(a),codomain(X0),compose(h,compose(codomain(X0),codomain(compose(h,codomain(X0))))),compose(h,codomain(X0))),compose(h,codomain(X0))) = compose(h,codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f20,f55513]) ).

fof(f55635,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),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)],[f478,f5685]) ).

fof(f55636,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(g,a))),compose(compose(codomain(X1),codomain(X0)),compose(g,a))),compose(compose(codomain(X1),codomain(X0)),compose(g,a))) = compose(compose(codomain(X1),codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5685]) ).

fof(f55637,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(h),ifeq(codomain(X1),codomain(X0),compose(codomain(X1),compose(codomain(X0),compose(h,a))),compose(compose(codomain(X1),codomain(X0)),compose(h,a))),compose(compose(codomain(X1),codomain(X0)),compose(h,a))) = compose(compose(codomain(X1),codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5685]) ).

fof(f55681,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)],[f20,f5685]) ).

fof(f55939,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)],[f18,f55681]) ).

fof(f55940,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)],[f20,f55939]) ).

fof(f55941,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)],[f20,f55940]) ).

fof(f56132,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),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(paramodulation,[status(thm)],[f478,f5829]) ).

fof(f56133,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(codomain(X0),compose(g,a))),codomain(X0),compose(codomain(X0),compose(g,a)),compose(compose(domain(compose(codomain(X0),compose(g,a))),codomain(X0)),compose(g,a))),compose(compose(domain(compose(codomain(X0),compose(g,a))),codomain(X0)),compose(g,a))) = compose(compose(domain(compose(codomain(X0),compose(g,a))),codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5829]) ).

fof(f56134,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(compose(codomain(X0),compose(h,a))),codomain(X0),compose(codomain(X0),compose(h,a)),compose(compose(domain(compose(codomain(X0),compose(h,a))),codomain(X0)),compose(h,a))),compose(compose(domain(compose(codomain(X0),compose(h,a))),codomain(X0)),compose(h,a))) = compose(compose(domain(compose(codomain(X0),compose(h,a))),codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5829]) ).

fof(f56975,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(compose(g,a),codomain(X0))),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),codomain(compose(compose(g,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)],[f1583,f5884]) ).

fof(f56976,plain,
    ! [X0] : ifeq(codomain(X0),codomain(compose(compose(h,a),codomain(X0))),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),codomain(compose(compose(h,a),codomain(X0))))),compose(compose(h,a),codomain(X0))),compose(compose(h,a),codomain(X0))) = compose(compose(h,a),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f5884]) ).

fof(f56978,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)],[f975,f5884]) ).

fof(f57759,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),g)),domain(h),compose(compose(h,compose(a,b)),g),compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g)),compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g)) = compose(compose(domain(compose(compose(h,compose(a,b)),g)),compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f478,f6329]) ).

fof(f57760,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),compose(g,a))),domain(h),compose(compose(h,compose(a,b)),compose(g,a)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(g,a))),compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f6329]) ).

fof(f57761,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),compose(h,a))),domain(h),compose(compose(h,compose(a,b)),compose(h,a)),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,a))),compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f6329]) ).

fof(f57762,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f6329]) ).

fof(f57764,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(compose(compose(h,compose(a,b)),domain(X0))),domain(h),compose(compose(h,compose(a,b)),domain(X0)),compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0))),compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0))) = compose(compose(domain(compose(compose(h,compose(a,b)),domain(X0))),compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f35,f6329]) ).

fof(f58225,plain,
    ifeq(domain(a),domain(h),ifeq(domain(compose(g,g)),domain(h),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)],[f478,f6331]) ).

fof(f58226,plain,
    ifeq(domain(a),domain(h),ifeq(domain(compose(g,compose(g,a))),domain(h),compose(g,compose(g,a)),compose(compose(domain(compose(g,compose(g,a))),g),compose(g,a))),compose(compose(domain(compose(g,compose(g,a))),g),compose(g,a))) = compose(compose(domain(compose(g,compose(g,a))),g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f6331]) ).

fof(f58227,plain,
    ifeq(domain(a),domain(h),ifeq(domain(compose(g,compose(h,a))),domain(h),compose(g,compose(h,a)),compose(compose(domain(compose(g,compose(h,a))),g),compose(h,a))),compose(compose(domain(compose(g,compose(h,a))),g),compose(h,a))) = compose(compose(domain(compose(g,compose(h,a))),g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f6331]) ).

fof(f58228,plain,
    ifeq(domain(a),domain(h),ifeq(domain(compose(g,compose(h,compose(a,b)))),domain(h),compose(g,compose(h,compose(a,b))),compose(compose(domain(compose(g,compose(h,compose(a,b)))),g),compose(h,compose(a,b)))),compose(compose(domain(compose(g,compose(h,compose(a,b)))),g),compose(h,compose(a,b)))) = compose(compose(domain(compose(g,compose(h,compose(a,b)))),g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f6331]) ).

fof(f58230,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(compose(g,domain(X0))),domain(h),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)],[f35,f6331]) ).

fof(f58372,plain,
    ifeq(domain(a),domain(h),ifeq(domain(compose(h,g)),domain(h),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)],[f478,f6233]) ).

fof(f58373,plain,
    ifeq(domain(a),domain(h),ifeq(domain(compose(h,compose(g,a))),domain(h),compose(h,compose(g,a)),compose(compose(domain(compose(h,compose(g,a))),h),compose(g,a))),compose(compose(domain(compose(h,compose(g,a))),h),compose(g,a))) = compose(compose(domain(compose(h,compose(g,a))),h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f6233]) ).

fof(f58374,plain,
    ifeq(domain(a),domain(h),ifeq(domain(compose(h,compose(h,a))),domain(h),compose(h,compose(h,a)),compose(compose(domain(compose(h,compose(h,a))),h),compose(h,a))),compose(compose(domain(compose(h,compose(h,a))),h),compose(h,a))) = compose(compose(domain(compose(h,compose(h,a))),h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f6233]) ).

fof(f58375,plain,
    ifeq(domain(a),domain(h),ifeq(domain(compose(h,compose(h,compose(a,b)))),domain(h),compose(h,compose(h,compose(a,b))),compose(compose(domain(compose(h,compose(h,compose(a,b)))),h),compose(h,compose(a,b)))),compose(compose(domain(compose(h,compose(h,compose(a,b)))),h),compose(h,compose(a,b)))) = compose(compose(domain(compose(h,compose(h,compose(a,b)))),h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f6233]) ).

fof(f58377,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(compose(h,domain(X0))),domain(h),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)],[f35,f6233]) ).

fof(f58500,plain,
    ! [X0] : ifeq(compose(domain(b),a),X0,ifeq(compose(g,a),X0,g,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f9946]) ).

fof(f58738,plain,
    ! [X0] : ifeq(compose(domain(b),a),X0,ifeq(compose(h,a),X0,h,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f9947]) ).

fof(f58986,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),compose(h,compose(a,b)))),domain(compose(g,a)),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f6240]) ).

fof(f58987,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),compose(h,compose(a,b)))),domain(compose(h,a)),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f6240]) ).

fof(f59010,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),compose(h,compose(a,b)))),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(g,a),compose(h,compose(a,b)))),compose(g,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f2123,f58986]) ).

fof(f59011,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),compose(h,compose(a,b)))),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b)))),compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(domain(compose(compose(h,a),compose(h,compose(a,b)))),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f58987]) ).

fof(f60616,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(g,a),domain(X0))),domain(compose(g,a)),compose(compose(g,a),domain(X0)),compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0))),compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0))) = compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f6242]) ).

fof(f60617,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(h,a),domain(X0))),domain(compose(h,a)),compose(compose(h,a),domain(X0)),compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0))),compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0))) = compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f6242]) ).

fof(f60709,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(g,a),domain(X0))),domain(h),compose(compose(g,a),domain(X0)),compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0))),compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0))) = compose(compose(domain(compose(compose(g,a),domain(X0))),compose(g,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f2123,f60616]) ).

fof(f60710,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(compose(compose(h,a),domain(X0))),domain(h),compose(compose(h,a),domain(X0)),compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0))),compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0))) = compose(compose(domain(compose(compose(h,a),domain(X0))),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f60617]) ).

fof(f61927,plain,
    ifeq(codomain(b),domain(h),domain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),domain(h)) = domain(h),
    inference(forward_demodulation,[status(thm)],[f22238,f17250]) ).

fof(f61982,plain,
    ifeq(codomain(b),domain(h),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),codomain(b)) = codomain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f17595]) ).

fof(f61984,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f7000]) ).

fof(f61985,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f7000]) ).

fof(f61987,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),domain(h)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),domain(h)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f7000]) ).

fof(f62023,plain,
    ! [X0] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(g,b),X0,g,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f18090]) ).

fof(f62326,plain,
    ! [X0] : ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,b),X0,h,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f18245]) ).

fof(f62705,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),b,compose(h,a),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f21129]) ).

fof(f62706,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(g,a),compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f1583,f7183]) ).

fof(f62707,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(h,a),compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f1465,f7183]) ).

fof(f62709,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(b))) = compose(compose(compose(a,b),compose(h,compose(a,b))),codomain(b)),
    inference(paramodulation,[status(thm)],[f975,f7183]) ).

fof(f62735,plain,
    ifeq(domain(b),domain(a),ifeq(b,compose(h,compose(a,b)),compose(h,a),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f21153]) ).

fof(f63275,plain,
    ifeq(codomain(b),codomain(compose(compose(g,a),compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),codomain(compose(compose(g,a),compose(h,compose(a,b)))))),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,a),compose(h,compose(a,b)))) = compose(compose(g,a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f7461]) ).

fof(f63276,plain,
    ifeq(codomain(b),codomain(compose(compose(h,a),compose(h,compose(a,b)))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),codomain(compose(compose(h,a),compose(h,compose(a,b)))))),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,a),compose(h,compose(a,b)))) = compose(compose(h,a),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f7461]) ).

fof(f63277,plain,
    ifeq(codomain(b),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),codomain(compose(compose(h,compose(a,b)),compose(h,compose(a,b)))))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))) = compose(compose(h,compose(a,b)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f7461]) ).

fof(f63278,plain,
    ifeq(codomain(b),codomain(compose(compose(a,b),compose(h,compose(a,b)))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),codomain(compose(compose(a,b),compose(h,compose(a,b)))))),compose(compose(a,b),compose(h,compose(a,b)))),compose(compose(a,b),compose(h,compose(a,b)))) = compose(compose(a,b),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f7461]) ).

fof(f63279,plain,
    ifeq(codomain(b),codomain(compose(g,compose(h,compose(a,b)))),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),codomain(compose(g,compose(h,compose(a,b)))))),compose(g,compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f316,f7461]) ).

fof(f63280,plain,
    ifeq(codomain(b),codomain(compose(h,compose(h,compose(a,b)))),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),codomain(compose(h,compose(h,compose(a,b)))))),compose(h,compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f147,f7461]) ).

fof(f63281,plain,
    ! [X0] : ifeq(codomain(b),codomain(compose(codomain(X0),compose(h,compose(a,b)))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),codomain(compose(codomain(X0),compose(h,compose(a,b)))))),compose(codomain(X0),compose(h,compose(a,b)))),compose(codomain(X0),compose(h,compose(a,b)))) = compose(codomain(X0),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f36,f7461]) ).

fof(f63476,plain,
    ifeq(domain(a),codomain(compose(compose(g,a),g)),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,codomain(compose(compose(g,a),g)))),compose(compose(g,a),g)),compose(compose(g,a),g)) = compose(compose(g,a),g),
    inference(paramodulation,[status(thm)],[f1583,f7463]) ).

fof(f63477,plain,
    ifeq(domain(a),codomain(compose(compose(h,a),g)),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,codomain(compose(compose(h,a),g)))),compose(compose(h,a),g)),compose(compose(h,a),g)) = compose(compose(h,a),g),
    inference(paramodulation,[status(thm)],[f1465,f7463]) ).

fof(f63478,plain,
    ifeq(domain(a),codomain(compose(compose(h,compose(a,b)),g)),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,codomain(compose(compose(h,compose(a,b)),g)))),compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
    inference(paramodulation,[status(thm)],[f1016,f7463]) ).

fof(f63479,plain,
    ifeq(domain(a),codomain(compose(compose(a,b),g)),ifeq(codomain(b),domain(h),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)],[f975,f7463]) ).

fof(f63480,plain,
    ifeq(domain(a),codomain(compose(g,g)),ifeq(domain(a),domain(h),compose(g,compose(g,codomain(compose(g,g)))),compose(g,g)),compose(g,g)) = compose(g,g),
    inference(paramodulation,[status(thm)],[f316,f7463]) ).

fof(f63481,plain,
    ifeq(domain(a),codomain(compose(h,g)),ifeq(domain(a),domain(h),compose(h,compose(g,codomain(compose(h,g)))),compose(h,g)),compose(h,g)) = compose(h,g),
    inference(paramodulation,[status(thm)],[f147,f7463]) ).

fof(f63482,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(codomain(X0),g)),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,codomain(compose(codomain(X0),g)))),compose(codomain(X0),g)),compose(codomain(X0),g)) = compose(codomain(X0),g),
    inference(paramodulation,[status(thm)],[f36,f7463]) ).

fof(f63552,plain,
    ifeq(domain(a),codomain(compose(compose(g,a),h)),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,codomain(compose(compose(g,a),h)))),compose(compose(g,a),h)),compose(compose(g,a),h)) = compose(compose(g,a),h),
    inference(paramodulation,[status(thm)],[f1583,f7367]) ).

fof(f63553,plain,
    ifeq(domain(a),codomain(compose(compose(h,a),h)),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,codomain(compose(compose(h,a),h)))),compose(compose(h,a),h)),compose(compose(h,a),h)) = compose(compose(h,a),h),
    inference(paramodulation,[status(thm)],[f1465,f7367]) ).

fof(f63554,plain,
    ifeq(domain(a),codomain(compose(compose(h,compose(a,b)),h)),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,codomain(compose(compose(h,compose(a,b)),h)))),compose(compose(h,compose(a,b)),h)),compose(compose(h,compose(a,b)),h)) = compose(compose(h,compose(a,b)),h),
    inference(paramodulation,[status(thm)],[f1016,f7367]) ).

fof(f63555,plain,
    ifeq(domain(a),codomain(compose(compose(a,b),h)),ifeq(codomain(b),domain(h),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)],[f975,f7367]) ).

fof(f63556,plain,
    ifeq(domain(a),codomain(compose(g,h)),ifeq(domain(a),domain(h),compose(g,compose(h,codomain(compose(g,h)))),compose(g,h)),compose(g,h)) = compose(g,h),
    inference(paramodulation,[status(thm)],[f316,f7367]) ).

fof(f63557,plain,
    ifeq(domain(a),codomain(compose(h,h)),ifeq(domain(a),domain(h),compose(h,compose(h,codomain(compose(h,h)))),compose(h,h)),compose(h,h)) = compose(h,h),
    inference(paramodulation,[status(thm)],[f147,f7367]) ).

fof(f63558,plain,
    ! [X0] : ifeq(domain(a),codomain(compose(codomain(X0),h)),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,codomain(compose(codomain(X0),h)))),compose(codomain(X0),h)),compose(codomain(X0),h)) = compose(codomain(X0),h),
    inference(paramodulation,[status(thm)],[f36,f7367]) ).

fof(f63797,plain,
    ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),compose(g,a))),ifeq(codomain(b),domain(compose(g,a)),compose(compose(h,compose(a,b)),compose(compose(g,a),codomain(compose(compose(h,compose(a,b)),compose(g,a))))),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f7393]) ).

fof(f63798,plain,
    ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),compose(h,a))),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(compose(h,a),codomain(compose(compose(h,compose(a,b)),compose(h,a))))),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f7393]) ).

fof(f63821,plain,
    ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),compose(g,a))),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),codomain(compose(compose(h,compose(a,b)),compose(g,a))))),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f63797]) ).

fof(f63822,plain,
    ifeq(domain(b),codomain(compose(compose(h,compose(a,b)),compose(h,a))),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),codomain(compose(compose(h,compose(a,b)),compose(h,a))))),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f63798]) ).

fof(f63909,plain,
    ifeq(domain(b),codomain(compose(g,compose(g,a))),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(compose(g,a),codomain(compose(g,compose(g,a))))),compose(g,compose(g,a))),compose(g,compose(g,a))) = compose(g,compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f7395]) ).

fof(f63910,plain,
    ifeq(domain(b),codomain(compose(g,compose(h,a))),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),codomain(compose(g,compose(h,a))))),compose(g,compose(h,a))),compose(g,compose(h,a))) = compose(g,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f7395]) ).

fof(f63940,plain,
    ifeq(domain(b),codomain(compose(g,compose(g,a))),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),codomain(compose(g,compose(g,a))))),compose(g,compose(g,a))),compose(g,compose(g,a))) = compose(g,compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f63909]) ).

fof(f63941,plain,
    ifeq(domain(b),codomain(compose(g,compose(h,a))),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),codomain(compose(g,compose(h,a))))),compose(g,compose(h,a))),compose(g,compose(h,a))) = compose(g,compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f63910]) ).

fof(f64086,plain,
    ifeq(domain(b),codomain(compose(h,compose(g,a))),ifeq(domain(a),domain(compose(g,a)),compose(h,compose(compose(g,a),codomain(compose(h,compose(g,a))))),compose(h,compose(g,a))),compose(h,compose(g,a))) = compose(h,compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f7396]) ).

fof(f64087,plain,
    ifeq(domain(b),codomain(compose(h,compose(h,a))),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),codomain(compose(h,compose(h,a))))),compose(h,compose(h,a))),compose(h,compose(h,a))) = compose(h,compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f7396]) ).

fof(f64115,plain,
    ifeq(domain(b),codomain(compose(h,compose(g,a))),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),codomain(compose(h,compose(g,a))))),compose(h,compose(g,a))),compose(h,compose(g,a))) = compose(h,compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f64086]) ).

fof(f64116,plain,
    ifeq(domain(b),codomain(compose(h,compose(h,a))),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),codomain(compose(h,compose(h,a))))),compose(h,compose(h,a))),compose(h,compose(h,a))) = compose(h,compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f64087]) ).

fof(f64237,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(codomain(X0),compose(g,a))),ifeq(codomain(X0),domain(compose(g,a)),compose(codomain(X0),compose(compose(g,a),codomain(compose(codomain(X0),compose(g,a))))),compose(codomain(X0),compose(g,a))),compose(codomain(X0),compose(g,a))) = compose(codomain(X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f7397]) ).

fof(f64238,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(codomain(X0),compose(h,a))),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(compose(h,a),codomain(compose(codomain(X0),compose(h,a))))),compose(codomain(X0),compose(h,a))),compose(codomain(X0),compose(h,a))) = compose(codomain(X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f7397]) ).

fof(f64315,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(codomain(X0),compose(g,a))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),codomain(compose(codomain(X0),compose(g,a))))),compose(codomain(X0),compose(g,a))),compose(codomain(X0),compose(g,a))) = compose(codomain(X0),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f64237]) ).

fof(f64316,plain,
    ! [X0] : ifeq(domain(b),codomain(compose(codomain(X0),compose(h,a))),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),codomain(compose(codomain(X0),compose(h,a))))),compose(codomain(X0),compose(h,a))),compose(codomain(X0),compose(h,a))) = compose(codomain(X0),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f64238]) ).

fof(f65327,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(codomain(compose(g,a)),a),X0,ifeq(compose(a,a),X0,a,codomain(compose(g,a))),codomain(compose(g,a))),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f9711]) ).

fof(f65383,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(codomain(compose(g,a)),a),X0,ifeq(compose(a,a),X0,a,codomain(compose(g,a))),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f65327]) ).

fof(f65384,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(a,a),X0,a,codomain(compose(g,a))),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f65383]) ).

fof(f65385,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(a,a),X0,a,domain(b)),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f65384]) ).

fof(f65386,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(a,a),X0,a,domain(b)),domain(b)),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f65385]) ).

fof(f65387,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(a,a),X0,a,domain(b)),domain(b)),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f65386]) ).

fof(f65388,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(a,a),X0,a,domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f65387]) ).

fof(f66267,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(domain(b),domain(b),ifeq(compose(codomain(compose(g,a)),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),codomain(compose(g,a))),codomain(compose(g,a))),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f9736]) ).

fof(f66356,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(codomain(compose(g,a)),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),codomain(compose(g,a))),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f16,f66267]) ).

fof(f66357,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),codomain(compose(g,a))),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f66356]) ).

fof(f66358,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),domain(b)),codomain(compose(g,a))),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f66357]) ).

fof(f66359,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),domain(b)),domain(b)),codomain(compose(g,a))) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f66358]) ).

fof(f66360,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),domain(b)),domain(b)),domain(b)) = codomain(compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1583,f66359]) ).

fof(f66361,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(domain(X0),a),X1,domain(X0),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f1583,f66360]) ).

fof(f67356,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(compose(h,compose(a,b)),a),X0,compose(h,compose(a,b)),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f9892]) ).

fof(f67364,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(domain(X0),a),compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f16,f9892]) ).

fof(f67373,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f16,f9892]) ).

fof(f67669,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(b),a),X1,ifeq(compose(codomain(X0),a),X1,codomain(X0),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f9896]) ).

fof(f68057,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1583,f9899]) ).

fof(f68058,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1465,f9899]) ).

fof(f68060,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(domain(b),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f975,f9899]) ).

fof(f68068,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,a),compose(domain(b),a),X0,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f9899]) ).

fof(f68071,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(b),a),compose(X0,a),X0,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f16,f9899]) ).

fof(f68083,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(domain(b),a),compose(g,a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1583,f68068]) ).

fof(f68084,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(domain(b),a),compose(h,a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1465,f68068]) ).

fof(f68085,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(domain(b),a),compose(h,compose(a,b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1016,f68068]) ).

fof(f68086,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),a),compose(domain(b),a),compose(a,b),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f975,f68068]) ).

fof(f68089,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(codomain(X0),a),compose(domain(b),a),codomain(X0),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f36,f68068]) ).

fof(f68090,plain,
    ifeq(domain(b),domain(a),ifeq(compose(a,a),compose(domain(b),a),a,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f24,f68068]) ).

fof(f68091,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(X0),a),compose(domain(b),a),domain(X0),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f17,f68068]) ).

fof(f68104,plain,
    ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),compose(compose(g,a),a),compose(g,a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1583,f68071]) ).

fof(f68105,plain,
    ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),compose(compose(h,a),a),compose(h,a),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1465,f68071]) ).

fof(f68106,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(domain(b),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f1016,f68071]) ).

fof(f68107,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(domain(b),a),compose(compose(a,b),a),compose(a,b),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f975,f68071]) ).

fof(f68110,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(domain(b),a),compose(codomain(X0),a),codomain(X0),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f36,f68071]) ).

fof(f68111,plain,
    ifeq(domain(b),domain(a),ifeq(compose(domain(b),a),compose(a,a),a,domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f24,f68071]) ).

fof(f68112,plain,
    ! [X0] : ifeq(domain(X0),domain(a),ifeq(compose(domain(b),a),compose(domain(X0),a),domain(X0),domain(b)),domain(b)) = domain(b),
    inference(paramodulation,[status(thm)],[f17,f68071]) ).

fof(f68480,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(g,a),a),compose(domain(X0),a),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1583,f9907]) ).

fof(f68481,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(h,a),a),compose(domain(X0),a),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1465,f9907]) ).

fof(f68483,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(a,b),a),compose(domain(X0),a),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f975,f9907]) ).

fof(f68724,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(compose(g,a),a),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1583,f9916]) ).

fof(f68725,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(compose(h,a),a),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1465,f9916]) ).

fof(f68727,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),a),compose(compose(a,b),a),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f975,f9916]) ).

fof(f68969,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(compose(g,a),a),compose(h,a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1465,f10288]) ).

fof(f68970,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(g,a),a),compose(h,compose(a,b)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1016,f10288]) ).

fof(f68971,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),a),compose(compose(g,a),a),compose(a,b),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f975,f10288]) ).

fof(f68989,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(compose(h,a),a),compose(g,a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1583,f10289]) ).

fof(f68991,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(h,a),a),compose(h,compose(a,b)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1016,f10289]) ).

fof(f68992,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),a),compose(compose(h,a),a),compose(a,b),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f975,f10289]) ).

fof(f69010,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(g,a),a),compose(codomain(X0),a),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1583,f10280]) ).

fof(f69011,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,a),a),compose(codomain(X0),a),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1465,f10280]) ).

fof(f69012,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(codomain(X0),a),compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1016,f10280]) ).

fof(f69013,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(a,b),a),compose(codomain(X0),a),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f975,f10280]) ).

fof(f69313,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(g,a),a),a,compose(g,a),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1583,f10293]) ).

fof(f69314,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,a),a),a,compose(h,a),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1465,f10293]) ).

fof(f69315,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(h,compose(a,b)),a),a,compose(h,compose(a,b)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1016,f10293]) ).

fof(f69316,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(compose(a,b),a),a,compose(a,b),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f975,f10293]) ).

fof(f69334,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(compose(g,a),a),compose(g,a),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1583,f10355]) ).

fof(f69335,plain,
    ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(compose(h,a),a),compose(h,a),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1465,f10355]) ).

fof(f69336,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f1016,f10355]) ).

fof(f69337,plain,
    ifeq(codomain(b),domain(a),ifeq(domain(a),domain(b),ifeq(a,compose(compose(a,b),a),compose(a,b),domain(a)),domain(a)),domain(a)) = domain(a),
    inference(paramodulation,[status(thm)],[f975,f10355]) ).

fof(f69357,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),compose(compose(h,a),a),compose(h,a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1465,f10406]) ).

fof(f69358,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(g,a),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1016,f10406]) ).

fof(f69359,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(g,a),a),compose(compose(a,b),a),compose(a,b),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f975,f10406]) ).

fof(f69379,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),compose(compose(g,a),a),compose(g,a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1583,f10407]) ).

fof(f69381,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1016,f10407]) ).

fof(f69382,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),a),compose(compose(a,b),a),compose(a,b),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f975,f10407]) ).

fof(f69402,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(compose(g,a),a),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1583,f10397]) ).

fof(f69403,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(compose(h,a),a),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1465,f10397]) ).

fof(f69404,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1016,f10397]) ).

fof(f69405,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),a),compose(compose(a,b),a),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f975,f10397]) ).

fof(f69706,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(g,a),b),compose(domain(X0),b),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1583,f10666]) ).

fof(f69707,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(h,a),b),compose(domain(X0),b),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1465,f10666]) ).

fof(f69708,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(domain(X0),b),compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1016,f10666]) ).

fof(f69709,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(compose(a,b),b),compose(domain(X0),b),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f975,f10666]) ).

fof(f69760,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(domain(X0),b),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f446,f69706]) ).

fof(f69761,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(domain(X0),b),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f22238,f69707]) ).

fof(f69950,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(compose(g,a),b),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1583,f10675]) ).

fof(f69951,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(compose(h,a),b),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1465,f10675]) ).

fof(f69952,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f1016,f10675]) ).

fof(f69953,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(compose(a,b),b),compose(a,b),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(paramodulation,[status(thm)],[f975,f10675]) ).

fof(f70005,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(h,compose(a,b)),compose(g,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f446,f69950]) ).

fof(f70006,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),compose(h,compose(a,b)),compose(h,a),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f22238,f69951]) ).

fof(f70195,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),compose(h,compose(a,b)),compose(h,a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1465,f10994]) ).

fof(f70196,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(h,compose(a,b)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1016,f10994]) ).

fof(f70197,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),b),compose(h,compose(a,b)),compose(a,b),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f975,f10994]) ).

fof(f70211,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(h,compose(a,b)),compose(h,a),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f22238,f70195]) ).

fof(f70212,plain,
    ifeq(domain(b),domain(a),compose(h,a),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f70211]) ).

fof(f70223,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(X0,b),compose(h,compose(a,b)),X0,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f10995]) ).

fof(f70224,plain,
    ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),b),compose(h,compose(a,b)),compose(g,a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1583,f70223]) ).

fof(f70226,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(h,compose(a,b)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1016,f70223]) ).

fof(f70227,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(a,b),b),compose(h,compose(a,b)),compose(a,b),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f975,f70223]) ).

fof(f70239,plain,
    ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(h,compose(a,b)),compose(g,a),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f446,f70224]) ).

fof(f70240,plain,
    ifeq(domain(b),domain(a),compose(g,a),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f70239]) ).

fof(f70253,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(g,a),b),compose(codomain(X0),b),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1583,f10982]) ).

fof(f70254,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,a),b),compose(codomain(X0),b),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1465,f10982]) ).

fof(f70255,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(codomain(X0),b),compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1016,f10982]) ).

fof(f70256,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(compose(a,b),b),compose(codomain(X0),b),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f975,f10982]) ).

fof(f70314,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(codomain(X0),b),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f446,f70253]) ).

fof(f70315,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(codomain(X0),b),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f22238,f70254]) ).

fof(f70570,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1016,f11322]) ).

fof(f70571,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(compose(a,b),b),compose(a,b),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f975,f11322]) ).

fof(f70597,plain,
    ! [X0] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),compose(X0,b),X0,compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f11323]) ).

fof(f70600,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1016,f70597]) ).

fof(f70601,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),compose(compose(a,b),b),compose(a,b),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f975,f70597]) ).

fof(f70628,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(compose(g,a),b),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1583,f11309]) ).

fof(f70629,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(compose(h,a),b),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1465,f11309]) ).

fof(f70630,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f1016,f11309]) ).

fof(f70631,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(compose(a,b),b),compose(a,b),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(paramodulation,[status(thm)],[f975,f11309]) ).

fof(f70690,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(h,compose(a,b)),compose(g,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f446,f70628]) ).

fof(f70691,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),compose(h,compose(a,b)),compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f22238,f70629]) ).

fof(f71899,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(a,b),a),compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10266]) ).

fof(f72285,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(g,a),a),compose(compose(h,compose(a,b)),a),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f10276]) ).

fof(f72286,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,a),a),compose(compose(h,compose(a,b)),a),compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f10276]) ).

fof(f72288,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(compose(h,compose(a,b)),a),compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f10276]) ).

fof(f72403,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10383]) ).

fof(f72419,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(g,a),a),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f10393]) ).

fof(f72420,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(h,a),a),compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f10393]) ).

fof(f72422,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),a),compose(compose(a,b),a),compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f10393]) ).

fof(f72525,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),domain(compose(g,a))),compose(g,a))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f6947]) ).

fof(f72526,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),domain(compose(h,a))),compose(h,a))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f6947]) ).

fof(f72547,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),domain(h)),compose(g,a))) = compose(compose(compose(g,a),domain(compose(g,a))),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f72525]) ).

fof(f72548,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),domain(h)),compose(g,a))) = compose(compose(compose(g,a),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f72547]) ).

fof(f72549,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),domain(h)),compose(h,a))) = compose(compose(compose(g,a),domain(compose(h,a))),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f72526]) ).

fof(f72550,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),domain(h)),compose(h,a))) = compose(compose(compose(g,a),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f72549]) ).

fof(f72589,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),domain(compose(g,a))),compose(g,a))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f6948]) ).

fof(f72590,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),domain(compose(h,a))),compose(h,a))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f6948]) ).

fof(f72611,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),domain(h)),compose(g,a))) = compose(compose(compose(h,a),domain(compose(g,a))),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f72589]) ).

fof(f72612,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),domain(h)),compose(g,a))) = compose(compose(compose(h,a),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f72611]) ).

fof(f72613,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),domain(h)),compose(h,a))) = compose(compose(compose(h,a),domain(compose(h,a))),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f72590]) ).

fof(f72614,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),domain(h)),compose(h,a))) = compose(compose(compose(h,a),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f72613]) ).

fof(f72652,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),domain(compose(g,a))),compose(g,a))) = compose(compose(compose(a,b),domain(compose(g,a))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f6950]) ).

fof(f72653,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),domain(compose(h,a))),compose(h,a))) = compose(compose(compose(a,b),domain(compose(h,a))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f6950]) ).

fof(f72669,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),domain(h)),compose(g,a))) = compose(compose(compose(a,b),domain(compose(g,a))),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f72652]) ).

fof(f72670,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),domain(h)),compose(g,a))) = compose(compose(compose(a,b),domain(h)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f72669]) ).

fof(f72671,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),domain(h)),compose(h,a))) = compose(compose(compose(a,b),domain(compose(h,a))),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f72653]) ).

fof(f72672,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),domain(h)),compose(h,a))) = compose(compose(compose(a,b),domain(h)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f72671]) ).

fof(f72706,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),compose(g,a)),codomain(compose(g,a)))) = compose(compose(compose(g,a),compose(g,a)),codomain(compose(g,a))),
    inference(paramodulation,[status(thm)],[f2123,f7118]) ).

fof(f72707,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),compose(h,a)),codomain(compose(h,a)))) = compose(compose(compose(g,a),compose(h,a)),codomain(compose(h,a))),
    inference(paramodulation,[status(thm)],[f1908,f7118]) ).

fof(f72732,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),compose(g,a)),domain(b))) = compose(compose(compose(g,a),compose(g,a)),codomain(compose(g,a))),
    inference(forward_demodulation,[status(thm)],[f1583,f72706]) ).

fof(f72733,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(compose(g,a),compose(g,a)),domain(b))) = compose(compose(compose(g,a),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f72732]) ).

fof(f72734,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),compose(h,a)),domain(b))) = compose(compose(compose(g,a),compose(h,a)),codomain(compose(h,a))),
    inference(forward_demodulation,[status(thm)],[f1465,f72707]) ).

fof(f72735,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(compose(g,a),compose(h,a)),domain(b))) = compose(compose(compose(g,a),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f72734]) ).

fof(f72789,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),compose(g,a)),codomain(compose(g,a)))) = compose(compose(compose(h,a),compose(g,a)),codomain(compose(g,a))),
    inference(paramodulation,[status(thm)],[f2123,f7119]) ).

fof(f72790,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),compose(h,a)),codomain(compose(h,a)))) = compose(compose(compose(h,a),compose(h,a)),codomain(compose(h,a))),
    inference(paramodulation,[status(thm)],[f1908,f7119]) ).

fof(f72815,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),compose(g,a)),domain(b))) = compose(compose(compose(h,a),compose(g,a)),codomain(compose(g,a))),
    inference(forward_demodulation,[status(thm)],[f1583,f72789]) ).

fof(f72816,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(compose(h,a),compose(g,a)),domain(b))) = compose(compose(compose(h,a),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f72815]) ).

fof(f72817,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),compose(h,a)),domain(b))) = compose(compose(compose(h,a),compose(h,a)),codomain(compose(h,a))),
    inference(forward_demodulation,[status(thm)],[f1465,f72790]) ).

fof(f72818,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(compose(h,a),compose(h,a)),domain(b))) = compose(compose(compose(h,a),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f72817]) ).

fof(f72871,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),compose(g,a)),codomain(compose(g,a)))) = compose(compose(compose(a,b),compose(g,a)),codomain(compose(g,a))),
    inference(paramodulation,[status(thm)],[f2123,f7121]) ).

fof(f72872,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),compose(h,a)),codomain(compose(h,a)))) = compose(compose(compose(a,b),compose(h,a)),codomain(compose(h,a))),
    inference(paramodulation,[status(thm)],[f1908,f7121]) ).

fof(f72892,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),compose(g,a)),domain(b))) = compose(compose(compose(a,b),compose(g,a)),codomain(compose(g,a))),
    inference(forward_demodulation,[status(thm)],[f1583,f72871]) ).

fof(f72893,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,a)),compose(compose(compose(a,b),compose(g,a)),domain(b))) = compose(compose(compose(a,b),compose(g,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1583,f72892]) ).

fof(f72894,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),compose(h,a)),domain(b))) = compose(compose(compose(a,b),compose(h,a)),codomain(compose(h,a))),
    inference(forward_demodulation,[status(thm)],[f1465,f72872]) ).

fof(f72895,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,a)),compose(compose(compose(a,b),compose(h,a)),domain(b))) = compose(compose(compose(a,b),compose(h,a)),domain(b)),
    inference(forward_demodulation,[status(thm)],[f1465,f72894]) ).

fof(f73066,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(g,a),a),compose(compose(a,b),a),compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10264]) ).

fof(f73084,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,a),a),compose(compose(a,b),a),compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10265]) ).

fof(f73120,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(compose(g,a),a),compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10381]) ).

fof(f73140,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),compose(compose(h,a),a),compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10382]) ).

fof(f73177,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(a,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),a),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f10631]) ).

fof(f73187,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(compose(a,b),b),compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10990]) ).

fof(f73211,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(h,compose(a,b)),compose(X0,b),compose(h,a),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f22238,f10967]) ).

fof(f73214,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),b),compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f73211]) ).

fof(f73215,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(compose(a,b),b),compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f73211]) ).

fof(f73268,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(h,compose(a,b)),compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f11318]) ).

fof(f73292,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),compose(h,compose(a,b)),compose(h,a),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f22238,f11294]) ).

fof(f73295,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1016,f73292]) ).

fof(f73296,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(h,compose(a,b)),compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f73292]) ).

fof(f78022,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(compose(a,b),b),compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f10968]) ).

fof(f78045,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(g,a),b),compose(compose(h,compose(a,b)),b),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f10978]) ).

fof(f78048,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(compose(h,compose(a,b)),b),compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f10978]) ).

fof(f78058,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),b),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f446,f78045]) ).

fof(f78075,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f11295]) ).

fof(f78100,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(compose(g,a),b),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f11305]) ).

fof(f78103,plain,
    ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(compose(a,b),b),compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f11305]) ).

fof(f78114,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f446,f78100]) ).

fof(f79260,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(g,a)),compose(X0,compose(compose(g,a),g)),compose(compose(X0,compose(g,a)),g)),compose(compose(X0,compose(g,a)),g)) = compose(compose(X0,compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f1583,f508]) ).

fof(f79261,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(compose(h,a),g)),compose(compose(X0,compose(h,a)),g)),compose(compose(X0,compose(h,a)),g)) = compose(compose(X0,compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f508]) ).

fof(f79269,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,g)),compose(compose(compose(g,a),X0),g)),compose(compose(compose(g,a),X0),g)) = compose(compose(compose(g,a),X0),g),
    inference(paramodulation,[status(thm)],[f1583,f508]) ).

fof(f79270,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,g)),compose(compose(compose(h,a),X0),g)),compose(compose(compose(h,a),X0),g)) = compose(compose(compose(h,a),X0),g),
    inference(paramodulation,[status(thm)],[f1465,f508]) ).

fof(f79272,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),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)],[f975,f508]) ).

fof(f79289,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(compose(h,a)),domain(b),compose(compose(h,a),compose(b,g)),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(paramodulation,[status(thm)],[f22238,f508]) ).

fof(f79326,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),g)),compose(compose(X0,compose(g,a)),g)),compose(compose(X0,compose(g,a)),g)) = compose(compose(X0,compose(g,a)),g),
    inference(forward_demodulation,[status(thm)],[f2123,f79260]) ).

fof(f79327,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),g)),compose(compose(X0,compose(h,a)),g)),compose(compose(X0,compose(h,a)),g)) = compose(compose(X0,compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f79261]) ).

fof(f79354,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(b),compose(compose(h,a),compose(b,g)),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f1465,f79289]) ).

fof(f79355,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f16,f79354]) ).

fof(f79356,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,g)),compose(compose(h,compose(a,b)),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f22238,f79355]) ).

fof(f79357,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
    inference(forward_demodulation,[status(thm)],[f22238,f79356]) ).

fof(f79544,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(compose(h,a),b),X0,compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f1465,f1030]) ).

fof(f79546,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f1030]) ).

fof(f79558,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(forward_demodulation,[status(thm)],[f22238,f79544]) ).

fof(f79627,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f1031]) ).

fof(f79642,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),b),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f79627]) ).

fof(f79643,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(a,b),b),X0,compose(a,b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f79642]) ).

fof(f79925,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f1583,f1032]) ).

fof(f79926,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f1465,f1032]) ).

fof(f79928,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(a,b),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(a,b)),compose(a,b)),compose(a,b)),compose(a,b)) = compose(a,b),
    inference(paramodulation,[status(thm)],[f975,f1032]) ).

fof(f80344,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(g,a)),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f1033]) ).

fof(f80345,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f1033]) ).

fof(f80356,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f16,f80344]) ).

fof(f80357,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(a,b),a),X0,compose(a,b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f80345]) ).

fof(f80360,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(compose(g,a)),compose(compose(a,b),compose(compose(g,a),X0)),compose(compose(compose(a,b),compose(g,a)),X0)),compose(compose(compose(a,b),compose(g,a)),X0)) = compose(compose(compose(a,b),compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f1034]) ).

fof(f80361,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),X0)),compose(compose(compose(a,b),compose(h,a)),X0)),compose(compose(compose(a,b),compose(h,a)),X0)) = compose(compose(compose(a,b),compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f1034]) ).

fof(f80370,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(g,a))),compose(compose(compose(a,b),X0),compose(g,a))),compose(compose(compose(a,b),X0),compose(g,a))) = compose(compose(compose(a,b),X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f1034]) ).

fof(f80371,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(X0,compose(h,a))),compose(compose(compose(a,b),X0),compose(h,a))),compose(compose(compose(a,b),X0),compose(h,a))) = compose(compose(compose(a,b),X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f1034]) ).

fof(f80384,plain,
    ifeq(codomain(compose(h,a)),domain(b),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(h,a)),b)),compose(compose(compose(a,b),compose(h,a)),b)) = compose(compose(compose(a,b),compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f1034]) ).

fof(f80408,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),X0)),compose(compose(compose(a,b),compose(g,a)),X0)),compose(compose(compose(a,b),compose(g,a)),X0)) = compose(compose(compose(a,b),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f80360]) ).

fof(f80409,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),X0)),compose(compose(compose(a,b),compose(h,a)),X0)),compose(compose(compose(a,b),compose(h,a)),X0)) = compose(compose(compose(a,b),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f80361]) ).

fof(f80426,plain,
    ifeq(domain(b),domain(b),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(h,a)),b)),compose(compose(compose(a,b),compose(h,a)),b)) = compose(compose(compose(a,b),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f80384]) ).

fof(f80427,plain,
    ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(h,a)),b)) = compose(compose(compose(a,b),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f80426]) ).

fof(f80428,plain,
    ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(a,b))),compose(compose(compose(a,b),compose(h,a)),b)) = compose(compose(compose(a,b),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f80427]) ).

fof(f81128,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1583,f1655]) ).

fof(f81129,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(g,a),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(paramodulation,[status(thm)],[f1465,f1655]) ).

fof(f81155,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f1612]) ).

fof(f81167,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(g,a),a),X0,compose(g,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f81155]) ).

fof(f81170,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(a,a),compose(compose(h,a),b),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f17035]) ).

fof(f81171,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),a),compose(a,a),compose(h,compose(a,b)),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f81170]) ).

fof(f81172,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(a,a),compose(compose(h,compose(a,b)),a),compose(compose(h,a),b),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f17058]) ).

fof(f81173,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(a,a),compose(compose(h,compose(a,b)),a),compose(h,compose(a,b)),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f81172]) ).

fof(f81174,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(g,a)),compose(compose(g,a),compose(compose(g,a),X0)),compose(compose(compose(g,a),compose(g,a)),X0)),compose(compose(compose(g,a),compose(g,a)),X0)) = compose(compose(compose(g,a),compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1583,f1613]) ).

fof(f81175,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),X0)),compose(compose(compose(g,a),compose(h,a)),X0)),compose(compose(compose(g,a),compose(h,a)),X0)) = compose(compose(compose(g,a),compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f1613]) ).

fof(f81184,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,compose(g,a))),compose(compose(compose(g,a),X0),compose(g,a))),compose(compose(compose(g,a),X0),compose(g,a))) = compose(compose(compose(g,a),X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f1613]) ).

fof(f81185,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(X0,compose(h,a))),compose(compose(compose(g,a),X0),compose(h,a))),compose(compose(compose(g,a),X0),compose(h,a))) = compose(compose(compose(g,a),X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f1613]) ).

fof(f81199,plain,
    ifeq(codomain(compose(h,a)),domain(b),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(h,a)),b)),compose(compose(compose(g,a),compose(h,a)),b)) = compose(compose(compose(g,a),compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f22238,f1613]) ).

fof(f81225,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),X0)),compose(compose(compose(g,a),compose(g,a)),X0)),compose(compose(compose(g,a),compose(g,a)),X0)) = compose(compose(compose(g,a),compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f81174]) ).

fof(f81226,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),X0)),compose(compose(compose(g,a),compose(h,a)),X0)),compose(compose(compose(g,a),compose(h,a)),X0)) = compose(compose(compose(g,a),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f81175]) ).

fof(f81245,plain,
    ifeq(domain(b),domain(b),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(h,a)),b)),compose(compose(compose(g,a),compose(h,a)),b)) = compose(compose(compose(g,a),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1465,f81199]) ).

fof(f81246,plain,
    ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(h,a)),b)) = compose(compose(compose(g,a),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f16,f81245]) ).

fof(f81247,plain,
    ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(a,b))),compose(compose(compose(g,a),compose(h,a)),b)) = compose(compose(compose(g,a),compose(h,a)),b),
    inference(forward_demodulation,[status(thm)],[f1908,f81246]) ).

fof(f81345,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),compose(a,b),compose(compose(h,a),b),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f17110]) ).

fof(f81346,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),compose(a,b),compose(h,compose(a,b)),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f81345]) ).

fof(f81347,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(h,compose(a,b)),b),compose(compose(h,a),b),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f17135]) ).

fof(f81348,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(a,b),compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),a),a) = a,
    inference(forward_demodulation,[status(thm)],[f22238,f81347]) ).

fof(f81349,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(X1,compose(compose(g,a),X0)),compose(compose(X1,compose(g,a)),X0)),compose(compose(X1,compose(g,a)),X0)) = compose(compose(X1,compose(g,a)),X0),
    inference(forward_demodulation,[status(thm)],[f2123,f1614]) ).

fof(f81352,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(g,a))),compose(compose(X0,compose(g,a)),compose(g,a))),compose(compose(X0,compose(g,a)),compose(g,a))) = compose(compose(X0,compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f81349]) ).

fof(f81353,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(g,a),compose(h,a))),compose(compose(X0,compose(g,a)),compose(h,a))),compose(compose(X0,compose(g,a)),compose(h,a))) = compose(compose(X0,compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f81349]) ).

fof(f81359,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),X0)),compose(compose(compose(h,a),compose(g,a)),X0)),compose(compose(compose(h,a),compose(g,a)),X0)) = compose(compose(compose(h,a),compose(g,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f81349]) ).

fof(f81413,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,g)),compose(compose(compose(g,a),a),g)),compose(compose(compose(g,a),a),g)) = compose(compose(compose(g,a),a),g),
    inference(paramodulation,[status(thm)],[f1583,f2269]) ).

fof(f81414,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,g)),compose(compose(compose(h,a),a),g)),compose(compose(compose(h,a),a),g)) = compose(compose(compose(h,a),a),g),
    inference(paramodulation,[status(thm)],[f1465,f2269]) ).

fof(f81416,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,g)),compose(compose(compose(a,b),a),g)),compose(compose(compose(a,b),a),g)) = compose(compose(compose(a,b),a),g),
    inference(paramodulation,[status(thm)],[f975,f2269]) ).

fof(f81437,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,compose(g,a))),compose(compose(compose(g,a),a),compose(g,a))),compose(compose(compose(g,a),a),compose(g,a))) = compose(compose(compose(g,a),a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2276]) ).

fof(f81438,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(a,compose(h,a))),compose(compose(compose(g,a),a),compose(h,a))),compose(compose(compose(g,a),a),compose(h,a))) = compose(compose(compose(g,a),a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2276]) ).

fof(f81461,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(g,a))),compose(compose(compose(a,b),a),compose(g,a))),compose(compose(compose(a,b),a),compose(g,a))) = compose(compose(compose(a,b),a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2279]) ).

fof(f81462,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(a,compose(h,a))),compose(compose(compose(a,b),a),compose(h,a))),compose(compose(compose(a,b),a),compose(h,a))) = compose(compose(compose(a,b),a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2279]) ).

fof(f81491,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),g)),compose(compose(compose(g,a),domain(X0)),g)),compose(compose(compose(g,a),domain(X0)),g)) = compose(compose(compose(g,a),domain(X0)),g),
    inference(paramodulation,[status(thm)],[f1583,f2644]) ).

fof(f81492,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),g)),compose(compose(compose(h,a),domain(X0)),g)),compose(compose(compose(h,a),domain(X0)),g)) = compose(compose(compose(h,a),domain(X0)),g),
    inference(paramodulation,[status(thm)],[f1465,f2644]) ).

fof(f81494,plain,
    ! [X0] : ifeq(domain(X0),domain(h),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)],[f975,f2644]) ).

fof(f81801,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,compose(g,a))),compose(compose(h,compose(a,b)),compose(g,a))) = compose(compose(h,compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f22543]) ).

fof(f81802,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,a),compose(b,compose(h,a))),compose(compose(h,compose(a,b)),compose(h,a))) = compose(compose(h,compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f22543]) ).

fof(f81824,plain,
    ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(a,b))),compose(compose(compose(h,a),compose(h,a)),b)) = compose(compose(compose(h,a),compose(h,a)),b),
    inference(paramodulation,[status(thm)],[f1465,f22550]) ).

fof(f81863,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),compose(g,a))),compose(compose(compose(g,a),domain(X0)),compose(g,a))),compose(compose(compose(g,a),domain(X0)),compose(g,a))) = compose(compose(compose(g,a),domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2651]) ).

fof(f81864,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(g,a),compose(domain(X0),compose(h,a))),compose(compose(compose(g,a),domain(X0)),compose(h,a))),compose(compose(compose(g,a),domain(X0)),compose(h,a))) = compose(compose(compose(g,a),domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2651]) ).

fof(f82128,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(g,a))),compose(compose(compose(a,b),domain(X0)),compose(g,a))),compose(compose(compose(a,b),domain(X0)),compose(g,a))) = compose(compose(compose(a,b),domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f2654]) ).

fof(f82129,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(codomain(b),domain(X0),compose(compose(a,b),compose(domain(X0),compose(h,a))),compose(compose(compose(a,b),domain(X0)),compose(h,a))),compose(compose(compose(a,b),domain(X0)),compose(h,a))) = compose(compose(compose(a,b),domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f2654]) ).

fof(f82374,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(a,b))),compose(compose(compose(g,a),compose(g,a)),compose(a,b))),compose(compose(compose(g,a),compose(g,a)),compose(a,b))) = compose(compose(compose(g,a),compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1583,f3028]) ).

fof(f82375,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(a,b))),compose(compose(compose(h,a),compose(g,a)),compose(a,b))),compose(compose(compose(h,a),compose(g,a)),compose(a,b))) = compose(compose(compose(h,a),compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f3028]) ).

fof(f82377,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(a,b))),compose(compose(compose(a,b),compose(g,a)),compose(a,b))),compose(compose(compose(a,b),compose(g,a)),compose(a,b))) = compose(compose(compose(a,b),compose(g,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f975,f3028]) ).

fof(f82408,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),compose(a,b))),compose(compose(compose(g,a),compose(h,a)),compose(a,b))),compose(compose(compose(g,a),compose(h,a)),compose(a,b))) = compose(compose(compose(g,a),compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2976]) ).

fof(f82434,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(a,b))),compose(compose(compose(g,a),compose(h,a)),compose(a,b))),compose(compose(compose(g,a),compose(h,a)),compose(a,b))) = compose(compose(compose(g,a),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f82408]) ).

fof(f82494,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),compose(a,b))),compose(compose(compose(a,b),compose(h,a)),compose(a,b))),compose(compose(compose(a,b),compose(h,a)),compose(a,b))) = compose(compose(compose(a,b),compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2979]) ).

fof(f82517,plain,
    ifeq(domain(b),domain(a),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(a,b))),compose(compose(compose(a,b),compose(h,a)),compose(a,b))),compose(compose(compose(a,b),compose(h,a)),compose(a,b))) = compose(compose(compose(a,b),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f82494]) ).

fof(f82578,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),codomain(X0))),compose(compose(compose(g,a),compose(g,a)),codomain(X0))),compose(compose(compose(g,a),compose(g,a)),codomain(X0))) = compose(compose(compose(g,a),compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f3695]) ).

fof(f82579,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),codomain(X0))),compose(compose(compose(h,a),compose(g,a)),codomain(X0))),compose(compose(compose(h,a),compose(g,a)),codomain(X0))) = compose(compose(compose(h,a),compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3695]) ).

fof(f82581,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),codomain(X0))),compose(compose(compose(a,b),compose(g,a)),codomain(X0))),compose(compose(compose(a,b),compose(g,a)),codomain(X0))) = compose(compose(compose(a,b),compose(g,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f975,f3695]) ).

fof(f84811,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),codomain(X0))),compose(compose(compose(g,a),compose(h,a)),codomain(X0))),compose(compose(compose(g,a),compose(h,a)),codomain(X0))) = compose(compose(compose(g,a),compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3609]) ).

fof(f84879,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),codomain(X0))),compose(compose(compose(g,a),compose(h,a)),codomain(X0))),compose(compose(compose(g,a),compose(h,a)),codomain(X0))) = compose(compose(compose(g,a),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f84811]) ).

fof(f85088,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),codomain(X0))),compose(compose(compose(a,b),compose(h,a)),codomain(X0))),compose(compose(compose(a,b),compose(h,a)),codomain(X0))) = compose(compose(compose(a,b),compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3612]) ).

fof(f85153,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),codomain(X0))),compose(compose(compose(a,b),compose(h,a)),codomain(X0))),compose(compose(compose(a,b),compose(h,a)),codomain(X0))) = compose(compose(compose(a,b),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f85088]) ).

fof(f85354,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),g)),compose(compose(a,compose(g,a)),g)),compose(compose(a,compose(g,a)),g)) = compose(compose(a,compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f478,f4203]) ).

fof(f85355,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(g,a))),compose(compose(a,compose(g,a)),compose(g,a))),compose(compose(a,compose(g,a)),compose(g,a))) = compose(compose(a,compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4203]) ).

fof(f85356,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(g,a),compose(h,a))),compose(compose(a,compose(g,a)),compose(h,a))),compose(compose(a,compose(g,a)),compose(h,a))) = compose(compose(a,compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4203]) ).

fof(f85384,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),g)),compose(compose(a,compose(h,a)),g)),compose(compose(a,compose(h,a)),g)) = compose(compose(a,compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f4164]) ).

fof(f85407,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),g)),compose(compose(a,compose(h,a)),g)),compose(compose(a,compose(h,a)),g)) = compose(compose(a,compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f85384]) ).

fof(f85452,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),g)),compose(compose(domain(X0),compose(g,a)),g)),compose(compose(domain(X0),compose(g,a)),g)) = compose(compose(domain(X0),compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f478,f4669]) ).

fof(f85453,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(g,a))),compose(compose(domain(X0),compose(g,a)),compose(g,a))),compose(compose(domain(X0),compose(g,a)),compose(g,a))) = compose(compose(domain(X0),compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f4669]) ).

fof(f85454,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(g,a),compose(h,a))),compose(compose(domain(X0),compose(g,a)),compose(h,a))),compose(compose(domain(X0),compose(g,a)),compose(h,a))) = compose(compose(domain(X0),compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f4669]) ).

fof(f85675,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(compose(h,a),g)),compose(compose(domain(X0),compose(h,a)),g)),compose(compose(domain(X0),compose(h,a)),g)) = compose(compose(domain(X0),compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f4590]) ).

fof(f85739,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),g)),compose(compose(domain(X0),compose(h,a)),g)),compose(compose(domain(X0),compose(h,a)),g)) = compose(compose(domain(X0),compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f85675]) ).

fof(f85947,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),g)),compose(compose(compose(g,a),compose(a,b)),g)),compose(compose(compose(g,a),compose(a,b)),g)) = compose(compose(compose(g,a),compose(a,b)),g),
    inference(paramodulation,[status(thm)],[f1583,f5142]) ).

fof(f85948,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),g)),compose(compose(compose(h,a),compose(a,b)),g)),compose(compose(compose(h,a),compose(a,b)),g)) = compose(compose(compose(h,a),compose(a,b)),g),
    inference(paramodulation,[status(thm)],[f1465,f5142]) ).

fof(f85950,plain,
    ifeq(codomain(b),domain(h),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)],[f975,f5142]) ).

fof(f85994,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(g,a))),compose(compose(compose(g,a),compose(a,b)),compose(g,a))),compose(compose(compose(g,a),compose(a,b)),compose(g,a))) = compose(compose(compose(g,a),compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5149]) ).

fof(f85995,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(g,a),compose(compose(a,b),compose(h,a))),compose(compose(compose(g,a),compose(a,b)),compose(h,a))),compose(compose(compose(g,a),compose(a,b)),compose(h,a))) = compose(compose(compose(g,a),compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5149]) ).

fof(f86018,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(g,a))),compose(compose(compose(a,b),compose(a,b)),compose(g,a))),compose(compose(compose(a,b),compose(a,b)),compose(g,a))) = compose(compose(compose(a,b),compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5152]) ).

fof(f86019,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(a),compose(compose(a,b),compose(compose(a,b),compose(h,a))),compose(compose(compose(a,b),compose(a,b)),compose(h,a))),compose(compose(compose(a,b),compose(a,b)),compose(h,a))) = compose(compose(compose(a,b),compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5152]) ).

fof(f86051,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),g)),compose(compose(compose(g,a),codomain(X0)),g)),compose(compose(compose(g,a),codomain(X0)),g)) = compose(compose(compose(g,a),codomain(X0)),g),
    inference(paramodulation,[status(thm)],[f1583,f5671]) ).

fof(f86052,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),g)),compose(compose(compose(h,a),codomain(X0)),g)),compose(compose(compose(h,a),codomain(X0)),g)) = compose(compose(compose(h,a),codomain(X0)),g),
    inference(paramodulation,[status(thm)],[f1465,f5671]) ).

fof(f86054,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),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)],[f975,f5671]) ).

fof(f86382,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),compose(g,a))),compose(compose(compose(g,a),codomain(X0)),compose(g,a))),compose(compose(compose(g,a),codomain(X0)),compose(g,a))) = compose(compose(compose(g,a),codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5679]) ).

fof(f86383,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(g,a),compose(codomain(X0),compose(h,a))),compose(compose(compose(g,a),codomain(X0)),compose(h,a))),compose(compose(compose(g,a),codomain(X0)),compose(h,a))) = compose(compose(compose(g,a),codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5679]) ).

fof(f86713,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(g,a))),compose(compose(compose(a,b),codomain(X0)),compose(g,a))),compose(compose(compose(a,b),codomain(X0)),compose(g,a))) = compose(compose(compose(a,b),codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f5682]) ).

fof(f86714,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(codomain(b),codomain(X0),compose(compose(a,b),compose(codomain(X0),compose(h,a))),compose(compose(compose(a,b),codomain(X0)),compose(h,a))),compose(compose(compose(a,b),codomain(X0)),compose(h,a))) = compose(compose(compose(a,b),codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f5682]) ).

fof(f87034,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),g)),domain(h),compose(compose(g,a),g),compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g)),compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g)) = compose(compose(domain(compose(compose(g,a),g)),compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f478,f6327]) ).

fof(f87035,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),compose(g,a))),domain(h),compose(compose(g,a),compose(g,a)),compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a))),compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a))) = compose(compose(domain(compose(compose(g,a),compose(g,a))),compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f6327]) ).

fof(f87036,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(g,a),compose(h,a))),domain(h),compose(compose(g,a),compose(h,a)),compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a))),compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a))) = compose(compose(domain(compose(compose(g,a),compose(h,a))),compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f6327]) ).

fof(f87163,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),g)),domain(compose(h,a)),compose(compose(h,a),g),compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g)),compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g)) = compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f6237]) ).

fof(f87187,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),g)),domain(h),compose(compose(h,a),g),compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g)),compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g)) = compose(compose(domain(compose(compose(h,a),g)),compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f87163]) ).

fof(f87282,plain,
    ifeq(domain(b),codomain(compose(compose(g,a),compose(g,a))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),codomain(compose(compose(g,a),compose(g,a))))),compose(compose(g,a),compose(g,a))),compose(compose(g,a),compose(g,a))) = compose(compose(g,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f7459]) ).

fof(f87283,plain,
    ifeq(domain(b),codomain(compose(compose(h,a),compose(g,a))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),codomain(compose(compose(h,a),compose(g,a))))),compose(compose(h,a),compose(g,a))),compose(compose(h,a),compose(g,a))) = compose(compose(h,a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f7459]) ).

fof(f87285,plain,
    ifeq(domain(b),codomain(compose(compose(a,b),compose(g,a))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),codomain(compose(compose(a,b),compose(g,a))))),compose(compose(a,b),compose(g,a))),compose(compose(a,b),compose(g,a))) = compose(compose(a,b),compose(g,a)),
    inference(paramodulation,[status(thm)],[f975,f7459]) ).

fof(f87358,plain,
    ifeq(domain(b),codomain(compose(compose(g,a),compose(h,a))),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),codomain(compose(compose(g,a),compose(h,a))))),compose(compose(g,a),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f7391]) ).

fof(f87387,plain,
    ifeq(domain(b),codomain(compose(compose(g,a),compose(h,a))),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),codomain(compose(compose(g,a),compose(h,a))))),compose(compose(g,a),compose(h,a))),compose(compose(g,a),compose(h,a))) = compose(compose(g,a),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f87358]) ).

fof(f87502,plain,
    ifeq(domain(b),codomain(compose(compose(a,b),compose(h,a))),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),codomain(compose(compose(a,b),compose(h,a))))),compose(compose(a,b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f7394]) ).

fof(f87526,plain,
    ifeq(domain(b),codomain(compose(compose(a,b),compose(h,a))),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),codomain(compose(compose(a,b),compose(h,a))))),compose(compose(a,b),compose(h,a))),compose(compose(a,b),compose(h,a))) = compose(compose(a,b),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f87502]) ).

fof(f96598,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(b,X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),domain(b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f11239]) ).

fof(f96601,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),b,compose(compose(h,a),b),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f21127]) ).

fof(f96602,plain,
    ifeq(codomain(b),domain(a),ifeq(compose(compose(h,compose(a,b)),b),b,compose(h,compose(a,b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f96601]) ).

fof(f96605,plain,
    ifeq(codomain(b),domain(a),ifeq(b,compose(compose(h,compose(a,b)),b),compose(compose(h,a),b),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f21151]) ).

fof(f96606,plain,
    ifeq(codomain(b),domain(a),ifeq(b,compose(compose(h,compose(a,b)),b),compose(h,compose(a,b)),domain(b)),domain(b)) = domain(b),
    inference(forward_demodulation,[status(thm)],[f22238,f96605]) ).

fof(f96613,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(X0,b),X1,ifeq(compose(h,compose(a,b)),X1,compose(h,a),X0),X0),X0),X0) = X0,
    inference(forward_demodulation,[status(thm)],[f22238,f1522]) ).

fof(f96615,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f96613]) ).

fof(f96630,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f96615]) ).

fof(f96631,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f96630]) ).

fof(f96640,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(b),domain(b),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(h,a)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(paramodulation,[status(thm)],[f1465,f1524]) ).

fof(f96652,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(compose(h,a),a),X0,ifeq(compose(compose(h,a),a),X0,compose(h,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f16,f96640]) ).

fof(f97053,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),domain(X0))),compose(compose(compose(g,a),compose(g,a)),domain(X0))),compose(compose(compose(g,a),compose(g,a)),domain(X0))) = compose(compose(compose(g,a),compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f11749]) ).

fof(f97054,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),domain(X0))),compose(compose(compose(h,a),compose(g,a)),domain(X0))),compose(compose(compose(h,a),compose(g,a)),domain(X0))) = compose(compose(compose(h,a),compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11749]) ).

fof(f97055,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f11749]) ).

fof(f97056,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),domain(X0))),compose(compose(compose(a,b),compose(g,a)),domain(X0))),compose(compose(compose(a,b),compose(g,a)),domain(X0))) = compose(compose(compose(a,b),compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f975,f11749]) ).

fof(f97057,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),domain(X0))),compose(compose(g,compose(g,a)),domain(X0))),compose(compose(g,compose(g,a)),domain(X0))) = compose(compose(g,compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f316,f11749]) ).

fof(f97058,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),domain(X0))),compose(compose(h,compose(g,a)),domain(X0))),compose(compose(h,compose(g,a)),domain(X0))) = compose(compose(h,compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f147,f11749]) ).

fof(f97059,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(g,a),domain(X0))),compose(compose(codomain(X1),compose(g,a)),domain(X0))),compose(compose(codomain(X1),compose(g,a)),domain(X0))) = compose(compose(codomain(X1),compose(g,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f36,f11749]) ).

fof(f97233,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(g,a),compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f11751]) ).

fof(f97234,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,a),compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11751]) ).

fof(f97235,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f11751]) ).

fof(f97236,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0))),compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0))) = compose(compose(compose(a,b),compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f975,f11751]) ).

fof(f97237,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(g,compose(h,compose(a,b))),domain(X0))),compose(compose(g,compose(h,compose(a,b))),domain(X0))) = compose(compose(g,compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f316,f11751]) ).

fof(f97238,plain,
    ! [X0] : ifeq(codomain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),domain(X0))),compose(compose(h,compose(h,compose(a,b))),domain(X0))),compose(compose(h,compose(h,compose(a,b))),domain(X0))) = compose(compose(h,compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f147,f11751]) ).

fof(f97239,plain,
    ! [X0,X1] : ifeq(codomain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,compose(a,b)),domain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0))),compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0))) = compose(compose(codomain(X1),compose(h,compose(a,b))),domain(X0)),
    inference(paramodulation,[status(thm)],[f36,f11751]) ).

fof(f98634,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,domain(X0))),compose(compose(compose(g,a),g),domain(X0))),compose(compose(compose(g,a),g),domain(X0))) = compose(compose(compose(g,a),g),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f11753]) ).

fof(f98635,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,domain(X0))),compose(compose(compose(h,a),g),domain(X0))),compose(compose(compose(h,a),g),domain(X0))) = compose(compose(compose(h,a),g),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11753]) ).

fof(f98636,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,domain(X0))),compose(compose(compose(h,compose(a,b)),g),domain(X0))),compose(compose(compose(h,compose(a,b)),g),domain(X0))) = compose(compose(compose(h,compose(a,b)),g),domain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f11753]) ).

fof(f98637,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),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)],[f975,f11753]) ).

fof(f98638,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),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)],[f316,f11753]) ).

fof(f98639,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(g,domain(X0))),compose(compose(h,g),domain(X0))),compose(compose(h,g),domain(X0))) = compose(compose(h,g),domain(X0)),
    inference(paramodulation,[status(thm)],[f147,f11753]) ).

fof(f98640,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),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)],[f36,f11753]) ).

fof(f98818,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,domain(X0))),compose(compose(compose(g,a),h),domain(X0))),compose(compose(compose(g,a),h),domain(X0))) = compose(compose(compose(g,a),h),domain(X0)),
    inference(paramodulation,[status(thm)],[f1583,f11650]) ).

fof(f98819,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,domain(X0))),compose(compose(compose(h,a),h),domain(X0))),compose(compose(compose(h,a),h),domain(X0))) = compose(compose(compose(h,a),h),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11650]) ).

fof(f98820,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,domain(X0))),compose(compose(compose(h,compose(a,b)),h),domain(X0))),compose(compose(compose(h,compose(a,b)),h),domain(X0))) = compose(compose(compose(h,compose(a,b)),h),domain(X0)),
    inference(paramodulation,[status(thm)],[f1016,f11650]) ).

fof(f98821,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(codomain(b),domain(h),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)],[f975,f11650]) ).

fof(f98822,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),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)],[f316,f11650]) ).

fof(f98823,plain,
    ! [X0] : ifeq(domain(a),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(h,domain(X0))),compose(compose(h,h),domain(X0))),compose(compose(h,h),domain(X0))) = compose(compose(h,h),domain(X0)),
    inference(paramodulation,[status(thm)],[f147,f11650]) ).

fof(f98824,plain,
    ! [X0,X1] : ifeq(domain(a),domain(X0),ifeq(codomain(X1),domain(h),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)],[f36,f11650]) ).

fof(f98988,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),domain(X0))),compose(compose(compose(g,a),compose(h,a)),domain(X0))),compose(compose(compose(g,a),compose(h,a)),domain(X0))) = compose(compose(compose(g,a),compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11662]) ).

fof(f99046,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),domain(X0))),compose(compose(compose(g,a),compose(h,a)),domain(X0))),compose(compose(compose(g,a),compose(h,a)),domain(X0))) = compose(compose(compose(g,a),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f98988]) ).

fof(f99223,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(compose(h,a),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11664]) ).

fof(f99278,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0))),compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f99223]) ).

fof(f99448,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),domain(X0))),compose(compose(compose(a,b),compose(h,a)),domain(X0))),compose(compose(compose(a,b),compose(h,a)),domain(X0))) = compose(compose(compose(a,b),compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11665]) ).

fof(f99503,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),domain(X0))),compose(compose(compose(a,b),compose(h,a)),domain(X0))),compose(compose(compose(a,b),compose(h,a)),domain(X0))) = compose(compose(compose(a,b),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f99448]) ).

fof(f99673,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),domain(X0))),compose(compose(g,compose(h,a)),domain(X0))),compose(compose(g,compose(h,a)),domain(X0))) = compose(compose(g,compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11666]) ).

fof(f99733,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),domain(X0))),compose(compose(g,compose(h,a)),domain(X0))),compose(compose(g,compose(h,a)),domain(X0))) = compose(compose(g,compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f99673]) ).

fof(f99929,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),domain(X0))),compose(compose(h,compose(h,a)),domain(X0))),compose(compose(h,compose(h,a)),domain(X0))) = compose(compose(h,compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11667]) ).

fof(f99987,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),domain(X0))),compose(compose(h,compose(h,a)),domain(X0))),compose(compose(h,compose(h,a)),domain(X0))) = compose(compose(h,compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f99929]) ).

fof(f100170,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(compose(h,a)),compose(codomain(X1),compose(compose(h,a),domain(X0))),compose(compose(codomain(X1),compose(h,a)),domain(X0))),compose(compose(codomain(X1),compose(h,a)),domain(X0))) = compose(compose(codomain(X1),compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11668]) ).

fof(f100261,plain,
    ! [X0,X1] : ifeq(domain(b),domain(X0),ifeq(codomain(X1),domain(h),compose(codomain(X1),compose(compose(h,a),domain(X0))),compose(compose(codomain(X1),compose(h,a)),domain(X0))),compose(compose(codomain(X1),compose(h,a)),domain(X0))) = compose(compose(codomain(X1),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f100170]) ).

fof(f100852,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),g)),compose(compose(codomain(X0),compose(g,a)),g)),compose(compose(codomain(X0),compose(g,a)),g)) = compose(compose(codomain(X0),compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f478,f12504]) ).

fof(f100853,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(g,a))),compose(compose(codomain(X0),compose(g,a)),compose(g,a))),compose(compose(codomain(X0),compose(g,a)),compose(g,a))) = compose(compose(codomain(X0),compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f12504]) ).

fof(f100854,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(h,a))),compose(compose(codomain(X0),compose(g,a)),compose(h,a))),compose(compose(codomain(X0),compose(g,a)),compose(h,a))) = compose(compose(codomain(X0),compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f12504]) ).

fof(f100855,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(g,a)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f12504]) ).

fof(f101061,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),g)),compose(compose(codomain(X0),compose(h,compose(a,b))),g)),compose(compose(codomain(X0),compose(h,compose(a,b))),g)) = compose(compose(codomain(X0),compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f478,f12506]) ).

fof(f101062,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f12506]) ).

fof(f101063,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f12506]) ).

fof(f101064,plain,
    ! [X0] : ifeq(codomain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f12506]) ).

fof(f101266,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),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)],[f478,f12508]) ).

fof(f101267,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,compose(g,a))),compose(compose(codomain(X0),g),compose(g,a))),compose(compose(codomain(X0),g),compose(g,a))) = compose(compose(codomain(X0),g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f12508]) ).

fof(f101268,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,compose(h,a))),compose(compose(codomain(X0),g),compose(h,a))),compose(compose(codomain(X0),g),compose(h,a))) = compose(compose(codomain(X0),g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f12508]) ).

fof(f101269,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(g,compose(h,compose(a,b)))),compose(compose(codomain(X0),g),compose(h,compose(a,b)))),compose(compose(codomain(X0),g),compose(h,compose(a,b)))) = compose(compose(codomain(X0),g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f12508]) ).

fof(f101478,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),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)],[f478,f12421]) ).

fof(f101479,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(g,a))),compose(compose(codomain(X0),h),compose(g,a))),compose(compose(codomain(X0),h),compose(g,a))) = compose(compose(codomain(X0),h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f12421]) ).

fof(f101480,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(h,a))),compose(compose(codomain(X0),h),compose(h,a))),compose(compose(codomain(X0),h),compose(h,a))) = compose(compose(codomain(X0),h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f12421]) ).

fof(f101481,plain,
    ! [X0] : ifeq(domain(a),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(h,compose(h,compose(a,b)))),compose(compose(codomain(X0),h),compose(h,compose(a,b)))),compose(compose(codomain(X0),h),compose(h,compose(a,b)))) = compose(compose(codomain(X0),h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f12421]) ).

fof(f101684,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(compose(h,a),g)),compose(compose(codomain(X0),compose(h,a)),g)),compose(compose(codomain(X0),compose(h,a)),g)) = compose(compose(codomain(X0),compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f12425]) ).

fof(f101742,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),g)),compose(compose(codomain(X0),compose(h,a)),g)),compose(compose(codomain(X0),compose(h,a)),g)) = compose(compose(codomain(X0),compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f101684]) ).

fof(f101931,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f12428]) ).

fof(f101989,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b)))),compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(codomain(X0),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f101931]) ).

fof(f103393,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),g)),compose(compose(h,compose(g,a)),g)),compose(compose(h,compose(g,a)),g)) = compose(compose(h,compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f478,f15765]) ).

fof(f103394,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(g,a))),compose(compose(h,compose(g,a)),compose(g,a))),compose(compose(h,compose(g,a)),compose(g,a))) = compose(compose(h,compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f15765]) ).

fof(f103395,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(h,a))),compose(compose(h,compose(g,a)),compose(h,a))),compose(compose(h,compose(g,a)),compose(h,a))) = compose(compose(h,compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f15765]) ).

fof(f103396,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(h,compose(g,a)),compose(h,compose(a,b)))),compose(compose(h,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(h,compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f15765]) ).

fof(f103422,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(h,compose(a,b))),g)),compose(compose(h,compose(h,compose(a,b))),g)) = compose(compose(h,compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f478,f15767]) ).

fof(f103423,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(h,compose(h,compose(a,b))),compose(g,a))),compose(compose(h,compose(h,compose(a,b))),compose(g,a))) = compose(compose(h,compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f15767]) ).

fof(f103424,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(h,compose(h,compose(a,b))),compose(h,a))),compose(compose(h,compose(h,compose(a,b))),compose(h,a))) = compose(compose(h,compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f15767]) ).

fof(f103425,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(h,compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f15767]) ).

fof(f103447,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,g)),compose(compose(h,g),g)),compose(compose(h,g),g)) = compose(compose(h,g),g),
    inference(paramodulation,[status(thm)],[f478,f15770]) ).

fof(f103448,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,compose(g,a))),compose(compose(h,g),compose(g,a))),compose(compose(h,g),compose(g,a))) = compose(compose(h,g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f15770]) ).

fof(f103449,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,compose(h,a))),compose(compose(h,g),compose(h,a))),compose(compose(h,g),compose(h,a))) = compose(compose(h,g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f15770]) ).

fof(f103450,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(g,compose(h,compose(a,b)))),compose(compose(h,g),compose(h,compose(a,b)))),compose(compose(h,g),compose(h,compose(a,b)))) = compose(compose(h,g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f15770]) ).

fof(f103479,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(h,g)),compose(compose(h,h),g)),compose(compose(h,h),g)) = compose(compose(h,h),g),
    inference(paramodulation,[status(thm)],[f478,f15713]) ).

fof(f103480,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(h,compose(g,a))),compose(compose(h,h),compose(g,a))),compose(compose(h,h),compose(g,a))) = compose(compose(h,h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f15713]) ).

fof(f103481,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(h,compose(h,a))),compose(compose(h,h),compose(h,a))),compose(compose(h,h),compose(h,a))) = compose(compose(h,h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f15713]) ).

fof(f103482,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(h,compose(h,compose(h,compose(a,b)))),compose(compose(h,h),compose(h,compose(a,b)))),compose(compose(h,h),compose(h,compose(a,b)))) = compose(compose(h,h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f15713]) ).

fof(f103507,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),g)),compose(compose(h,compose(h,a)),g)),compose(compose(h,compose(h,a)),g)) = compose(compose(h,compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f15717]) ).

fof(f103530,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),g)),compose(compose(h,compose(h,a)),g)),compose(compose(h,compose(h,a)),g)) = compose(compose(h,compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f103507]) ).

fof(f103579,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,compose(h,a)),compose(h,compose(a,b)))),compose(compose(h,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f15721]) ).

fof(f103602,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(h,compose(h,a)),compose(h,compose(a,b)))),compose(compose(h,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(h,compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f103579]) ).

fof(f103656,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,g)),compose(compose(compose(g,a),h),g)),compose(compose(compose(g,a),h),g)) = compose(compose(compose(g,a),h),g),
    inference(paramodulation,[status(thm)],[f1583,f15914]) ).

fof(f103657,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,g)),compose(compose(compose(h,a),h),g)),compose(compose(compose(h,a),h),g)) = compose(compose(compose(h,a),h),g),
    inference(paramodulation,[status(thm)],[f1465,f15914]) ).

fof(f103658,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,g)),compose(compose(compose(h,compose(a,b)),h),g)),compose(compose(compose(h,compose(a,b)),h),g)) = compose(compose(compose(h,compose(a,b)),h),g),
    inference(paramodulation,[status(thm)],[f1016,f15914]) ).

fof(f103659,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),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)],[f975,f15914]) ).

fof(f103660,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(h,g)),compose(compose(g,h),g)),compose(compose(g,h),g)) = compose(compose(g,h),g),
    inference(paramodulation,[status(thm)],[f316,f15914]) ).

fof(f104174,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(h,compose(a,b)))),compose(compose(compose(g,a),h),compose(h,compose(a,b)))),compose(compose(compose(g,a),h),compose(h,compose(a,b)))) = compose(compose(compose(g,a),h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f15918]) ).

fof(f104175,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(h,compose(a,b)))),compose(compose(compose(h,a),h),compose(h,compose(a,b)))),compose(compose(compose(h,a),h),compose(h,compose(a,b)))) = compose(compose(compose(h,a),h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f15918]) ).

fof(f104176,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),h),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),h),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f15918]) ).

fof(f104177,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(h,compose(a,b)))),compose(compose(compose(a,b),h),compose(h,compose(a,b)))),compose(compose(compose(a,b),h),compose(h,compose(a,b)))) = compose(compose(compose(a,b),h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f15918]) ).

fof(f104178,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(h,compose(h,compose(a,b)))),compose(compose(g,h),compose(h,compose(a,b)))),compose(compose(g,h),compose(h,compose(a,b)))) = compose(compose(g,h),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f316,f15918]) ).

fof(f104603,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(g,a))),compose(compose(compose(g,a),h),compose(g,a))),compose(compose(compose(g,a),h),compose(g,a))) = compose(compose(compose(g,a),h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f15923]) ).

fof(f104604,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(h,compose(h,a))),compose(compose(compose(g,a),h),compose(h,a))),compose(compose(compose(g,a),h),compose(h,a))) = compose(compose(compose(g,a),h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f15923]) ).

fof(f104962,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(g,a))),compose(compose(compose(h,compose(a,b)),h),compose(g,a))),compose(compose(compose(h,compose(a,b)),h),compose(g,a))) = compose(compose(compose(h,compose(a,b)),h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f15925]) ).

fof(f104963,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(h,compose(h,a))),compose(compose(compose(h,compose(a,b)),h),compose(h,a))),compose(compose(compose(h,compose(a,b)),h),compose(h,a))) = compose(compose(compose(h,compose(a,b)),h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f15925]) ).

fof(f104991,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(g,a)),compose(g,compose(compose(g,a),g)),compose(compose(g,compose(g,a)),g)),compose(compose(g,compose(g,a)),g)) = compose(compose(g,compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f1583,f15979]) ).

fof(f104992,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),g)),compose(compose(g,compose(h,a)),g)),compose(compose(g,compose(h,a)),g)) = compose(compose(g,compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f15979]) ).

fof(f104993,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(compose(h,compose(a,b))),compose(g,compose(compose(h,compose(a,b)),g)),compose(compose(g,compose(h,compose(a,b))),g)),compose(compose(g,compose(h,compose(a,b))),g)) = compose(compose(g,compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f1016,f15979]) ).

fof(f104995,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(g),compose(g,compose(g,g)),compose(compose(g,g),g)),compose(compose(g,g),g)) = compose(compose(g,g),g),
    inference(paramodulation,[status(thm)],[f316,f15979]) ).

fof(f105016,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),g)),compose(compose(g,compose(g,a)),g)),compose(compose(g,compose(g,a)),g)) = compose(compose(g,compose(g,a)),g),
    inference(forward_demodulation,[status(thm)],[f2123,f104991]) ).

fof(f105017,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),g)),compose(compose(g,compose(h,a)),g)),compose(compose(g,compose(h,a)),g)) = compose(compose(g,compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f104992]) ).

fof(f105018,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),g)),compose(compose(g,compose(h,compose(a,b))),g)),compose(compose(g,compose(h,compose(a,b))),g)) = compose(compose(g,compose(h,compose(a,b))),g),
    inference(forward_demodulation,[status(thm)],[f506,f104993]) ).

fof(f105023,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,g)),compose(compose(g,g),g)),compose(compose(g,g),g)) = compose(compose(g,g),g),
    inference(forward_demodulation,[status(thm)],[f478,f104995]) ).

fof(f105080,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(g,a))),compose(compose(compose(a,b),h),compose(g,a))),compose(compose(compose(a,b),h),compose(g,a))) = compose(compose(compose(a,b),h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f15926]) ).

fof(f105081,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(h,compose(h,a))),compose(compose(compose(a,b),h),compose(h,a))),compose(compose(compose(a,b),h),compose(h,a))) = compose(compose(compose(a,b),h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f15926]) ).

fof(f105106,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(h,compose(g,a))),compose(compose(g,h),compose(g,a))),compose(compose(g,h),compose(g,a))) = compose(compose(g,h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f15927]) ).

fof(f105107,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(h,compose(h,a))),compose(compose(g,h),compose(h,a))),compose(compose(g,h),compose(h,a))) = compose(compose(g,h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f15927]) ).

fof(f105828,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(g,a))),compose(compose(g,compose(g,a)),compose(g,a))),compose(compose(g,compose(g,a)),compose(g,a))) = compose(compose(g,compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f16030]) ).

fof(f105829,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(h,a))),compose(compose(g,compose(g,a)),compose(h,a))),compose(compose(g,compose(g,a)),compose(h,a))) = compose(compose(g,compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f16030]) ).

fof(f105830,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(g,compose(g,a)),compose(h,compose(a,b)))),compose(compose(g,compose(g,a)),compose(h,compose(a,b)))) = compose(compose(g,compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f16030]) ).

fof(f105857,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(g,compose(h,compose(a,b))),compose(g,a))),compose(compose(g,compose(h,compose(a,b))),compose(g,a))) = compose(compose(g,compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f16032]) ).

fof(f105858,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(g,compose(h,compose(a,b))),compose(h,a))),compose(compose(g,compose(h,compose(a,b))),compose(h,a))) = compose(compose(g,compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f16032]) ).

fof(f105859,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(g,compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f16032]) ).

fof(f105882,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,compose(g,a))),compose(compose(g,g),compose(g,a))),compose(compose(g,g),compose(g,a))) = compose(compose(g,g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f16037]) ).

fof(f105883,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,compose(h,a))),compose(compose(g,g),compose(h,a))),compose(compose(g,g),compose(h,a))) = compose(compose(g,g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f16037]) ).

fof(f105884,plain,
    ifeq(domain(a),domain(h),ifeq(domain(a),domain(h),compose(g,compose(g,compose(h,compose(a,b)))),compose(compose(g,g),compose(h,compose(a,b)))),compose(compose(g,g),compose(h,compose(a,b)))) = compose(compose(g,g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f16037]) ).

fof(f106042,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(g,compose(h,a)),compose(h,compose(a,b)))),compose(compose(g,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(g,compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f15983]) ).

fof(f106067,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(g,compose(h,a)),compose(h,compose(a,b)))),compose(compose(g,compose(h,a)),compose(h,compose(a,b)))) = compose(compose(g,compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f106042]) ).

fof(f106212,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,g)),compose(compose(compose(g,a),g),g)),compose(compose(compose(g,a),g),g)) = compose(compose(compose(g,a),g),g),
    inference(paramodulation,[status(thm)],[f1583,f16196]) ).

fof(f106213,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,g)),compose(compose(compose(h,a),g),g)),compose(compose(compose(h,a),g),g)) = compose(compose(compose(h,a),g),g),
    inference(paramodulation,[status(thm)],[f1465,f16196]) ).

fof(f106214,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,g)),compose(compose(compose(h,compose(a,b)),g),g)),compose(compose(compose(h,compose(a,b)),g),g)) = compose(compose(compose(h,compose(a,b)),g),g),
    inference(paramodulation,[status(thm)],[f1016,f16196]) ).

fof(f106215,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),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)],[f975,f16196]) ).

fof(f106245,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,compose(h,compose(a,b)))),compose(compose(compose(g,a),g),compose(h,compose(a,b)))),compose(compose(compose(g,a),g),compose(h,compose(a,b)))) = compose(compose(compose(g,a),g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f16200]) ).

fof(f106246,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,compose(h,compose(a,b)))),compose(compose(compose(h,a),g),compose(h,compose(a,b)))),compose(compose(compose(h,a),g),compose(h,compose(a,b)))) = compose(compose(compose(h,a),g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f16200]) ).

fof(f106247,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),g),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),g),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f16200]) ).

fof(f106248,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,compose(h,compose(a,b)))),compose(compose(compose(a,b),g),compose(h,compose(a,b)))),compose(compose(compose(a,b),g),compose(h,compose(a,b)))) = compose(compose(compose(a,b),g),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f16200]) ).

fof(f106280,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,compose(g,a))),compose(compose(compose(g,a),g),compose(g,a))),compose(compose(compose(g,a),g),compose(g,a))) = compose(compose(compose(g,a),g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f16205]) ).

fof(f106281,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(g,compose(h,a))),compose(compose(compose(g,a),g),compose(h,a))),compose(compose(compose(g,a),g),compose(h,a))) = compose(compose(compose(g,a),g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f16205]) ).

fof(f106312,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,compose(g,a))),compose(compose(compose(h,compose(a,b)),g),compose(g,a))),compose(compose(compose(h,compose(a,b)),g),compose(g,a))) = compose(compose(compose(h,compose(a,b)),g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f16207]) ).

fof(f106313,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(g,compose(h,a))),compose(compose(compose(h,compose(a,b)),g),compose(h,a))),compose(compose(compose(h,compose(a,b)),g),compose(h,a))) = compose(compose(compose(h,compose(a,b)),g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f16207]) ).

fof(f106343,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,compose(g,a))),compose(compose(compose(a,b),g),compose(g,a))),compose(compose(compose(a,b),g),compose(g,a))) = compose(compose(compose(a,b),g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f16208]) ).

fof(f106344,plain,
    ifeq(domain(a),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(g,compose(h,a))),compose(compose(compose(a,b),g),compose(h,a))),compose(compose(compose(a,b),g),compose(h,a))) = compose(compose(compose(a,b),g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f16208]) ).

fof(f106381,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(X0,b),X1,X0,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f1564]) ).

fof(f107237,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(b,X0,domain(b),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f11390]) ).

fof(f109576,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),g)),compose(compose(compose(g,a),compose(h,compose(a,b))),g)),compose(compose(compose(g,a),compose(h,compose(a,b))),g)) = compose(compose(compose(g,a),compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f1583,f17513]) ).

fof(f109577,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,a),compose(h,compose(a,b))),g)),compose(compose(compose(h,a),compose(h,compose(a,b))),g)) = compose(compose(compose(h,a),compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f1465,f17513]) ).

fof(f109578,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g)),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g)) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f1016,f17513]) ).

fof(f109579,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),g)),compose(compose(compose(a,b),compose(h,compose(a,b))),g)),compose(compose(compose(a,b),compose(h,compose(a,b))),g)) = compose(compose(compose(a,b),compose(h,compose(a,b))),g),
    inference(paramodulation,[status(thm)],[f975,f17513]) ).

fof(f110260,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f17517]) ).

fof(f110261,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f17517]) ).

fof(f110262,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f17517]) ).

fof(f110263,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f17517]) ).

fof(f113062,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f17522]) ).

fof(f113063,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(g,a),compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f17522]) ).

fof(f113588,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f17524]) ).

fof(f113589,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f17524]) ).

fof(f114188,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f17525]) ).

fof(f114189,plain,
    ifeq(codomain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(a,b),compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f17525]) ).

fof(f115075,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1583,f17749]) ).

fof(f115076,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f17749]) ).

fof(f115077,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1016,f17749]) ).

fof(f115078,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(g,a)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(g,a)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(g,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f975,f17749]) ).

fof(f115109,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f17688]) ).

fof(f115134,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(g,a),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f115109]) ).

fof(f115186,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f17690]) ).

fof(f115208,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f115186]) ).

fof(f115253,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f1465,f17691]) ).

fof(f115275,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(a,b),compose(h,a)),compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f1908,f115253]) ).

fof(f115343,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(a,b),X0,a,compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f10532]) ).

fof(f115450,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f22238,f16952]) ).

fof(f115451,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f22238,f115450]) ).

fof(f115452,plain,
    ifeq(codomain(b),domain(h),compose(domain(h),compose(compose(h,compose(a,b)),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
    inference(forward_demodulation,[status(thm)],[f22238,f115451]) ).

fof(f115551,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),g)),compose(compose(compose(h,a),b),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f22238,f17005]) ).

fof(f115552,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(compose(h,a),b),g),
    inference(forward_demodulation,[status(thm)],[f22238,f115551]) ).

fof(f115553,plain,
    ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(codomain(b),g)),compose(compose(h,compose(a,b)),g)) = compose(compose(h,compose(a,b)),g),
    inference(forward_demodulation,[status(thm)],[f22238,f115552]) ).

fof(f115658,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(h,compose(a,b)))),compose(g,compose(compose(h,a),b))) = compose(g,compose(compose(h,a),b)),
    inference(forward_demodulation,[status(thm)],[f22238,f17291]) ).

fof(f115659,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(g,compose(compose(h,a),b)),
    inference(forward_demodulation,[status(thm)],[f22238,f115658]) ).

fof(f115660,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(g,compose(h,compose(a,b)))),compose(g,compose(h,compose(a,b)))) = compose(g,compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f22238,f115659]) ).

fof(f115663,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(g,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),g),g),g),g) = g,
    inference(forward_demodulation,[status(thm)],[f22238,f18472]) ).

fof(f115670,plain,
    ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(h,compose(a,b)))),compose(a,compose(compose(h,a),b))) = compose(a,compose(compose(h,a),b)),
    inference(forward_demodulation,[status(thm)],[f22238,f18575]) ).

fof(f115671,plain,
    ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(a,compose(compose(h,a),b)),
    inference(forward_demodulation,[status(thm)],[f22238,f115670]) ).

fof(f115672,plain,
    ifeq(domain(b),domain(h),compose(domain(a),compose(a,compose(h,compose(a,b)))),compose(a,compose(h,compose(a,b)))) = compose(a,compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f22238,f115671]) ).

fof(f115675,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(domain(a),domain(b),ifeq(compose(h,b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),h),h),h),h) = h,
    inference(forward_demodulation,[status(thm)],[f22238,f18606]) ).

fof(f115682,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(h,compose(a,b)))),compose(h,compose(compose(h,a),b))) = compose(h,compose(compose(h,a),b)),
    inference(forward_demodulation,[status(thm)],[f22238,f19086]) ).

fof(f115683,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(h,compose(compose(h,a),b)),
    inference(forward_demodulation,[status(thm)],[f22238,f115682]) ).

fof(f115684,plain,
    ifeq(domain(a),domain(h),compose(domain(h),compose(h,compose(h,compose(a,b)))),compose(h,compose(h,compose(a,b)))) = compose(h,compose(h,compose(a,b))),
    inference(forward_demodulation,[status(thm)],[f22238,f115683]) ).

fof(f117001,plain,
    ! [X0,X1] : ifeq(domain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(domain(X0),b),X1,domain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f10593]) ).

fof(f117177,plain,
    ! [X0,X1] : ifeq(codomain(X0),domain(a),ifeq(compose(h,compose(a,b)),X1,ifeq(compose(codomain(X0),b),X1,codomain(X0),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f18329]) ).

fof(f117274,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),g)),compose(compose(compose(h,compose(a,b)),compose(g,a)),g)),compose(compose(compose(h,compose(a,b)),compose(g,a)),g)) = compose(compose(compose(h,compose(a,b)),compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f478,f20051]) ).

fof(f117275,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f20051]) ).

fof(f117276,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(g,a),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f20051]) ).

fof(f117369,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(h,a)),compose(compose(h,compose(a,b)),compose(compose(h,a),g)),compose(compose(compose(h,compose(a,b)),compose(h,a)),g)),compose(compose(compose(h,compose(a,b)),compose(h,a)),g)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f20008]) ).

fof(f117391,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),g)),compose(compose(compose(h,compose(a,b)),compose(h,a)),g)),compose(compose(compose(h,compose(a,b)),compose(h,a)),g)) = compose(compose(compose(h,compose(a,b)),compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f117369]) ).

fof(f127259,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(domain(X0),domain(b),ifeq(compose(domain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(h,a),domain(X0)),domain(X0)),domain(X0)),domain(X0)) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f22238,f10650]) ).

fof(f127955,plain,
    ! [X0,X1] : ifeq(domain(b),domain(a),ifeq(codomain(X0),domain(b),ifeq(compose(codomain(X0),b),X1,ifeq(compose(h,compose(a,b)),X1,compose(h,a),codomain(X0)),codomain(X0)),codomain(X0)),codomain(X0)) = codomain(X0),
    inference(forward_demodulation,[status(thm)],[f22238,f18625]) ).

fof(f152936,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(h,a)),compose(compose(h,a),compose(compose(h,a),X0)),compose(compose(compose(h,a),compose(h,a)),X0)),compose(compose(compose(h,a),compose(h,a)),X0)) = compose(compose(compose(h,a),compose(h,a)),X0),
    inference(paramodulation,[status(thm)],[f1465,f1525]) ).

fof(f152945,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,compose(g,a))),compose(compose(compose(h,a),X0),compose(g,a))),compose(compose(compose(h,a),X0),compose(g,a))) = compose(compose(compose(h,a),X0),compose(g,a)),
    inference(paramodulation,[status(thm)],[f2123,f1525]) ).

fof(f152946,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(X0,compose(h,a))),compose(compose(compose(h,a),X0),compose(h,a))),compose(compose(compose(h,a),X0),compose(h,a))) = compose(compose(compose(h,a),X0),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1908,f1525]) ).

fof(f152990,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),X0)),compose(compose(compose(h,a),compose(h,a)),X0)),compose(compose(compose(h,a),compose(h,a)),X0)) = compose(compose(compose(h,a),compose(h,a)),X0),
    inference(forward_demodulation,[status(thm)],[f1908,f152936]) ).

fof(f153515,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(compose(h,a),compose(h,a))),compose(compose(X0,compose(h,a)),compose(h,a))),compose(compose(X0,compose(h,a)),compose(h,a))) = compose(compose(X0,compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f1949]) ).

fof(f153581,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(h,a))),compose(compose(X0,compose(h,a)),compose(h,a))),compose(compose(X0,compose(h,a)),compose(h,a))) = compose(compose(X0,compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f153515]) ).

fof(f153798,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(h,a)),compose(X0,compose(compose(h,a),compose(g,a))),compose(compose(X0,compose(h,a)),compose(g,a))),compose(compose(X0,compose(h,a)),compose(g,a))) = compose(compose(X0,compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f2169]) ).

fof(f153864,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(X0,compose(compose(h,a),compose(g,a))),compose(compose(X0,compose(h,a)),compose(g,a))),compose(compose(X0,compose(h,a)),compose(g,a))) = compose(compose(X0,compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f153798]) ).

fof(f161851,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,compose(a,b)),X0,compose(g,a),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f19200]) ).

fof(f161856,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(g,a)),compose(g,a)),compose(g,a)) = compose(g,a),
    inference(forward_demodulation,[status(thm)],[f22238,f19210]) ).

fof(f172418,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),compose(g,a))),compose(compose(a,compose(h,a)),compose(g,a))),compose(compose(a,compose(h,a)),compose(g,a))) = compose(compose(a,compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f4165]) ).

fof(f172441,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(g,a))),compose(compose(a,compose(h,a)),compose(g,a))),compose(compose(a,compose(h,a)),compose(g,a))) = compose(compose(a,compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f172418]) ).

fof(f172486,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(a,compose(compose(h,a),compose(h,a))),compose(compose(a,compose(h,a)),compose(h,a))),compose(compose(a,compose(h,a)),compose(h,a))) = compose(compose(a,compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f4166]) ).

fof(f172509,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(a,compose(compose(h,a),compose(h,a))),compose(compose(a,compose(h,a)),compose(h,a))),compose(compose(a,compose(h,a)),compose(h,a))) = compose(compose(a,compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f172486]) ).

fof(f172566,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),compose(g,a))),compose(compose(h,compose(h,a)),compose(g,a))),compose(compose(h,compose(h,a)),compose(g,a))) = compose(compose(h,compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f15719]) ).

fof(f172589,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(g,a))),compose(compose(h,compose(h,a)),compose(g,a))),compose(compose(h,compose(h,a)),compose(g,a))) = compose(compose(h,compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f172566]) ).

fof(f172638,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(h,a)),compose(h,compose(compose(h,a),compose(h,a))),compose(compose(h,compose(h,a)),compose(h,a))),compose(compose(h,compose(h,a)),compose(h,a))) = compose(compose(h,compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f15720]) ).

fof(f172661,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(h,compose(compose(h,a),compose(h,a))),compose(compose(h,compose(h,a)),compose(h,a))),compose(compose(h,compose(h,a)),compose(h,a))) = compose(compose(h,compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f172638]) ).

fof(f172710,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),compose(g,a))),compose(compose(g,compose(h,a)),compose(g,a))),compose(compose(g,compose(h,a)),compose(g,a))) = compose(compose(g,compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f15981]) ).

fof(f172735,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(g,a))),compose(compose(g,compose(h,a)),compose(g,a))),compose(compose(g,compose(h,a)),compose(g,a))) = compose(compose(g,compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f172710]) ).

fof(f172797,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(compose(h,a)),compose(g,compose(compose(h,a),compose(h,a))),compose(compose(g,compose(h,a)),compose(h,a))),compose(compose(g,compose(h,a)),compose(h,a))) = compose(compose(g,compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f15982]) ).

fof(f172822,plain,
    ifeq(domain(b),domain(h),ifeq(domain(a),domain(h),compose(g,compose(compose(h,a),compose(h,a))),compose(compose(g,compose(h,a)),compose(h,a))),compose(compose(g,compose(h,a)),compose(h,a))) = compose(compose(g,compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f172797]) ).

fof(f172886,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(g,a)),compose(compose(g,a),compose(compose(g,a),g)),compose(compose(compose(g,a),compose(g,a)),g)),compose(compose(compose(g,a),compose(g,a)),g)) = compose(compose(compose(g,a),compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f1583,f79269]) ).

fof(f172887,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),g)),compose(compose(compose(g,a),compose(h,a)),g)),compose(compose(compose(g,a),compose(h,a)),g)) = compose(compose(compose(g,a),compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f79269]) ).

fof(f172911,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),g)),compose(compose(compose(g,a),compose(g,a)),g)),compose(compose(compose(g,a),compose(g,a)),g)) = compose(compose(compose(g,a),compose(g,a)),g),
    inference(forward_demodulation,[status(thm)],[f2123,f172886]) ).

fof(f172912,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),g)),compose(compose(compose(g,a),compose(h,a)),g)),compose(compose(compose(g,a),compose(h,a)),g)) = compose(compose(compose(g,a),compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f172887]) ).

fof(f172963,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(g,a)),compose(compose(h,a),compose(compose(g,a),g)),compose(compose(compose(h,a),compose(g,a)),g)),compose(compose(compose(h,a),compose(g,a)),g)) = compose(compose(compose(h,a),compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f1583,f79270]) ).

fof(f172964,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(compose(h,a),compose(compose(h,a),g)),compose(compose(compose(h,a),compose(h,a)),g)),compose(compose(compose(h,a),compose(h,a)),g)) = compose(compose(compose(h,a),compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f79270]) ).

fof(f172988,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),g)),compose(compose(compose(h,a),compose(g,a)),g)),compose(compose(compose(h,a),compose(g,a)),g)) = compose(compose(compose(h,a),compose(g,a)),g),
    inference(forward_demodulation,[status(thm)],[f2123,f172963]) ).

fof(f172989,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),g)),compose(compose(compose(h,a),compose(h,a)),g)),compose(compose(compose(h,a),compose(h,a)),g)) = compose(compose(compose(h,a),compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f172964]) ).

fof(f173040,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(g,a)),compose(compose(a,b),compose(compose(g,a),g)),compose(compose(compose(a,b),compose(g,a)),g)),compose(compose(compose(a,b),compose(g,a)),g)) = compose(compose(compose(a,b),compose(g,a)),g),
    inference(paramodulation,[status(thm)],[f1583,f79272]) ).

fof(f173041,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),g)),compose(compose(compose(a,b),compose(h,a)),g)),compose(compose(compose(a,b),compose(h,a)),g)) = compose(compose(compose(a,b),compose(h,a)),g),
    inference(paramodulation,[status(thm)],[f1465,f79272]) ).

fof(f173062,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),g)),compose(compose(compose(a,b),compose(g,a)),g)),compose(compose(compose(a,b),compose(g,a)),g)) = compose(compose(compose(a,b),compose(g,a)),g),
    inference(forward_demodulation,[status(thm)],[f2123,f173040]) ).

fof(f173063,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),g)),compose(compose(compose(a,b),compose(h,a)),g)),compose(compose(compose(a,b),compose(h,a)),g)) = compose(compose(compose(a,b),compose(h,a)),g),
    inference(forward_demodulation,[status(thm)],[f1908,f173041]) ).

fof(f173463,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,compose(g,a))),compose(compose(compose(h,a),a),compose(g,a))),compose(compose(compose(h,a),a),compose(g,a))) = compose(compose(compose(h,a),a),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f2270]) ).

fof(f173485,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(a,compose(h,a))),compose(compose(compose(h,a),a),compose(h,a))),compose(compose(compose(h,a),a),compose(h,a))) = compose(compose(compose(h,a),a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f2271]) ).

fof(f173596,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(g,a))),compose(compose(compose(h,a),h),compose(g,a))),compose(compose(compose(h,a),h),compose(g,a))) = compose(compose(compose(h,a),h),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f15916]) ).

fof(f173616,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(h,compose(h,a))),compose(compose(compose(h,a),h),compose(h,a))),compose(compose(compose(h,a),h),compose(h,a))) = compose(compose(compose(h,a),h),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f15917]) ).

fof(f173694,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,compose(g,a))),compose(compose(compose(h,a),g),compose(g,a))),compose(compose(compose(h,a),g),compose(g,a))) = compose(compose(compose(h,a),g),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f16198]) ).

fof(f173727,plain,
    ifeq(domain(a),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(g,compose(h,a))),compose(compose(compose(h,a),g),compose(h,a))),compose(compose(compose(h,a),g),compose(h,a))) = compose(compose(compose(h,a),g),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f16199]) ).

fof(f176549,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),compose(g,a))),compose(compose(compose(h,a),domain(X0)),compose(g,a))),compose(compose(compose(h,a),domain(X0)),compose(g,a))) = compose(compose(compose(h,a),domain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f2645]) ).

fof(f176866,plain,
    ! [X0] : ifeq(domain(X0),domain(h),ifeq(domain(b),domain(X0),compose(compose(h,a),compose(domain(X0),compose(h,a))),compose(compose(compose(h,a),domain(X0)),compose(h,a))),compose(compose(compose(h,a),domain(X0)),compose(h,a))) = compose(compose(compose(h,a),domain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f2646]) ).

fof(f177441,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(compose(h,a)),compose(compose(h,a),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,a),compose(h,a)),codomain(X0))),compose(compose(compose(h,a),compose(h,a)),codomain(X0))) = compose(compose(compose(h,a),compose(h,a)),codomain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f3610]) ).

fof(f177509,plain,
    ! [X0] : ifeq(domain(b),codomain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),codomain(X0))),compose(compose(compose(h,a),compose(h,a)),codomain(X0))),compose(compose(compose(h,a),compose(h,a)),codomain(X0))) = compose(compose(compose(h,a),compose(h,a)),codomain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f177441]) ).

fof(f177717,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(compose(h,a),compose(g,a))),compose(compose(domain(X0),compose(h,a)),compose(g,a))),compose(compose(domain(X0),compose(h,a)),compose(g,a))) = compose(compose(domain(X0),compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f4591]) ).

fof(f177781,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(g,a))),compose(compose(domain(X0),compose(h,a)),compose(g,a))),compose(compose(domain(X0),compose(h,a)),compose(g,a))) = compose(compose(domain(X0),compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f177717]) ).

fof(f177990,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(compose(h,a)),compose(domain(X0),compose(compose(h,a),compose(h,a))),compose(compose(domain(X0),compose(h,a)),compose(h,a))),compose(compose(domain(X0),compose(h,a)),compose(h,a))) = compose(compose(domain(X0),compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f4592]) ).

fof(f178054,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(domain(X0),domain(h),compose(domain(X0),compose(compose(h,a),compose(h,a))),compose(compose(domain(X0),compose(h,a)),compose(h,a))),compose(compose(domain(X0),compose(h,a)),compose(h,a))) = compose(compose(domain(X0),compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f177990]) ).

fof(f178273,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),compose(g,a))),compose(compose(compose(h,a),codomain(X0)),compose(g,a))),compose(compose(compose(h,a),codomain(X0)),compose(g,a))) = compose(compose(compose(h,a),codomain(X0)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f5672]) ).

fof(f178604,plain,
    ! [X0] : ifeq(codomain(X0),domain(h),ifeq(domain(b),codomain(X0),compose(compose(h,a),compose(codomain(X0),compose(h,a))),compose(compose(compose(h,a),codomain(X0)),compose(h,a))),compose(compose(compose(h,a),codomain(X0)),compose(h,a))) = compose(compose(compose(h,a),codomain(X0)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f5673]) ).

fof(f179256,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(compose(h,a)),compose(compose(h,a),compose(compose(h,a),domain(X0))),compose(compose(compose(h,a),compose(h,a)),domain(X0))),compose(compose(compose(h,a),compose(h,a)),domain(X0))) = compose(compose(compose(h,a),compose(h,a)),domain(X0)),
    inference(paramodulation,[status(thm)],[f1465,f11663]) ).

fof(f179314,plain,
    ! [X0] : ifeq(domain(b),domain(X0),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),domain(X0))),compose(compose(compose(h,a),compose(h,a)),domain(X0))),compose(compose(compose(h,a),compose(h,a)),domain(X0))) = compose(compose(compose(h,a),compose(h,a)),domain(X0)),
    inference(forward_demodulation,[status(thm)],[f1908,f179256]) ).

fof(f179491,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(compose(h,a),compose(g,a))),compose(compose(codomain(X0),compose(h,a)),compose(g,a))),compose(compose(codomain(X0),compose(h,a)),compose(g,a))) = compose(compose(codomain(X0),compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f12426]) ).

fof(f179549,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(g,a))),compose(compose(codomain(X0),compose(h,a)),compose(g,a))),compose(compose(codomain(X0),compose(h,a)),compose(g,a))) = compose(compose(codomain(X0),compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f179491]) ).

fof(f179738,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(compose(h,a)),compose(codomain(X0),compose(compose(h,a),compose(h,a))),compose(compose(codomain(X0),compose(h,a)),compose(h,a))),compose(compose(codomain(X0),compose(h,a)),compose(h,a))) = compose(compose(codomain(X0),compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f12427]) ).

fof(f179796,plain,
    ! [X0] : ifeq(domain(b),domain(h),ifeq(codomain(X0),domain(h),compose(codomain(X0),compose(compose(h,a),compose(h,a))),compose(compose(codomain(X0),compose(h,a)),compose(h,a))),compose(compose(codomain(X0),compose(h,a)),compose(h,a))) = compose(compose(codomain(X0),compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f179738]) ).

fof(f186125,plain,
    ifeq(domain(b),codomain(compose(compose(h,a),compose(h,a))),ifeq(domain(b),domain(compose(h,a)),compose(compose(h,a),compose(compose(h,a),codomain(compose(compose(h,a),compose(h,a))))),compose(compose(h,a),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f7392]) ).

fof(f186154,plain,
    ifeq(domain(b),codomain(compose(compose(h,a),compose(h,a))),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),codomain(compose(compose(h,a),compose(h,a))))),compose(compose(h,a),compose(h,a))),compose(compose(h,a),compose(h,a))) = compose(compose(h,a),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f186125]) ).

fof(f186669,plain,
    ! [X0] : ifeq(codomain(b),domain(a),ifeq(compose(h,compose(a,b)),X0,ifeq(compose(compose(h,compose(a,b)),b),X0,compose(h,compose(a,b)),compose(h,a)),compose(h,a)),compose(h,a)) = compose(h,a),
    inference(forward_demodulation,[status(thm)],[f22238,f19895]) ).

fof(f225854,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(compose(h,a)),compose(compose(h,a),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,a),compose(h,a)),compose(a,b))),compose(compose(compose(h,a),compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),compose(h,a)),compose(a,b)),
    inference(paramodulation,[status(thm)],[f1465,f2977]) ).

fof(f225881,plain,
    ifeq(domain(b),domain(a),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(a,b))),compose(compose(compose(h,a),compose(h,a)),compose(a,b))),compose(compose(compose(h,a),compose(h,a)),compose(a,b))) = compose(compose(compose(h,a),compose(h,a)),compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f1908,f225854]) ).

fof(f227034,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(g,a)),compose(compose(a,b),compose(compose(g,a),compose(g,a))),compose(compose(compose(a,b),compose(g,a)),compose(g,a))),compose(compose(compose(a,b),compose(g,a)),compose(g,a))) = compose(compose(compose(a,b),compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f80370]) ).

fof(f227035,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),compose(g,a))),compose(compose(compose(a,b),compose(h,a)),compose(g,a))),compose(compose(compose(a,b),compose(h,a)),compose(g,a))) = compose(compose(compose(a,b),compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f80370]) ).

fof(f227056,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(g,a))),compose(compose(compose(a,b),compose(g,a)),compose(g,a))),compose(compose(compose(a,b),compose(g,a)),compose(g,a))) = compose(compose(compose(a,b),compose(g,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f227034]) ).

fof(f227057,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(g,a))),compose(compose(compose(a,b),compose(h,a)),compose(g,a))),compose(compose(compose(a,b),compose(h,a)),compose(g,a))) = compose(compose(compose(a,b),compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f227035]) ).

fof(f227101,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(g,a)),compose(compose(a,b),compose(compose(g,a),compose(h,a))),compose(compose(compose(a,b),compose(g,a)),compose(h,a))),compose(compose(compose(a,b),compose(g,a)),compose(h,a))) = compose(compose(compose(a,b),compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1583,f80371]) ).

fof(f227102,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(compose(h,a)),compose(compose(a,b),compose(compose(h,a),compose(h,a))),compose(compose(compose(a,b),compose(h,a)),compose(h,a))),compose(compose(compose(a,b),compose(h,a)),compose(h,a))) = compose(compose(compose(a,b),compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f80371]) ).

fof(f227123,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(g,a),compose(h,a))),compose(compose(compose(a,b),compose(g,a)),compose(h,a))),compose(compose(compose(a,b),compose(g,a)),compose(h,a))) = compose(compose(compose(a,b),compose(g,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f227101]) ).

fof(f227124,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(a,b),compose(compose(h,a),compose(h,a))),compose(compose(compose(a,b),compose(h,a)),compose(h,a))),compose(compose(compose(a,b),compose(h,a)),compose(h,a))) = compose(compose(compose(a,b),compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f227102]) ).

fof(f227168,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(g,a)),compose(compose(g,a),compose(compose(g,a),compose(g,a))),compose(compose(compose(g,a),compose(g,a)),compose(g,a))),compose(compose(compose(g,a),compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f81184]) ).

fof(f227169,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),compose(g,a))),compose(compose(compose(g,a),compose(h,a)),compose(g,a))),compose(compose(compose(g,a),compose(h,a)),compose(g,a))) = compose(compose(compose(g,a),compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f81184]) ).

fof(f227193,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(g,a))),compose(compose(compose(g,a),compose(g,a)),compose(g,a))),compose(compose(compose(g,a),compose(g,a)),compose(g,a))) = compose(compose(compose(g,a),compose(g,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f227168]) ).

fof(f227194,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(g,a))),compose(compose(compose(g,a),compose(h,a)),compose(g,a))),compose(compose(compose(g,a),compose(h,a)),compose(g,a))) = compose(compose(compose(g,a),compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f227169]) ).

fof(f227245,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(g,a)),compose(compose(g,a),compose(compose(g,a),compose(h,a))),compose(compose(compose(g,a),compose(g,a)),compose(h,a))),compose(compose(compose(g,a),compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1583,f81185]) ).

fof(f227246,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(compose(g,a),compose(compose(h,a),compose(h,a))),compose(compose(compose(g,a),compose(h,a)),compose(h,a))),compose(compose(compose(g,a),compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f81185]) ).

fof(f227270,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(g,a),compose(h,a))),compose(compose(compose(g,a),compose(g,a)),compose(h,a))),compose(compose(compose(g,a),compose(g,a)),compose(h,a))) = compose(compose(compose(g,a),compose(g,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f227245]) ).

fof(f227271,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(g,a),compose(compose(h,a),compose(h,a))),compose(compose(compose(g,a),compose(h,a)),compose(h,a))),compose(compose(compose(g,a),compose(h,a)),compose(h,a))) = compose(compose(compose(g,a),compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f227246]) ).

fof(f227322,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(g,a)),compose(compose(h,a),compose(compose(g,a),compose(g,a))),compose(compose(compose(h,a),compose(g,a)),compose(g,a))),compose(compose(compose(h,a),compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),compose(g,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1583,f152945]) ).

fof(f227323,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(compose(h,a),compose(compose(h,a),compose(g,a))),compose(compose(compose(h,a),compose(h,a)),compose(g,a))),compose(compose(compose(h,a),compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1465,f152945]) ).

fof(f227324,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(compose(h,compose(a,b))),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1016,f152945]) ).

fof(f227325,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(compose(a,b)),compose(compose(h,a),compose(compose(a,b),compose(g,a))),compose(compose(compose(h,a),compose(a,b)),compose(g,a))),compose(compose(compose(h,a),compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),compose(a,b)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f975,f152945]) ).

fof(f227347,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(g,a))),compose(compose(compose(h,a),compose(g,a)),compose(g,a))),compose(compose(compose(h,a),compose(g,a)),compose(g,a))) = compose(compose(compose(h,a),compose(g,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f227322]) ).

fof(f227348,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(g,a))),compose(compose(compose(h,a),compose(h,a)),compose(g,a))),compose(compose(compose(h,a),compose(h,a)),compose(g,a))) = compose(compose(compose(h,a),compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f227323]) ).

fof(f227349,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(g,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f506,f227324]) ).

fof(f227350,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(g,a))),compose(compose(compose(h,a),compose(a,b)),compose(g,a))),compose(compose(compose(h,a),compose(a,b)),compose(g,a))) = compose(compose(compose(h,a),compose(a,b)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f261,f227325]) ).

fof(f227399,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(g,a)),compose(compose(h,a),compose(compose(g,a),compose(h,a))),compose(compose(compose(h,a),compose(g,a)),compose(h,a))),compose(compose(compose(h,a),compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),compose(g,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1583,f152946]) ).

fof(f227400,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(compose(h,a)),compose(compose(h,a),compose(compose(h,a),compose(h,a))),compose(compose(compose(h,a),compose(h,a)),compose(h,a))),compose(compose(compose(h,a),compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1465,f152946]) ).

fof(f227401,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(compose(h,compose(a,b))),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1016,f152946]) ).

fof(f227402,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(compose(a,b)),compose(compose(h,a),compose(compose(a,b),compose(h,a))),compose(compose(compose(h,a),compose(a,b)),compose(h,a))),compose(compose(compose(h,a),compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),compose(a,b)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f975,f152946]) ).

fof(f227424,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(g,a),compose(h,a))),compose(compose(compose(h,a),compose(g,a)),compose(h,a))),compose(compose(compose(h,a),compose(g,a)),compose(h,a))) = compose(compose(compose(h,a),compose(g,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f2123,f227399]) ).

fof(f227425,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(h,a))),compose(compose(compose(h,a),compose(h,a)),compose(h,a))),compose(compose(compose(h,a),compose(h,a)),compose(h,a))) = compose(compose(compose(h,a),compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f1908,f227400]) ).

fof(f227426,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,compose(a,b)),compose(h,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))),compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a))) = compose(compose(compose(h,a),compose(h,compose(a,b))),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f506,f227401]) ).

fof(f227427,plain,
    ifeq(codomain(b),domain(h),ifeq(domain(b),domain(a),compose(compose(h,a),compose(compose(a,b),compose(h,a))),compose(compose(compose(h,a),compose(a,b)),compose(h,a))),compose(compose(compose(h,a),compose(a,b)),compose(h,a))) = compose(compose(compose(h,a),compose(a,b)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f261,f227402]) ).

fof(f229979,plain,
    ifeq(domain(b),domain(h),ifeq(domain(b),domain(h),compose(compose(h,a),compose(compose(h,a),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b)))),compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b)))) = compose(compose(compose(h,a),compose(h,a)),compose(h,compose(a,b))),
    inference(paramodulation,[status(thm)],[f506,f152990]) ).

fof(f230007,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f1016,f153581]) ).

fof(f230014,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(compose(h,a),compose(h,a)))),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a))),compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a))) = compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a)),
    inference(paramodulation,[status(thm)],[f19,f153581]) ).

fof(f230019,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),compose(h,a))),domain(h),compose(compose(h,a),compose(h,a)),compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a))),compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a))) = compose(compose(domain(compose(compose(h,a),compose(h,a))),compose(h,a)),compose(h,a)),
    inference(forward_demodulation,[status(thm)],[f17,f230014]) ).

fof(f230040,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(b),domain(h),compose(compose(h,compose(a,b)),compose(compose(h,a),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(g,a))),compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(g,a))) = compose(compose(compose(h,compose(a,b)),compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f1016,f153864]) ).

fof(f230047,plain,
    ifeq(domain(b),domain(h),ifeq(codomain(domain(compose(compose(h,a),compose(g,a)))),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a))),compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a))) = compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a)),
    inference(paramodulation,[status(thm)],[f19,f153864]) ).

fof(f230052,plain,
    ifeq(domain(b),domain(h),ifeq(domain(compose(compose(h,a),compose(g,a))),domain(h),compose(compose(h,a),compose(g,a)),compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a))),compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a))) = compose(compose(domain(compose(compose(h,a),compose(g,a))),compose(h,a)),compose(g,a)),
    inference(forward_demodulation,[status(thm)],[f17,f230047]) ).

fof(f230696,plain,
    ! [X0] : ifeq(domain(b),domain(a),ifeq(codomain(b),domain(b),ifeq(compose(compose(h,compose(a,b)),b),X0,ifeq(compose(h,compose(a,b)),X0,compose(h,a),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))),compose(h,compose(a,b))) = compose(h,compose(a,b)),
    inference(forward_demodulation,[status(thm)],[f22238,f19861]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : CAT002-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04  % Command  : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.40  % Computer : n010.cluster.edu
% 0.12/10.40  % Model    : x86_64 x86_64
% 0.12/10.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40  % Memory   : 8046.5625MB
% 0.12/10.40  % OS       : Linux 6.8.0-71-generic
% 0.12/10.40  % CPULimit : 300
% 0.12/10.40  % WCLimit  : 300
% 0.12/10.40  % DateTime : Mon Sep 21 13:55:38 UTC 2026
% 0.12/10.40  % CPUTime  : 
% 0.12/10.41  % Drodi V4.1.1
% 92.47/22.69  % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 92.47/22.69  % SZS output start Saturation for theBenchmark
% See solution above
% 7.54/23.18  % Elapsed time: 12.748495 seconds
% 7.54/23.18  % CPU time: 99.574534 seconds
% 7.54/23.18  % Total memory used: 1.410 GB
% 7.54/23.18  % Net memory used: 1.401 GB
%------------------------------------------------------------------------------