%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : CAT001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.22s 5.94s
% Output : Saturation 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : codomain(domain(X)) = domain(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : domain(codomain(X)) = codomain(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : compose(domain(X),X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : compose(X,codomain(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( domain(compose(X,Y)) = domain(X)
| codomain(X) != domain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( codomain(compose(X,Y)) = codomain(Y)
| codomain(X) != domain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z)
| codomain(Y) != domain(Z)
| codomain(X) != domain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
! [X,Y,Z] :
( X = Z
| compose(Z,compose(a,b)) != Y
| codomain(Z) != domain(compose(a,b))
| compose(X,compose(a,b)) != Y
| codomain(X) != domain(compose(a,b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
codomain(a) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
codomain(a) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
compose(a,h) = compose(a,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0] : codomain(domain(X0)) = domain(X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0] : domain(codomain(X0)) = codomain(X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : compose(domain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0] : compose(X0,codomain(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [X0,X1] :
( domain(compose(X0,X1)) = domain(X0)
| codomain(X0) != domain(X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0,X1] :
( codomain(compose(X0,X1)) = codomain(X1)
| codomain(X0) != domain(X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0,X1,X2] :
( compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2)
| codomain(X1) != domain(X2)
| codomain(X0) != domain(X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [X,Z] :
( X = Z
| ! [Y] :
( compose(Z,compose(a,b)) != Y
| codomain(Z) != domain(compose(a,b))
| compose(X,compose(a,b)) != Y
| codomain(X) != domain(compose(a,b)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( X0 = X2
| compose(X2,compose(a,b)) != X1
| codomain(X2) != domain(compose(a,b))
| compose(X0,compose(a,b)) != X1
| codomain(X0) != domain(compose(a,b)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
codomain(a) = domain(b),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
codomain(a) = domain(h),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
codomain(a) = domain(g),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
compose(a,h) = compose(a,g),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
h != g,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
domain(h) = domain(g),
inference(forward_demodulation,[status(thm)],[f24,f25]) ).
fof(f31,plain,
compose(domain(h),g) = g,
inference(paramodulation,[status(thm)],[f28,f16]) ).
fof(f32,plain,
! [X0] : compose(domain(X0),domain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f14,f17]) ).
fof(f34,plain,
! [X0] : domain(domain(X0)) = codomain(domain(X0)),
inference(paramodulation,[status(thm)],[f14,f15]) ).
fof(f36,plain,
! [X0] : compose(codomain(X0),codomain(X0)) = codomain(X0),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f37,plain,
! [X0] : codomain(codomain(X0)) = domain(codomain(X0)),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f38,plain,
! [X0] : domain(domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f14,f34]) ).
fof(f40,plain,
! [X0] : codomain(codomain(X0)) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f15,f37]) ).
fof(f44,plain,
domain(b) = domain(h),
inference(backward_demodulation,[status(thm)],[f23,f24]) ).
fof(f46,plain,
compose(a,domain(b)) = a,
inference(paramodulation,[status(thm)],[f23,f17]) ).
fof(f51,plain,
compose(domain(b),g) = g,
inference(backward_demodulation,[status(thm)],[f44,f31]) ).
fof(f52,plain,
domain(b) = domain(g),
inference(backward_demodulation,[status(thm)],[f44,f28]) ).
fof(f53,plain,
compose(domain(b),h) = h,
inference(paramodulation,[status(thm)],[f44,f16]) ).
fof(f117,plain,
domain(compose(a,b)) = domain(a),
inference(resolution,[status(thm)],[f18,f23]) ).
fof(f119,plain,
! [X0,X1] :
( domain(compose(codomain(X0),X1)) = domain(codomain(X0))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f40,f18]) ).
fof(f120,plain,
! [X0,X1] :
( domain(compose(domain(X0),X1)) = domain(domain(X0))
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f14,f18]) ).
fof(f121,plain,
! [X0] :
( domain(compose(a,X0)) = domain(a)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f23,f18]) ).
fof(f122,plain,
! [X0,X1] :
( domain(compose(X0,domain(X1))) = domain(X0)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f18]) ).
fof(f123,plain,
! [X0,X1] :
( domain(compose(X0,codomain(X1))) = domain(X0)
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f18]) ).
fof(f125,plain,
! [X0,X1] :
( domain(compose(codomain(X0),X1)) = codomain(X0)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f15,f119]) ).
fof(f126,plain,
! [X0,X1] :
( domain(compose(domain(X0),X1)) = domain(X0)
| domain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f38,f120]) ).
fof(f128,plain,
codomain(compose(a,b)) = codomain(b),
inference(resolution,[status(thm)],[f19,f23]) ).
fof(f130,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),X1)) = codomain(X1)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f40,f19]) ).
fof(f131,plain,
! [X0,X1] :
( codomain(compose(domain(X0),X1)) = codomain(X1)
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f14,f19]) ).
fof(f132,plain,
! [X0] :
( codomain(compose(a,X0)) = codomain(X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f23,f19]) ).
fof(f133,plain,
! [X0,X1] :
( codomain(compose(X0,domain(X1))) = codomain(domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f19]) ).
fof(f134,plain,
! [X0,X1] :
( codomain(compose(X0,codomain(X1))) = codomain(codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f19]) ).
fof(f136,plain,
! [X0,X1] :
( codomain(compose(X0,domain(X1))) = domain(X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f14,f133]) ).
fof(f137,plain,
! [X0,X1] :
( codomain(compose(X0,codomain(X1))) = codomain(X1)
| codomain(X0) != codomain(X1) ),
inference(forward_demodulation,[status(thm)],[f40,f134]) ).
fof(f138,plain,
! [X0,X1] :
( compose(domain(X0),compose(X0,X1)) = compose(compose(domain(X0),X0),X1)
| codomain(X0) != domain(X1) ),
inference(resolution,[status(thm)],[f20,f14]) ).
fof(f139,plain,
! [X0] :
( compose(a,compose(b,X0)) = compose(compose(a,b),X0)
| codomain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f20,f23]) ).
fof(f140,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),X1)) = compose(compose(X0,codomain(X0)),X1)
| codomain(codomain(X0)) != domain(X1) ),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f141,plain,
! [X0,X1,X2] :
( compose(codomain(X0),compose(X1,X2)) = compose(compose(codomain(X0),X1),X2)
| codomain(X1) != domain(X2)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f40,f20]) ).
fof(f142,plain,
! [X0,X1,X2] :
( compose(domain(X0),compose(X1,X2)) = compose(compose(domain(X0),X1),X2)
| codomain(X1) != domain(X2)
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f14,f20]) ).
fof(f143,plain,
! [X0,X1] :
( compose(a,compose(X0,X1)) = compose(compose(a,X0),X1)
| codomain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f23,f20]) ).
fof(f144,plain,
! [X0,X1,X2] :
( compose(X0,compose(domain(X1),X2)) = compose(compose(X0,domain(X1)),X2)
| codomain(domain(X1)) != domain(X2)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f20]) ).
fof(f145,plain,
! [X0,X1,X2] :
( compose(X0,compose(codomain(X1),X2)) = compose(compose(X0,codomain(X1)),X2)
| codomain(codomain(X1)) != domain(X2)
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f20]) ).
fof(f146,plain,
! [X0,X1] :
( compose(domain(X0),compose(X0,X1)) = compose(X0,X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f16,f138]) ).
fof(f147,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),X1)) = compose(compose(X0,codomain(X0)),X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f40,f140]) ).
fof(f148,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),X1)) = compose(X0,X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f17,f147]) ).
fof(f149,plain,
! [X0,X1,X2] :
( compose(X0,compose(domain(X1),X2)) = compose(compose(X0,domain(X1)),X2)
| domain(X1) != domain(X2)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f14,f144]) ).
fof(f150,plain,
! [X0,X1,X2] :
( compose(X0,compose(codomain(X1),X2)) = compose(compose(X0,codomain(X1)),X2)
| codomain(X1) != domain(X2)
| codomain(X0) != codomain(X1) ),
inference(forward_demodulation,[status(thm)],[f40,f145]) ).
fof(f151,plain,
! [X0,X1] :
( compose(X0,compose(compose(a,b),X1)) = compose(compose(X0,compose(a,b)),X1)
| codomain(compose(a,b)) != domain(X1)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f20]) ).
fof(f152,plain,
! [X0] :
( codomain(compose(X0,compose(a,b))) = codomain(compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f19]) ).
fof(f153,plain,
! [X0] :
( domain(compose(X0,compose(a,b))) = domain(X0)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f18]) ).
fof(f157,plain,
compose(domain(a),compose(a,b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f117,f16]) ).
fof(f165,plain,
! [X0,X1,X2] :
( X0 = X2
| compose(X2,compose(a,b)) != X1
| codomain(X2) != domain(compose(a,b))
| compose(X0,compose(a,b)) != X1
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f117,f22]) ).
fof(f166,plain,
! [X0,X1,X2] :
( X0 = X2
| compose(X2,compose(a,b)) != X1
| codomain(X2) != domain(a)
| compose(X0,compose(a,b)) != X1
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f117,f165]) ).
fof(f167,plain,
! [X0] :
( domain(compose(a,b)) = X0
| compose(X0,compose(a,b)) != compose(a,b)
| codomain(X0) != domain(a)
| codomain(domain(compose(a,b))) != domain(a) ),
inference(resolution,[status(thm)],[f166,f16]) ).
fof(f168,plain,
! [X0,X1] :
( X0 = X1
| compose(X1,compose(a,b)) != compose(domain(compose(X0,compose(a,b))),compose(X0,compose(a,b)))
| codomain(X1) != domain(a)
| codomain(X0) != domain(a) ),
inference(resolution,[status(thm)],[f166,f16]) ).
fof(f170,plain,
! [X0,X1] :
( domain(compose(a,b)) = X1
| compose(X1,compose(a,b)) != X0
| codomain(X1) != domain(a)
| compose(a,b) != X0
| codomain(domain(compose(a,b))) != domain(a) ),
inference(paramodulation,[status(thm)],[f16,f166]) ).
fof(f172,definition,
( sQ0_spl
<=> codomain(domain(compose(a,b))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( sQ0_spl
| codomain(domain(compose(a,b))) != domain(a) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
! [X0] :
( sQ1_spl
<=> ( domain(compose(a,b)) = X0
| compose(X0,compose(a,b)) != compose(a,b)
| codomain(X0) != domain(a) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0] :
( ~ sQ1_spl
| domain(compose(a,b)) = X0
| compose(X0,compose(a,b)) != compose(a,b)
| codomain(X0) != domain(a) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f167,f172,f175]) ).
fof(f179,plain,
! [X0,X1] :
( X0 = X1
| compose(X1,compose(a,b)) != compose(X0,compose(a,b))
| codomain(X1) != domain(a)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f16,f168]) ).
fof(f181,definition,
! [X0,X1] :
( sQ2_spl
<=> ( domain(compose(a,b)) = X1
| compose(X1,compose(a,b)) != X0
| codomain(X1) != domain(a)
| compose(a,b) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0,X1] :
( ~ sQ2_spl
| domain(compose(a,b)) = X1
| compose(X1,compose(a,b)) != X0
| codomain(X1) != domain(a)
| compose(a,b) != X0 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f170,f172,f181]) ).
fof(f185,plain,
( sQ0_spl
| domain(compose(a,b)) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f14,f174]) ).
fof(f186,plain,
( sQ0_spl
| domain(a) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f117,f185]) ).
fof(f187,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f186]) ).
fof(f188,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f189,plain,
! [X0] :
( ~ sQ1_spl
| domain(a) = X0
| compose(X0,compose(a,b)) != compose(a,b)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f117,f176]) ).
fof(f190,plain,
! [X0,X1] :
( ~ sQ2_spl
| domain(a) = X1
| compose(X1,compose(a,b)) != X0
| codomain(X1) != domain(a)
| compose(a,b) != X0 ),
inference(forward_demodulation,[status(thm)],[f117,f182]) ).
fof(f192,plain,
! [X0,X1] :
( compose(compose(a,b),compose(X0,X1)) = compose(compose(compose(a,b),X0),X1)
| codomain(X0) != domain(X1)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f20]) ).
fof(f193,plain,
! [X0] :
( codomain(compose(compose(a,b),X0)) = codomain(X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f19]) ).
fof(f194,plain,
! [X0] :
( domain(compose(compose(a,b),X0)) = domain(compose(a,b))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f18]) ).
fof(f199,plain,
compose(compose(a,b),codomain(b)) = compose(a,b),
inference(paramodulation,[status(thm)],[f128,f17]) ).
fof(f200,plain,
! [X0] :
( domain(compose(compose(a,b),X0)) = domain(a)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f117,f194]) ).
fof(f214,plain,
! [X0] :
( domain(compose(codomain(X0),compose(a,b))) = codomain(X0)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f125]) ).
fof(f215,plain,
! [X0,X1] :
( domain(compose(codomain(X0),domain(X1))) = codomain(X0)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f125]) ).
fof(f216,plain,
! [X0,X1] :
( domain(compose(codomain(X0),codomain(X1))) = codomain(X0)
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f125]) ).
fof(f243,plain,
! [X0] :
( domain(compose(domain(X0),compose(a,b))) = domain(X0)
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f126]) ).
fof(f244,plain,
! [X0,X1] :
( domain(compose(domain(X0),domain(X1))) = domain(X0)
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f126]) ).
fof(f245,plain,
! [X0] :
( domain(compose(domain(X0),g)) = domain(X0)
| domain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f126]) ).
fof(f246,plain,
! [X0] :
( domain(compose(domain(X0),h)) = domain(X0)
| domain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f126]) ).
fof(f247,plain,
! [X0,X1] :
( domain(compose(domain(X0),codomain(X1))) = domain(X0)
| domain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f126]) ).
fof(f273,plain,
( domain(compose(domain(compose(a,b)),g)) = domain(compose(a,b))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f117,f245]) ).
fof(f275,plain,
( domain(compose(domain(g),g)) = domain(g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f245]) ).
fof(f276,plain,
( domain(compose(domain(h),g)) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f245]) ).
fof(f277,plain,
! [X0] :
( domain(compose(domain(codomain(X0)),g)) = domain(codomain(X0))
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f15,f245]) ).
fof(f285,definition,
( sQ3_spl
<=> domain(a) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ3_spl
| domain(a) != domain(b) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,definition,
( sQ4_spl
<=> domain(compose(domain(compose(a,b)),g)) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f273,f285,f288]) ).
fof(f294,definition,
( sQ5_spl
<=> domain(b) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ5_spl
| domain(b) != domain(b) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,definition,
( sQ6_spl
<=> domain(compose(domain(g),g)) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f275,f294,f297]) ).
fof(f301,definition,
( sQ7_spl
<=> domain(compose(domain(h),g)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f276,f294,f301]) ).
fof(f305,plain,
! [X0] :
( domain(compose(codomain(X0),g)) = domain(codomain(X0))
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f277]) ).
fof(f306,plain,
! [X0] :
( domain(compose(codomain(X0),g)) = codomain(X0)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f305]) ).
fof(f308,plain,
( sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f296]) ).
fof(f309,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f308]) ).
fof(f316,plain,
( domain(compose(domain(compose(a,b)),h)) = domain(compose(a,b))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f117,f246]) ).
fof(f318,plain,
( domain(compose(domain(g),h)) = domain(g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f246]) ).
fof(f319,plain,
( domain(compose(domain(h),h)) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f246]) ).
fof(f320,plain,
! [X0] :
( domain(compose(domain(codomain(X0)),h)) = domain(codomain(X0))
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f15,f246]) ).
fof(f328,definition,
( sQ8_spl
<=> domain(compose(domain(compose(a,b)),h)) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ8_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f316,f285,f328]) ).
fof(f334,definition,
( sQ9_spl
<=> domain(compose(domain(g),h)) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f318,f294,f334]) ).
fof(f338,definition,
( sQ10_spl
<=> domain(compose(domain(h),h)) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ10_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f319,f294,f338]) ).
fof(f342,plain,
! [X0] :
( domain(compose(codomain(X0),h)) = domain(codomain(X0))
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f320]) ).
fof(f343,plain,
! [X0] :
( domain(compose(codomain(X0),h)) = codomain(X0)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f342]) ).
fof(f350,plain,
( domain(compose(codomain(compose(a,b)),g)) = codomain(compose(a,b))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f128,f306]) ).
fof(f353,plain,
( domain(compose(codomain(a),g)) = codomain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f306]) ).
fof(f360,definition,
( sQ11_spl
<=> codomain(b) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( sQ11_spl
| codomain(b) != domain(b) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,definition,
( sQ12_spl
<=> domain(compose(codomain(compose(a,b)),g)) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f350,f360,f363]) ).
fof(f371,definition,
( sQ13_spl
<=> domain(compose(codomain(a),g)) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ13_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f353,f294,f371]) ).
fof(f380,plain,
( domain(compose(codomain(compose(a,b)),h)) = codomain(compose(a,b))
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f128,f343]) ).
fof(f383,plain,
( domain(compose(codomain(a),h)) = codomain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f343]) ).
fof(f390,definition,
( sQ14_spl
<=> domain(compose(codomain(compose(a,b)),h)) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ14_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f380,f360,f390]) ).
fof(f398,definition,
( sQ15_spl
<=> domain(compose(codomain(a),h)) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ15_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f383,f294,f398]) ).
fof(f405,plain,
domain(compose(a,g)) = domain(a),
inference(resolution,[status(thm)],[f121,f52]) ).
fof(f408,plain,
( domain(compose(a,compose(a,b))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f121]) ).
fof(f409,plain,
! [X0] :
( domain(compose(a,domain(X0))) = domain(a)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f121]) ).
fof(f410,plain,
( domain(compose(a,g)) = domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f121]) ).
fof(f411,plain,
( domain(compose(a,h)) = domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f121]) ).
fof(f412,plain,
! [X0] :
( domain(compose(a,codomain(X0))) = domain(a)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f121]) ).
fof(f414,plain,
domain(compose(a,h)) = domain(a),
inference(forward_demodulation,[status(thm)],[f26,f405]) ).
fof(f415,definition,
( sQ16_spl
<=> domain(compose(a,compose(a,b))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( sQ16_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f408,f285,f415]) ).
fof(f419,definition,
( sQ17_spl
<=> domain(compose(a,g)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( sQ17_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f410,f294,f419]) ).
fof(f423,definition,
( sQ18_spl
<=> domain(compose(a,h)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f426,plain,
( sQ18_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f411,f294,f423]) ).
fof(f429,plain,
domain(compose(domain(a),compose(a,h))) = domain(a),
inference(resolution,[status(thm)],[f414,f126]) ).
fof(f430,plain,
( domain(compose(a,compose(a,h))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f121]) ).
fof(f431,plain,
( domain(compose(domain(compose(a,h)),h)) = domain(compose(a,h))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f414,f246]) ).
fof(f432,plain,
( domain(compose(domain(compose(a,h)),g)) = domain(compose(a,h))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f414,f245]) ).
fof(f433,plain,
! [X0] :
( domain(compose(domain(X0),compose(a,h))) = domain(X0)
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f126]) ).
fof(f435,plain,
! [X0] :
( domain(compose(codomain(X0),compose(a,h))) = codomain(X0)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f125]) ).
fof(f436,plain,
! [X0,X1] :
( compose(X0,compose(compose(a,h),X1)) = compose(compose(X0,compose(a,h)),X1)
| codomain(compose(a,h)) != domain(X1)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f20]) ).
fof(f437,plain,
! [X0] :
( codomain(compose(X0,compose(a,h))) = codomain(compose(a,h))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f19]) ).
fof(f438,plain,
! [X0] :
( domain(compose(X0,compose(a,h))) = domain(X0)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f18]) ).
fof(f442,plain,
compose(domain(a),compose(a,h)) = compose(a,h),
inference(paramodulation,[status(thm)],[f414,f16]) ).
fof(f446,definition,
( sQ19_spl
<=> domain(compose(a,compose(a,h))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ19_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f430,f285,f446]) ).
fof(f450,definition,
( sQ20_spl
<=> domain(compose(domain(compose(a,h)),h)) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( sQ20_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f431,f285,f450]) ).
fof(f454,definition,
( sQ21_spl
<=> domain(compose(domain(compose(a,h)),g)) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ21_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f432,f285,f454]) ).
fof(f469,plain,
! [X0] :
( domain(compose(compose(a,b),domain(X0))) = domain(compose(a,b))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f122]) ).
fof(f478,plain,
! [X0] :
( domain(compose(compose(a,b),domain(X0))) = domain(a)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f117,f469]) ).
fof(f489,plain,
! [X0] :
( domain(compose(compose(a,b),codomain(X0))) = domain(compose(a,b))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f128,f123]) ).
fof(f501,plain,
! [X0] :
( domain(compose(compose(a,b),codomain(X0))) = domain(a)
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f117,f489]) ).
fof(f515,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(a,h))) = codomain(compose(a,h))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f130]) ).
fof(f516,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(a,b))) = codomain(compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f130]) ).
fof(f517,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),domain(X1))) = codomain(domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f130]) ).
fof(f518,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),codomain(X1))) = codomain(codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f130]) ).
fof(f525,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(a,b))) = codomain(b)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f128,f516]) ).
fof(f526,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),domain(X1))) = domain(X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f14,f517]) ).
fof(f527,plain,
! [X0,X1] :
( codomain(compose(codomain(X0),codomain(X1))) = codomain(X1)
| codomain(X0) != codomain(X1) ),
inference(forward_demodulation,[status(thm)],[f40,f518]) ).
fof(f544,plain,
! [X0] :
( codomain(compose(domain(X0),compose(a,h))) = codomain(compose(a,h))
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f131]) ).
fof(f545,plain,
! [X0] :
( codomain(compose(domain(X0),compose(a,b))) = codomain(compose(a,b))
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f131]) ).
fof(f546,plain,
! [X0,X1] :
( codomain(compose(domain(X0),domain(X1))) = codomain(domain(X1))
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f131]) ).
fof(f547,plain,
! [X0] :
( codomain(compose(domain(X0),g)) = codomain(g)
| domain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f131]) ).
fof(f548,plain,
! [X0] :
( codomain(compose(domain(X0),h)) = codomain(h)
| domain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f131]) ).
fof(f549,plain,
! [X0,X1] :
( codomain(compose(domain(X0),codomain(X1))) = codomain(codomain(X1))
| domain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f131]) ).
fof(f563,plain,
! [X0] :
( codomain(compose(domain(X0),compose(a,b))) = codomain(b)
| domain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f128,f545]) ).
fof(f564,plain,
! [X0,X1] :
( codomain(compose(domain(X0),domain(X1))) = domain(X1)
| domain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f14,f546]) ).
fof(f565,plain,
! [X0,X1] :
( codomain(compose(domain(X0),codomain(X1))) = codomain(X1)
| domain(X0) != codomain(X1) ),
inference(forward_demodulation,[status(thm)],[f40,f549]) ).
fof(f566,plain,
codomain(compose(a,g)) = codomain(g),
inference(resolution,[status(thm)],[f132,f52]) ).
fof(f567,plain,
codomain(compose(a,h)) = codomain(h),
inference(resolution,[status(thm)],[f132,f44]) ).
fof(f569,plain,
( codomain(compose(a,compose(a,h))) = codomain(compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f132]) ).
fof(f570,plain,
( codomain(compose(a,compose(a,b))) = codomain(compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f132]) ).
fof(f571,plain,
! [X0] :
( codomain(compose(a,domain(X0))) = codomain(domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f132]) ).
fof(f572,plain,
( codomain(compose(a,g)) = codomain(g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f132]) ).
fof(f573,plain,
( codomain(compose(a,h)) = codomain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f132]) ).
fof(f574,plain,
! [X0] :
( codomain(compose(a,codomain(X0))) = codomain(codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f132]) ).
fof(f576,plain,
codomain(compose(a,h)) = codomain(g),
inference(forward_demodulation,[status(thm)],[f26,f566]) ).
fof(f579,definition,
( sQ22_spl
<=> codomain(compose(a,compose(a,h))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( sQ22_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f569,f285,f579]) ).
fof(f583,definition,
( sQ23_spl
<=> codomain(compose(a,compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( sQ23_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f570,f285,f583]) ).
fof(f587,plain,
! [X0] :
( codomain(compose(a,domain(X0))) = domain(X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f14,f571]) ).
fof(f588,definition,
( sQ24_spl
<=> codomain(compose(a,g)) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( sQ24_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f572,f294,f588]) ).
fof(f592,definition,
( sQ25_spl
<=> codomain(compose(a,h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f595,plain,
( sQ25_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f573,f294,f592]) ).
fof(f596,plain,
! [X0] :
( codomain(compose(a,codomain(X0))) = codomain(X0)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f40,f574]) ).
fof(f598,plain,
domain(compose(compose(a,h),codomain(g))) = domain(compose(a,h)),
inference(resolution,[status(thm)],[f576,f123]) ).
fof(f602,plain,
! [X0] :
( domain(compose(compose(a,h),codomain(X0))) = domain(compose(a,h))
| codomain(g) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f576,f123]) ).
fof(f603,plain,
! [X0] :
( domain(compose(compose(a,h),domain(X0))) = domain(compose(a,h))
| codomain(g) != domain(X0) ),
inference(paramodulation,[status(thm)],[f576,f122]) ).
fof(f604,plain,
( domain(compose(codomain(compose(a,h)),h)) = codomain(compose(a,h))
| codomain(g) != domain(b) ),
inference(paramodulation,[status(thm)],[f576,f343]) ).
fof(f605,plain,
( domain(compose(codomain(compose(a,h)),g)) = codomain(compose(a,h))
| codomain(g) != domain(b) ),
inference(paramodulation,[status(thm)],[f576,f306]) ).
fof(f607,plain,
! [X0,X1] :
( compose(compose(a,h),compose(X0,X1)) = compose(compose(compose(a,h),X0),X1)
| codomain(X0) != domain(X1)
| codomain(g) != domain(X0) ),
inference(paramodulation,[status(thm)],[f576,f20]) ).
fof(f608,plain,
! [X0] :
( codomain(compose(compose(a,h),X0)) = codomain(X0)
| codomain(g) != domain(X0) ),
inference(paramodulation,[status(thm)],[f576,f19]) ).
fof(f609,plain,
! [X0] :
( domain(compose(compose(a,h),X0)) = domain(compose(a,h))
| codomain(g) != domain(X0) ),
inference(paramodulation,[status(thm)],[f576,f18]) ).
fof(f614,plain,
compose(compose(a,h),codomain(g)) = compose(a,h),
inference(paramodulation,[status(thm)],[f576,f17]) ).
fof(f615,plain,
domain(compose(compose(a,h),codomain(g))) = domain(a),
inference(forward_demodulation,[status(thm)],[f414,f598]) ).
fof(f619,plain,
! [X0] :
( domain(compose(compose(a,h),codomain(X0))) = domain(a)
| codomain(g) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f414,f602]) ).
fof(f620,plain,
! [X0] :
( domain(compose(compose(a,h),domain(X0))) = domain(a)
| codomain(g) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f414,f603]) ).
fof(f621,definition,
( sQ26_spl
<=> codomain(g) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( sQ26_spl
| codomain(g) != domain(b) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,definition,
( sQ27_spl
<=> domain(compose(codomain(compose(a,h)),h)) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f627,plain,
( sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f604,f621,f624]) ).
fof(f628,definition,
( sQ28_spl
<=> domain(compose(codomain(compose(a,h)),g)) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f631,plain,
( sQ28_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f605,f621,f628]) ).
fof(f634,plain,
! [X0] :
( domain(compose(compose(a,h),X0)) = domain(a)
| codomain(g) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f414,f609]) ).
fof(f641,plain,
codomain(h) = codomain(g),
inference(backward_demodulation,[status(thm)],[f567,f576]) ).
fof(f648,plain,
( domain(compose(codomain(compose(a,h)),h)) = codomain(compose(a,h))
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f567,f343]) ).
fof(f649,plain,
( domain(compose(codomain(compose(a,h)),g)) = codomain(compose(a,h))
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f567,f306]) ).
fof(f665,definition,
( sQ29_spl
<=> codomain(h) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( sQ29_spl
| codomain(h) != domain(b) ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( sQ27_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f648,f665,f624]) ).
fof(f669,plain,
( sQ28_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f649,f665,f628]) ).
fof(f685,plain,
! [X0] :
( codomain(compose(compose(a,h),codomain(X0))) = codomain(X0)
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f567,f137]) ).
fof(f686,plain,
! [X0] :
( codomain(compose(compose(a,b),codomain(X0))) = codomain(X0)
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f128,f137]) ).
fof(f716,plain,
! [X0] :
( compose(domain(compose(a,h)),compose(compose(a,h),X0)) = compose(compose(a,h),X0)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f567,f146]) ).
fof(f717,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(compose(a,b),X0)) = compose(compose(a,b),X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f146]) ).
fof(f718,plain,
! [X0,X1] :
( compose(domain(codomain(X0)),compose(codomain(X0),X1)) = compose(codomain(X0),X1)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f40,f146]) ).
fof(f719,plain,
! [X0,X1] :
( compose(domain(domain(X0)),compose(domain(X0),X1)) = compose(domain(X0),X1)
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f14,f146]) ).
fof(f721,plain,
! [X0] :
( compose(domain(X0),compose(X0,compose(a,h))) = compose(X0,compose(a,h))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f146]) ).
fof(f722,plain,
! [X0] :
( compose(domain(X0),compose(X0,compose(a,b))) = compose(X0,compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f146]) ).
fof(f723,plain,
! [X0,X1] :
( compose(domain(X0),compose(X0,domain(X1))) = compose(X0,domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f146]) ).
fof(f724,plain,
! [X0,X1] :
( compose(domain(X0),compose(X0,codomain(X1))) = compose(X0,codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f146]) ).
fof(f728,plain,
! [X0] :
( compose(domain(a),compose(compose(a,h),X0)) = compose(compose(a,h),X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f414,f716]) ).
fof(f729,plain,
! [X0] :
( compose(domain(a),compose(compose(a,b),X0)) = compose(compose(a,b),X0)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f117,f717]) ).
fof(f730,plain,
! [X0,X1] :
( compose(codomain(X0),compose(codomain(X0),X1)) = compose(codomain(X0),X1)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f15,f718]) ).
fof(f731,plain,
! [X0,X1] :
( compose(domain(X0),compose(domain(X0),X1)) = compose(domain(X0),X1)
| domain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f38,f719]) ).
fof(f733,plain,
( compose(a,compose(b,compose(a,h))) = compose(compose(a,b),compose(a,h))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f139]) ).
fof(f734,plain,
( compose(a,compose(b,compose(a,b))) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f139]) ).
fof(f735,plain,
! [X0] :
( compose(a,compose(b,domain(X0))) = compose(compose(a,b),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f139]) ).
fof(f736,plain,
! [X0] :
( compose(a,compose(b,codomain(X0))) = compose(compose(a,b),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f139]) ).
fof(f738,definition,
( sQ30_spl
<=> codomain(b) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f740,plain,
( sQ30_spl
| codomain(b) != domain(a) ),
inference(component_clause,[status(thm)],[f738]) ).
fof(f741,definition,
( sQ31_spl
<=> compose(a,compose(b,compose(a,h))) = compose(compose(a,b),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f744,plain,
( sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f733,f738,f741]) ).
fof(f745,definition,
( sQ32_spl
<=> compose(a,compose(b,compose(a,b))) = compose(compose(a,b),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f748,plain,
( sQ32_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f734,f738,f745]) ).
fof(f749,plain,
( sQ26_spl
| codomain(h) != domain(b) ),
inference(backward_demodulation,[status(thm)],[f641,f623]) ).
fof(f756,plain,
! [X0] :
( codomain(compose(g,codomain(X0))) = codomain(X0)
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f641,f137]) ).
fof(f759,plain,
! [X0] :
( domain(compose(g,codomain(X0))) = domain(g)
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f641,f123]) ).
fof(f760,plain,
! [X0] :
( domain(compose(g,domain(X0))) = domain(g)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f641,f122]) ).
fof(f761,plain,
( domain(compose(codomain(g),h)) = codomain(g)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f641,f343]) ).
fof(f762,plain,
( domain(compose(codomain(g),g)) = codomain(g)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f641,f306]) ).
fof(f764,plain,
! [X0,X1] :
( compose(g,compose(X0,X1)) = compose(compose(g,X0),X1)
| codomain(X0) != domain(X1)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f641,f20]) ).
fof(f765,plain,
! [X0] :
( codomain(compose(g,X0)) = codomain(X0)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f641,f19]) ).
fof(f766,plain,
! [X0] :
( domain(compose(g,X0)) = domain(g)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f641,f18]) ).
fof(f771,plain,
compose(g,codomain(h)) = g,
inference(paramodulation,[status(thm)],[f641,f17]) ).
fof(f781,plain,
! [X0] :
( domain(compose(g,codomain(X0))) = domain(b)
| codomain(h) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f52,f759]) ).
fof(f782,plain,
! [X0] :
( domain(compose(g,domain(X0))) = domain(b)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f52,f760]) ).
fof(f783,definition,
( sQ33_spl
<=> domain(compose(codomain(g),h)) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f786,plain,
( sQ33_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f761,f665,f783]) ).
fof(f787,definition,
( sQ34_spl
<=> domain(compose(codomain(g),g)) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f790,plain,
( sQ34_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f762,f665,f787]) ).
fof(f793,plain,
! [X0] :
( domain(compose(g,X0)) = domain(b)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f52,f766]) ).
fof(f800,plain,
! [X0] :
( codomain(compose(domain(X0),g)) = codomain(h)
| domain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f641,f547]) ).
fof(f804,plain,
( codomain(compose(domain(compose(a,h)),g)) = codomain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f414,f800]) ).
fof(f805,plain,
( codomain(compose(domain(compose(a,b)),g)) = codomain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f117,f800]) ).
fof(f807,plain,
( codomain(compose(domain(g),g)) = codomain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f800]) ).
fof(f808,plain,
( codomain(compose(domain(h),g)) = codomain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f800]) ).
fof(f809,plain,
! [X0] :
( codomain(compose(domain(codomain(X0)),g)) = codomain(h)
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f15,f800]) ).
fof(f816,definition,
( sQ35_spl
<=> codomain(compose(domain(compose(a,h)),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f819,plain,
( sQ35_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f804,f285,f816]) ).
fof(f820,definition,
( sQ36_spl
<=> codomain(compose(domain(compose(a,b)),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f823,plain,
( sQ36_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f805,f285,f820]) ).
fof(f825,definition,
( sQ37_spl
<=> codomain(compose(domain(g),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f828,plain,
( sQ37_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f807,f294,f825]) ).
fof(f829,definition,
( sQ38_spl
<=> codomain(compose(domain(h),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f832,plain,
( sQ38_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f808,f294,f829]) ).
fof(f833,plain,
! [X0] :
( codomain(compose(codomain(X0),g)) = codomain(h)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f809]) ).
fof(f842,plain,
( codomain(compose(g,compose(a,h))) = codomain(compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f765]) ).
fof(f843,plain,
( codomain(compose(g,compose(a,b))) = codomain(compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f765]) ).
fof(f844,plain,
! [X0] :
( codomain(compose(g,domain(X0))) = codomain(domain(X0))
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f765]) ).
fof(f848,definition,
( sQ39_spl
<=> codomain(h) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f850,plain,
( sQ39_spl
| codomain(h) != domain(a) ),
inference(component_clause,[status(thm)],[f848]) ).
fof(f851,definition,
( sQ40_spl
<=> codomain(compose(g,compose(a,h))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f854,plain,
( sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f842,f848,f851]) ).
fof(f855,definition,
( sQ41_spl
<=> codomain(compose(g,compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f858,plain,
( sQ41_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f843,f848,f855]) ).
fof(f859,plain,
! [X0] :
( codomain(compose(g,domain(X0))) = domain(X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f14,f844]) ).
fof(f865,plain,
( codomain(compose(g,compose(domain(a),compose(a,h)))) = codomain(compose(domain(a),compose(a,h)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f429,f765]) ).
fof(f866,plain,
( codomain(compose(domain(compose(domain(a),compose(a,h))),g)) = codomain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f429,f800]) ).
fof(f867,plain,
( compose(a,compose(b,compose(domain(a),compose(a,h)))) = compose(compose(a,b),compose(domain(a),compose(a,h)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f429,f139]) ).
fof(f869,plain,
( codomain(compose(a,compose(domain(a),compose(a,h)))) = codomain(compose(domain(a),compose(a,h)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f429,f132]) ).
fof(f874,plain,
( domain(compose(a,compose(domain(a),compose(a,h)))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f429,f121]) ).
fof(f875,plain,
( domain(compose(domain(compose(domain(a),compose(a,h))),h)) = domain(compose(domain(a),compose(a,h)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f429,f246]) ).
fof(f876,plain,
( domain(compose(domain(compose(domain(a),compose(a,h))),g)) = domain(compose(domain(a),compose(a,h)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f429,f245]) ).
fof(f891,definition,
( sQ42_spl
<=> codomain(compose(g,compose(domain(a),compose(a,h)))) = codomain(compose(domain(a),compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f894,plain,
( sQ42_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f865,f848,f891]) ).
fof(f895,definition,
( sQ43_spl
<=> codomain(compose(domain(compose(domain(a),compose(a,h))),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f898,plain,
( sQ43_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f866,f285,f895]) ).
fof(f899,definition,
( sQ44_spl
<=> compose(a,compose(b,compose(domain(a),compose(a,h)))) = compose(compose(a,b),compose(domain(a),compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f902,plain,
( sQ44_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f867,f738,f899]) ).
fof(f903,definition,
( sQ45_spl
<=> codomain(compose(a,compose(domain(a),compose(a,h)))) = codomain(compose(domain(a),compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f906,plain,
( sQ45_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f869,f285,f903]) ).
fof(f909,definition,
( sQ46_spl
<=> domain(compose(a,compose(domain(a),compose(a,h)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f912,plain,
( sQ46_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f874,f285,f909]) ).
fof(f913,definition,
( sQ47_spl
<=> domain(compose(domain(compose(domain(a),compose(a,h))),h)) = domain(compose(domain(a),compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f916,plain,
( sQ47_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f875,f285,f913]) ).
fof(f917,definition,
( sQ48_spl
<=> domain(compose(domain(compose(domain(a),compose(a,h))),g)) = domain(compose(domain(a),compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f920,plain,
( sQ48_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f876,f285,f917]) ).
fof(f932,plain,
( codomain(compose(domain(compose(domain(a),compose(a,h))),h)) = codomain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f429,f548]) ).
fof(f933,plain,
( codomain(compose(domain(compose(a,h)),h)) = codomain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f414,f548]) ).
fof(f934,plain,
( codomain(compose(domain(compose(a,b)),h)) = codomain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f117,f548]) ).
fof(f936,plain,
( codomain(compose(domain(g),h)) = codomain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f548]) ).
fof(f937,plain,
( codomain(compose(domain(h),h)) = codomain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f548]) ).
fof(f938,plain,
! [X0] :
( codomain(compose(domain(codomain(X0)),h)) = codomain(h)
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f15,f548]) ).
fof(f942,definition,
( sQ49_spl
<=> codomain(compose(domain(compose(domain(a),compose(a,h))),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f945,plain,
( sQ49_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f932,f285,f942]) ).
fof(f946,definition,
( sQ50_spl
<=> codomain(compose(domain(compose(a,h)),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f949,plain,
( sQ50_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f933,f285,f946]) ).
fof(f950,definition,
( sQ51_spl
<=> codomain(compose(domain(compose(a,b)),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f953,plain,
( sQ51_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f934,f285,f950]) ).
fof(f955,definition,
( sQ52_spl
<=> codomain(compose(domain(g),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f958,plain,
( sQ52_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f936,f294,f955]) ).
fof(f959,definition,
( sQ53_spl
<=> codomain(compose(domain(h),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f962,plain,
( sQ53_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f937,f294,f959]) ).
fof(f963,plain,
! [X0] :
( codomain(compose(codomain(X0),h)) = codomain(h)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f938]) ).
fof(f969,plain,
( domain(compose(domain(compose(domain(a),compose(a,h))),compose(a,h))) = domain(compose(domain(a),compose(a,h)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f429,f433]) ).
fof(f970,plain,
( domain(compose(domain(compose(a,h)),compose(a,h))) = domain(compose(a,h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f433]) ).
fof(f971,plain,
( domain(compose(domain(compose(a,b)),compose(a,h))) = domain(compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f433]) ).
fof(f973,plain,
( domain(compose(domain(g),compose(a,h))) = domain(g)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f52,f433]) ).
fof(f974,plain,
( domain(compose(domain(h),compose(a,h))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f44,f433]) ).
fof(f981,definition,
( sQ54_spl
<=> domain(a) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f983,plain,
( sQ54_spl
| domain(a) != domain(a) ),
inference(component_clause,[status(thm)],[f981]) ).
fof(f984,definition,
( sQ55_spl
<=> domain(compose(domain(compose(domain(a),compose(a,h))),compose(a,h))) = domain(compose(domain(a),compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f987,plain,
( sQ55_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f969,f981,f984]) ).
fof(f988,definition,
( sQ56_spl
<=> domain(compose(domain(compose(a,h)),compose(a,h))) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f991,plain,
( sQ56_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f970,f981,f988]) ).
fof(f992,definition,
( sQ57_spl
<=> domain(compose(domain(compose(a,b)),compose(a,h))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f995,plain,
( sQ57_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f971,f981,f992]) ).
fof(f998,definition,
( sQ58_spl
<=> domain(compose(domain(g),compose(a,h))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1001,plain,
( sQ58_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f973,f285,f998]) ).
fof(f1002,definition,
( sQ59_spl
<=> domain(compose(domain(h),compose(a,h))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
( sQ59_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f974,f285,f1002]) ).
fof(f1008,plain,
( sQ54_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f983]) ).
fof(f1009,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f1008]) ).
fof(f1016,plain,
! [X0] :
( codomain(compose(compose(a,h),domain(X0))) = domain(X0)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f567,f136]) ).
fof(f1017,plain,
! [X0] :
( codomain(compose(compose(a,b),domain(X0))) = domain(X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f136]) ).
fof(f1040,plain,
! [X0] :
( domain(a) = X0
| compose(X0,compose(a,b)) != compose(a,b)
| codomain(X0) != domain(a)
| codomain(domain(a)) != domain(a) ),
inference(resolution,[status(thm)],[f157,f166]) ).
fof(f1041,plain,
! [X0,X1] :
( domain(a) = X1
| compose(X1,compose(a,b)) != X0
| codomain(X1) != domain(a)
| compose(a,b) != X0
| codomain(domain(a)) != domain(a) ),
inference(paramodulation,[status(thm)],[f157,f166]) ).
fof(f1042,definition,
( sQ60_spl
<=> codomain(domain(a)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1044,plain,
( sQ60_spl
| codomain(domain(a)) != domain(a) ),
inference(component_clause,[status(thm)],[f1042]) ).
fof(f1045,definition,
! [X0] :
( sQ61_spl
<=> ( domain(a) = X0
| compose(X0,compose(a,b)) != compose(a,b)
| codomain(X0) != domain(a) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1046,plain,
! [X0] :
( ~ sQ61_spl
| domain(a) = X0
| compose(X0,compose(a,b)) != compose(a,b)
| codomain(X0) != domain(a) ),
inference(component_clause,[status(thm)],[f1045]) ).
fof(f1048,plain,
( sQ61_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f1040,f1042,f1045]) ).
fof(f1049,definition,
! [X0,X1] :
( sQ62_spl
<=> ( domain(a) = X1
| compose(X1,compose(a,b)) != X0
| codomain(X1) != domain(a)
| compose(a,b) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1050,plain,
! [X0,X1] :
( ~ sQ62_spl
| domain(a) = X1
| compose(X1,compose(a,b)) != X0
| codomain(X1) != domain(a)
| compose(a,b) != X0 ),
inference(component_clause,[status(thm)],[f1049]) ).
fof(f1052,plain,
( sQ62_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f1041,f1042,f1049]) ).
fof(f1053,plain,
( sQ60_spl
| domain(a) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f14,f1044]) ).
fof(f1054,plain,
( sQ60_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1053]) ).
fof(f1055,plain,
sQ60_spl,
inference(contradiction_clause,[status(thm)],[f1054]) ).
fof(f1060,plain,
domain(compose(compose(a,h),codomain(h))) = domain(a),
inference(forward_demodulation,[status(thm)],[f641,f615]) ).
fof(f1067,plain,
( domain(compose(domain(compose(compose(a,h),codomain(h))),compose(a,h))) = domain(compose(compose(a,h),codomain(h)))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f1060,f433]) ).
fof(f1068,plain,
( codomain(compose(domain(compose(compose(a,h),codomain(h))),h)) = codomain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f1060,f548]) ).
fof(f1069,plain,
( codomain(compose(g,compose(compose(a,h),codomain(h)))) = codomain(compose(compose(a,h),codomain(h)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f1060,f765]) ).
fof(f1070,plain,
( codomain(compose(domain(compose(compose(a,h),codomain(h))),g)) = codomain(h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f1060,f800]) ).
fof(f1071,plain,
( compose(a,compose(b,compose(compose(a,h),codomain(h)))) = compose(compose(a,b),compose(compose(a,h),codomain(h)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f1060,f139]) ).
fof(f1073,plain,
( codomain(compose(a,compose(compose(a,h),codomain(h)))) = codomain(compose(compose(a,h),codomain(h)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f1060,f132]) ).
fof(f1078,plain,
( domain(compose(a,compose(compose(a,h),codomain(h)))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f1060,f121]) ).
fof(f1079,plain,
( domain(compose(domain(compose(compose(a,h),codomain(h))),h)) = domain(compose(compose(a,h),codomain(h)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f1060,f246]) ).
fof(f1080,plain,
( domain(compose(domain(compose(compose(a,h),codomain(h))),g)) = domain(compose(compose(a,h),codomain(h)))
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f1060,f245]) ).
fof(f1100,definition,
( sQ63_spl
<=> domain(compose(domain(compose(compose(a,h),codomain(h))),compose(a,h))) = domain(compose(compose(a,h),codomain(h))) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1103,plain,
( sQ63_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1067,f981,f1100]) ).
fof(f1104,definition,
( sQ64_spl
<=> codomain(compose(domain(compose(compose(a,h),codomain(h))),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1107,plain,
( sQ64_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1068,f285,f1104]) ).
fof(f1108,definition,
( sQ65_spl
<=> codomain(compose(g,compose(compose(a,h),codomain(h)))) = codomain(compose(compose(a,h),codomain(h))) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1111,plain,
( sQ65_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1069,f848,f1108]) ).
fof(f1112,definition,
( sQ66_spl
<=> codomain(compose(domain(compose(compose(a,h),codomain(h))),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1115,plain,
( sQ66_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1070,f285,f1112]) ).
fof(f1116,definition,
( sQ67_spl
<=> compose(a,compose(b,compose(compose(a,h),codomain(h)))) = compose(compose(a,b),compose(compose(a,h),codomain(h))) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1119,plain,
( sQ67_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1071,f738,f1116]) ).
fof(f1120,definition,
( sQ68_spl
<=> codomain(compose(a,compose(compose(a,h),codomain(h)))) = codomain(compose(compose(a,h),codomain(h))) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1123,plain,
( sQ68_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1073,f285,f1120]) ).
fof(f1126,definition,
( sQ69_spl
<=> domain(compose(a,compose(compose(a,h),codomain(h)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1129,plain,
( sQ69_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1078,f285,f1126]) ).
fof(f1130,definition,
( sQ70_spl
<=> domain(compose(domain(compose(compose(a,h),codomain(h))),h)) = domain(compose(compose(a,h),codomain(h))) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1133,plain,
( sQ70_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1079,f285,f1130]) ).
fof(f1134,definition,
( sQ71_spl
<=> domain(compose(domain(compose(compose(a,h),codomain(h))),g)) = domain(compose(compose(a,h),codomain(h))) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1137,plain,
( sQ71_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1080,f285,f1134]) ).
fof(f1152,plain,
! [X0] :
( compose(g,compose(codomain(g),X0)) = compose(g,X0)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f641,f148]) ).
fof(f1153,plain,
! [X0] :
( compose(compose(a,h),compose(codomain(compose(a,h)),X0)) = compose(compose(a,h),X0)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f567,f148]) ).
fof(f1154,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(compose(a,b)),X0)) = compose(compose(a,b),X0)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f148]) ).
fof(f1157,plain,
! [X0] :
( compose(a,compose(codomain(a),X0)) = compose(a,X0)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f23,f148]) ).
fof(f1159,plain,
! [X0] :
( compose(X0,compose(codomain(X0),compose(a,h))) = compose(X0,compose(a,h))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f148]) ).
fof(f1160,plain,
! [X0] :
( compose(X0,compose(codomain(X0),compose(a,b))) = compose(X0,compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f148]) ).
fof(f1161,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),domain(X1))) = compose(X0,domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f148]) ).
fof(f1162,plain,
! [X0,X1] :
( compose(X0,compose(codomain(X0),codomain(X1))) = compose(X0,codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f148]) ).
fof(f1165,plain,
! [X0] :
( compose(g,compose(codomain(h),X0)) = compose(g,X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f641,f1152]) ).
fof(f1166,plain,
! [X0] :
( compose(compose(a,h),compose(codomain(h),X0)) = compose(compose(a,h),X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f567,f1153]) ).
fof(f1167,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(b),X0)) = compose(compose(a,b),X0)
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f128,f1154]) ).
fof(f1170,plain,
! [X0] :
( compose(a,compose(domain(b),X0)) = compose(a,X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f23,f1157]) ).
fof(f1171,plain,
! [X0] :
( compose(domain(compose(compose(a,h),codomain(h))),compose(a,X0)) = compose(compose(domain(compose(compose(a,h),codomain(h))),a),X0)
| codomain(a) != domain(X0) ),
inference(resolution,[status(thm)],[f142,f1060]) ).
fof(f1175,plain,
! [X0] :
( compose(domain(b),compose(g,X0)) = compose(compose(domain(b),g),X0)
| codomain(g) != domain(X0) ),
inference(resolution,[status(thm)],[f142,f52]) ).
fof(f1176,plain,
! [X0] :
( compose(domain(b),compose(h,X0)) = compose(compose(domain(b),h),X0)
| codomain(h) != domain(X0) ),
inference(resolution,[status(thm)],[f142,f44]) ).
fof(f1191,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(a,h),X1)) = compose(compose(domain(X0),compose(a,h)),X1)
| codomain(compose(a,h)) != domain(X1)
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f142]) ).
fof(f1192,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(a,b),X1)) = compose(compose(domain(X0),compose(a,b)),X1)
| codomain(compose(a,b)) != domain(X1)
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f142]) ).
fof(f1193,plain,
! [X0,X1,X2] :
( compose(domain(X0),compose(domain(X1),X2)) = compose(compose(domain(X0),domain(X1)),X2)
| codomain(domain(X1)) != domain(X2)
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f142]) ).
fof(f1194,plain,
! [X0,X1] :
( compose(domain(X0),compose(g,X1)) = compose(compose(domain(X0),g),X1)
| codomain(g) != domain(X1)
| domain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f142]) ).
fof(f1195,plain,
! [X0,X1] :
( compose(domain(X0),compose(h,X1)) = compose(compose(domain(X0),h),X1)
| codomain(h) != domain(X1)
| domain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f142]) ).
fof(f1196,plain,
! [X0,X1,X2] :
( compose(domain(X0),compose(codomain(X1),X2)) = compose(compose(domain(X0),codomain(X1)),X2)
| codomain(codomain(X1)) != domain(X2)
| domain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f142]) ).
fof(f1198,plain,
! [X0] :
( compose(domain(compose(compose(a,h),codomain(h))),compose(a,X0)) = compose(compose(domain(compose(compose(a,h),codomain(h))),a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f23,f1171]) ).
fof(f1199,plain,
! [X0] :
( compose(domain(a),compose(a,X0)) = compose(compose(domain(compose(compose(a,h),codomain(h))),a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f1060,f1198]) ).
fof(f1200,plain,
! [X0] :
( compose(domain(a),compose(a,X0)) = compose(compose(domain(a),a),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f1060,f1199]) ).
fof(f1201,plain,
! [X0] :
( compose(domain(a),compose(a,X0)) = compose(a,X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f1200]) ).
fof(f1213,plain,
! [X0] :
( compose(domain(b),compose(g,X0)) = compose(compose(domain(b),g),X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f641,f1175]) ).
fof(f1214,plain,
! [X0] :
( compose(domain(b),compose(g,X0)) = compose(g,X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f51,f1213]) ).
fof(f1215,plain,
! [X0] :
( compose(domain(b),compose(h,X0)) = compose(h,X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f53,f1176]) ).
fof(f1242,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(a,h),X1)) = compose(compose(domain(X0),compose(a,h)),X1)
| codomain(h) != domain(X1)
| domain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f567,f1191]) ).
fof(f1243,plain,
! [X0,X1] :
( compose(domain(X0),compose(compose(a,b),X1)) = compose(compose(domain(X0),compose(a,b)),X1)
| codomain(b) != domain(X1)
| domain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f128,f1192]) ).
fof(f1244,plain,
! [X0,X1,X2] :
( compose(domain(X0),compose(domain(X1),X2)) = compose(compose(domain(X0),domain(X1)),X2)
| domain(X1) != domain(X2)
| domain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f14,f1193]) ).
fof(f1245,plain,
! [X0,X1] :
( compose(domain(X0),compose(g,X1)) = compose(compose(domain(X0),g),X1)
| codomain(h) != domain(X1)
| domain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f641,f1194]) ).
fof(f1246,plain,
! [X0,X1,X2] :
( compose(domain(X0),compose(codomain(X1),X2)) = compose(compose(domain(X0),codomain(X1)),X2)
| codomain(X1) != domain(X2)
| domain(X0) != codomain(X1) ),
inference(forward_demodulation,[status(thm)],[f40,f1196]) ).
fof(f1248,plain,
! [X0] :
( compose(a,compose(domain(X0),X0)) = compose(compose(a,domain(X0)),X0)
| domain(b) != domain(domain(X0)) ),
inference(resolution,[status(thm)],[f143,f14]) ).
fof(f1249,plain,
( compose(a,compose(a,b)) = compose(compose(a,a),b)
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f143,f23]) ).
fof(f1250,plain,
! [X0] :
( compose(a,compose(X0,codomain(X0))) = compose(compose(a,X0),codomain(X0))
| domain(b) != domain(X0) ),
inference(resolution,[status(thm)],[f143,f15]) ).
fof(f1251,plain,
! [X0] :
( compose(a,compose(g,X0)) = compose(compose(a,g),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f641,f143]) ).
fof(f1252,plain,
! [X0] :
( compose(a,compose(compose(a,h),X0)) = compose(compose(a,compose(a,h)),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(compose(a,h)) ),
inference(paramodulation,[status(thm)],[f567,f143]) ).
fof(f1253,plain,
! [X0] :
( compose(a,compose(compose(a,b),X0)) = compose(compose(a,compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f128,f143]) ).
fof(f1254,plain,
! [X0,X1] :
( compose(a,compose(codomain(X0),X1)) = compose(compose(a,codomain(X0)),X1)
| codomain(X0) != domain(X1)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f40,f143]) ).
fof(f1255,plain,
! [X0,X1] :
( compose(a,compose(domain(X0),X1)) = compose(compose(a,domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f14,f143]) ).
fof(f1256,plain,
! [X0] :
( compose(a,compose(a,X0)) = compose(compose(a,a),X0)
| domain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f143]) ).
fof(f1258,plain,
! [X0] :
( compose(a,compose(X0,compose(a,h))) = compose(compose(a,X0),compose(a,h))
| codomain(X0) != domain(a)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f414,f143]) ).
fof(f1259,plain,
! [X0] :
( compose(a,compose(X0,compose(a,b))) = compose(compose(a,X0),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f117,f143]) ).
fof(f1260,plain,
! [X0,X1] :
( compose(a,compose(X0,domain(X1))) = compose(compose(a,X0),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f143]) ).
fof(f1261,plain,
! [X0,X1] :
( compose(a,compose(X0,codomain(X1))) = compose(compose(a,X0),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f15,f143]) ).
fof(f1262,plain,
! [X0] :
( compose(a,compose(domain(X0),X0)) = compose(compose(a,domain(X0)),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f1248]) ).
fof(f1263,plain,
! [X0] :
( compose(a,X0) = compose(compose(a,domain(X0)),X0)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f16,f1262]) ).
fof(f1264,definition,
( sQ72_spl
<=> compose(a,compose(a,b)) = compose(compose(a,a),b) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1267,plain,
( sQ72_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1249,f285,f1264]) ).
fof(f1268,plain,
! [X0] :
( compose(a,X0) = compose(compose(a,X0),codomain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f17,f1250]) ).
fof(f1269,definition,
( sQ73_spl
<=> domain(b) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1271,plain,
( sQ73_spl
| domain(b) != domain(g) ),
inference(component_clause,[status(thm)],[f1269]) ).
fof(f1272,definition,
! [X0] :
( sQ74_spl
<=> ( compose(a,compose(g,X0)) = compose(compose(a,g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1273,plain,
! [X0] :
( ~ sQ74_spl
| compose(a,compose(g,X0)) = compose(compose(a,g),X0)
| codomain(h) != domain(X0) ),
inference(component_clause,[status(thm)],[f1272]) ).
fof(f1275,plain,
( sQ74_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f1251,f1269,f1272]) ).
fof(f1276,definition,
( sQ75_spl
<=> domain(b) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1278,plain,
( sQ75_spl
| domain(b) != domain(compose(a,h)) ),
inference(component_clause,[status(thm)],[f1276]) ).
fof(f1279,definition,
! [X0] :
( sQ76_spl
<=> ( compose(a,compose(compose(a,h),X0)) = compose(compose(a,compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1280,plain,
! [X0] :
( ~ sQ76_spl
| compose(a,compose(compose(a,h),X0)) = compose(compose(a,compose(a,h)),X0)
| codomain(h) != domain(X0) ),
inference(component_clause,[status(thm)],[f1279]) ).
fof(f1282,plain,
( sQ76_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f1252,f1276,f1279]) ).
fof(f1283,definition,
( sQ77_spl
<=> domain(b) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1285,plain,
( sQ77_spl
| domain(b) != domain(compose(a,b)) ),
inference(component_clause,[status(thm)],[f1283]) ).
fof(f1286,definition,
! [X0] :
( sQ78_spl
<=> ( compose(a,compose(compose(a,b),X0)) = compose(compose(a,compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1287,plain,
! [X0] :
( ~ sQ78_spl
| compose(a,compose(compose(a,b),X0)) = compose(compose(a,compose(a,b)),X0)
| codomain(b) != domain(X0) ),
inference(component_clause,[status(thm)],[f1286]) ).
fof(f1289,plain,
( sQ78_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f1253,f1283,f1286]) ).
fof(f1290,plain,
! [X0,X1] :
( compose(a,compose(codomain(X0),X1)) = compose(compose(a,codomain(X0)),X1)
| codomain(X0) != domain(X1)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f1254]) ).
fof(f1291,plain,
! [X0,X1] :
( compose(a,compose(domain(X0),X1)) = compose(compose(a,domain(X0)),X1)
| domain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f1255]) ).
fof(f1292,definition,
! [X0] :
( sQ79_spl
<=> ( compose(a,compose(a,X0)) = compose(compose(a,a),X0)
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1295,plain,
( sQ79_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1256,f285,f1292]) ).
fof(f1296,plain,
( sQ77_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f117,f1285]) ).
fof(f1297,plain,
( sQ75_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f414,f1278]) ).
fof(f1298,plain,
( sQ73_spl
| domain(b) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f52,f1271]) ).
fof(f1299,plain,
( sQ73_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1298]) ).
fof(f1300,plain,
sQ73_spl,
inference(contradiction_clause,[status(thm)],[f1299]) ).
fof(f1301,plain,
! [X0] :
( ~ sQ74_spl
| compose(a,compose(g,X0)) = compose(compose(a,h),X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f26,f1273]) ).
fof(f1303,plain,
compose(compose(a,h),codomain(h)) = compose(a,h),
inference(forward_demodulation,[status(thm)],[f641,f614]) ).
fof(f1307,plain,
( compose(domain(b),compose(g,compose(a,h))) = compose(g,compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1214]) ).
fof(f1308,plain,
( compose(domain(b),compose(g,compose(a,b))) = compose(g,compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1214]) ).
fof(f1309,plain,
! [X0] :
( compose(domain(b),compose(g,domain(X0))) = compose(g,domain(X0))
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f1214]) ).
fof(f1310,plain,
! [X0] :
( compose(domain(b),compose(g,codomain(X0))) = compose(g,codomain(X0))
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f1214]) ).
fof(f1313,definition,
( sQ80_spl
<=> compose(domain(b),compose(g,compose(a,h))) = compose(g,compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1316,plain,
( sQ80_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1307,f848,f1313]) ).
fof(f1317,definition,
( sQ81_spl
<=> compose(domain(b),compose(g,compose(a,b))) = compose(g,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1320,plain,
( sQ81_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1308,f848,f1317]) ).
fof(f1322,plain,
( domain(compose(g,compose(a,h))) = domain(b)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f793]) ).
fof(f1323,plain,
( domain(compose(g,compose(a,b))) = domain(b)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f793]) ).
fof(f1327,definition,
( sQ82_spl
<=> domain(compose(g,compose(a,h))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1330,plain,
( sQ82_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1322,f848,f1327]) ).
fof(f1331,definition,
( sQ83_spl
<=> domain(compose(g,compose(a,b))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1334,plain,
( sQ83_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1323,f848,f1331]) ).
fof(f1338,plain,
( codomain(compose(g,codomain(g))) = codomain(g)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f756]) ).
fof(f1339,plain,
( codomain(compose(g,codomain(compose(a,h)))) = codomain(compose(a,h))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f756]) ).
fof(f1340,plain,
( codomain(compose(g,codomain(compose(a,b)))) = codomain(compose(a,b))
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f756]) ).
fof(f1350,definition,
( sQ84_spl
<=> codomain(h) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1352,plain,
( sQ84_spl
| codomain(h) != codomain(h) ),
inference(component_clause,[status(thm)],[f1350]) ).
fof(f1353,definition,
( sQ85_spl
<=> codomain(compose(g,codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1356,plain,
( sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f1338,f1350,f1353]) ).
fof(f1357,definition,
( sQ86_spl
<=> codomain(compose(g,codomain(compose(a,h)))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1360,plain,
( sQ86_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f1339,f1350,f1357]) ).
fof(f1361,definition,
( sQ87_spl
<=> codomain(h) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1363,plain,
( sQ87_spl
| codomain(h) != codomain(b) ),
inference(component_clause,[status(thm)],[f1361]) ).
fof(f1364,definition,
( sQ88_spl
<=> codomain(compose(g,codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1367,plain,
( sQ88_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f1340,f1361,f1364]) ).
fof(f1373,plain,
( sQ84_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1352]) ).
fof(f1374,plain,
sQ84_spl,
inference(contradiction_clause,[status(thm)],[f1373]) ).
fof(f1379,plain,
( codomain(compose(g,domain(compose(a,h)))) = domain(compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f859]) ).
fof(f1380,plain,
( codomain(compose(g,domain(compose(a,b)))) = domain(compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f859]) ).
fof(f1386,definition,
( sQ89_spl
<=> codomain(compose(g,domain(compose(a,h)))) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1389,plain,
( sQ89_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1379,f848,f1386]) ).
fof(f1390,definition,
( sQ90_spl
<=> codomain(compose(g,domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1393,plain,
( sQ90_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1380,f848,f1390]) ).
fof(f1401,plain,
( domain(compose(g,codomain(g))) = domain(b)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f781]) ).
fof(f1402,plain,
( domain(compose(g,codomain(compose(a,h)))) = domain(b)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f781]) ).
fof(f1403,plain,
( domain(compose(g,codomain(compose(a,b)))) = domain(b)
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f781]) ).
fof(f1412,definition,
( sQ91_spl
<=> domain(compose(g,codomain(g))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1415,plain,
( sQ91_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f1401,f1350,f1412]) ).
fof(f1416,definition,
( sQ92_spl
<=> domain(compose(g,codomain(compose(a,h)))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1419,plain,
( sQ92_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f1402,f1350,f1416]) ).
fof(f1420,definition,
( sQ93_spl
<=> domain(compose(g,codomain(compose(a,b)))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1423,plain,
( sQ93_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f1403,f1361,f1420]) ).
fof(f1431,plain,
( compose(domain(b),compose(h,compose(a,h))) = compose(h,compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1215]) ).
fof(f1432,plain,
( compose(domain(b),compose(h,compose(a,b))) = compose(h,compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1215]) ).
fof(f1433,plain,
! [X0] :
( compose(domain(b),compose(h,domain(X0))) = compose(h,domain(X0))
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f1215]) ).
fof(f1434,plain,
! [X0] :
( compose(domain(b),compose(h,codomain(X0))) = compose(h,codomain(X0))
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f1215]) ).
fof(f1437,definition,
( sQ94_spl
<=> compose(domain(b),compose(h,compose(a,h))) = compose(h,compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1440,plain,
( sQ94_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1431,f848,f1437]) ).
fof(f1441,definition,
( sQ95_spl
<=> compose(domain(b),compose(h,compose(a,b))) = compose(h,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1444,plain,
( sQ95_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1432,f848,f1441]) ).
fof(f1448,plain,
! [X0] :
( compose(domain(compose(a,h)),compose(g,X0)) = compose(compose(domain(compose(a,h)),g),X0)
| codomain(h) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f414,f1245]) ).
fof(f1449,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(g,X0)) = compose(compose(domain(compose(a,b)),g),X0)
| codomain(h) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f117,f1245]) ).
fof(f1451,plain,
! [X0] :
( compose(domain(g),compose(g,X0)) = compose(compose(domain(g),g),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f1245]) ).
fof(f1452,plain,
! [X0] :
( compose(domain(h),compose(g,X0)) = compose(compose(domain(h),g),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f1245]) ).
fof(f1453,plain,
! [X0,X1] :
( compose(domain(codomain(X0)),compose(g,X1)) = compose(compose(domain(codomain(X0)),g),X1)
| codomain(h) != domain(X1)
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f15,f1245]) ).
fof(f1463,definition,
! [X0] :
( sQ96_spl
<=> ( compose(domain(compose(a,h)),compose(g,X0)) = compose(compose(domain(compose(a,h)),g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1466,plain,
( sQ96_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1448,f285,f1463]) ).
fof(f1467,definition,
! [X0] :
( sQ97_spl
<=> ( compose(domain(compose(a,b)),compose(g,X0)) = compose(compose(domain(compose(a,b)),g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1470,plain,
( sQ97_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1449,f285,f1467]) ).
fof(f1473,definition,
! [X0] :
( sQ98_spl
<=> ( compose(domain(g),compose(g,X0)) = compose(compose(domain(g),g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1476,plain,
( sQ98_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1451,f294,f1473]) ).
fof(f1477,definition,
! [X0] :
( sQ99_spl
<=> ( compose(domain(h),compose(g,X0)) = compose(compose(domain(h),g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1480,plain,
( sQ99_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1452,f294,f1477]) ).
fof(f1481,plain,
! [X0,X1] :
( compose(codomain(X0),compose(g,X1)) = compose(compose(domain(codomain(X0)),g),X1)
| codomain(h) != domain(X1)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f1453]) ).
fof(f1482,plain,
! [X0,X1] :
( compose(codomain(X0),compose(g,X1)) = compose(compose(codomain(X0),g),X1)
| codomain(h) != domain(X1)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f1481]) ).
fof(f1688,plain,
! [X0,X1] :
( compose(g,compose(codomain(X0),X1)) = compose(compose(g,codomain(X0)),X1)
| codomain(X0) != domain(X1)
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f641,f150]) ).
fof(f1689,plain,
! [X0,X1] :
( compose(compose(a,h),compose(codomain(X0),X1)) = compose(compose(compose(a,h),codomain(X0)),X1)
| codomain(X0) != domain(X1)
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f567,f150]) ).
fof(f1690,plain,
! [X0,X1] :
( compose(compose(a,b),compose(codomain(X0),X1)) = compose(compose(compose(a,b),codomain(X0)),X1)
| codomain(X0) != domain(X1)
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f128,f150]) ).
fof(f1691,plain,
! [X0,X1,X2] :
( compose(codomain(X0),compose(codomain(X1),X2)) = compose(compose(codomain(X0),codomain(X1)),X2)
| codomain(X1) != domain(X2)
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f40,f150]) ).
fof(f1750,plain,
( domain(compose(g,domain(compose(a,h)))) = domain(b)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f782]) ).
fof(f1751,plain,
( domain(compose(g,domain(compose(a,b)))) = domain(b)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f782]) ).
fof(f1756,definition,
( sQ100_spl
<=> domain(compose(g,domain(compose(a,h)))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1759,plain,
( sQ100_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1750,f848,f1756]) ).
fof(f1760,definition,
( sQ101_spl
<=> domain(compose(g,domain(compose(a,b)))) = domain(b) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1763,plain,
( sQ101_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1751,f848,f1760]) ).
fof(f1768,plain,
( codomain(compose(codomain(g),g)) = codomain(h)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f641,f833]) ).
fof(f1769,plain,
( codomain(compose(codomain(compose(a,h)),g)) = codomain(h)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f567,f833]) ).
fof(f1770,plain,
( codomain(compose(codomain(compose(a,b)),g)) = codomain(h)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f128,f833]) ).
fof(f1773,plain,
( codomain(compose(codomain(a),g)) = codomain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f833]) ).
fof(f1778,definition,
( sQ102_spl
<=> codomain(compose(codomain(g),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1781,plain,
( sQ102_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1768,f665,f1778]) ).
fof(f1782,definition,
( sQ103_spl
<=> codomain(compose(codomain(compose(a,h)),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1785,plain,
( sQ103_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1769,f665,f1782]) ).
fof(f1786,definition,
( sQ104_spl
<=> codomain(compose(codomain(compose(a,b)),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1789,plain,
( sQ104_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1770,f360,f1786]) ).
fof(f1792,definition,
( sQ105_spl
<=> codomain(compose(codomain(a),g)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1795,plain,
( sQ105_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1773,f294,f1792]) ).
fof(f1800,plain,
( codomain(compose(codomain(g),h)) = codomain(h)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f641,f963]) ).
fof(f1801,plain,
( codomain(compose(codomain(compose(a,h)),h)) = codomain(h)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f567,f963]) ).
fof(f1802,plain,
( codomain(compose(codomain(compose(a,b)),h)) = codomain(h)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f128,f963]) ).
fof(f1805,plain,
( codomain(compose(codomain(a),h)) = codomain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f963]) ).
fof(f1808,definition,
( sQ106_spl
<=> codomain(compose(codomain(g),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1811,plain,
( sQ106_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1800,f665,f1808]) ).
fof(f1812,definition,
( sQ107_spl
<=> codomain(compose(codomain(compose(a,h)),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1815,plain,
( sQ107_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1801,f665,f1812]) ).
fof(f1816,definition,
( sQ108_spl
<=> codomain(compose(codomain(compose(a,b)),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1819,plain,
( sQ108_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1802,f360,f1816]) ).
fof(f1822,definition,
( sQ109_spl
<=> codomain(compose(codomain(a),h)) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1825,plain,
( sQ109_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1805,f294,f1822]) ).
fof(f1830,plain,
! [X0] :
( compose(domain(compose(a,h)),compose(h,X0)) = compose(compose(domain(compose(a,h)),h),X0)
| codomain(h) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f414,f1195]) ).
fof(f1831,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(h,X0)) = compose(compose(domain(compose(a,b)),h),X0)
| codomain(h) != domain(X0)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f117,f1195]) ).
fof(f1833,plain,
! [X0] :
( compose(domain(g),compose(h,X0)) = compose(compose(domain(g),h),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f1195]) ).
fof(f1834,plain,
! [X0] :
( compose(domain(h),compose(h,X0)) = compose(compose(domain(h),h),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f1195]) ).
fof(f1835,plain,
! [X0,X1] :
( compose(domain(codomain(X0)),compose(h,X1)) = compose(compose(domain(codomain(X0)),h),X1)
| codomain(h) != domain(X1)
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f15,f1195]) ).
fof(f1845,definition,
! [X0] :
( sQ110_spl
<=> ( compose(domain(compose(a,h)),compose(h,X0)) = compose(compose(domain(compose(a,h)),h),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1848,plain,
( sQ110_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1830,f285,f1845]) ).
fof(f1849,definition,
! [X0] :
( sQ111_spl
<=> ( compose(domain(compose(a,b)),compose(h,X0)) = compose(compose(domain(compose(a,b)),h),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1852,plain,
( sQ111_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1831,f285,f1849]) ).
fof(f1855,definition,
! [X0] :
( sQ112_spl
<=> ( compose(domain(g),compose(h,X0)) = compose(compose(domain(g),h),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1858,plain,
( sQ112_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1833,f294,f1855]) ).
fof(f1859,definition,
! [X0] :
( sQ113_spl
<=> ( compose(domain(h),compose(h,X0)) = compose(compose(domain(h),h),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1862,plain,
( sQ113_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1834,f294,f1859]) ).
fof(f1863,plain,
! [X0,X1] :
( compose(codomain(X0),compose(h,X1)) = compose(compose(domain(codomain(X0)),h),X1)
| codomain(h) != domain(X1)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f1835]) ).
fof(f1864,plain,
! [X0,X1] :
( compose(codomain(X0),compose(h,X1)) = compose(compose(codomain(X0),h),X1)
| codomain(h) != domain(X1)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f1863]) ).
fof(f1872,plain,
( domain(compose(g,compose(a,h))) = domain(g)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f438]) ).
fof(f1873,plain,
( domain(compose(compose(a,h),compose(a,h))) = domain(compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f438]) ).
fof(f1874,plain,
( domain(compose(compose(a,b),compose(a,h))) = domain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f438]) ).
fof(f1880,definition,
( sQ114_spl
<=> domain(compose(g,compose(a,h))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1883,plain,
( sQ114_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1872,f848,f1880]) ).
fof(f1884,definition,
( sQ115_spl
<=> domain(compose(compose(a,h),compose(a,h))) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1887,plain,
( sQ115_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1873,f848,f1884]) ).
fof(f1888,definition,
( sQ116_spl
<=> domain(compose(compose(a,b),compose(a,h))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1891,plain,
( sQ116_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1874,f738,f1888]) ).
fof(f1895,plain,
! [X0] :
( codomain(compose(compose(a,h),X0)) = codomain(X0)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f641,f608]) ).
fof(f1897,plain,
( codomain(compose(compose(a,h),compose(a,h))) = codomain(compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1895]) ).
fof(f1898,plain,
( codomain(compose(compose(a,h),compose(a,b))) = codomain(compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1895]) ).
fof(f1903,definition,
( sQ117_spl
<=> codomain(compose(compose(a,h),compose(a,h))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1906,plain,
( sQ117_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1897,f848,f1903]) ).
fof(f1907,definition,
( sQ118_spl
<=> codomain(compose(compose(a,h),compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1910,plain,
( sQ118_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1898,f848,f1907]) ).
fof(f1913,plain,
! [X0] :
( domain(compose(compose(a,h),X0)) = domain(a)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f641,f634]) ).
fof(f1915,plain,
( domain(compose(compose(a,h),compose(a,h))) = domain(a)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1913]) ).
fof(f1916,plain,
( domain(compose(compose(a,h),compose(a,b))) = domain(a)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1913]) ).
fof(f1920,definition,
( sQ119_spl
<=> domain(compose(compose(a,h),compose(a,h))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1923,plain,
( sQ119_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1915,f848,f1920]) ).
fof(f1924,definition,
( sQ120_spl
<=> domain(compose(compose(a,h),compose(a,b))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1927,plain,
( sQ120_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1916,f848,f1924]) ).
fof(f1929,plain,
( domain(compose(codomain(g),compose(a,h))) = codomain(g)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f435]) ).
fof(f1930,plain,
( domain(compose(codomain(compose(a,h)),compose(a,h))) = codomain(compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f435]) ).
fof(f1931,plain,
( domain(compose(codomain(compose(a,b)),compose(a,h))) = codomain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f435]) ).
fof(f1934,plain,
( domain(compose(codomain(a),compose(a,h))) = codomain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f435]) ).
fof(f1938,definition,
( sQ121_spl
<=> domain(compose(codomain(g),compose(a,h))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1941,plain,
( sQ121_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1929,f848,f1938]) ).
fof(f1942,definition,
( sQ122_spl
<=> domain(compose(codomain(compose(a,h)),compose(a,h))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1945,plain,
( sQ122_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1930,f848,f1942]) ).
fof(f1946,definition,
( sQ123_spl
<=> domain(compose(codomain(compose(a,b)),compose(a,h))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1949,plain,
( sQ123_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1931,f738,f1946]) ).
fof(f1954,definition,
( sQ124_spl
<=> domain(compose(codomain(a),compose(a,h))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1957,plain,
( sQ124_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1934,f285,f1954]) ).
fof(f1958,plain,
! [X0,X1] :
( compose(X0,compose(compose(a,h),X1)) = compose(compose(X0,compose(a,h)),X1)
| codomain(h) != domain(X1)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f567,f436]) ).
fof(f1960,plain,
! [X0] :
( compose(g,compose(compose(a,h),X0)) = compose(compose(g,compose(a,h)),X0)
| codomain(h) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f1958]) ).
fof(f1961,plain,
! [X0] :
( compose(compose(a,h),compose(compose(a,h),X0)) = compose(compose(compose(a,h),compose(a,h)),X0)
| codomain(h) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f1958]) ).
fof(f1962,plain,
! [X0] :
( compose(compose(a,b),compose(compose(a,h),X0)) = compose(compose(compose(a,b),compose(a,h)),X0)
| codomain(h) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f1958]) ).
fof(f1965,plain,
! [X0] :
( compose(a,compose(compose(a,h),X0)) = compose(compose(a,compose(a,h)),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f1958]) ).
fof(f1967,definition,
! [X0] :
( sQ125_spl
<=> ( compose(g,compose(compose(a,h),X0)) = compose(compose(g,compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1970,plain,
( sQ125_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1960,f848,f1967]) ).
fof(f1971,definition,
! [X0] :
( sQ126_spl
<=> ( compose(compose(a,h),compose(compose(a,h),X0)) = compose(compose(compose(a,h),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1974,plain,
( sQ126_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1961,f848,f1971]) ).
fof(f1975,definition,
! [X0] :
( sQ127_spl
<=> ( compose(compose(a,b),compose(compose(a,h),X0)) = compose(compose(compose(a,b),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1978,plain,
( sQ127_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1962,f738,f1975]) ).
fof(f1979,plain,
( sQ76_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1965,f285,f1279]) ).
fof(f2173,plain,
( codomain(compose(a,domain(compose(a,h)))) = domain(compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f587]) ).
fof(f2174,plain,
( codomain(compose(a,domain(compose(a,b)))) = domain(compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f587]) ).
fof(f2176,plain,
( codomain(compose(a,domain(g))) = domain(g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f587]) ).
fof(f2177,plain,
( codomain(compose(a,domain(h))) = domain(h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f587]) ).
fof(f2189,definition,
( sQ128_spl
<=> codomain(compose(a,domain(compose(a,h)))) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f2192,plain,
( sQ128_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2173,f285,f2189]) ).
fof(f2193,definition,
( sQ129_spl
<=> codomain(compose(a,domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f2196,plain,
( sQ129_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2174,f285,f2193]) ).
fof(f2199,definition,
( sQ130_spl
<=> codomain(compose(a,domain(g))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f2202,plain,
( sQ130_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2176,f294,f2199]) ).
fof(f2203,definition,
( sQ131_spl
<=> codomain(compose(a,domain(h))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f2206,plain,
( sQ131_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2177,f294,f2203]) ).
fof(f2218,plain,
( codomain(compose(a,codomain(g))) = codomain(g)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f596]) ).
fof(f2219,plain,
( codomain(compose(a,codomain(compose(a,h)))) = codomain(compose(a,h))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f596]) ).
fof(f2220,plain,
( codomain(compose(a,codomain(compose(a,b)))) = codomain(compose(a,b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f596]) ).
fof(f2223,plain,
( codomain(compose(a,codomain(a))) = codomain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f596]) ).
fof(f2227,definition,
( sQ132_spl
<=> codomain(compose(a,codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f2230,plain,
( sQ132_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f2218,f665,f2227]) ).
fof(f2231,definition,
( sQ133_spl
<=> codomain(compose(a,codomain(compose(a,h)))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f2234,plain,
( sQ133_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f2219,f665,f2231]) ).
fof(f2235,definition,
( sQ134_spl
<=> codomain(compose(a,codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f2238,plain,
( sQ134_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2220,f360,f2235]) ).
fof(f2243,definition,
( sQ135_spl
<=> codomain(compose(a,codomain(a))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f2246,plain,
( sQ135_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2223,f294,f2243]) ).
fof(f2247,plain,
( ~ sQ1_spl
| domain(a) = domain(a)
| codomain(domain(a)) != domain(a) ),
inference(resolution,[status(thm)],[f189,f157]) ).
fof(f2248,plain,
( ~ sQ1_spl
| domain(a) = domain(compose(a,b))
| codomain(domain(compose(a,b))) != domain(a) ),
inference(resolution,[status(thm)],[f189,f16]) ).
fof(f2251,plain,
( ~ sQ1_spl
| sQ54_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f2247,f1042,f981,f175]) ).
fof(f2252,definition,
( sQ136_spl
<=> domain(a) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f2255,plain,
( ~ sQ1_spl
| sQ136_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f2248,f172,f2252,f175]) ).
fof(f2256,definition,
( sQ137_spl
<=> compose(a,b) = compose(a,b) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f2261,plain,
( ~ sQ2_spl
| domain(a) = domain(a)
| codomain(domain(a)) != domain(a)
| compose(a,b) != compose(a,b) ),
inference(resolution,[status(thm)],[f190,f157]) ).
fof(f2262,plain,
( ~ sQ2_spl
| domain(a) = domain(compose(a,b))
| codomain(domain(compose(a,b))) != domain(a)
| compose(a,b) != compose(a,b) ),
inference(resolution,[status(thm)],[f190,f16]) ).
fof(f2263,plain,
! [X0] :
( ~ sQ2_spl
| domain(a) = X0
| codomain(X0) != domain(a)
| compose(a,b) != compose(domain(compose(X0,compose(a,b))),compose(X0,compose(a,b))) ),
inference(resolution,[status(thm)],[f190,f16]) ).
fof(f2264,plain,
! [X0] :
( ~ sQ2_spl
| domain(a) = X0
| codomain(X0) != domain(a)
| compose(a,b) != compose(compose(X0,compose(a,b)),codomain(compose(X0,compose(a,b)))) ),
inference(resolution,[status(thm)],[f190,f17]) ).
fof(f2265,plain,
! [X0] :
( ~ sQ2_spl
| domain(a) = domain(a)
| compose(a,b) != X0
| codomain(domain(a)) != domain(a)
| compose(a,b) != X0 ),
inference(paramodulation,[status(thm)],[f157,f190]) ).
fof(f2266,plain,
! [X0] :
( ~ sQ2_spl
| domain(a) = domain(compose(a,b))
| compose(a,b) != X0
| codomain(domain(compose(a,b))) != domain(a)
| compose(a,b) != X0 ),
inference(paramodulation,[status(thm)],[f16,f190]) ).
fof(f2267,plain,
! [X0] :
( ~ sQ2_spl
| domain(a) = X0
| codomain(X0) != domain(a)
| compose(a,b) != compose(X0,compose(a,b)) ),
inference(equality_resolution,[status(thm)],[f190]) ).
fof(f2268,plain,
( ~ sQ2_spl
| sQ54_spl
| ~ sQ60_spl
| ~ sQ137_spl ),
inference(split_clause,[status(thm)],[f2261,f2256,f1042,f981,f181]) ).
fof(f2269,plain,
( ~ sQ2_spl
| sQ136_spl
| ~ sQ0_spl
| ~ sQ137_spl ),
inference(split_clause,[status(thm)],[f2262,f2256,f172,f2252,f181]) ).
fof(f2270,plain,
! [X0] :
( ~ sQ2_spl
| domain(a) = X0
| codomain(X0) != domain(a)
| compose(a,b) != compose(X0,compose(a,b)) ),
inference(forward_demodulation,[status(thm)],[f16,f2263]) ).
fof(f2271,plain,
! [X0] :
( ~ sQ2_spl
| domain(a) = X0
| codomain(X0) != domain(a)
| compose(a,b) != compose(X0,compose(a,b)) ),
inference(forward_demodulation,[status(thm)],[f17,f2264]) ).
fof(f2272,definition,
! [X0] :
( sQ138_spl
<=> ( compose(a,b) != X0
| compose(a,b) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f2275,plain,
( ~ sQ2_spl
| sQ54_spl
| ~ sQ60_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f2265,f2272,f1042,f981,f181]) ).
fof(f2276,plain,
( ~ sQ2_spl
| sQ136_spl
| ~ sQ0_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f2266,f2272,f172,f2252,f181]) ).
fof(f2280,plain,
( codomain(compose(compose(a,h),codomain(g))) = codomain(g)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f685]) ).
fof(f2281,plain,
( codomain(compose(compose(a,h),codomain(compose(a,h)))) = codomain(compose(a,h))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f685]) ).
fof(f2282,plain,
( codomain(compose(compose(a,h),codomain(compose(a,b)))) = codomain(compose(a,b))
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f685]) ).
fof(f2292,definition,
( sQ139_spl
<=> codomain(compose(compose(a,h),codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f2295,plain,
( sQ139_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f2280,f1350,f2292]) ).
fof(f2296,definition,
( sQ140_spl
<=> codomain(compose(compose(a,h),codomain(compose(a,h)))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f2299,plain,
( sQ140_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f2281,f1350,f2296]) ).
fof(f2300,definition,
( sQ141_spl
<=> codomain(compose(compose(a,h),codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f2303,plain,
( sQ141_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f2282,f1361,f2300]) ).
fof(f2313,plain,
( codomain(compose(compose(a,h),domain(compose(a,h)))) = domain(compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1016]) ).
fof(f2314,plain,
( codomain(compose(compose(a,h),domain(compose(a,b)))) = domain(compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1016]) ).
fof(f2320,definition,
( sQ142_spl
<=> codomain(compose(compose(a,h),domain(compose(a,h)))) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f2323,plain,
( sQ142_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2313,f848,f2320]) ).
fof(f2324,definition,
( sQ143_spl
<=> codomain(compose(compose(a,h),domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f2327,plain,
( sQ143_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2314,f848,f2324]) ).
fof(f2332,plain,
! [X0] :
( codomain(compose(X0,compose(a,h))) = codomain(h)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f567,f437]) ).
fof(f2334,plain,
( codomain(compose(g,compose(a,h))) = codomain(h)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f2332]) ).
fof(f2335,plain,
( codomain(compose(compose(a,h),compose(a,h))) = codomain(h)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f2332]) ).
fof(f2336,plain,
( codomain(compose(compose(a,b),compose(a,h))) = codomain(h)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f2332]) ).
fof(f2339,plain,
( codomain(compose(a,compose(a,h))) = codomain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f2332]) ).
fof(f2341,definition,
( sQ144_spl
<=> codomain(compose(g,compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f2344,plain,
( sQ144_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2334,f848,f2341]) ).
fof(f2345,definition,
( sQ145_spl
<=> codomain(compose(compose(a,h),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f2348,plain,
( sQ145_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2335,f848,f2345]) ).
fof(f2349,definition,
( sQ146_spl
<=> codomain(compose(compose(a,b),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f2352,plain,
( sQ146_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2336,f738,f2349]) ).
fof(f2353,definition,
( sQ147_spl
<=> codomain(compose(a,compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f2356,plain,
( sQ147_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2339,f285,f2353]) ).
fof(f2358,plain,
( compose(g,compose(codomain(h),compose(a,h))) = compose(g,compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1165]) ).
fof(f2359,plain,
( compose(g,compose(codomain(h),compose(a,b))) = compose(g,compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1165]) ).
fof(f2360,plain,
! [X0] :
( compose(g,compose(codomain(h),domain(X0))) = compose(g,domain(X0))
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f1165]) ).
fof(f2361,plain,
! [X0] :
( compose(g,compose(codomain(h),codomain(X0))) = compose(g,codomain(X0))
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f1165]) ).
fof(f2362,definition,
( sQ148_spl
<=> compose(g,compose(codomain(h),compose(a,h))) = compose(g,compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f2365,plain,
( sQ148_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2358,f848,f2362]) ).
fof(f2366,definition,
( sQ149_spl
<=> compose(g,compose(codomain(h),compose(a,b))) = compose(g,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f2369,plain,
( sQ149_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2359,f848,f2366]) ).
fof(f2373,plain,
( compose(domain(a),compose(a,compose(a,h))) = compose(a,compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1201]) ).
fof(f2374,plain,
( compose(domain(a),compose(a,compose(a,b))) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1201]) ).
fof(f2375,plain,
! [X0] :
( compose(domain(a),compose(a,domain(X0))) = compose(a,domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f1201]) ).
fof(f2376,plain,
( compose(domain(a),compose(a,g)) = compose(a,g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f1201]) ).
fof(f2377,plain,
( compose(domain(a),compose(a,h)) = compose(a,h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f1201]) ).
fof(f2378,plain,
! [X0] :
( compose(domain(a),compose(a,codomain(X0))) = compose(a,codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f1201]) ).
fof(f2384,definition,
( sQ150_spl
<=> compose(domain(a),compose(a,compose(a,h))) = compose(a,compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f2387,plain,
( sQ150_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2373,f285,f2384]) ).
fof(f2388,definition,
( sQ151_spl
<=> compose(domain(a),compose(a,compose(a,b))) = compose(a,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f2391,plain,
( sQ151_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2374,f285,f2388]) ).
fof(f2392,definition,
( sQ152_spl
<=> compose(domain(a),compose(a,g)) = compose(a,g) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2395,plain,
( sQ152_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2376,f294,f2392]) ).
fof(f2396,definition,
( sQ153_spl
<=> compose(domain(a),compose(a,h)) = compose(a,h) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f2399,plain,
( sQ153_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2377,f294,f2396]) ).
fof(f2402,plain,
! [X0] :
( codomain(compose(codomain(X0),compose(a,h))) = codomain(h)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f567,f515]) ).
fof(f2404,plain,
( codomain(compose(codomain(g),compose(a,h))) = codomain(h)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f2402]) ).
fof(f2405,plain,
( codomain(compose(codomain(compose(a,h)),compose(a,h))) = codomain(h)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f2402]) ).
fof(f2406,plain,
( codomain(compose(codomain(compose(a,b)),compose(a,h))) = codomain(h)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f2402]) ).
fof(f2409,plain,
( codomain(compose(codomain(a),compose(a,h))) = codomain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f2402]) ).
fof(f2412,definition,
( sQ154_spl
<=> codomain(compose(codomain(g),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2415,plain,
( sQ154_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2404,f848,f2412]) ).
fof(f2416,definition,
( sQ155_spl
<=> codomain(compose(codomain(compose(a,h)),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2419,plain,
( sQ155_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2405,f848,f2416]) ).
fof(f2420,definition,
( sQ156_spl
<=> codomain(compose(codomain(compose(a,b)),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2423,plain,
( sQ156_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2406,f738,f2420]) ).
fof(f2426,definition,
( sQ157_spl
<=> codomain(compose(codomain(a),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2429,plain,
( sQ157_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2409,f285,f2426]) ).
fof(f2430,plain,
! [X0] :
( codomain(compose(domain(X0),compose(a,h))) = codomain(h)
| domain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f567,f544]) ).
fof(f2434,plain,
( codomain(compose(domain(compose(a,h)),compose(a,h))) = codomain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2430]) ).
fof(f2435,plain,
( codomain(compose(domain(compose(a,b)),compose(a,h))) = codomain(h)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2430]) ).
fof(f2437,plain,
( codomain(compose(domain(g),compose(a,h))) = codomain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f52,f2430]) ).
fof(f2438,plain,
( codomain(compose(domain(h),compose(a,h))) = codomain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f44,f2430]) ).
fof(f2446,definition,
( sQ158_spl
<=> codomain(compose(domain(compose(a,h)),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2449,plain,
( sQ158_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2434,f981,f2446]) ).
fof(f2450,definition,
( sQ159_spl
<=> codomain(compose(domain(compose(a,b)),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2453,plain,
( sQ159_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2435,f981,f2450]) ).
fof(f2455,definition,
( sQ160_spl
<=> codomain(compose(domain(g),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2458,plain,
( sQ160_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2437,f285,f2455]) ).
fof(f2459,definition,
( sQ161_spl
<=> codomain(compose(domain(h),compose(a,h))) = codomain(h) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f2462,plain,
( sQ161_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2438,f285,f2459]) ).
fof(f2471,plain,
( domain(compose(a,domain(compose(a,h)))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f409]) ).
fof(f2472,plain,
( domain(compose(a,domain(compose(a,b)))) = domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f409]) ).
fof(f2474,plain,
( domain(compose(a,domain(g))) = domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f409]) ).
fof(f2475,plain,
( domain(compose(a,domain(h))) = domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f409]) ).
fof(f2481,definition,
( sQ162_spl
<=> domain(compose(a,domain(compose(a,h)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f2484,plain,
( sQ162_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2471,f285,f2481]) ).
fof(f2485,definition,
( sQ163_spl
<=> domain(compose(a,domain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2488,plain,
( sQ163_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2472,f285,f2485]) ).
fof(f2490,definition,
( sQ164_spl
<=> domain(compose(a,domain(g))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f2493,plain,
( sQ164_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2474,f294,f2490]) ).
fof(f2494,definition,
( sQ165_spl
<=> domain(compose(a,domain(h))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f2497,plain,
( sQ165_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2475,f294,f2494]) ).
fof(f2503,plain,
( domain(compose(a,codomain(g))) = domain(a)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f412]) ).
fof(f2504,plain,
( domain(compose(a,codomain(compose(a,h)))) = domain(a)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f412]) ).
fof(f2505,plain,
( domain(compose(a,codomain(compose(a,b)))) = domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f412]) ).
fof(f2508,plain,
( domain(compose(a,codomain(a))) = domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f412]) ).
fof(f2510,definition,
( sQ166_spl
<=> domain(compose(a,codomain(g))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f2513,plain,
( sQ166_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f2503,f665,f2510]) ).
fof(f2514,definition,
( sQ167_spl
<=> domain(compose(a,codomain(compose(a,h)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f2517,plain,
( sQ167_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f2504,f665,f2514]) ).
fof(f2518,definition,
( sQ168_spl
<=> domain(compose(a,codomain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f2521,plain,
( sQ168_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2505,f360,f2518]) ).
fof(f2524,definition,
( sQ169_spl
<=> domain(compose(a,codomain(a))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f2527,plain,
( sQ169_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2508,f294,f2524]) ).
fof(f2537,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(a,h),X1)) = compose(compose(codomain(X0),compose(a,h)),X1)
| codomain(compose(a,h)) != domain(X1)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f141]) ).
fof(f2538,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(a,b),X1)) = compose(compose(codomain(X0),compose(a,b)),X1)
| codomain(compose(a,b)) != domain(X1)
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f141]) ).
fof(f2539,plain,
! [X0,X1,X2] :
( compose(codomain(X0),compose(domain(X1),X2)) = compose(compose(codomain(X0),domain(X1)),X2)
| codomain(domain(X1)) != domain(X2)
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f141]) ).
fof(f2561,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(a,h),X1)) = compose(compose(codomain(X0),compose(a,h)),X1)
| codomain(h) != domain(X1)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f567,f2537]) ).
fof(f2562,plain,
! [X0,X1] :
( compose(codomain(X0),compose(compose(a,b),X1)) = compose(compose(codomain(X0),compose(a,b)),X1)
| codomain(b) != domain(X1)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f128,f2538]) ).
fof(f2563,plain,
! [X0,X1,X2] :
( compose(codomain(X0),compose(domain(X1),X2)) = compose(compose(codomain(X0),domain(X1)),X2)
| domain(X1) != domain(X2)
| codomain(X0) != domain(X1) ),
inference(forward_demodulation,[status(thm)],[f14,f2539]) ).
fof(f2568,plain,
! [X0,X1] :
( compose(g,compose(domain(X0),X1)) = compose(compose(g,domain(X0)),X1)
| domain(X0) != domain(X1)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f641,f149]) ).
fof(f2569,plain,
! [X0,X1] :
( compose(compose(a,h),compose(domain(X0),X1)) = compose(compose(compose(a,h),domain(X0)),X1)
| domain(X0) != domain(X1)
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f567,f149]) ).
fof(f2570,plain,
! [X0,X1] :
( compose(compose(a,b),compose(domain(X0),X1)) = compose(compose(compose(a,b),domain(X0)),X1)
| domain(X0) != domain(X1)
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f149]) ).
fof(f2596,plain,
! [X0,X1] :
( compose(X0,compose(compose(a,b),X1)) = compose(compose(X0,compose(a,b)),X1)
| codomain(b) != domain(X1)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f128,f151]) ).
fof(f2598,plain,
! [X0] :
( compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(b) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f2596]) ).
fof(f2599,plain,
! [X0] :
( compose(compose(a,h),compose(compose(a,b),X0)) = compose(compose(compose(a,h),compose(a,b)),X0)
| codomain(b) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f2596]) ).
fof(f2600,plain,
! [X0] :
( compose(compose(a,b),compose(compose(a,b),X0)) = compose(compose(compose(a,b),compose(a,b)),X0)
| codomain(b) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f2596]) ).
fof(f2603,plain,
! [X0] :
( compose(a,compose(compose(a,b),X0)) = compose(compose(a,compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f2596]) ).
fof(f2605,definition,
! [X0] :
( sQ170_spl
<=> ( compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f2608,plain,
( sQ170_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2598,f848,f2605]) ).
fof(f2609,definition,
! [X0] :
( sQ171_spl
<=> ( compose(compose(a,h),compose(compose(a,b),X0)) = compose(compose(compose(a,h),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f2612,plain,
( sQ171_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2599,f848,f2609]) ).
fof(f2613,definition,
! [X0] :
( sQ172_spl
<=> ( compose(compose(a,b),compose(compose(a,b),X0)) = compose(compose(compose(a,b),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f2616,plain,
( sQ172_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2600,f738,f2613]) ).
fof(f2617,plain,
( sQ78_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2603,f285,f1286]) ).
fof(f2618,plain,
! [X0] :
( domain(compose(compose(a,h),codomain(X0))) = domain(a)
| codomain(h) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f641,f619]) ).
fof(f2622,plain,
( domain(compose(compose(a,h),codomain(g))) = domain(a)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f2618]) ).
fof(f2623,plain,
( domain(compose(compose(a,h),codomain(compose(a,h)))) = domain(a)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f2618]) ).
fof(f2624,plain,
( domain(compose(compose(a,h),codomain(compose(a,b)))) = domain(a)
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f2618]) ).
fof(f2633,definition,
( sQ173_spl
<=> domain(compose(compose(a,h),codomain(g))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f2636,plain,
( sQ173_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f2622,f1350,f2633]) ).
fof(f2637,definition,
( sQ174_spl
<=> domain(compose(compose(a,h),codomain(compose(a,h)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2640,plain,
( sQ174_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f2623,f1350,f2637]) ).
fof(f2641,definition,
( sQ175_spl
<=> domain(compose(compose(a,h),codomain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2644,plain,
( sQ175_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f2624,f1361,f2641]) ).
fof(f2651,plain,
! [X0] :
( domain(compose(compose(a,h),domain(X0))) = domain(a)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f641,f620]) ).
fof(f2653,plain,
( domain(compose(compose(a,h),domain(compose(a,h)))) = domain(a)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2651]) ).
fof(f2654,plain,
( domain(compose(compose(a,h),domain(compose(a,b)))) = domain(a)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2651]) ).
fof(f2659,definition,
( sQ176_spl
<=> domain(compose(compose(a,h),domain(compose(a,h)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f2662,plain,
( sQ176_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2653,f848,f2659]) ).
fof(f2663,definition,
( sQ177_spl
<=> domain(compose(compose(a,h),domain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f2666,plain,
( sQ177_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2654,f848,f2663]) ).
fof(f2669,plain,
! [X0,X1] :
( compose(compose(a,h),compose(X0,X1)) = compose(compose(compose(a,h),X0),X1)
| codomain(X0) != domain(X1)
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f641,f607]) ).
fof(f2671,plain,
! [X0] :
( compose(compose(a,h),compose(compose(a,h),X0)) = compose(compose(compose(a,h),compose(a,h)),X0)
| codomain(compose(a,h)) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2669]) ).
fof(f2672,plain,
! [X0] :
( compose(compose(a,h),compose(compose(a,b),X0)) = compose(compose(compose(a,h),compose(a,b)),X0)
| codomain(compose(a,b)) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2669]) ).
fof(f2677,definition,
! [X0] :
( sQ178_spl
<=> ( compose(compose(a,h),compose(compose(a,h),X0)) = compose(compose(compose(a,h),compose(a,h)),X0)
| codomain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2680,plain,
( sQ178_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2671,f848,f2677]) ).
fof(f2681,definition,
! [X0] :
( sQ179_spl
<=> ( compose(compose(a,h),compose(compose(a,b),X0)) = compose(compose(compose(a,h),compose(a,b)),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2684,plain,
( sQ179_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2672,f848,f2681]) ).
fof(f2692,plain,
( compose(domain(a),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f728]) ).
fof(f2693,plain,
( compose(domain(a),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f728]) ).
fof(f2694,plain,
! [X0] :
( compose(domain(a),compose(compose(a,h),domain(X0))) = compose(compose(a,h),domain(X0))
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f728]) ).
fof(f2695,plain,
! [X0] :
( compose(domain(a),compose(compose(a,h),codomain(X0))) = compose(compose(a,h),codomain(X0))
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f728]) ).
fof(f2698,definition,
( sQ180_spl
<=> compose(domain(a),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2701,plain,
( sQ180_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2692,f848,f2698]) ).
fof(f2702,definition,
( sQ181_spl
<=> compose(domain(a),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f2705,plain,
( sQ181_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2693,f848,f2702]) ).
fof(f2707,plain,
( domain(compose(g,compose(a,b))) = domain(g)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f153]) ).
fof(f2708,plain,
( domain(compose(compose(a,h),compose(a,b))) = domain(compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f153]) ).
fof(f2709,plain,
( domain(compose(compose(a,b),compose(a,b))) = domain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f153]) ).
fof(f2715,definition,
( sQ182_spl
<=> domain(compose(g,compose(a,b))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2718,plain,
( sQ182_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2707,f848,f2715]) ).
fof(f2719,definition,
( sQ183_spl
<=> domain(compose(compose(a,h),compose(a,b))) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f2722,plain,
( sQ183_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2708,f848,f2719]) ).
fof(f2723,definition,
( sQ184_spl
<=> domain(compose(compose(a,b),compose(a,b))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f2726,plain,
( sQ184_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2709,f738,f2723]) ).
fof(f2731,plain,
( codomain(compose(compose(a,b),compose(a,h))) = codomain(compose(a,h))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f193]) ).
fof(f2732,plain,
( codomain(compose(compose(a,b),compose(a,b))) = codomain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f193]) ).
fof(f2737,definition,
( sQ185_spl
<=> codomain(compose(compose(a,b),compose(a,h))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2740,plain,
( sQ185_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2731,f738,f2737]) ).
fof(f2741,definition,
( sQ186_spl
<=> codomain(compose(compose(a,b),compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f2744,plain,
( sQ186_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2732,f738,f2741]) ).
fof(f2748,plain,
( domain(compose(compose(a,b),compose(a,h))) = domain(a)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f200]) ).
fof(f2749,plain,
( domain(compose(compose(a,b),compose(a,b))) = domain(a)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f200]) ).
fof(f2753,definition,
( sQ187_spl
<=> domain(compose(compose(a,b),compose(a,h))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f2756,plain,
( sQ187_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2748,f738,f2753]) ).
fof(f2757,definition,
( sQ188_spl
<=> domain(compose(compose(a,b),compose(a,b))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f2760,plain,
( sQ188_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2749,f738,f2757]) ).
fof(f2764,plain,
( compose(a,compose(a,h)) = compose(compose(a,domain(compose(a,h))),compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1263]) ).
fof(f2765,plain,
( compose(a,compose(a,b)) = compose(compose(a,domain(compose(a,b))),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1263]) ).
fof(f2766,plain,
! [X0] :
( compose(a,domain(X0)) = compose(compose(a,domain(domain(X0))),domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f1263]) ).
fof(f2767,plain,
( compose(a,g) = compose(compose(a,domain(g)),g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f1263]) ).
fof(f2768,plain,
( compose(a,h) = compose(compose(a,domain(h)),h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f1263]) ).
fof(f2769,plain,
! [X0] :
( compose(a,codomain(X0)) = compose(compose(a,domain(codomain(X0))),codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f1263]) ).
fof(f2778,definition,
( sQ189_spl
<=> compose(a,compose(a,h)) = compose(compose(a,domain(compose(a,h))),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2781,plain,
( sQ189_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2764,f285,f2778]) ).
fof(f2782,definition,
( sQ190_spl
<=> compose(a,compose(a,b)) = compose(compose(a,domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f2785,plain,
( sQ190_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2765,f285,f2782]) ).
fof(f2786,plain,
! [X0] :
( compose(a,domain(X0)) = compose(compose(a,domain(X0)),domain(X0))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f2766]) ).
fof(f2787,definition,
( sQ191_spl
<=> compose(a,g) = compose(compose(a,domain(g)),g) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f2790,plain,
( sQ191_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2767,f294,f2787]) ).
fof(f2791,definition,
( sQ192_spl
<=> compose(a,h) = compose(compose(a,domain(h)),h) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2794,plain,
( sQ192_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2768,f294,f2791]) ).
fof(f2795,plain,
! [X0] :
( compose(a,codomain(X0)) = compose(compose(a,codomain(X0)),codomain(X0))
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f2769]) ).
fof(f2803,plain,
( compose(a,compose(a,h)) = compose(compose(a,compose(a,h)),codomain(compose(a,h)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1268]) ).
fof(f2804,plain,
( compose(a,compose(a,b)) = compose(compose(a,compose(a,b)),codomain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1268]) ).
fof(f2806,plain,
( compose(a,g) = compose(compose(a,g),codomain(g))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f1268]) ).
fof(f2807,plain,
( compose(a,h) = compose(compose(a,h),codomain(h))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f1268]) ).
fof(f2816,definition,
( sQ193_spl
<=> compose(a,compose(a,h)) = compose(compose(a,compose(a,h)),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2819,plain,
( sQ193_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2803,f285,f2816]) ).
fof(f2820,definition,
( sQ194_spl
<=> compose(a,compose(a,b)) = compose(compose(a,compose(a,b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f2823,plain,
( sQ194_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2804,f285,f2820]) ).
fof(f2825,definition,
( sQ195_spl
<=> compose(a,g) = compose(compose(a,g),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f2828,plain,
( sQ195_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2806,f294,f2825]) ).
fof(f2829,definition,
( sQ196_spl
<=> compose(a,h) = compose(compose(a,h),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2832,plain,
( sQ196_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2807,f294,f2829]) ).
fof(f2837,plain,
! [X0] :
( codomain(compose(X0,compose(a,b))) = codomain(b)
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f128,f152]) ).
fof(f2839,plain,
( codomain(compose(g,compose(a,b))) = codomain(b)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f2837]) ).
fof(f2840,plain,
( codomain(compose(compose(a,h),compose(a,b))) = codomain(b)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f2837]) ).
fof(f2841,plain,
( codomain(compose(compose(a,b),compose(a,b))) = codomain(b)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f2837]) ).
fof(f2844,plain,
( codomain(compose(a,compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f2837]) ).
fof(f2846,definition,
( sQ197_spl
<=> codomain(compose(g,compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2849,plain,
( sQ197_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2839,f848,f2846]) ).
fof(f2850,definition,
( sQ198_spl
<=> codomain(compose(compose(a,h),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2853,plain,
( sQ198_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2840,f848,f2850]) ).
fof(f2854,definition,
( sQ199_spl
<=> codomain(compose(compose(a,b),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2857,plain,
( sQ199_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2841,f738,f2854]) ).
fof(f2858,definition,
( sQ200_spl
<=> codomain(compose(a,compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2861,plain,
( sQ200_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2844,f285,f2858]) ).
fof(f2863,plain,
! [X0] :
( compose(compose(a,b),compose(compose(a,h),X0)) = compose(compose(compose(a,b),compose(a,h)),X0)
| codomain(compose(a,h)) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f192]) ).
fof(f2864,plain,
! [X0] :
( compose(compose(a,b),compose(compose(a,b),X0)) = compose(compose(compose(a,b),compose(a,b)),X0)
| codomain(compose(a,b)) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f192]) ).
fof(f2869,definition,
! [X0] :
( sQ201_spl
<=> ( compose(compose(a,b),compose(compose(a,h),X0)) = compose(compose(compose(a,b),compose(a,h)),X0)
| codomain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2872,plain,
( sQ201_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2863,f738,f2869]) ).
fof(f2873,definition,
! [X0] :
( sQ202_spl
<=> ( compose(compose(a,b),compose(compose(a,b),X0)) = compose(compose(compose(a,b),compose(a,b)),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2876,plain,
( sQ202_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2864,f738,f2873]) ).
fof(f2882,plain,
( domain(compose(domain(compose(a,h)),compose(a,b))) = domain(compose(a,h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f243]) ).
fof(f2883,plain,
( domain(compose(domain(compose(a,b)),compose(a,b))) = domain(compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f243]) ).
fof(f2885,plain,
( domain(compose(domain(g),compose(a,b))) = domain(g)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f52,f243]) ).
fof(f2886,plain,
( domain(compose(domain(h),compose(a,b))) = domain(h)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f44,f243]) ).
fof(f2895,definition,
( sQ203_spl
<=> domain(compose(domain(compose(a,h)),compose(a,b))) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2898,plain,
( sQ203_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2882,f981,f2895]) ).
fof(f2899,definition,
( sQ204_spl
<=> domain(compose(domain(compose(a,b)),compose(a,b))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2902,plain,
( sQ204_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2883,f981,f2899]) ).
fof(f2905,definition,
( sQ205_spl
<=> domain(compose(domain(g),compose(a,b))) = domain(g) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2908,plain,
( sQ205_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2885,f285,f2905]) ).
fof(f2909,definition,
( sQ206_spl
<=> domain(compose(domain(h),compose(a,b))) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2912,plain,
( sQ206_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2886,f285,f2909]) ).
fof(f2920,plain,
( ~ sQ74_spl
| compose(a,compose(g,compose(a,h))) = compose(compose(a,h),compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1301]) ).
fof(f2921,plain,
( ~ sQ74_spl
| compose(a,compose(g,compose(a,b))) = compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1301]) ).
fof(f2922,plain,
! [X0] :
( ~ sQ74_spl
| compose(a,compose(g,domain(X0))) = compose(compose(a,h),domain(X0))
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f1301]) ).
fof(f2923,plain,
! [X0] :
( ~ sQ74_spl
| compose(a,compose(g,codomain(X0))) = compose(compose(a,h),codomain(X0))
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f1301]) ).
fof(f2926,definition,
( sQ207_spl
<=> compose(a,compose(g,compose(a,h))) = compose(compose(a,h),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2929,plain,
( ~ sQ74_spl
| sQ207_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2920,f848,f2926,f1272]) ).
fof(f2930,definition,
( sQ208_spl
<=> compose(a,compose(g,compose(a,b))) = compose(compose(a,h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2933,plain,
( ~ sQ74_spl
| sQ208_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2921,f848,f2930,f1272]) ).
fof(f2937,plain,
( compose(domain(b),compose(g,domain(compose(a,h)))) = compose(g,domain(compose(a,h)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1309]) ).
fof(f2938,plain,
( compose(domain(b),compose(g,domain(compose(a,b)))) = compose(g,domain(compose(a,b)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1309]) ).
fof(f2945,definition,
( sQ209_spl
<=> compose(domain(b),compose(g,domain(compose(a,h)))) = compose(g,domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2948,plain,
( sQ209_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2937,f848,f2945]) ).
fof(f2949,definition,
( sQ210_spl
<=> compose(domain(b),compose(g,domain(compose(a,b)))) = compose(g,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2952,plain,
( sQ210_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2938,f848,f2949]) ).
fof(f2958,plain,
( compose(domain(g),compose(g,compose(a,h))) = compose(g,compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f721]) ).
fof(f2959,plain,
( compose(domain(compose(a,h)),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f721]) ).
fof(f2960,plain,
( compose(domain(compose(a,b)),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f721]) ).
fof(f2961,plain,
! [X0] :
( compose(domain(codomain(X0)),compose(codomain(X0),compose(a,h))) = compose(codomain(X0),compose(a,h))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f40,f721]) ).
fof(f2962,plain,
! [X0] :
( compose(domain(domain(X0)),compose(domain(X0),compose(a,h))) = compose(domain(X0),compose(a,h))
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f14,f721]) ).
fof(f2965,definition,
( sQ211_spl
<=> compose(domain(g),compose(g,compose(a,h))) = compose(g,compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2968,plain,
( sQ211_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2958,f848,f2965]) ).
fof(f2969,definition,
( sQ212_spl
<=> compose(domain(compose(a,h)),compose(compose(a,h),compose(a,h))) = compose(compose(a,h),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2972,plain,
( sQ212_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2959,f848,f2969]) ).
fof(f2973,definition,
( sQ213_spl
<=> compose(domain(compose(a,b)),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2976,plain,
( sQ213_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2960,f738,f2973]) ).
fof(f2977,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),compose(a,h))) = compose(codomain(X0),compose(a,h))
| codomain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f15,f2961]) ).
fof(f2978,plain,
! [X0] :
( compose(domain(X0),compose(domain(X0),compose(a,h))) = compose(domain(X0),compose(a,h))
| domain(X0) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f38,f2962]) ).
fof(f2983,plain,
( compose(domain(b),compose(g,codomain(g))) = compose(g,codomain(g))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f1310]) ).
fof(f2984,plain,
( compose(domain(b),compose(g,codomain(compose(a,h)))) = compose(g,codomain(compose(a,h)))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f1310]) ).
fof(f2985,plain,
( compose(domain(b),compose(g,codomain(compose(a,b)))) = compose(g,codomain(compose(a,b)))
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f1310]) ).
fof(f2999,definition,
( sQ214_spl
<=> compose(domain(b),compose(g,codomain(g))) = compose(g,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f3002,plain,
( sQ214_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f2983,f1350,f2999]) ).
fof(f3003,definition,
( sQ215_spl
<=> compose(domain(b),compose(g,codomain(compose(a,h)))) = compose(g,codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f3006,plain,
( sQ215_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f2984,f1350,f3003]) ).
fof(f3007,definition,
( sQ216_spl
<=> compose(domain(b),compose(g,codomain(compose(a,b)))) = compose(g,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f3010,plain,
( sQ216_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f2985,f1361,f3007]) ).
fof(f3024,plain,
( compose(domain(b),compose(h,domain(compose(a,h)))) = compose(h,domain(compose(a,h)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1433]) ).
fof(f3025,plain,
( compose(domain(b),compose(h,domain(compose(a,b)))) = compose(h,domain(compose(a,b)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1433]) ).
fof(f3032,definition,
( sQ217_spl
<=> compose(domain(b),compose(h,domain(compose(a,h)))) = compose(h,domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f3035,plain,
( sQ217_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3024,f848,f3032]) ).
fof(f3036,definition,
( sQ218_spl
<=> compose(domain(b),compose(h,domain(compose(a,b)))) = compose(h,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f3039,plain,
( sQ218_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3025,f848,f3036]) ).
fof(f3047,plain,
( compose(domain(b),compose(h,codomain(g))) = compose(h,codomain(g))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f1434]) ).
fof(f3048,plain,
( compose(domain(b),compose(h,codomain(compose(a,h)))) = compose(h,codomain(compose(a,h)))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f1434]) ).
fof(f3049,plain,
( compose(domain(b),compose(h,codomain(compose(a,b)))) = compose(h,codomain(compose(a,b)))
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f1434]) ).
fof(f3065,definition,
( sQ219_spl
<=> compose(domain(b),compose(h,codomain(g))) = compose(h,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f3068,plain,
( sQ219_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f3047,f1350,f3065]) ).
fof(f3069,definition,
( sQ220_spl
<=> compose(domain(b),compose(h,codomain(compose(a,h)))) = compose(h,codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f3072,plain,
( sQ220_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f3048,f1350,f3069]) ).
fof(f3073,definition,
( sQ221_spl
<=> compose(domain(b),compose(h,codomain(compose(a,b)))) = compose(h,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f3076,plain,
( sQ221_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f3049,f1361,f3073]) ).
fof(f3092,plain,
( compose(g,compose(codomain(h),domain(compose(a,h)))) = compose(g,domain(compose(a,h)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2360]) ).
fof(f3093,plain,
( compose(g,compose(codomain(h),domain(compose(a,b)))) = compose(g,domain(compose(a,b)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2360]) ).
fof(f3100,definition,
( sQ222_spl
<=> compose(g,compose(codomain(h),domain(compose(a,h)))) = compose(g,domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f3103,plain,
( sQ222_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3092,f848,f3100]) ).
fof(f3104,definition,
( sQ223_spl
<=> compose(g,compose(codomain(h),domain(compose(a,b)))) = compose(g,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f3107,plain,
( sQ223_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3093,f848,f3104]) ).
fof(f3115,plain,
( compose(g,compose(codomain(h),codomain(g))) = compose(g,codomain(g))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f2361]) ).
fof(f3116,plain,
( compose(g,compose(codomain(h),codomain(compose(a,h)))) = compose(g,codomain(compose(a,h)))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f2361]) ).
fof(f3117,plain,
( compose(g,compose(codomain(h),codomain(compose(a,b)))) = compose(g,codomain(compose(a,b)))
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f2361]) ).
fof(f3131,definition,
( sQ224_spl
<=> compose(g,compose(codomain(h),codomain(g))) = compose(g,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f3134,plain,
( sQ224_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f3115,f1350,f3131]) ).
fof(f3135,definition,
( sQ225_spl
<=> compose(g,compose(codomain(h),codomain(compose(a,h)))) = compose(g,codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f3138,plain,
( sQ225_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f3116,f1350,f3135]) ).
fof(f3139,definition,
( sQ226_spl
<=> compose(g,compose(codomain(h),codomain(compose(a,b)))) = compose(g,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f3142,plain,
( sQ226_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f3117,f1361,f3139]) ).
fof(f3157,plain,
( compose(domain(a),compose(a,domain(compose(a,h)))) = compose(a,domain(compose(a,h)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2375]) ).
fof(f3158,plain,
( compose(domain(a),compose(a,domain(compose(a,b)))) = compose(a,domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2375]) ).
fof(f3160,plain,
( compose(domain(a),compose(a,domain(g))) = compose(a,domain(g))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f2375]) ).
fof(f3161,plain,
( compose(domain(a),compose(a,domain(h))) = compose(a,domain(h))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f2375]) ).
fof(f3176,definition,
( sQ227_spl
<=> compose(domain(a),compose(a,domain(compose(a,h)))) = compose(a,domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f3179,plain,
( sQ227_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3157,f285,f3176]) ).
fof(f3180,definition,
( sQ228_spl
<=> compose(domain(a),compose(a,domain(compose(a,b)))) = compose(a,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f3183,plain,
( sQ228_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3158,f285,f3180]) ).
fof(f3186,definition,
( sQ229_spl
<=> compose(domain(a),compose(a,domain(g))) = compose(a,domain(g)) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f3189,plain,
( sQ229_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3160,f294,f3186]) ).
fof(f3190,definition,
( sQ230_spl
<=> compose(domain(a),compose(a,domain(h))) = compose(a,domain(h)) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f3193,plain,
( sQ230_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3161,f294,f3190]) ).
fof(f3208,plain,
( compose(domain(a),compose(a,codomain(g))) = compose(a,codomain(g))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f2378]) ).
fof(f3209,plain,
( compose(domain(a),compose(a,codomain(compose(a,h)))) = compose(a,codomain(compose(a,h)))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f2378]) ).
fof(f3210,plain,
( compose(domain(a),compose(a,codomain(compose(a,b)))) = compose(a,codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f2378]) ).
fof(f3213,plain,
( compose(domain(a),compose(a,codomain(a))) = compose(a,codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f2378]) ).
fof(f3220,definition,
( sQ231_spl
<=> compose(domain(a),compose(a,codomain(g))) = compose(a,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f3223,plain,
( sQ231_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f3208,f665,f3220]) ).
fof(f3224,definition,
( sQ232_spl
<=> compose(domain(a),compose(a,codomain(compose(a,h)))) = compose(a,codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f3227,plain,
( sQ232_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f3209,f665,f3224]) ).
fof(f3228,definition,
( sQ233_spl
<=> compose(domain(a),compose(a,codomain(compose(a,b)))) = compose(a,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f3231,plain,
( sQ233_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3210,f360,f3228]) ).
fof(f3236,definition,
( sQ234_spl
<=> compose(domain(a),compose(a,codomain(a))) = compose(a,codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3239,plain,
( sQ234_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3213,f294,f3236]) ).
fof(f3243,plain,
! [X0] :
( compose(g,compose(compose(a,h),X0)) = compose(compose(g,compose(a,h)),X0)
| codomain(compose(a,h)) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f764]) ).
fof(f3244,plain,
! [X0] :
( compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(compose(a,b)) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f764]) ).
fof(f3249,definition,
! [X0] :
( sQ235_spl
<=> ( compose(g,compose(compose(a,h),X0)) = compose(compose(g,compose(a,h)),X0)
| codomain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f3252,plain,
( sQ235_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3243,f848,f3249]) ).
fof(f3253,definition,
! [X0] :
( sQ236_spl
<=> ( compose(g,compose(compose(a,b),X0)) = compose(compose(g,compose(a,b)),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f3256,plain,
( sQ236_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3244,f848,f3253]) ).
fof(f3260,plain,
( compose(compose(a,h),compose(codomain(h),compose(a,h))) = compose(compose(a,h),compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1166]) ).
fof(f3261,plain,
( compose(compose(a,h),compose(codomain(h),compose(a,b))) = compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1166]) ).
fof(f3262,plain,
! [X0] :
( compose(compose(a,h),compose(codomain(h),domain(X0))) = compose(compose(a,h),domain(X0))
| codomain(h) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f1166]) ).
fof(f3263,plain,
! [X0] :
( compose(compose(a,h),compose(codomain(h),codomain(X0))) = compose(compose(a,h),codomain(X0))
| codomain(h) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f1166]) ).
fof(f3264,definition,
( sQ237_spl
<=> compose(compose(a,h),compose(codomain(h),compose(a,h))) = compose(compose(a,h),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f3267,plain,
( sQ237_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3260,f848,f3264]) ).
fof(f3268,definition,
( sQ238_spl
<=> compose(compose(a,h),compose(codomain(h),compose(a,b))) = compose(compose(a,h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f3271,plain,
( sQ238_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3261,f848,f3268]) ).
fof(f3273,plain,
( domain(compose(codomain(g),compose(a,b))) = codomain(g)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f214]) ).
fof(f3274,plain,
( domain(compose(codomain(compose(a,h)),compose(a,b))) = codomain(compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f214]) ).
fof(f3275,plain,
( domain(compose(codomain(compose(a,b)),compose(a,b))) = codomain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f214]) ).
fof(f3278,plain,
( domain(compose(codomain(a),compose(a,b))) = codomain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f214]) ).
fof(f3282,definition,
( sQ239_spl
<=> domain(compose(codomain(g),compose(a,b))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f3285,plain,
( sQ239_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3273,f848,f3282]) ).
fof(f3286,definition,
( sQ240_spl
<=> domain(compose(codomain(compose(a,h)),compose(a,b))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f3289,plain,
( sQ240_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3274,f848,f3286]) ).
fof(f3290,definition,
( sQ241_spl
<=> domain(compose(codomain(compose(a,b)),compose(a,b))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f3293,plain,
( sQ241_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3275,f738,f3290]) ).
fof(f3298,definition,
( sQ242_spl
<=> domain(compose(codomain(a),compose(a,b))) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f3301,plain,
( sQ242_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3278,f285,f3298]) ).
fof(f3304,plain,
( codomain(compose(compose(a,b),codomain(g))) = codomain(g)
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f686]) ).
fof(f3305,plain,
( codomain(compose(compose(a,b),codomain(compose(a,h)))) = codomain(compose(a,h))
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f686]) ).
fof(f3306,plain,
( codomain(compose(compose(a,b),codomain(compose(a,b)))) = codomain(compose(a,b))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f686]) ).
fof(f3313,definition,
( sQ243_spl
<=> codomain(compose(compose(a,b),codomain(g))) = codomain(g) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f3316,plain,
( sQ243_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f3304,f1361,f3313]) ).
fof(f3317,definition,
( sQ244_spl
<=> codomain(compose(compose(a,b),codomain(compose(a,h)))) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f3320,plain,
( sQ244_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f3305,f1361,f3317]) ).
fof(f3321,definition,
( sQ245_spl
<=> codomain(b) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f3323,plain,
( sQ245_spl
| codomain(b) != codomain(b) ),
inference(component_clause,[status(thm)],[f3321]) ).
fof(f3324,definition,
( sQ246_spl
<=> codomain(compose(compose(a,b),codomain(compose(a,b)))) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f3327,plain,
( sQ246_spl
| ~ sQ245_spl ),
inference(split_clause,[status(thm)],[f3306,f3321,f3324]) ).
fof(f3333,plain,
( sQ245_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3323]) ).
fof(f3334,plain,
sQ245_spl,
inference(contradiction_clause,[status(thm)],[f3333]) ).
fof(f3345,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),compose(a,b))) = compose(codomain(X0),compose(a,b))
| codomain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f730]) ).
fof(f3346,plain,
! [X0,X1] :
( compose(codomain(X0),compose(codomain(X0),domain(X1))) = compose(codomain(X0),domain(X1))
| codomain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f730]) ).
fof(f3347,plain,
! [X0,X1] :
( compose(codomain(X0),compose(codomain(X0),codomain(X1))) = compose(codomain(X0),codomain(X1))
| codomain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f730]) ).
fof(f3393,plain,
! [X0] :
( compose(domain(X0),compose(domain(X0),compose(a,b))) = compose(domain(X0),compose(a,b))
| domain(X0) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f731]) ).
fof(f3394,plain,
! [X0,X1] :
( compose(domain(X0),compose(domain(X0),domain(X1))) = compose(domain(X0),domain(X1))
| domain(X0) != domain(X1) ),
inference(paramodulation,[status(thm)],[f38,f731]) ).
fof(f3395,plain,
! [X0] :
( compose(domain(X0),compose(domain(X0),g)) = compose(domain(X0),g)
| domain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f731]) ).
fof(f3396,plain,
! [X0] :
( compose(domain(X0),compose(domain(X0),h)) = compose(domain(X0),h)
| domain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f731]) ).
fof(f3397,plain,
! [X0,X1] :
( compose(domain(X0),compose(domain(X0),codomain(X1))) = compose(domain(X0),codomain(X1))
| domain(X0) != codomain(X1) ),
inference(paramodulation,[status(thm)],[f15,f731]) ).
fof(f3447,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f723]) ).
fof(f3464,plain,
! [X0] :
( compose(domain(a),compose(compose(a,b),domain(X0))) = compose(compose(a,b),domain(X0))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f117,f3447]) ).
fof(f3485,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f128,f724]) ).
fof(f3526,plain,
! [X0] :
( compose(domain(a),compose(compose(a,b),codomain(X0))) = compose(compose(a,b),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f117,f3485]) ).
fof(f3544,plain,
( codomain(compose(compose(a,b),domain(compose(a,h)))) = domain(compose(a,h))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1017]) ).
fof(f3545,plain,
( codomain(compose(compose(a,b),domain(compose(a,b)))) = domain(compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1017]) ).
fof(f3551,definition,
( sQ247_spl
<=> codomain(compose(compose(a,b),domain(compose(a,h)))) = domain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f3554,plain,
( sQ247_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3544,f738,f3551]) ).
fof(f3555,definition,
( sQ248_spl
<=> codomain(compose(compose(a,b),domain(compose(a,b)))) = domain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f3558,plain,
( sQ248_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3545,f738,f3555]) ).
fof(f3566,plain,
( compose(a,compose(domain(b),compose(a,h))) = compose(a,compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1170]) ).
fof(f3567,plain,
( compose(a,compose(domain(b),compose(a,b))) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1170]) ).
fof(f3568,plain,
! [X0] :
( compose(a,compose(domain(b),domain(X0))) = compose(a,domain(X0))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f38,f1170]) ).
fof(f3569,plain,
( compose(a,compose(domain(b),g)) = compose(a,g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f1170]) ).
fof(f3570,plain,
( compose(a,compose(domain(b),h)) = compose(a,h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f1170]) ).
fof(f3571,plain,
! [X0] :
( compose(a,compose(domain(b),codomain(X0))) = compose(a,codomain(X0))
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f15,f1170]) ).
fof(f3573,definition,
( sQ249_spl
<=> compose(a,compose(domain(b),compose(a,h))) = compose(a,compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3576,plain,
( sQ249_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3566,f285,f3573]) ).
fof(f3577,definition,
( sQ250_spl
<=> compose(a,compose(domain(b),compose(a,b))) = compose(a,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f3580,plain,
( sQ250_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3567,f285,f3577]) ).
fof(f3581,definition,
( sQ251_spl
<=> compose(a,compose(domain(b),g)) = compose(a,g) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f3584,plain,
( sQ251_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3569,f294,f3581]) ).
fof(f3585,definition,
( sQ252_spl
<=> compose(a,compose(domain(b),h)) = compose(a,h) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f3588,plain,
( sQ252_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3570,f294,f3585]) ).
fof(f3591,plain,
( domain(compose(compose(a,b),codomain(g))) = domain(a)
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f501]) ).
fof(f3592,plain,
( domain(compose(compose(a,b),codomain(compose(a,h)))) = domain(a)
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f501]) ).
fof(f3593,plain,
( domain(compose(compose(a,b),codomain(compose(a,b)))) = domain(a)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f501]) ).
fof(f3600,definition,
( sQ253_spl
<=> domain(compose(compose(a,b),codomain(g))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3603,plain,
( sQ253_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f3591,f1361,f3600]) ).
fof(f3604,definition,
( sQ254_spl
<=> domain(compose(compose(a,b),codomain(compose(a,h)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3607,plain,
( sQ254_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f3592,f1361,f3604]) ).
fof(f3608,definition,
( sQ255_spl
<=> domain(compose(compose(a,b),codomain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3611,plain,
( sQ255_spl
| ~ sQ245_spl ),
inference(split_clause,[status(thm)],[f3593,f3321,f3608]) ).
fof(f3619,plain,
( codomain(compose(domain(compose(a,h)),compose(a,b))) = codomain(b)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f563]) ).
fof(f3620,plain,
( codomain(compose(domain(compose(a,b)),compose(a,b))) = codomain(b)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f563]) ).
fof(f3622,plain,
( codomain(compose(domain(g),compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f52,f563]) ).
fof(f3623,plain,
( codomain(compose(domain(h),compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f44,f563]) ).
fof(f3631,definition,
( sQ256_spl
<=> codomain(compose(domain(compose(a,h)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3634,plain,
( sQ256_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3619,f981,f3631]) ).
fof(f3635,definition,
( sQ257_spl
<=> codomain(compose(domain(compose(a,b)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3638,plain,
( sQ257_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3620,f981,f3635]) ).
fof(f3640,definition,
( sQ258_spl
<=> codomain(compose(domain(g),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3643,plain,
( sQ258_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3622,f285,f3640]) ).
fof(f3644,definition,
( sQ259_spl
<=> codomain(compose(domain(h),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f3647,plain,
( sQ259_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3623,f285,f3644]) ).
fof(f3654,plain,
( compose(domain(a),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f729]) ).
fof(f3655,plain,
( compose(domain(a),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f729]) ).
fof(f3660,definition,
( sQ260_spl
<=> compose(domain(a),compose(compose(a,b),compose(a,h))) = compose(compose(a,b),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f3663,plain,
( sQ260_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3654,f738,f3660]) ).
fof(f3664,definition,
( sQ261_spl
<=> compose(domain(a),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3667,plain,
( sQ261_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3655,f738,f3664]) ).
fof(f3671,plain,
( compose(domain(compose(a,h)),compose(domain(compose(a,h)),g)) = compose(domain(compose(a,h)),g)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f414,f3395]) ).
fof(f3672,plain,
( compose(domain(compose(a,b)),compose(domain(compose(a,b)),g)) = compose(domain(compose(a,b)),g)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f117,f3395]) ).
fof(f3674,plain,
( compose(domain(g),compose(domain(g),g)) = compose(domain(g),g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f3395]) ).
fof(f3675,plain,
( compose(domain(h),compose(domain(h),g)) = compose(domain(h),g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f3395]) ).
fof(f3676,plain,
! [X0] :
( compose(domain(codomain(X0)),compose(domain(codomain(X0)),g)) = compose(domain(codomain(X0)),g)
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f15,f3395]) ).
fof(f3691,definition,
( sQ262_spl
<=> compose(domain(compose(a,h)),compose(domain(compose(a,h)),g)) = compose(domain(compose(a,h)),g) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f3694,plain,
( sQ262_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3671,f285,f3691]) ).
fof(f3695,definition,
( sQ263_spl
<=> compose(domain(compose(a,b)),compose(domain(compose(a,b)),g)) = compose(domain(compose(a,b)),g) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3698,plain,
( sQ263_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3672,f285,f3695]) ).
fof(f3702,definition,
( sQ264_spl
<=> compose(domain(g),compose(domain(g),g)) = compose(domain(g),g) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3705,plain,
( sQ264_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3674,f294,f3702]) ).
fof(f3706,definition,
( sQ265_spl
<=> compose(domain(h),compose(domain(h),g)) = compose(domain(h),g) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f3709,plain,
( sQ265_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3675,f294,f3706]) ).
fof(f3710,plain,
! [X0] :
( compose(codomain(X0),compose(domain(codomain(X0)),g)) = compose(domain(codomain(X0)),g)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f3676]) ).
fof(f3711,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),g)) = compose(domain(codomain(X0)),g)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f3710]) ).
fof(f3712,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),g)) = compose(codomain(X0),g)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f3711]) ).
fof(f3724,plain,
( compose(domain(compose(a,h)),compose(domain(compose(a,h)),h)) = compose(domain(compose(a,h)),h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f414,f3396]) ).
fof(f3725,plain,
( compose(domain(compose(a,b)),compose(domain(compose(a,b)),h)) = compose(domain(compose(a,b)),h)
| domain(a) != domain(b) ),
inference(paramodulation,[status(thm)],[f117,f3396]) ).
fof(f3727,plain,
( compose(domain(g),compose(domain(g),h)) = compose(domain(g),h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f3396]) ).
fof(f3728,plain,
( compose(domain(h),compose(domain(h),h)) = compose(domain(h),h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f3396]) ).
fof(f3729,plain,
! [X0] :
( compose(domain(codomain(X0)),compose(domain(codomain(X0)),h)) = compose(domain(codomain(X0)),h)
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f15,f3396]) ).
fof(f3744,definition,
( sQ266_spl
<=> compose(domain(compose(a,h)),compose(domain(compose(a,h)),h)) = compose(domain(compose(a,h)),h) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f3747,plain,
( sQ266_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3724,f285,f3744]) ).
fof(f3748,definition,
( sQ267_spl
<=> compose(domain(compose(a,b)),compose(domain(compose(a,b)),h)) = compose(domain(compose(a,b)),h) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3751,plain,
( sQ267_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3725,f285,f3748]) ).
fof(f3755,definition,
( sQ268_spl
<=> compose(domain(g),compose(domain(g),h)) = compose(domain(g),h) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3758,plain,
( sQ268_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3727,f294,f3755]) ).
fof(f3759,definition,
( sQ269_spl
<=> compose(domain(h),compose(domain(h),h)) = compose(domain(h),h) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3762,plain,
( sQ269_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3728,f294,f3759]) ).
fof(f3763,plain,
! [X0] :
( compose(codomain(X0),compose(domain(codomain(X0)),h)) = compose(domain(codomain(X0)),h)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f3729]) ).
fof(f3764,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),h)) = compose(domain(codomain(X0)),h)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f3763]) ).
fof(f3765,plain,
! [X0] :
( compose(codomain(X0),compose(codomain(X0),h)) = compose(codomain(X0),h)
| codomain(X0) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f15,f3764]) ).
fof(f3776,plain,
( compose(codomain(g),compose(codomain(g),g)) = compose(codomain(g),g)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f641,f3712]) ).
fof(f3777,plain,
( compose(codomain(compose(a,h)),compose(codomain(compose(a,h)),g)) = compose(codomain(compose(a,h)),g)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f567,f3712]) ).
fof(f3778,plain,
( compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),g)) = compose(codomain(compose(a,b)),g)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f128,f3712]) ).
fof(f3781,plain,
( compose(codomain(a),compose(codomain(a),g)) = compose(codomain(a),g)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f3712]) ).
fof(f3792,definition,
( sQ270_spl
<=> compose(codomain(g),compose(codomain(g),g)) = compose(codomain(g),g) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3795,plain,
( sQ270_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f3776,f665,f3792]) ).
fof(f3796,definition,
( sQ271_spl
<=> compose(codomain(compose(a,h)),compose(codomain(compose(a,h)),g)) = compose(codomain(compose(a,h)),g) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f3799,plain,
( sQ271_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f3777,f665,f3796]) ).
fof(f3800,definition,
( sQ272_spl
<=> compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),g)) = compose(codomain(compose(a,b)),g) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f3803,plain,
( sQ272_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3778,f360,f3800]) ).
fof(f3810,definition,
( sQ273_spl
<=> compose(codomain(a),compose(codomain(a),g)) = compose(codomain(a),g) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f3813,plain,
( sQ273_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3781,f294,f3810]) ).
fof(f3821,plain,
( compose(codomain(g),compose(codomain(g),h)) = compose(codomain(g),h)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f641,f3765]) ).
fof(f3822,plain,
( compose(codomain(compose(a,h)),compose(codomain(compose(a,h)),h)) = compose(codomain(compose(a,h)),h)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f567,f3765]) ).
fof(f3823,plain,
( compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),h)) = compose(codomain(compose(a,b)),h)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f128,f3765]) ).
fof(f3826,plain,
( compose(codomain(a),compose(codomain(a),h)) = compose(codomain(a),h)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f3765]) ).
fof(f3837,definition,
( sQ274_spl
<=> compose(codomain(g),compose(codomain(g),h)) = compose(codomain(g),h) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f3840,plain,
( sQ274_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f3821,f665,f3837]) ).
fof(f3841,definition,
( sQ275_spl
<=> compose(codomain(compose(a,h)),compose(codomain(compose(a,h)),h)) = compose(codomain(compose(a,h)),h) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3844,plain,
( sQ275_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f3822,f665,f3841]) ).
fof(f3845,definition,
( sQ276_spl
<=> compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),h)) = compose(codomain(compose(a,b)),h) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f3848,plain,
( sQ276_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3823,f360,f3845]) ).
fof(f3855,definition,
( sQ277_spl
<=> compose(codomain(a),compose(codomain(a),h)) = compose(codomain(a),h) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3858,plain,
( sQ277_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3826,f294,f3855]) ).
fof(f3865,plain,
( compose(g,compose(codomain(g),compose(a,h))) = compose(g,compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f1159]) ).
fof(f3866,plain,
( compose(compose(a,h),compose(codomain(compose(a,h)),compose(a,h))) = compose(compose(a,h),compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f1159]) ).
fof(f3867,plain,
( compose(compose(a,b),compose(codomain(compose(a,b)),compose(a,h))) = compose(compose(a,b),compose(a,h))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f1159]) ).
fof(f3870,plain,
( compose(a,compose(codomain(a),compose(a,h))) = compose(a,compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f1159]) ).
fof(f3872,definition,
( sQ278_spl
<=> compose(g,compose(codomain(g),compose(a,h))) = compose(g,compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f3875,plain,
( sQ278_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3865,f848,f3872]) ).
fof(f3876,definition,
( sQ279_spl
<=> compose(compose(a,h),compose(codomain(compose(a,h)),compose(a,h))) = compose(compose(a,h),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f3879,plain,
( sQ279_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3866,f848,f3876]) ).
fof(f3880,definition,
( sQ280_spl
<=> compose(compose(a,b),compose(codomain(compose(a,b)),compose(a,h))) = compose(compose(a,b),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3883,plain,
( sQ280_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3867,f738,f3880]) ).
fof(f3886,definition,
( sQ281_spl
<=> compose(a,compose(codomain(a),compose(a,h))) = compose(a,compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3889,plain,
( sQ281_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3870,f285,f3886]) ).
fof(f3895,plain,
( ~ sQ74_spl
| compose(a,compose(g,domain(compose(a,h)))) = compose(compose(a,h),domain(compose(a,h)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2922]) ).
fof(f3896,plain,
( ~ sQ74_spl
| compose(a,compose(g,domain(compose(a,b)))) = compose(compose(a,h),domain(compose(a,b)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2922]) ).
fof(f3903,definition,
( sQ282_spl
<=> compose(a,compose(g,domain(compose(a,h)))) = compose(compose(a,h),domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3906,plain,
( ~ sQ74_spl
| sQ282_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3895,f848,f3903,f1272]) ).
fof(f3907,definition,
( sQ283_spl
<=> compose(a,compose(g,domain(compose(a,b)))) = compose(compose(a,h),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3910,plain,
( ~ sQ74_spl
| sQ283_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3896,f848,f3907,f1272]) ).
fof(f3918,plain,
! [X0] :
( compose(domain(compose(a,h)),compose(compose(a,h),X0)) = compose(compose(domain(compose(a,h)),compose(a,h)),X0)
| codomain(h) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1242]) ).
fof(f3919,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(compose(a,h),X0)) = compose(compose(domain(compose(a,b)),compose(a,h)),X0)
| codomain(h) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1242]) ).
fof(f3921,plain,
! [X0] :
( compose(domain(g),compose(compose(a,h),X0)) = compose(compose(domain(g),compose(a,h)),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f52,f1242]) ).
fof(f3922,plain,
! [X0] :
( compose(domain(h),compose(compose(a,h),X0)) = compose(compose(domain(h),compose(a,h)),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f44,f1242]) ).
fof(f3933,definition,
! [X0] :
( sQ284_spl
<=> ( compose(domain(compose(a,h)),compose(compose(a,h),X0)) = compose(compose(domain(compose(a,h)),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3936,plain,
( sQ284_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3918,f981,f3933]) ).
fof(f3937,definition,
! [X0] :
( sQ285_spl
<=> ( compose(domain(compose(a,b)),compose(compose(a,h),X0)) = compose(compose(domain(compose(a,b)),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3940,plain,
( sQ285_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3919,f981,f3937]) ).
fof(f3943,definition,
! [X0] :
( sQ286_spl
<=> ( compose(domain(g),compose(compose(a,h),X0)) = compose(compose(domain(g),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3946,plain,
( sQ286_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3921,f285,f3943]) ).
fof(f3947,definition,
! [X0] :
( sQ287_spl
<=> ( compose(domain(h),compose(compose(a,h),X0)) = compose(compose(domain(h),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f3950,plain,
( sQ287_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3922,f285,f3947]) ).
fof(f3964,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(compose(a,b)),domain(X0))) = compose(compose(a,b),domain(X0))
| codomain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f128,f1161]) ).
fof(f3980,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(b),domain(X0))) = compose(compose(a,b),domain(X0))
| codomain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f128,f3964]) ).
fof(f4002,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(a,b),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f128,f1162]) ).
fof(f4034,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(b),codomain(X0))) = compose(compose(a,b),codomain(X0))
| codomain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f128,f4002]) ).
fof(f4051,plain,
( compose(domain(g),compose(g,compose(a,b))) = compose(g,compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f722]) ).
fof(f4052,plain,
( compose(domain(compose(a,h)),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f722]) ).
fof(f4053,plain,
( compose(domain(compose(a,b)),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f722]) ).
fof(f4058,definition,
( sQ288_spl
<=> compose(domain(g),compose(g,compose(a,b))) = compose(g,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f4061,plain,
( sQ288_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4051,f848,f4058]) ).
fof(f4062,definition,
( sQ289_spl
<=> compose(domain(compose(a,h)),compose(compose(a,h),compose(a,b))) = compose(compose(a,h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f4065,plain,
( sQ289_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4052,f848,f4062]) ).
fof(f4066,definition,
( sQ290_spl
<=> compose(domain(compose(a,b)),compose(compose(a,b),compose(a,b))) = compose(compose(a,b),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f4069,plain,
( sQ290_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4053,f738,f4066]) ).
fof(f4074,plain,
( compose(a,compose(b,domain(compose(a,h)))) = compose(compose(a,b),domain(compose(a,h)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f735]) ).
fof(f4075,plain,
( compose(a,compose(b,domain(compose(a,b)))) = compose(compose(a,b),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f735]) ).
fof(f4081,definition,
( sQ291_spl
<=> compose(a,compose(b,domain(compose(a,h)))) = compose(compose(a,b),domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f4084,plain,
( sQ291_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4074,f738,f4081]) ).
fof(f4085,definition,
( sQ292_spl
<=> compose(a,compose(b,domain(compose(a,b)))) = compose(compose(a,b),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f4088,plain,
( sQ292_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4075,f738,f4085]) ).
fof(f4095,plain,
( compose(a,compose(b,codomain(g))) = compose(compose(a,b),codomain(g))
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f736]) ).
fof(f4096,plain,
( compose(a,compose(b,codomain(compose(a,h)))) = compose(compose(a,b),codomain(compose(a,h)))
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f736]) ).
fof(f4097,plain,
( compose(a,compose(b,codomain(compose(a,b)))) = compose(compose(a,b),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f736]) ).
fof(f4106,definition,
( sQ293_spl
<=> compose(a,compose(b,codomain(g))) = compose(compose(a,b),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f4109,plain,
( sQ293_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f4095,f1361,f4106]) ).
fof(f4110,definition,
( sQ294_spl
<=> compose(a,compose(b,codomain(compose(a,h)))) = compose(compose(a,b),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f4113,plain,
( sQ294_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f4096,f1361,f4110]) ).
fof(f4114,definition,
( sQ295_spl
<=> compose(a,compose(b,codomain(compose(a,b)))) = compose(compose(a,b),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f4117,plain,
( sQ295_spl
| ~ sQ245_spl ),
inference(split_clause,[status(thm)],[f4097,f3321,f4114]) ).
fof(f4128,plain,
( ~ sQ74_spl
| compose(a,compose(g,codomain(g))) = compose(compose(a,h),codomain(g))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f2923]) ).
fof(f4129,plain,
( ~ sQ74_spl
| compose(a,compose(g,codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h)))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f2923]) ).
fof(f4130,plain,
( ~ sQ74_spl
| compose(a,compose(g,codomain(compose(a,b)))) = compose(compose(a,h),codomain(compose(a,b)))
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f2923]) ).
fof(f4144,definition,
( sQ296_spl
<=> compose(a,compose(g,codomain(g))) = compose(compose(a,h),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f4147,plain,
( ~ sQ74_spl
| sQ296_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f4128,f1350,f4144,f1272]) ).
fof(f4148,definition,
( sQ297_spl
<=> compose(a,compose(g,codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f4151,plain,
( ~ sQ74_spl
| sQ297_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f4129,f1350,f4148,f1272]) ).
fof(f4152,definition,
( sQ298_spl
<=> compose(a,compose(g,codomain(compose(a,b)))) = compose(compose(a,h),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f4155,plain,
( ~ sQ74_spl
| sQ298_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f4130,f1361,f4152,f1272]) ).
fof(f4170,plain,
( compose(a,compose(domain(a),compose(a,h))) = compose(compose(a,domain(a)),compose(a,h))
| domain(b) != domain(domain(a)) ),
inference(resolution,[status(thm)],[f1258,f14]) ).
fof(f4171,plain,
( compose(a,compose(g,compose(a,h))) = compose(compose(a,g),compose(a,h))
| codomain(h) != domain(a)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f641,f1258]) ).
fof(f4172,plain,
( compose(a,compose(compose(a,h),compose(a,h))) = compose(compose(a,compose(a,h)),compose(a,h))
| codomain(h) != domain(a)
| domain(b) != domain(compose(a,h)) ),
inference(paramodulation,[status(thm)],[f567,f1258]) ).
fof(f4173,plain,
( compose(a,compose(compose(a,b),compose(a,h))) = compose(compose(a,compose(a,b)),compose(a,h))
| codomain(b) != domain(a)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f128,f1258]) ).
fof(f4174,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(a,h))) = compose(compose(a,codomain(X0)),compose(a,h))
| codomain(X0) != domain(a)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f40,f1258]) ).
fof(f4175,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(a,h))) = compose(compose(a,domain(X0)),compose(a,h))
| domain(X0) != domain(a)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f14,f1258]) ).
fof(f4176,plain,
( compose(a,compose(a,compose(a,h))) = compose(compose(a,a),compose(a,h))
| domain(b) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f1258]) ).
fof(f4177,definition,
( sQ299_spl
<=> domain(b) = domain(domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f4179,plain,
( sQ299_spl
| domain(b) != domain(domain(a)) ),
inference(component_clause,[status(thm)],[f4177]) ).
fof(f4180,definition,
( sQ300_spl
<=> compose(a,compose(domain(a),compose(a,h))) = compose(compose(a,domain(a)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f4183,plain,
( sQ300_spl
| ~ sQ299_spl ),
inference(split_clause,[status(thm)],[f4170,f4177,f4180]) ).
fof(f4184,definition,
( sQ301_spl
<=> compose(a,compose(g,compose(a,h))) = compose(compose(a,g),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f4187,plain,
( sQ301_spl
| ~ sQ39_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f4171,f1269,f848,f4184]) ).
fof(f4188,definition,
( sQ302_spl
<=> compose(a,compose(compose(a,h),compose(a,h))) = compose(compose(a,compose(a,h)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f4191,plain,
( sQ302_spl
| ~ sQ39_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f4172,f1276,f848,f4188]) ).
fof(f4192,definition,
( sQ303_spl
<=> compose(a,compose(compose(a,b),compose(a,h))) = compose(compose(a,compose(a,b)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f4195,plain,
( sQ303_spl
| ~ sQ30_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f4173,f1283,f738,f4192]) ).
fof(f4196,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(a,h))) = compose(compose(a,codomain(X0)),compose(a,h))
| codomain(X0) != domain(a)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f4174]) ).
fof(f4197,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(a,h))) = compose(compose(a,domain(X0)),compose(a,h))
| domain(X0) != domain(a)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f4175]) ).
fof(f4198,definition,
( sQ304_spl
<=> compose(a,compose(a,compose(a,h))) = compose(compose(a,a),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f4201,plain,
( sQ304_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4176,f285,f4198]) ).
fof(f4202,plain,
( sQ299_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f38,f4179]) ).
fof(f4206,plain,
! [X0] :
( compose(g,compose(codomain(g),X0)) = compose(compose(g,codomain(g)),X0)
| codomain(g) != domain(X0)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f1688]) ).
fof(f4207,plain,
! [X0] :
( compose(g,compose(codomain(compose(a,h)),X0)) = compose(compose(g,codomain(compose(a,h))),X0)
| codomain(compose(a,h)) != domain(X0)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f1688]) ).
fof(f4208,plain,
! [X0] :
( compose(g,compose(codomain(compose(a,b)),X0)) = compose(compose(g,codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f1688]) ).
fof(f4223,definition,
! [X0] :
( sQ305_spl
<=> ( compose(g,compose(codomain(g),X0)) = compose(compose(g,codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f4226,plain,
( sQ305_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f4206,f1350,f4223]) ).
fof(f4227,definition,
! [X0] :
( sQ306_spl
<=> ( compose(g,compose(codomain(compose(a,h)),X0)) = compose(compose(g,codomain(compose(a,h))),X0)
| codomain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f4230,plain,
( sQ306_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f4207,f1350,f4227]) ).
fof(f4231,definition,
! [X0] :
( sQ307_spl
<=> ( compose(g,compose(codomain(compose(a,b)),X0)) = compose(compose(g,codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f4234,plain,
( sQ307_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f4208,f1361,f4231]) ).
fof(f4250,plain,
! [X0] :
( compose(g,compose(domain(compose(a,h)),X0)) = compose(compose(g,domain(compose(a,h))),X0)
| domain(compose(a,h)) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2568]) ).
fof(f4251,plain,
! [X0] :
( compose(g,compose(domain(compose(a,b)),X0)) = compose(compose(g,domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2568]) ).
fof(f4258,definition,
! [X0] :
( sQ308_spl
<=> ( compose(g,compose(domain(compose(a,h)),X0)) = compose(compose(g,domain(compose(a,h))),X0)
| domain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f4261,plain,
( sQ308_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4250,f848,f4258]) ).
fof(f4262,definition,
! [X0] :
( sQ309_spl
<=> ( compose(g,compose(domain(compose(a,b)),X0)) = compose(compose(g,domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f4265,plain,
( sQ309_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4251,f848,f4262]) ).
fof(f4274,plain,
! [X0] :
( compose(codomain(g),compose(g,X0)) = compose(compose(codomain(g),g),X0)
| codomain(h) != domain(X0)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f641,f1482]) ).
fof(f4275,plain,
! [X0] :
( compose(codomain(compose(a,h)),compose(g,X0)) = compose(compose(codomain(compose(a,h)),g),X0)
| codomain(h) != domain(X0)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f567,f1482]) ).
fof(f4276,plain,
! [X0] :
( compose(codomain(compose(a,b)),compose(g,X0)) = compose(compose(codomain(compose(a,b)),g),X0)
| codomain(h) != domain(X0)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f128,f1482]) ).
fof(f4279,plain,
! [X0] :
( compose(codomain(a),compose(g,X0)) = compose(compose(codomain(a),g),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f1482]) ).
fof(f4286,definition,
! [X0] :
( sQ310_spl
<=> ( compose(codomain(g),compose(g,X0)) = compose(compose(codomain(g),g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f4289,plain,
( sQ310_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f4274,f665,f4286]) ).
fof(f4290,definition,
! [X0] :
( sQ311_spl
<=> ( compose(codomain(compose(a,h)),compose(g,X0)) = compose(compose(codomain(compose(a,h)),g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f4293,plain,
( sQ311_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f4275,f665,f4290]) ).
fof(f4294,definition,
! [X0] :
( sQ312_spl
<=> ( compose(codomain(compose(a,b)),compose(g,X0)) = compose(compose(codomain(compose(a,b)),g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f4297,plain,
( sQ312_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4276,f360,f4294]) ).
fof(f4302,definition,
! [X0] :
( sQ313_spl
<=> ( compose(codomain(a),compose(g,X0)) = compose(compose(codomain(a),g),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f4305,plain,
( sQ313_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4279,f294,f4302]) ).
fof(f4312,plain,
! [X0] :
( compose(compose(a,h),compose(codomain(g),X0)) = compose(compose(compose(a,h),codomain(g)),X0)
| codomain(g) != domain(X0)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f1689]) ).
fof(f4313,plain,
! [X0] :
( compose(compose(a,h),compose(codomain(compose(a,h)),X0)) = compose(compose(compose(a,h),codomain(compose(a,h))),X0)
| codomain(compose(a,h)) != domain(X0)
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f1689]) ).
fof(f4314,plain,
! [X0] :
( compose(compose(a,h),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(a,h),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f1689]) ).
fof(f4329,definition,
! [X0] :
( sQ314_spl
<=> ( compose(compose(a,h),compose(codomain(g),X0)) = compose(compose(compose(a,h),codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f4332,plain,
( sQ314_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f4312,f1350,f4329]) ).
fof(f4333,definition,
! [X0] :
( sQ315_spl
<=> ( compose(compose(a,h),compose(codomain(compose(a,h)),X0)) = compose(compose(compose(a,h),codomain(compose(a,h))),X0)
| codomain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f4336,plain,
( sQ315_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f4313,f1350,f4333]) ).
fof(f4337,definition,
! [X0] :
( sQ316_spl
<=> ( compose(compose(a,h),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(a,h),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f4340,plain,
( sQ316_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f4314,f1361,f4337]) ).
fof(f4356,plain,
( domain(compose(compose(a,b),domain(compose(a,h)))) = domain(a)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f478]) ).
fof(f4357,plain,
( domain(compose(compose(a,b),domain(compose(a,b)))) = domain(a)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f478]) ).
fof(f4362,definition,
( sQ317_spl
<=> domain(compose(compose(a,b),domain(compose(a,h)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f4365,plain,
( sQ317_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4356,f738,f4362]) ).
fof(f4366,definition,
( sQ318_spl
<=> domain(compose(compose(a,b),domain(compose(a,b)))) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f4369,plain,
( sQ318_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4357,f738,f4366]) ).
fof(f4373,plain,
( codomain(compose(codomain(g),compose(a,b))) = codomain(b)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f525]) ).
fof(f4374,plain,
( codomain(compose(codomain(compose(a,h)),compose(a,b))) = codomain(b)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f525]) ).
fof(f4375,plain,
( codomain(compose(codomain(compose(a,b)),compose(a,b))) = codomain(b)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f525]) ).
fof(f4378,plain,
( codomain(compose(codomain(a),compose(a,b))) = codomain(b)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f525]) ).
fof(f4381,definition,
( sQ319_spl
<=> codomain(compose(codomain(g),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f4384,plain,
( sQ319_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4373,f848,f4381]) ).
fof(f4385,definition,
( sQ320_spl
<=> codomain(compose(codomain(compose(a,h)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f4388,plain,
( sQ320_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4374,f848,f4385]) ).
fof(f4389,definition,
( sQ321_spl
<=> codomain(compose(codomain(compose(a,b)),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f4392,plain,
( sQ321_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4375,f738,f4389]) ).
fof(f4395,definition,
( sQ322_spl
<=> codomain(compose(codomain(a),compose(a,b))) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f4398,plain,
( sQ322_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4378,f285,f4395]) ).
fof(f4400,plain,
( compose(compose(a,b),compose(codomain(b),compose(a,h))) = compose(compose(a,b),compose(a,h))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1167]) ).
fof(f4401,plain,
( compose(compose(a,b),compose(codomain(b),compose(a,b))) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1167]) ).
fof(f4404,definition,
( sQ323_spl
<=> compose(compose(a,b),compose(codomain(b),compose(a,h))) = compose(compose(a,b),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f4407,plain,
( sQ323_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4400,f738,f4404]) ).
fof(f4408,definition,
( sQ324_spl
<=> compose(compose(a,b),compose(codomain(b),compose(a,b))) = compose(compose(a,b),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f4411,plain,
( sQ324_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4401,f738,f4408]) ).
fof(f4413,plain,
( compose(g,compose(codomain(g),compose(a,b))) = compose(g,compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f1160]) ).
fof(f4414,plain,
( compose(compose(a,h),compose(codomain(compose(a,h)),compose(a,b))) = compose(compose(a,h),compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f1160]) ).
fof(f4415,plain,
( compose(compose(a,b),compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(a,b),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f1160]) ).
fof(f4418,plain,
( compose(a,compose(codomain(a),compose(a,b))) = compose(a,compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f1160]) ).
fof(f4420,definition,
( sQ325_spl
<=> compose(g,compose(codomain(g),compose(a,b))) = compose(g,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f4423,plain,
( sQ325_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4413,f848,f4420]) ).
fof(f4424,definition,
( sQ326_spl
<=> compose(compose(a,h),compose(codomain(compose(a,h)),compose(a,b))) = compose(compose(a,h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f4427,plain,
( sQ326_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4414,f848,f4424]) ).
fof(f4428,definition,
( sQ327_spl
<=> compose(compose(a,b),compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(a,b),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f4431,plain,
( sQ327_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4415,f738,f4428]) ).
fof(f4434,definition,
( sQ328_spl
<=> compose(a,compose(codomain(a),compose(a,b))) = compose(a,compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f4437,plain,
( sQ328_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4418,f285,f4434]) ).
fof(f4444,plain,
! [X0] :
( compose(codomain(g),compose(h,X0)) = compose(compose(codomain(g),h),X0)
| codomain(h) != domain(X0)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f641,f1864]) ).
fof(f4445,plain,
! [X0] :
( compose(codomain(compose(a,h)),compose(h,X0)) = compose(compose(codomain(compose(a,h)),h),X0)
| codomain(h) != domain(X0)
| codomain(h) != domain(b) ),
inference(paramodulation,[status(thm)],[f567,f1864]) ).
fof(f4446,plain,
! [X0] :
( compose(codomain(compose(a,b)),compose(h,X0)) = compose(compose(codomain(compose(a,b)),h),X0)
| codomain(h) != domain(X0)
| codomain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f128,f1864]) ).
fof(f4449,plain,
! [X0] :
( compose(codomain(a),compose(h,X0)) = compose(compose(codomain(a),h),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f1864]) ).
fof(f4456,definition,
! [X0] :
( sQ329_spl
<=> ( compose(codomain(g),compose(h,X0)) = compose(compose(codomain(g),h),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f4459,plain,
( sQ329_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f4444,f665,f4456]) ).
fof(f4460,definition,
! [X0] :
( sQ330_spl
<=> ( compose(codomain(compose(a,h)),compose(h,X0)) = compose(compose(codomain(compose(a,h)),h),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f4463,plain,
( sQ330_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f4445,f665,f4460]) ).
fof(f4464,definition,
! [X0] :
( sQ331_spl
<=> ( compose(codomain(compose(a,b)),compose(h,X0)) = compose(compose(codomain(compose(a,b)),h),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f4467,plain,
( sQ331_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4446,f360,f4464]) ).
fof(f4472,definition,
! [X0] :
( sQ332_spl
<=> ( compose(codomain(a),compose(h,X0)) = compose(compose(codomain(a),h),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f4475,plain,
( sQ332_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4449,f294,f4472]) ).
fof(f4480,plain,
( compose(codomain(g),compose(codomain(g),compose(a,h))) = compose(codomain(g),compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f2977]) ).
fof(f4481,plain,
( compose(codomain(compose(a,h)),compose(codomain(compose(a,h)),compose(a,h))) = compose(codomain(compose(a,h)),compose(a,h))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f2977]) ).
fof(f4482,plain,
( compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(a,h))) = compose(codomain(compose(a,b)),compose(a,h))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f2977]) ).
fof(f4485,plain,
( compose(codomain(a),compose(codomain(a),compose(a,h))) = compose(codomain(a),compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f2977]) ).
fof(f4491,definition,
( sQ333_spl
<=> compose(codomain(g),compose(codomain(g),compose(a,h))) = compose(codomain(g),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f4494,plain,
( sQ333_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4480,f848,f4491]) ).
fof(f4495,definition,
( sQ334_spl
<=> compose(codomain(compose(a,h)),compose(codomain(compose(a,h)),compose(a,h))) = compose(codomain(compose(a,h)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f4498,plain,
( sQ334_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4481,f848,f4495]) ).
fof(f4499,definition,
( sQ335_spl
<=> compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(a,h))) = compose(codomain(compose(a,b)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f4502,plain,
( sQ335_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4482,f738,f4499]) ).
fof(f4509,definition,
( sQ336_spl
<=> compose(codomain(a),compose(codomain(a),compose(a,h))) = compose(codomain(a),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f4512,plain,
( sQ336_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4485,f285,f4509]) ).
fof(f4514,plain,
! [X0] :
( compose(codomain(g),compose(compose(a,h),X0)) = compose(compose(codomain(g),compose(a,h)),X0)
| codomain(h) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f2561]) ).
fof(f4515,plain,
! [X0] :
( compose(codomain(compose(a,h)),compose(compose(a,h),X0)) = compose(compose(codomain(compose(a,h)),compose(a,h)),X0)
| codomain(h) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f2561]) ).
fof(f4516,plain,
! [X0] :
( compose(codomain(compose(a,b)),compose(compose(a,h),X0)) = compose(compose(codomain(compose(a,b)),compose(a,h)),X0)
| codomain(h) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f2561]) ).
fof(f4519,plain,
! [X0] :
( compose(codomain(a),compose(compose(a,h),X0)) = compose(compose(codomain(a),compose(a,h)),X0)
| codomain(h) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f2561]) ).
fof(f4523,definition,
! [X0] :
( sQ337_spl
<=> ( compose(codomain(g),compose(compose(a,h),X0)) = compose(compose(codomain(g),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f4526,plain,
( sQ337_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4514,f848,f4523]) ).
fof(f4527,definition,
! [X0] :
( sQ338_spl
<=> ( compose(codomain(compose(a,h)),compose(compose(a,h),X0)) = compose(compose(codomain(compose(a,h)),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f4530,plain,
( sQ338_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4515,f848,f4527]) ).
fof(f4531,definition,
! [X0] :
( sQ339_spl
<=> ( compose(codomain(compose(a,b)),compose(compose(a,h),X0)) = compose(compose(codomain(compose(a,b)),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f4534,plain,
( sQ339_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4516,f738,f4531]) ).
fof(f4539,definition,
! [X0] :
( sQ340_spl
<=> ( compose(codomain(a),compose(compose(a,h),X0)) = compose(compose(codomain(a),compose(a,h)),X0)
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f4542,plain,
( sQ340_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4519,f285,f4539]) ).
fof(f4546,plain,
( compose(domain(compose(a,h)),compose(domain(compose(a,h)),compose(a,h))) = compose(domain(compose(a,h)),compose(a,h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2978]) ).
fof(f4547,plain,
( compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(a,h))) = compose(domain(compose(a,b)),compose(a,h))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2978]) ).
fof(f4549,plain,
( compose(domain(g),compose(domain(g),compose(a,h))) = compose(domain(g),compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f52,f2978]) ).
fof(f4550,plain,
( compose(domain(h),compose(domain(h),compose(a,h))) = compose(domain(h),compose(a,h))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f44,f2978]) ).
fof(f4566,definition,
( sQ341_spl
<=> compose(domain(compose(a,h)),compose(domain(compose(a,h)),compose(a,h))) = compose(domain(compose(a,h)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f4569,plain,
( sQ341_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f4546,f981,f4566]) ).
fof(f4570,definition,
( sQ342_spl
<=> compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(a,h))) = compose(domain(compose(a,b)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f4573,plain,
( sQ342_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f4547,f981,f4570]) ).
fof(f4577,definition,
( sQ343_spl
<=> compose(domain(g),compose(domain(g),compose(a,h))) = compose(domain(g),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f4580,plain,
( sQ343_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4549,f285,f4577]) ).
fof(f4581,definition,
( sQ344_spl
<=> compose(domain(h),compose(domain(h),compose(a,h))) = compose(domain(h),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f4584,plain,
( sQ344_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4550,f285,f4581]) ).
fof(f4597,plain,
( compose(domain(a),compose(compose(a,h),domain(compose(a,h)))) = compose(compose(a,h),domain(compose(a,h)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2694]) ).
fof(f4598,plain,
( compose(domain(a),compose(compose(a,h),domain(compose(a,b)))) = compose(compose(a,h),domain(compose(a,b)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2694]) ).
fof(f4605,definition,
( sQ345_spl
<=> compose(domain(a),compose(compose(a,h),domain(compose(a,h)))) = compose(compose(a,h),domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f4608,plain,
( sQ345_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4597,f848,f4605]) ).
fof(f4609,definition,
( sQ346_spl
<=> compose(domain(a),compose(compose(a,h),domain(compose(a,b)))) = compose(compose(a,h),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f4612,plain,
( sQ346_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4598,f848,f4609]) ).
fof(f4620,plain,
( compose(domain(a),compose(compose(a,h),codomain(g))) = compose(compose(a,h),codomain(g))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f2695]) ).
fof(f4621,plain,
( compose(domain(a),compose(compose(a,h),codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h)))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f2695]) ).
fof(f4622,plain,
( compose(domain(a),compose(compose(a,h),codomain(compose(a,b)))) = compose(compose(a,h),codomain(compose(a,b)))
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f2695]) ).
fof(f4636,definition,
( sQ347_spl
<=> compose(domain(a),compose(compose(a,h),codomain(g))) = compose(compose(a,h),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f4639,plain,
( sQ347_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f4620,f1350,f4636]) ).
fof(f4640,definition,
( sQ348_spl
<=> compose(domain(a),compose(compose(a,h),codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f4643,plain,
( sQ348_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f4621,f1350,f4640]) ).
fof(f4644,definition,
( sQ349_spl
<=> compose(domain(a),compose(compose(a,h),codomain(compose(a,b)))) = compose(compose(a,h),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f4647,plain,
( sQ349_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f4622,f1361,f4644]) ).
fof(f4661,plain,
! [X0] :
( compose(compose(a,h),compose(domain(compose(a,h)),X0)) = compose(compose(compose(a,h),domain(compose(a,h))),X0)
| domain(compose(a,h)) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2569]) ).
fof(f4662,plain,
! [X0] :
( compose(compose(a,h),compose(domain(compose(a,b)),X0)) = compose(compose(compose(a,h),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2569]) ).
fof(f4669,definition,
! [X0] :
( sQ350_spl
<=> ( compose(compose(a,h),compose(domain(compose(a,h)),X0)) = compose(compose(compose(a,h),domain(compose(a,h))),X0)
| domain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f4672,plain,
( sQ350_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4661,f848,f4669]) ).
fof(f4673,definition,
! [X0] :
( sQ351_spl
<=> ( compose(compose(a,h),compose(domain(compose(a,b)),X0)) = compose(compose(compose(a,h),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f4676,plain,
( sQ351_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f4662,f848,f4673]) ).
fof(f4686,plain,
( compose(a,domain(compose(a,h))) = compose(compose(a,domain(compose(a,h))),domain(compose(a,h)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2786]) ).
fof(f4687,plain,
( compose(a,domain(compose(a,b))) = compose(compose(a,domain(compose(a,b))),domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2786]) ).
fof(f4689,plain,
( compose(a,domain(g)) = compose(compose(a,domain(g)),domain(g))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f2786]) ).
fof(f4690,plain,
( compose(a,domain(h)) = compose(compose(a,domain(h)),domain(h))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f2786]) ).
fof(f4708,definition,
( sQ352_spl
<=> compose(a,domain(compose(a,h))) = compose(compose(a,domain(compose(a,h))),domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f4711,plain,
( sQ352_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4686,f285,f4708]) ).
fof(f4712,definition,
( sQ353_spl
<=> compose(a,domain(compose(a,b))) = compose(compose(a,domain(compose(a,b))),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f4715,plain,
( sQ353_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4687,f285,f4712]) ).
fof(f4719,definition,
( sQ354_spl
<=> compose(a,domain(g)) = compose(compose(a,domain(g)),domain(g)) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f4722,plain,
( sQ354_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4689,f294,f4719]) ).
fof(f4723,definition,
( sQ355_spl
<=> compose(a,domain(h)) = compose(compose(a,domain(h)),domain(h)) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f4726,plain,
( sQ355_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4690,f294,f4723]) ).
fof(f4744,plain,
( compose(a,codomain(g)) = compose(compose(a,codomain(g)),codomain(g))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f2795]) ).
fof(f4745,plain,
( compose(a,codomain(compose(a,h))) = compose(compose(a,codomain(compose(a,h))),codomain(compose(a,h)))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f2795]) ).
fof(f4746,plain,
( compose(a,codomain(compose(a,b))) = compose(compose(a,codomain(compose(a,b))),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f2795]) ).
fof(f4749,plain,
( compose(a,codomain(a)) = compose(compose(a,codomain(a)),codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f2795]) ).
fof(f4757,definition,
( sQ356_spl
<=> compose(a,codomain(g)) = compose(compose(a,codomain(g)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f4760,plain,
( sQ356_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f4744,f665,f4757]) ).
fof(f4761,definition,
( sQ357_spl
<=> compose(a,codomain(compose(a,h))) = compose(compose(a,codomain(compose(a,h))),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f4764,plain,
( sQ357_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f4745,f665,f4761]) ).
fof(f4765,definition,
( sQ358_spl
<=> compose(a,codomain(compose(a,b))) = compose(compose(a,codomain(compose(a,b))),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f4768,plain,
( sQ358_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4746,f360,f4765]) ).
fof(f4775,definition,
( sQ359_spl
<=> compose(a,codomain(a)) = compose(compose(a,codomain(a)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f4778,plain,
( sQ359_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4749,f294,f4775]) ).
fof(f5064,plain,
! [X0] :
( compose(domain(compose(a,h)),compose(compose(a,b),X0)) = compose(compose(domain(compose(a,h)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1243]) ).
fof(f5065,plain,
! [X0] :
( compose(domain(compose(a,b)),compose(compose(a,b),X0)) = compose(compose(domain(compose(a,b)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1243]) ).
fof(f5067,plain,
! [X0] :
( compose(domain(g),compose(compose(a,b),X0)) = compose(compose(domain(g),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f52,f1243]) ).
fof(f5068,plain,
! [X0] :
( compose(domain(h),compose(compose(a,b),X0)) = compose(compose(domain(h),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f44,f1243]) ).
fof(f5079,definition,
! [X0] :
( sQ360_spl
<=> ( compose(domain(compose(a,h)),compose(compose(a,b),X0)) = compose(compose(domain(compose(a,h)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f5082,plain,
( sQ360_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f5064,f981,f5079]) ).
fof(f5083,definition,
! [X0] :
( sQ361_spl
<=> ( compose(domain(compose(a,b)),compose(compose(a,b),X0)) = compose(compose(domain(compose(a,b)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f5086,plain,
( sQ361_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f5065,f981,f5083]) ).
fof(f5089,definition,
! [X0] :
( sQ362_spl
<=> ( compose(domain(g),compose(compose(a,b),X0)) = compose(compose(domain(g),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f5092,plain,
( sQ362_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5067,f285,f5089]) ).
fof(f5093,definition,
! [X0] :
( sQ363_spl
<=> ( compose(domain(h),compose(compose(a,b),X0)) = compose(compose(domain(h),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f5096,plain,
( sQ363_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5068,f285,f5093]) ).
fof(f5194,plain,
( compose(compose(a,h),compose(codomain(h),domain(compose(a,h)))) = compose(compose(a,h),domain(compose(a,h)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f3262]) ).
fof(f5195,plain,
( compose(compose(a,h),compose(codomain(h),domain(compose(a,b)))) = compose(compose(a,h),domain(compose(a,b)))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f3262]) ).
fof(f5202,definition,
( sQ364_spl
<=> compose(compose(a,h),compose(codomain(h),domain(compose(a,h)))) = compose(compose(a,h),domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f5205,plain,
( sQ364_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f5194,f848,f5202]) ).
fof(f5206,definition,
( sQ365_spl
<=> compose(compose(a,h),compose(codomain(h),domain(compose(a,b)))) = compose(compose(a,h),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f5209,plain,
( sQ365_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f5195,f848,f5206]) ).
fof(f5217,plain,
( compose(compose(a,h),compose(codomain(h),codomain(g))) = compose(compose(a,h),codomain(g))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f3263]) ).
fof(f5218,plain,
( compose(compose(a,h),compose(codomain(h),codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h)))
| codomain(h) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f3263]) ).
fof(f5219,plain,
( compose(compose(a,h),compose(codomain(h),codomain(compose(a,b)))) = compose(compose(a,h),codomain(compose(a,b)))
| codomain(h) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f3263]) ).
fof(f5233,definition,
( sQ366_spl
<=> compose(compose(a,h),compose(codomain(h),codomain(g))) = compose(compose(a,h),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f5236,plain,
( sQ366_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f5217,f1350,f5233]) ).
fof(f5237,definition,
( sQ367_spl
<=> compose(compose(a,h),compose(codomain(h),codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f5240,plain,
( sQ367_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f5218,f1350,f5237]) ).
fof(f5241,definition,
( sQ368_spl
<=> compose(compose(a,h),compose(codomain(h),codomain(compose(a,b)))) = compose(compose(a,h),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f5244,plain,
( sQ368_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f5219,f1361,f5241]) ).
fof(f5283,plain,
( compose(a,compose(domain(b),domain(compose(a,h)))) = compose(a,domain(compose(a,h)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f3568]) ).
fof(f5284,plain,
( compose(a,compose(domain(b),domain(compose(a,b)))) = compose(a,domain(compose(a,b)))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f3568]) ).
fof(f5286,plain,
( compose(a,compose(domain(b),domain(g))) = compose(a,domain(g))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f3568]) ).
fof(f5287,plain,
( compose(a,compose(domain(b),domain(h))) = compose(a,domain(h))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f3568]) ).
fof(f5302,definition,
( sQ369_spl
<=> compose(a,compose(domain(b),domain(compose(a,h)))) = compose(a,domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f5305,plain,
( sQ369_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5283,f285,f5302]) ).
fof(f5306,definition,
( sQ370_spl
<=> compose(a,compose(domain(b),domain(compose(a,b)))) = compose(a,domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f5309,plain,
( sQ370_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5284,f285,f5306]) ).
fof(f5312,definition,
( sQ371_spl
<=> compose(a,compose(domain(b),domain(g))) = compose(a,domain(g)) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f5315,plain,
( sQ371_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5286,f294,f5312]) ).
fof(f5316,definition,
( sQ372_spl
<=> compose(a,compose(domain(b),domain(h))) = compose(a,domain(h)) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f5319,plain,
( sQ372_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5287,f294,f5316]) ).
fof(f5332,plain,
( compose(a,compose(domain(b),codomain(g))) = compose(a,codomain(g))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f3571]) ).
fof(f5333,plain,
( compose(a,compose(domain(b),codomain(compose(a,h)))) = compose(a,codomain(compose(a,h)))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f3571]) ).
fof(f5334,plain,
( compose(a,compose(domain(b),codomain(compose(a,b)))) = compose(a,codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f3571]) ).
fof(f5337,plain,
( compose(a,compose(domain(b),codomain(a))) = compose(a,codomain(a))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f3571]) ).
fof(f5344,definition,
( sQ373_spl
<=> compose(a,compose(domain(b),codomain(g))) = compose(a,codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f5347,plain,
( sQ373_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f5332,f665,f5344]) ).
fof(f5348,definition,
( sQ374_spl
<=> compose(a,compose(domain(b),codomain(compose(a,h)))) = compose(a,codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f5351,plain,
( sQ374_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f5333,f665,f5348]) ).
fof(f5352,definition,
( sQ375_spl
<=> compose(a,compose(domain(b),codomain(compose(a,b)))) = compose(a,codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f5355,plain,
( sQ375_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5334,f360,f5352]) ).
fof(f5360,definition,
( sQ376_spl
<=> compose(a,compose(domain(b),codomain(a))) = compose(a,codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f5363,plain,
( sQ376_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5337,f294,f5360]) ).
fof(f5417,plain,
! [X0] :
( compose(a,compose(codomain(g),X0)) = compose(compose(a,codomain(g)),X0)
| codomain(g) != domain(X0)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f1290]) ).
fof(f5418,plain,
! [X0] :
( compose(a,compose(codomain(compose(a,h)),X0)) = compose(compose(a,codomain(compose(a,h))),X0)
| codomain(compose(a,h)) != domain(X0)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f1290]) ).
fof(f5419,plain,
! [X0] :
( compose(a,compose(codomain(compose(a,b)),X0)) = compose(compose(a,codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f1290]) ).
fof(f5422,plain,
! [X0] :
( compose(a,compose(codomain(a),X0)) = compose(compose(a,codomain(a)),X0)
| codomain(a) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f1290]) ).
fof(f5430,definition,
! [X0] :
( sQ377_spl
<=> ( compose(a,compose(codomain(g),X0)) = compose(compose(a,codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f5433,plain,
( sQ377_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f5417,f665,f5430]) ).
fof(f5434,definition,
! [X0] :
( sQ378_spl
<=> ( compose(a,compose(codomain(compose(a,h)),X0)) = compose(compose(a,codomain(compose(a,h))),X0)
| codomain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f5437,plain,
( sQ378_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f5418,f665,f5434]) ).
fof(f5438,definition,
! [X0] :
( sQ379_spl
<=> ( compose(a,compose(codomain(compose(a,b)),X0)) = compose(compose(a,codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f5441,plain,
( sQ379_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5419,f360,f5438]) ).
fof(f5448,definition,
! [X0] :
( sQ380_spl
<=> ( compose(a,compose(codomain(a),X0)) = compose(compose(a,codomain(a)),X0)
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f5451,plain,
( sQ380_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5422,f294,f5448]) ).
fof(f5458,plain,
! [X0] :
( compose(a,compose(domain(compose(a,h)),X0)) = compose(compose(a,domain(compose(a,h))),X0)
| domain(compose(a,h)) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f1291]) ).
fof(f5459,plain,
! [X0] :
( compose(a,compose(domain(compose(a,b)),X0)) = compose(compose(a,domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f1291]) ).
fof(f5461,plain,
! [X0] :
( compose(a,compose(domain(g),X0)) = compose(compose(a,domain(g)),X0)
| domain(g) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f1291]) ).
fof(f5462,plain,
! [X0] :
( compose(a,compose(domain(h),X0)) = compose(compose(a,domain(h)),X0)
| domain(h) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f1291]) ).
fof(f5477,definition,
! [X0] :
( sQ381_spl
<=> ( compose(a,compose(domain(compose(a,h)),X0)) = compose(compose(a,domain(compose(a,h))),X0)
| domain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f5480,plain,
( sQ381_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5458,f285,f5477]) ).
fof(f5481,definition,
! [X0] :
( sQ382_spl
<=> ( compose(a,compose(domain(compose(a,b)),X0)) = compose(compose(a,domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f5484,plain,
( sQ382_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5459,f285,f5481]) ).
fof(f5488,definition,
! [X0] :
( sQ383_spl
<=> ( compose(a,compose(domain(g),X0)) = compose(compose(a,domain(g)),X0)
| domain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f5491,plain,
( sQ383_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5461,f294,f5488]) ).
fof(f5492,definition,
! [X0] :
( sQ384_spl
<=> ( compose(a,compose(domain(h),X0)) = compose(compose(a,domain(h)),X0)
| domain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f5495,plain,
( sQ384_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5462,f294,f5492]) ).
fof(f5516,plain,
( compose(a,compose(codomain(domain(b)),compose(a,h))) = compose(compose(a,codomain(domain(b))),compose(a,h))
| codomain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f4196,f14]) ).
fof(f5517,plain,
( compose(a,compose(codomain(a),compose(a,h))) = compose(compose(a,codomain(a)),compose(a,h))
| codomain(a) != domain(a) ),
inference(resolution,[status(thm)],[f4196,f23]) ).
fof(f5518,plain,
( compose(a,compose(codomain(g),compose(a,h))) = compose(compose(a,codomain(g)),compose(a,h))
| codomain(g) != domain(a)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f4196]) ).
fof(f5519,plain,
( compose(a,compose(codomain(compose(a,h)),compose(a,h))) = compose(compose(a,codomain(compose(a,h))),compose(a,h))
| codomain(compose(a,h)) != domain(a)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f4196]) ).
fof(f5520,plain,
( compose(a,compose(codomain(compose(a,b)),compose(a,h))) = compose(compose(a,codomain(compose(a,b))),compose(a,h))
| codomain(compose(a,b)) != domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f4196]) ).
fof(f5523,plain,
( compose(a,compose(codomain(a),compose(a,h))) = compose(compose(a,codomain(a)),compose(a,h))
| codomain(a) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f4196]) ).
fof(f5524,definition,
( sQ385_spl
<=> codomain(domain(b)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f5526,plain,
( sQ385_spl
| codomain(domain(b)) != domain(a) ),
inference(component_clause,[status(thm)],[f5524]) ).
fof(f5527,definition,
( sQ386_spl
<=> compose(a,compose(codomain(domain(b)),compose(a,h))) = compose(compose(a,codomain(domain(b))),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f5530,plain,
( sQ386_spl
| ~ sQ385_spl ),
inference(split_clause,[status(thm)],[f5516,f5524,f5527]) ).
fof(f5531,definition,
( sQ387_spl
<=> codomain(a) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f5533,plain,
( sQ387_spl
| codomain(a) != domain(a) ),
inference(component_clause,[status(thm)],[f5531]) ).
fof(f5534,definition,
( sQ388_spl
<=> compose(a,compose(codomain(a),compose(a,h))) = compose(compose(a,codomain(a)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f5537,plain,
( sQ388_spl
| ~ sQ387_spl ),
inference(split_clause,[status(thm)],[f5517,f5531,f5534]) ).
fof(f5538,definition,
( sQ389_spl
<=> codomain(g) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f5541,definition,
( sQ390_spl
<=> compose(a,compose(codomain(g),compose(a,h))) = compose(compose(a,codomain(g)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f5544,plain,
( sQ390_spl
| ~ sQ389_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f5518,f665,f5538,f5541]) ).
fof(f5545,definition,
( sQ391_spl
<=> codomain(compose(a,h)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f5548,definition,
( sQ392_spl
<=> compose(a,compose(codomain(compose(a,h)),compose(a,h))) = compose(compose(a,codomain(compose(a,h))),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f5551,plain,
( sQ392_spl
| ~ sQ391_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f5519,f665,f5545,f5548]) ).
fof(f5552,definition,
( sQ393_spl
<=> codomain(compose(a,b)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f5555,definition,
( sQ394_spl
<=> compose(a,compose(codomain(compose(a,b)),compose(a,h))) = compose(compose(a,codomain(compose(a,b))),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f5558,plain,
( sQ394_spl
| ~ sQ393_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5520,f360,f5552,f5555]) ).
fof(f5565,plain,
( sQ388_spl
| ~ sQ387_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5523,f294,f5531,f5534]) ).
fof(f5566,plain,
( sQ387_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f23,f5533]) ).
fof(f5567,plain,
( sQ385_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f14,f5526]) ).
fof(f5568,plain,
( compose(a,compose(domain(g),compose(a,h))) = compose(compose(a,domain(g)),compose(a,h))
| domain(g) != domain(a) ),
inference(resolution,[status(thm)],[f4197,f52]) ).
fof(f5569,plain,
( compose(a,compose(domain(h),compose(a,h))) = compose(compose(a,domain(h)),compose(a,h))
| domain(h) != domain(a) ),
inference(resolution,[status(thm)],[f4197,f44]) ).
fof(f5570,plain,
( compose(a,compose(domain(domain(b)),compose(a,h))) = compose(compose(a,domain(domain(b))),compose(a,h))
| domain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f4197,f38]) ).
fof(f5571,plain,
( compose(a,compose(domain(compose(a,h)),compose(a,h))) = compose(compose(a,domain(compose(a,h))),compose(a,h))
| domain(compose(a,h)) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f4197]) ).
fof(f5572,plain,
( compose(a,compose(domain(compose(a,b)),compose(a,h))) = compose(compose(a,domain(compose(a,b))),compose(a,h))
| domain(compose(a,b)) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f4197]) ).
fof(f5574,plain,
( compose(a,compose(domain(g),compose(a,h))) = compose(compose(a,domain(g)),compose(a,h))
| domain(g) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f4197]) ).
fof(f5575,plain,
( compose(a,compose(domain(h),compose(a,h))) = compose(compose(a,domain(h)),compose(a,h))
| domain(h) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f4197]) ).
fof(f5577,plain,
( compose(a,compose(domain(b),compose(a,h))) = compose(compose(a,domain(b)),compose(a,h))
| domain(b) != domain(a) ),
inference(equality_resolution,[status(thm)],[f4197]) ).
fof(f5578,definition,
( sQ395_spl
<=> domain(g) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f5580,plain,
( sQ395_spl
| domain(g) != domain(a) ),
inference(component_clause,[status(thm)],[f5578]) ).
fof(f5581,definition,
( sQ396_spl
<=> compose(a,compose(domain(g),compose(a,h))) = compose(compose(a,domain(g)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f5584,plain,
( sQ396_spl
| ~ sQ395_spl ),
inference(split_clause,[status(thm)],[f5568,f5578,f5581]) ).
fof(f5585,definition,
( sQ397_spl
<=> domain(h) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f5587,plain,
( sQ397_spl
| domain(h) != domain(a) ),
inference(component_clause,[status(thm)],[f5585]) ).
fof(f5588,definition,
( sQ398_spl
<=> compose(a,compose(domain(h),compose(a,h))) = compose(compose(a,domain(h)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f5591,plain,
( sQ398_spl
| ~ sQ397_spl ),
inference(split_clause,[status(thm)],[f5569,f5585,f5588]) ).
fof(f5592,definition,
( sQ399_spl
<=> domain(domain(b)) = domain(a) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f5594,plain,
( sQ399_spl
| domain(domain(b)) != domain(a) ),
inference(component_clause,[status(thm)],[f5592]) ).
fof(f5595,definition,
( sQ400_spl
<=> compose(a,compose(domain(domain(b)),compose(a,h))) = compose(compose(a,domain(domain(b))),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f5598,plain,
( sQ400_spl
| ~ sQ399_spl ),
inference(split_clause,[status(thm)],[f5570,f5592,f5595]) ).
fof(f5599,definition,
( sQ401_spl
<=> compose(a,compose(domain(compose(a,h)),compose(a,h))) = compose(compose(a,domain(compose(a,h))),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f5602,plain,
( sQ401_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5571,f285,f423,f5599]) ).
fof(f5603,definition,
( sQ402_spl
<=> compose(a,compose(domain(compose(a,b)),compose(a,h))) = compose(compose(a,domain(compose(a,b))),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f5606,plain,
( sQ402_spl
| ~ sQ136_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5572,f285,f2252,f5603]) ).
fof(f5610,plain,
( sQ396_spl
| ~ sQ395_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5574,f294,f5578,f5581]) ).
fof(f5611,plain,
( sQ398_spl
| ~ sQ397_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5575,f294,f5585,f5588]) ).
fof(f5615,definition,
( sQ403_spl
<=> compose(a,compose(domain(b),compose(a,h))) = compose(compose(a,domain(b)),compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f5618,plain,
( sQ403_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5577,f285,f5615]) ).
fof(f5619,plain,
( sQ395_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f52,f5580]) ).
fof(f5620,plain,
( sQ397_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f44,f5587]) ).
fof(f5621,plain,
( sQ399_spl
| domain(b) != domain(a) ),
inference(forward_demodulation,[status(thm)],[f38,f5594]) ).
fof(f5633,plain,
( compose(a,compose(domain(a),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b))
| domain(b) != domain(domain(a)) ),
inference(resolution,[status(thm)],[f1259,f14]) ).
fof(f5634,plain,
( compose(a,compose(g,compose(a,b))) = compose(compose(a,g),compose(a,b))
| codomain(h) != domain(a)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f641,f1259]) ).
fof(f5635,plain,
( compose(a,compose(compose(a,h),compose(a,b))) = compose(compose(a,compose(a,h)),compose(a,b))
| codomain(h) != domain(a)
| domain(b) != domain(compose(a,h)) ),
inference(paramodulation,[status(thm)],[f567,f1259]) ).
fof(f5636,plain,
( compose(a,compose(compose(a,b),compose(a,b))) = compose(compose(a,compose(a,b)),compose(a,b))
| codomain(b) != domain(a)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f128,f1259]) ).
fof(f5637,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(a,b))) = compose(compose(a,codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f40,f1259]) ).
fof(f5638,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(a,b))) = compose(compose(a,domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f14,f1259]) ).
fof(f5639,plain,
( compose(a,compose(a,compose(a,b))) = compose(compose(a,a),compose(a,b))
| domain(b) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f1259]) ).
fof(f5640,definition,
( sQ404_spl
<=> compose(a,compose(domain(a),compose(a,b))) = compose(compose(a,domain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f5643,plain,
( sQ404_spl
| ~ sQ299_spl ),
inference(split_clause,[status(thm)],[f5633,f4177,f5640]) ).
fof(f5644,definition,
( sQ405_spl
<=> compose(a,compose(g,compose(a,b))) = compose(compose(a,g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f5647,plain,
( sQ405_spl
| ~ sQ39_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f5634,f1269,f848,f5644]) ).
fof(f5648,definition,
( sQ406_spl
<=> compose(a,compose(compose(a,h),compose(a,b))) = compose(compose(a,compose(a,h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f5651,plain,
( sQ406_spl
| ~ sQ39_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f5635,f1276,f848,f5648]) ).
fof(f5652,definition,
( sQ407_spl
<=> compose(a,compose(compose(a,b),compose(a,b))) = compose(compose(a,compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f5655,plain,
( sQ407_spl
| ~ sQ30_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f5636,f1283,f738,f5652]) ).
fof(f5656,plain,
! [X0] :
( compose(a,compose(codomain(X0),compose(a,b))) = compose(compose(a,codomain(X0)),compose(a,b))
| codomain(X0) != domain(a)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f5637]) ).
fof(f5657,plain,
! [X0] :
( compose(a,compose(domain(X0),compose(a,b))) = compose(compose(a,domain(X0)),compose(a,b))
| domain(X0) != domain(a)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f5638]) ).
fof(f5658,definition,
( sQ408_spl
<=> compose(a,compose(a,compose(a,b))) = compose(compose(a,a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f5661,plain,
( sQ408_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5639,f285,f5658]) ).
fof(f5663,plain,
( compose(a,compose(a,domain(b))) = compose(compose(a,a),domain(b))
| domain(b) != domain(a) ),
inference(resolution,[status(thm)],[f1260,f23]) ).
fof(f5665,plain,
! [X0] :
( compose(a,compose(g,domain(X0))) = compose(compose(a,g),domain(X0))
| codomain(h) != domain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f641,f1260]) ).
fof(f5666,plain,
! [X0] :
( compose(a,compose(compose(a,h),domain(X0))) = compose(compose(a,compose(a,h)),domain(X0))
| codomain(h) != domain(X0)
| domain(b) != domain(compose(a,h)) ),
inference(paramodulation,[status(thm)],[f567,f1260]) ).
fof(f5667,plain,
! [X0] :
( compose(a,compose(compose(a,b),domain(X0))) = compose(compose(a,compose(a,b)),domain(X0))
| codomain(b) != domain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f128,f1260]) ).
fof(f5668,plain,
! [X0,X1] :
( compose(a,compose(codomain(X0),domain(X1))) = compose(compose(a,codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f40,f1260]) ).
fof(f5669,plain,
! [X0,X1] :
( compose(a,compose(domain(X0),domain(X1))) = compose(compose(a,domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f14,f1260]) ).
fof(f5670,plain,
! [X0] :
( compose(a,compose(a,domain(X0))) = compose(compose(a,a),domain(X0))
| domain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f1260]) ).
fof(f5677,definition,
( sQ409_spl
<=> compose(a,compose(a,domain(b))) = compose(compose(a,a),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f5680,plain,
( sQ409_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5663,f285,f5677]) ).
fof(f5684,definition,
! [X0] :
( sQ410_spl
<=> ( compose(a,compose(g,domain(X0))) = compose(compose(a,g),domain(X0))
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f5685,plain,
! [X0] :
( ~ sQ410_spl
| compose(a,compose(g,domain(X0))) = compose(compose(a,g),domain(X0))
| codomain(h) != domain(X0) ),
inference(component_clause,[status(thm)],[f5684]) ).
fof(f5687,plain,
( sQ410_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f5665,f1269,f5684]) ).
fof(f5688,definition,
! [X0] :
( sQ411_spl
<=> ( compose(a,compose(compose(a,h),domain(X0))) = compose(compose(a,compose(a,h)),domain(X0))
| codomain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f5691,plain,
( sQ411_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f5666,f1276,f5688]) ).
fof(f5692,definition,
! [X0] :
( sQ412_spl
<=> ( compose(a,compose(compose(a,b),domain(X0))) = compose(compose(a,compose(a,b)),domain(X0))
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f5695,plain,
( sQ412_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f5667,f1283,f5692]) ).
fof(f5696,plain,
! [X0,X1] :
( compose(a,compose(codomain(X0),domain(X1))) = compose(compose(a,codomain(X0)),domain(X1))
| codomain(X0) != domain(X1)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f5668]) ).
fof(f5697,plain,
! [X0,X1] :
( compose(a,compose(domain(X0),domain(X1))) = compose(compose(a,domain(X0)),domain(X1))
| domain(X0) != domain(X1)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f5669]) ).
fof(f5698,definition,
! [X0] :
( sQ413_spl
<=> ( compose(a,compose(a,domain(X0))) = compose(compose(a,a),domain(X0))
| domain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f5701,plain,
( sQ413_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5670,f285,f5698]) ).
fof(f5710,plain,
! [X0] :
( ~ sQ410_spl
| compose(a,compose(g,domain(X0))) = compose(compose(a,h),domain(X0))
| codomain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f26,f5685]) ).
fof(f5711,plain,
( compose(a,compose(h,codomain(g))) = compose(compose(a,h),codomain(g))
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f1261,f641]) ).
fof(f5712,plain,
( compose(a,compose(compose(a,h),codomain(h))) = compose(compose(a,compose(a,h)),codomain(h))
| domain(b) != domain(compose(a,h)) ),
inference(resolution,[status(thm)],[f1261,f567]) ).
fof(f5713,plain,
( compose(a,compose(compose(a,b),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b))
| domain(b) != domain(compose(a,b)) ),
inference(resolution,[status(thm)],[f1261,f128]) ).
fof(f5715,plain,
( compose(a,compose(g,codomain(h))) = compose(compose(a,g),codomain(h))
| domain(b) != domain(g) ),
inference(resolution,[status(thm)],[f1261,f641]) ).
fof(f5716,plain,
( compose(a,compose(h,codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h)))
| domain(b) != domain(h) ),
inference(resolution,[status(thm)],[f1261,f567]) ).
fof(f5717,plain,
( compose(a,compose(b,codomain(compose(a,b)))) = compose(compose(a,b),codomain(compose(a,b)))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f1261,f128]) ).
fof(f5719,plain,
! [X0] :
( compose(a,compose(g,codomain(X0))) = compose(compose(a,g),codomain(X0))
| codomain(h) != codomain(X0)
| domain(b) != domain(g) ),
inference(paramodulation,[status(thm)],[f641,f1261]) ).
fof(f5720,plain,
! [X0] :
( compose(a,compose(compose(a,h),codomain(X0))) = compose(compose(a,compose(a,h)),codomain(X0))
| codomain(h) != codomain(X0)
| domain(b) != domain(compose(a,h)) ),
inference(paramodulation,[status(thm)],[f567,f1261]) ).
fof(f5721,plain,
! [X0] :
( compose(a,compose(compose(a,b),codomain(X0))) = compose(compose(a,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f128,f1261]) ).
fof(f5722,plain,
! [X0,X1] :
( compose(a,compose(codomain(X0),codomain(X1))) = compose(compose(a,codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != domain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f40,f1261]) ).
fof(f5723,plain,
! [X0,X1] :
( compose(a,compose(domain(X0),codomain(X1))) = compose(compose(a,domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(b) != domain(domain(X0)) ),
inference(paramodulation,[status(thm)],[f14,f1261]) ).
fof(f5724,plain,
! [X0] :
( compose(a,compose(a,codomain(X0))) = compose(compose(a,a),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f1261]) ).
fof(f5732,definition,
( sQ414_spl
<=> domain(b) = domain(h) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f5734,plain,
( sQ414_spl
| domain(b) != domain(h) ),
inference(component_clause,[status(thm)],[f5732]) ).
fof(f5735,definition,
( sQ415_spl
<=> compose(a,compose(h,codomain(g))) = compose(compose(a,h),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f5738,plain,
( sQ415_spl
| ~ sQ414_spl ),
inference(split_clause,[status(thm)],[f5711,f5732,f5735]) ).
fof(f5739,definition,
( sQ416_spl
<=> compose(a,compose(compose(a,h),codomain(h))) = compose(compose(a,compose(a,h)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f5742,plain,
( sQ416_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f5712,f1276,f5739]) ).
fof(f5743,definition,
( sQ417_spl
<=> compose(a,compose(compose(a,b),codomain(b))) = compose(compose(a,compose(a,b)),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f5746,plain,
( sQ417_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f5713,f1283,f5743]) ).
fof(f5749,definition,
( sQ418_spl
<=> compose(a,compose(g,codomain(h))) = compose(compose(a,g),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f5752,plain,
( sQ418_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f5715,f1269,f5749]) ).
fof(f5753,definition,
( sQ419_spl
<=> compose(a,compose(h,codomain(compose(a,h)))) = compose(compose(a,h),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f5756,plain,
( sQ419_spl
| ~ sQ414_spl ),
inference(split_clause,[status(thm)],[f5716,f5732,f5753]) ).
fof(f5757,plain,
( sQ295_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5717,f294,f4114]) ).
fof(f5761,definition,
! [X0] :
( sQ420_spl
<=> ( compose(a,compose(g,codomain(X0))) = compose(compose(a,g),codomain(X0))
| codomain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f5762,plain,
! [X0] :
( ~ sQ420_spl
| compose(a,compose(g,codomain(X0))) = compose(compose(a,g),codomain(X0))
| codomain(h) != codomain(X0) ),
inference(component_clause,[status(thm)],[f5761]) ).
fof(f5764,plain,
( sQ420_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f5719,f1269,f5761]) ).
fof(f5765,definition,
! [X0] :
( sQ421_spl
<=> ( compose(a,compose(compose(a,h),codomain(X0))) = compose(compose(a,compose(a,h)),codomain(X0))
| codomain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f5768,plain,
( sQ421_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f5720,f1276,f5765]) ).
fof(f5769,definition,
! [X0] :
( sQ422_spl
<=> ( compose(a,compose(compose(a,b),codomain(X0))) = compose(compose(a,compose(a,b)),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f5772,plain,
( sQ422_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f5721,f1283,f5769]) ).
fof(f5773,plain,
! [X0,X1] :
( compose(a,compose(codomain(X0),codomain(X1))) = compose(compose(a,codomain(X0)),codomain(X1))
| codomain(X0) != codomain(X1)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f15,f5722]) ).
fof(f5774,plain,
! [X0,X1] :
( compose(a,compose(domain(X0),codomain(X1))) = compose(compose(a,domain(X0)),codomain(X1))
| domain(X0) != codomain(X1)
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f38,f5723]) ).
fof(f5775,definition,
! [X0] :
( sQ423_spl
<=> ( compose(a,compose(a,codomain(X0))) = compose(compose(a,a),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f5778,plain,
( sQ423_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5724,f285,f5775]) ).
fof(f5792,plain,
( sQ414_spl
| domain(b) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f44,f5734]) ).
fof(f5793,plain,
( sQ414_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5792]) ).
fof(f5794,plain,
sQ414_spl,
inference(contradiction_clause,[status(thm)],[f5793]) ).
fof(f5798,plain,
! [X0] :
( ~ sQ420_spl
| compose(a,compose(g,codomain(X0))) = compose(compose(a,h),codomain(X0))
| codomain(h) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f26,f5762]) ).
fof(f5806,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(g),X0)) = compose(compose(compose(a,b),codomain(g)),X0)
| codomain(g) != domain(X0)
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f1690]) ).
fof(f5807,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(compose(a,h)),X0)) = compose(compose(compose(a,b),codomain(compose(a,h))),X0)
| codomain(compose(a,h)) != domain(X0)
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f1690]) ).
fof(f5808,plain,
! [X0] :
( compose(compose(a,b),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(a,b),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0)
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f1690]) ).
fof(f5819,definition,
! [X0] :
( sQ424_spl
<=> ( compose(compose(a,b),compose(codomain(g),X0)) = compose(compose(compose(a,b),codomain(g)),X0)
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f5822,plain,
( sQ424_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f5806,f1361,f5819]) ).
fof(f5823,definition,
! [X0] :
( sQ425_spl
<=> ( compose(compose(a,b),compose(codomain(compose(a,h)),X0)) = compose(compose(compose(a,b),codomain(compose(a,h))),X0)
| codomain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f5826,plain,
( sQ425_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f5807,f1361,f5823]) ).
fof(f5827,definition,
! [X0] :
( sQ426_spl
<=> ( compose(compose(a,b),compose(codomain(compose(a,b)),X0)) = compose(compose(compose(a,b),codomain(compose(a,b))),X0)
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f5830,plain,
( sQ426_spl
| ~ sQ245_spl ),
inference(split_clause,[status(thm)],[f5808,f3321,f5827]) ).
fof(f5968,plain,
! [X0] :
( compose(codomain(g),compose(compose(a,b),X0)) = compose(compose(codomain(g),compose(a,b)),X0)
| codomain(b) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f2562]) ).
fof(f5969,plain,
! [X0] :
( compose(codomain(compose(a,h)),compose(compose(a,b),X0)) = compose(compose(codomain(compose(a,h)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f2562]) ).
fof(f5970,plain,
! [X0] :
( compose(codomain(compose(a,b)),compose(compose(a,b),X0)) = compose(compose(codomain(compose(a,b)),compose(a,b)),X0)
| codomain(b) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f2562]) ).
fof(f5973,plain,
! [X0] :
( compose(codomain(a),compose(compose(a,b),X0)) = compose(compose(codomain(a),compose(a,b)),X0)
| codomain(b) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f2562]) ).
fof(f5977,definition,
! [X0] :
( sQ427_spl
<=> ( compose(codomain(g),compose(compose(a,b),X0)) = compose(compose(codomain(g),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f5980,plain,
( sQ427_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f5968,f848,f5977]) ).
fof(f5981,definition,
! [X0] :
( sQ428_spl
<=> ( compose(codomain(compose(a,h)),compose(compose(a,b),X0)) = compose(compose(codomain(compose(a,h)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f5984,plain,
( sQ428_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f5969,f848,f5981]) ).
fof(f5985,definition,
! [X0] :
( sQ429_spl
<=> ( compose(codomain(compose(a,b)),compose(compose(a,b),X0)) = compose(compose(codomain(compose(a,b)),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f5988,plain,
( sQ429_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f5970,f738,f5985]) ).
fof(f5993,definition,
! [X0] :
( sQ430_spl
<=> ( compose(codomain(a),compose(compose(a,b),X0)) = compose(compose(codomain(a),compose(a,b)),X0)
| codomain(b) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f5996,plain,
( sQ430_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5973,f285,f5993]) ).
fof(f5998,plain,
! [X0] :
( compose(compose(a,b),compose(domain(compose(a,h)),X0)) = compose(compose(compose(a,b),domain(compose(a,h))),X0)
| domain(compose(a,h)) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f2570]) ).
fof(f5999,plain,
! [X0] :
( compose(compose(a,b),compose(domain(compose(a,b)),X0)) = compose(compose(compose(a,b),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0)
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f2570]) ).
fof(f6006,definition,
! [X0] :
( sQ431_spl
<=> ( compose(compose(a,b),compose(domain(compose(a,h)),X0)) = compose(compose(compose(a,b),domain(compose(a,h))),X0)
| domain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f6009,plain,
( sQ431_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f5998,f738,f6006]) ).
fof(f6010,definition,
! [X0] :
( sQ432_spl
<=> ( compose(compose(a,b),compose(domain(compose(a,b)),X0)) = compose(compose(compose(a,b),domain(compose(a,b))),X0)
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f6013,plain,
( sQ432_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f5999,f738,f6010]) ).
fof(f6021,plain,
( compose(codomain(g),compose(codomain(g),compose(a,b))) = compose(codomain(g),compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f641,f3345]) ).
fof(f6022,plain,
( compose(codomain(compose(a,h)),compose(codomain(compose(a,h)),compose(a,b))) = compose(codomain(compose(a,h)),compose(a,b))
| codomain(h) != domain(a) ),
inference(paramodulation,[status(thm)],[f567,f3345]) ).
fof(f6023,plain,
( compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(a,b))) = compose(codomain(compose(a,b)),compose(a,b))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f128,f3345]) ).
fof(f6026,plain,
( compose(codomain(a),compose(codomain(a),compose(a,b))) = compose(codomain(a),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f23,f3345]) ).
fof(f6032,definition,
( sQ433_spl
<=> compose(codomain(g),compose(codomain(g),compose(a,b))) = compose(codomain(g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f6035,plain,
( sQ433_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f6021,f848,f6032]) ).
fof(f6036,definition,
( sQ434_spl
<=> compose(codomain(compose(a,h)),compose(codomain(compose(a,h)),compose(a,b))) = compose(codomain(compose(a,h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f6039,plain,
( sQ434_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f6022,f848,f6036]) ).
fof(f6040,definition,
( sQ435_spl
<=> compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),compose(a,b))) = compose(codomain(compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f6043,plain,
( sQ435_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6023,f738,f6040]) ).
fof(f6050,definition,
( sQ436_spl
<=> compose(codomain(a),compose(codomain(a),compose(a,b))) = compose(codomain(a),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f6053,plain,
( sQ436_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6026,f285,f6050]) ).
fof(f6057,plain,
( compose(domain(compose(a,h)),compose(domain(compose(a,h)),compose(a,b))) = compose(domain(compose(a,h)),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f3393]) ).
fof(f6058,plain,
( compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(a,b))) = compose(domain(compose(a,b)),compose(a,b))
| domain(a) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f3393]) ).
fof(f6060,plain,
( compose(domain(g),compose(domain(g),compose(a,b))) = compose(domain(g),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f52,f3393]) ).
fof(f6061,plain,
( compose(domain(h),compose(domain(h),compose(a,b))) = compose(domain(h),compose(a,b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f44,f3393]) ).
fof(f6077,definition,
( sQ437_spl
<=> compose(domain(compose(a,h)),compose(domain(compose(a,h)),compose(a,b))) = compose(domain(compose(a,h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f6080,plain,
( sQ437_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6057,f981,f6077]) ).
fof(f6081,definition,
( sQ438_spl
<=> compose(domain(compose(a,b)),compose(domain(compose(a,b)),compose(a,b))) = compose(domain(compose(a,b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f6084,plain,
( sQ438_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6058,f981,f6081]) ).
fof(f6088,definition,
( sQ439_spl
<=> compose(domain(g),compose(domain(g),compose(a,b))) = compose(domain(g),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f6091,plain,
( sQ439_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6060,f285,f6088]) ).
fof(f6092,definition,
( sQ440_spl
<=> compose(domain(h),compose(domain(h),compose(a,b))) = compose(domain(h),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ440_spl])],[split_symbol_definition]) ).
fof(f6095,plain,
( sQ440_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6061,f285,f6092]) ).
fof(f6108,plain,
( compose(domain(a),compose(compose(a,b),domain(compose(a,h)))) = compose(compose(a,b),domain(compose(a,h)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f3464]) ).
fof(f6109,plain,
( compose(domain(a),compose(compose(a,b),domain(compose(a,b)))) = compose(compose(a,b),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f3464]) ).
fof(f6116,definition,
( sQ441_spl
<=> compose(domain(a),compose(compose(a,b),domain(compose(a,h)))) = compose(compose(a,b),domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f6119,plain,
( sQ441_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6108,f738,f6116]) ).
fof(f6120,definition,
( sQ442_spl
<=> compose(domain(a),compose(compose(a,b),domain(compose(a,b)))) = compose(compose(a,b),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f6123,plain,
( sQ442_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6109,f738,f6120]) ).
fof(f6130,plain,
( compose(domain(a),compose(compose(a,b),codomain(g))) = compose(compose(a,b),codomain(g))
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f3526]) ).
fof(f6131,plain,
( compose(domain(a),compose(compose(a,b),codomain(compose(a,h)))) = compose(compose(a,b),codomain(compose(a,h)))
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f3526]) ).
fof(f6132,plain,
( compose(domain(a),compose(compose(a,b),codomain(compose(a,b)))) = compose(compose(a,b),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f3526]) ).
fof(f6142,definition,
( sQ443_spl
<=> compose(domain(a),compose(compose(a,b),codomain(g))) = compose(compose(a,b),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ443_spl])],[split_symbol_definition]) ).
fof(f6145,plain,
( sQ443_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f6130,f1361,f6142]) ).
fof(f6146,definition,
( sQ444_spl
<=> compose(domain(a),compose(compose(a,b),codomain(compose(a,h)))) = compose(compose(a,b),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f6149,plain,
( sQ444_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f6131,f1361,f6146]) ).
fof(f6150,definition,
( sQ445_spl
<=> compose(domain(a),compose(compose(a,b),codomain(compose(a,b)))) = compose(compose(a,b),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f6153,plain,
( sQ445_spl
| ~ sQ245_spl ),
inference(split_clause,[status(thm)],[f6132,f3321,f6150]) ).
fof(f6163,plain,
( compose(compose(a,b),compose(codomain(b),domain(compose(a,h)))) = compose(compose(a,b),domain(compose(a,h)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f3980]) ).
fof(f6164,plain,
( compose(compose(a,b),compose(codomain(b),domain(compose(a,b)))) = compose(compose(a,b),domain(compose(a,b)))
| codomain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f3980]) ).
fof(f6171,definition,
( sQ446_spl
<=> compose(compose(a,b),compose(codomain(b),domain(compose(a,h)))) = compose(compose(a,b),domain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f6174,plain,
( sQ446_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6163,f738,f6171]) ).
fof(f6175,definition,
( sQ447_spl
<=> compose(compose(a,b),compose(codomain(b),domain(compose(a,b)))) = compose(compose(a,b),domain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f6178,plain,
( sQ447_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6164,f738,f6175]) ).
fof(f6185,plain,
( compose(compose(a,b),compose(codomain(b),codomain(g))) = compose(compose(a,b),codomain(g))
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f4034]) ).
fof(f6186,plain,
( compose(compose(a,b),compose(codomain(b),codomain(compose(a,h)))) = compose(compose(a,b),codomain(compose(a,h)))
| codomain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f4034]) ).
fof(f6187,plain,
( compose(compose(a,b),compose(codomain(b),codomain(compose(a,b)))) = compose(compose(a,b),codomain(compose(a,b)))
| codomain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f4034]) ).
fof(f6197,definition,
( sQ448_spl
<=> compose(compose(a,b),compose(codomain(b),codomain(g))) = compose(compose(a,b),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f6200,plain,
( sQ448_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f6185,f1361,f6197]) ).
fof(f6201,definition,
( sQ449_spl
<=> compose(compose(a,b),compose(codomain(b),codomain(compose(a,h)))) = compose(compose(a,b),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f6204,plain,
( sQ449_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f6186,f1361,f6201]) ).
fof(f6205,definition,
( sQ450_spl
<=> compose(compose(a,b),compose(codomain(b),codomain(compose(a,b)))) = compose(compose(a,b),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f6208,plain,
( sQ450_spl
| ~ sQ245_spl ),
inference(split_clause,[status(thm)],[f6187,f3321,f6205]) ).
fof(f6218,plain,
! [X0] :
( compose(a,compose(codomain(g),domain(X0))) = compose(compose(a,codomain(g)),domain(X0))
| codomain(g) != domain(X0)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f5696]) ).
fof(f6219,plain,
! [X0] :
( compose(a,compose(codomain(compose(a,h)),domain(X0))) = compose(compose(a,codomain(compose(a,h))),domain(X0))
| codomain(compose(a,h)) != domain(X0)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f5696]) ).
fof(f6220,plain,
! [X0] :
( compose(a,compose(codomain(compose(a,b)),domain(X0))) = compose(compose(a,codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f5696]) ).
fof(f6223,plain,
! [X0] :
( compose(a,compose(codomain(a),domain(X0))) = compose(compose(a,codomain(a)),domain(X0))
| codomain(a) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f5696]) ).
fof(f6231,definition,
! [X0] :
( sQ451_spl
<=> ( compose(a,compose(codomain(g),domain(X0))) = compose(compose(a,codomain(g)),domain(X0))
| codomain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f6234,plain,
( sQ451_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6218,f665,f6231]) ).
fof(f6235,definition,
! [X0] :
( sQ452_spl
<=> ( compose(a,compose(codomain(compose(a,h)),domain(X0))) = compose(compose(a,codomain(compose(a,h))),domain(X0))
| codomain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f6238,plain,
( sQ452_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6219,f665,f6235]) ).
fof(f6239,definition,
! [X0] :
( sQ453_spl
<=> ( compose(a,compose(codomain(compose(a,b)),domain(X0))) = compose(compose(a,codomain(compose(a,b))),domain(X0))
| codomain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f6242,plain,
( sQ453_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6220,f360,f6239]) ).
fof(f6249,definition,
! [X0] :
( sQ454_spl
<=> ( compose(a,compose(codomain(a),domain(X0))) = compose(compose(a,codomain(a)),domain(X0))
| codomain(a) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f6252,plain,
( sQ454_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6223,f294,f6249]) ).
fof(f6259,plain,
! [X0] :
( compose(a,compose(domain(compose(a,h)),domain(X0))) = compose(compose(a,domain(compose(a,h))),domain(X0))
| domain(compose(a,h)) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f5697]) ).
fof(f6260,plain,
! [X0] :
( compose(a,compose(domain(compose(a,b)),domain(X0))) = compose(compose(a,domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f5697]) ).
fof(f6262,plain,
! [X0] :
( compose(a,compose(domain(g),domain(X0))) = compose(compose(a,domain(g)),domain(X0))
| domain(g) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f5697]) ).
fof(f6263,plain,
! [X0] :
( compose(a,compose(domain(h),domain(X0))) = compose(compose(a,domain(h)),domain(X0))
| domain(h) != domain(X0)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f5697]) ).
fof(f6278,definition,
! [X0] :
( sQ455_spl
<=> ( compose(a,compose(domain(compose(a,h)),domain(X0))) = compose(compose(a,domain(compose(a,h))),domain(X0))
| domain(compose(a,h)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f6281,plain,
( sQ455_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6259,f285,f6278]) ).
fof(f6282,definition,
! [X0] :
( sQ456_spl
<=> ( compose(a,compose(domain(compose(a,b)),domain(X0))) = compose(compose(a,domain(compose(a,b))),domain(X0))
| domain(compose(a,b)) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f6285,plain,
( sQ456_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6260,f285,f6282]) ).
fof(f6289,definition,
! [X0] :
( sQ457_spl
<=> ( compose(a,compose(domain(g),domain(X0))) = compose(compose(a,domain(g)),domain(X0))
| domain(g) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f6292,plain,
( sQ457_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6262,f294,f6289]) ).
fof(f6293,definition,
! [X0] :
( sQ458_spl
<=> ( compose(a,compose(domain(h),domain(X0))) = compose(compose(a,domain(h)),domain(X0))
| domain(h) != domain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f6296,plain,
( sQ458_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6263,f294,f6293]) ).
fof(f6309,plain,
( compose(a,compose(codomain(h),codomain(g))) = compose(compose(a,codomain(h)),codomain(g))
| domain(b) != codomain(h) ),
inference(resolution,[status(thm)],[f5773,f641]) ).
fof(f6310,plain,
( compose(a,compose(codomain(compose(a,h)),codomain(h))) = compose(compose(a,codomain(compose(a,h))),codomain(h))
| domain(b) != codomain(compose(a,h)) ),
inference(resolution,[status(thm)],[f5773,f567]) ).
fof(f6311,plain,
( compose(a,compose(codomain(compose(a,b)),codomain(b))) = compose(compose(a,codomain(compose(a,b))),codomain(b))
| domain(b) != codomain(compose(a,b)) ),
inference(resolution,[status(thm)],[f5773,f128]) ).
fof(f6313,plain,
( compose(a,compose(codomain(g),codomain(h))) = compose(compose(a,codomain(g)),codomain(h))
| domain(b) != codomain(g) ),
inference(resolution,[status(thm)],[f5773,f641]) ).
fof(f6314,plain,
( compose(a,compose(codomain(h),codomain(compose(a,h)))) = compose(compose(a,codomain(h)),codomain(compose(a,h)))
| domain(b) != codomain(h) ),
inference(resolution,[status(thm)],[f5773,f567]) ).
fof(f6315,plain,
( compose(a,compose(codomain(b),codomain(compose(a,b)))) = compose(compose(a,codomain(b)),codomain(compose(a,b)))
| domain(b) != codomain(b) ),
inference(resolution,[status(thm)],[f5773,f128]) ).
fof(f6317,plain,
! [X0] :
( compose(a,compose(codomain(g),codomain(X0))) = compose(compose(a,codomain(g)),codomain(X0))
| codomain(h) != codomain(X0)
| domain(b) != codomain(g) ),
inference(paramodulation,[status(thm)],[f641,f5773]) ).
fof(f6318,plain,
! [X0] :
( compose(a,compose(codomain(compose(a,h)),codomain(X0))) = compose(compose(a,codomain(compose(a,h))),codomain(X0))
| codomain(h) != codomain(X0)
| domain(b) != codomain(compose(a,h)) ),
inference(paramodulation,[status(thm)],[f567,f5773]) ).
fof(f6319,plain,
! [X0] :
( compose(a,compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(a,codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0)
| domain(b) != codomain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f128,f5773]) ).
fof(f6322,plain,
! [X0] :
( compose(a,compose(codomain(a),codomain(X0))) = compose(compose(a,codomain(a)),codomain(X0))
| domain(b) != codomain(X0)
| domain(b) != codomain(a) ),
inference(paramodulation,[status(thm)],[f23,f5773]) ).
fof(f6328,plain,
! [X0] :
( compose(a,compose(codomain(X0),codomain(a))) = compose(compose(a,codomain(X0)),codomain(a))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(paramodulation,[status(thm)],[f23,f5773]) ).
fof(f6330,definition,
( sQ459_spl
<=> compose(a,compose(codomain(h),codomain(g))) = compose(compose(a,codomain(h)),codomain(g)) ),
introduced(definition,[new_symbols(definition,[sQ459_spl])],[split_symbol_definition]) ).
fof(f6333,plain,
( sQ459_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6309,f665,f6330]) ).
fof(f6334,definition,
( sQ460_spl
<=> domain(b) = codomain(compose(a,h)) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f6336,plain,
( sQ460_spl
| domain(b) != codomain(compose(a,h)) ),
inference(component_clause,[status(thm)],[f6334]) ).
fof(f6337,definition,
( sQ461_spl
<=> compose(a,compose(codomain(compose(a,h)),codomain(h))) = compose(compose(a,codomain(compose(a,h))),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f6340,plain,
( sQ461_spl
| ~ sQ460_spl ),
inference(split_clause,[status(thm)],[f6310,f6334,f6337]) ).
fof(f6341,definition,
( sQ462_spl
<=> domain(b) = codomain(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ462_spl])],[split_symbol_definition]) ).
fof(f6343,plain,
( sQ462_spl
| domain(b) != codomain(compose(a,b)) ),
inference(component_clause,[status(thm)],[f6341]) ).
fof(f6344,definition,
( sQ463_spl
<=> compose(a,compose(codomain(compose(a,b)),codomain(b))) = compose(compose(a,codomain(compose(a,b))),codomain(b)) ),
introduced(definition,[new_symbols(definition,[sQ463_spl])],[split_symbol_definition]) ).
fof(f6347,plain,
( sQ463_spl
| ~ sQ462_spl ),
inference(split_clause,[status(thm)],[f6311,f6341,f6344]) ).
fof(f6352,definition,
( sQ464_spl
<=> compose(a,compose(codomain(g),codomain(h))) = compose(compose(a,codomain(g)),codomain(h)) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f6355,plain,
( sQ464_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6313,f621,f6352]) ).
fof(f6356,definition,
( sQ465_spl
<=> compose(a,compose(codomain(h),codomain(compose(a,h)))) = compose(compose(a,codomain(h)),codomain(compose(a,h))) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f6359,plain,
( sQ465_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6314,f665,f6356]) ).
fof(f6360,definition,
( sQ466_spl
<=> compose(a,compose(codomain(b),codomain(compose(a,b)))) = compose(compose(a,codomain(b)),codomain(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f6363,plain,
( sQ466_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6315,f360,f6360]) ).
fof(f6366,definition,
! [X0] :
( sQ467_spl
<=> ( compose(a,compose(codomain(g),codomain(X0))) = compose(compose(a,codomain(g)),codomain(X0))
| codomain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f6369,plain,
( sQ467_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6317,f621,f6366]) ).
fof(f6370,definition,
! [X0] :
( sQ468_spl
<=> ( compose(a,compose(codomain(compose(a,h)),codomain(X0))) = compose(compose(a,codomain(compose(a,h))),codomain(X0))
| codomain(h) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f6373,plain,
( sQ468_spl
| ~ sQ460_spl ),
inference(split_clause,[status(thm)],[f6318,f6334,f6370]) ).
fof(f6374,definition,
! [X0] :
( sQ469_spl
<=> ( compose(a,compose(codomain(compose(a,b)),codomain(X0))) = compose(compose(a,codomain(compose(a,b))),codomain(X0))
| codomain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ469_spl])],[split_symbol_definition]) ).
fof(f6377,plain,
( sQ469_spl
| ~ sQ462_spl ),
inference(split_clause,[status(thm)],[f6319,f6341,f6374]) ).
fof(f6384,definition,
( sQ470_spl
<=> domain(b) = codomain(a) ),
introduced(definition,[new_symbols(definition,[sQ470_spl])],[split_symbol_definition]) ).
fof(f6386,plain,
( sQ470_spl
| domain(b) != codomain(a) ),
inference(component_clause,[status(thm)],[f6384]) ).
fof(f6387,definition,
! [X0] :
( sQ471_spl
<=> ( compose(a,compose(codomain(a),codomain(X0))) = compose(compose(a,codomain(a)),codomain(X0))
| domain(b) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ471_spl])],[split_symbol_definition]) ).
fof(f6390,plain,
( sQ471_spl
| ~ sQ470_spl ),
inference(split_clause,[status(thm)],[f6322,f6384,f6387]) ).
fof(f6401,plain,
! [X0] :
( compose(a,compose(codomain(X0),domain(b))) = compose(compose(a,codomain(X0)),codomain(a))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f23,f6328]) ).
fof(f6402,plain,
! [X0] :
( compose(a,compose(codomain(X0),domain(b))) = compose(compose(a,codomain(X0)),domain(b))
| codomain(X0) != domain(b)
| domain(b) != codomain(X0) ),
inference(forward_demodulation,[status(thm)],[f23,f6401]) ).
fof(f6403,plain,
! [X0] :
( compose(a,compose(codomain(X0),domain(b))) = compose(compose(a,codomain(X0)),domain(b))
| domain(b) != codomain(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f6402]) ).
fof(f6405,plain,
( sQ462_spl
| domain(b) != codomain(b) ),
inference(forward_demodulation,[status(thm)],[f128,f6343]) ).
fof(f6406,plain,
( sQ460_spl
| domain(b) != codomain(h) ),
inference(forward_demodulation,[status(thm)],[f567,f6336]) ).
fof(f6407,plain,
( sQ470_spl
| domain(b) != domain(b) ),
inference(forward_demodulation,[status(thm)],[f23,f6386]) ).
fof(f6408,plain,
( sQ470_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f6407]) ).
fof(f6409,plain,
sQ470_spl,
inference(contradiction_clause,[status(thm)],[f6408]) ).
fof(f6412,plain,
( compose(a,compose(codomain(domain(b)),compose(a,b))) = compose(compose(a,codomain(domain(b))),compose(a,b))
| codomain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f5656,f14]) ).
fof(f6413,plain,
( compose(a,compose(codomain(a),compose(a,b))) = compose(compose(a,codomain(a)),compose(a,b))
| codomain(a) != domain(a) ),
inference(resolution,[status(thm)],[f5656,f23]) ).
fof(f6414,plain,
( compose(a,compose(codomain(g),compose(a,b))) = compose(compose(a,codomain(g)),compose(a,b))
| codomain(g) != domain(a)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f5656]) ).
fof(f6415,plain,
( compose(a,compose(codomain(compose(a,h)),compose(a,b))) = compose(compose(a,codomain(compose(a,h))),compose(a,b))
| codomain(compose(a,h)) != domain(a)
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f5656]) ).
fof(f6416,plain,
( compose(a,compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(a,codomain(compose(a,b))),compose(a,b))
| codomain(compose(a,b)) != domain(a)
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f5656]) ).
fof(f6419,plain,
( compose(a,compose(codomain(a),compose(a,b))) = compose(compose(a,codomain(a)),compose(a,b))
| codomain(a) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f5656]) ).
fof(f6420,definition,
( sQ472_spl
<=> compose(a,compose(codomain(domain(b)),compose(a,b))) = compose(compose(a,codomain(domain(b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f6423,plain,
( sQ472_spl
| ~ sQ385_spl ),
inference(split_clause,[status(thm)],[f6412,f5524,f6420]) ).
fof(f6424,definition,
( sQ473_spl
<=> compose(a,compose(codomain(a),compose(a,b))) = compose(compose(a,codomain(a)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f6427,plain,
( sQ473_spl
| ~ sQ387_spl ),
inference(split_clause,[status(thm)],[f6413,f5531,f6424]) ).
fof(f6428,definition,
( sQ474_spl
<=> compose(a,compose(codomain(g),compose(a,b))) = compose(compose(a,codomain(g)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ474_spl])],[split_symbol_definition]) ).
fof(f6431,plain,
( sQ474_spl
| ~ sQ389_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6414,f665,f5538,f6428]) ).
fof(f6432,definition,
( sQ475_spl
<=> compose(a,compose(codomain(compose(a,h)),compose(a,b))) = compose(compose(a,codomain(compose(a,h))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f6435,plain,
( sQ475_spl
| ~ sQ391_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6415,f665,f5545,f6432]) ).
fof(f6436,definition,
( sQ476_spl
<=> compose(a,compose(codomain(compose(a,b)),compose(a,b))) = compose(compose(a,codomain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f6439,plain,
( sQ476_spl
| ~ sQ393_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6416,f360,f5552,f6436]) ).
fof(f6446,plain,
( sQ473_spl
| ~ sQ387_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6419,f294,f5531,f6424]) ).
fof(f6449,plain,
( compose(a,compose(codomain(g),domain(b))) = compose(compose(a,codomain(g)),domain(b))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f641,f6403]) ).
fof(f6450,plain,
( compose(a,compose(codomain(compose(a,h)),domain(b))) = compose(compose(a,codomain(compose(a,h))),domain(b))
| domain(b) != codomain(h) ),
inference(paramodulation,[status(thm)],[f567,f6403]) ).
fof(f6451,plain,
( compose(a,compose(codomain(compose(a,b)),domain(b))) = compose(compose(a,codomain(compose(a,b))),domain(b))
| domain(b) != codomain(b) ),
inference(paramodulation,[status(thm)],[f128,f6403]) ).
fof(f6453,plain,
! [X0] :
( compose(a,compose(codomain(domain(X0)),domain(b))) = compose(compose(a,codomain(domain(X0))),domain(b))
| domain(b) != domain(X0) ),
inference(paramodulation,[status(thm)],[f14,f6403]) ).
fof(f6454,plain,
( compose(a,compose(codomain(a),domain(b))) = compose(compose(a,codomain(a)),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f23,f6403]) ).
fof(f6464,definition,
( sQ477_spl
<=> compose(a,compose(codomain(g),domain(b))) = compose(compose(a,codomain(g)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f6467,plain,
( sQ477_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6449,f665,f6464]) ).
fof(f6468,definition,
( sQ478_spl
<=> compose(a,compose(codomain(compose(a,h)),domain(b))) = compose(compose(a,codomain(compose(a,h))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f6471,plain,
( sQ478_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6450,f665,f6468]) ).
fof(f6472,definition,
( sQ479_spl
<=> compose(a,compose(codomain(compose(a,b)),domain(b))) = compose(compose(a,codomain(compose(a,b))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ479_spl])],[split_symbol_definition]) ).
fof(f6475,plain,
( sQ479_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6451,f360,f6472]) ).
fof(f6478,plain,
! [X0] :
( compose(a,compose(domain(X0),domain(b))) = compose(compose(a,codomain(domain(X0))),domain(b))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f14,f6453]) ).
fof(f6479,plain,
! [X0] :
( compose(a,compose(domain(X0),domain(b))) = compose(compose(a,domain(X0)),domain(b))
| domain(b) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f14,f6478]) ).
fof(f6480,definition,
( sQ480_spl
<=> compose(a,compose(codomain(a),domain(b))) = compose(compose(a,codomain(a)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f6483,plain,
( sQ480_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6454,f294,f6480]) ).
fof(f6491,plain,
( compose(a,compose(domain(compose(a,h)),domain(b))) = compose(compose(a,domain(compose(a,h))),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f6479]) ).
fof(f6492,plain,
( compose(a,compose(domain(compose(a,b)),domain(b))) = compose(compose(a,domain(compose(a,b))),domain(b))
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f6479]) ).
fof(f6494,plain,
( compose(a,compose(domain(g),domain(b))) = compose(compose(a,domain(g)),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f6479]) ).
fof(f6495,plain,
( compose(a,compose(domain(h),domain(b))) = compose(compose(a,domain(h)),domain(b))
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f6479]) ).
fof(f6512,definition,
( sQ481_spl
<=> compose(a,compose(domain(compose(a,h)),domain(b))) = compose(compose(a,domain(compose(a,h))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f6515,plain,
( sQ481_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6491,f285,f6512]) ).
fof(f6516,definition,
( sQ482_spl
<=> compose(a,compose(domain(compose(a,b)),domain(b))) = compose(compose(a,domain(compose(a,b))),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f6519,plain,
( sQ482_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6492,f285,f6516]) ).
fof(f6522,definition,
( sQ483_spl
<=> compose(a,compose(domain(g),domain(b))) = compose(compose(a,domain(g)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f6525,plain,
( sQ483_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6494,f294,f6522]) ).
fof(f6526,definition,
( sQ484_spl
<=> compose(a,compose(domain(h),domain(b))) = compose(compose(a,domain(h)),domain(b)) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f6529,plain,
( sQ484_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6495,f294,f6526]) ).
fof(f6547,plain,
( compose(a,compose(domain(b),codomain(a))) = compose(compose(a,domain(b)),codomain(a))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[f5774,f23]) ).
fof(f6548,plain,
! [X0] :
( compose(a,compose(domain(compose(a,h)),codomain(X0))) = compose(compose(a,domain(compose(a,h))),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(compose(a,h)) ),
inference(paramodulation,[status(thm)],[f414,f5774]) ).
fof(f6549,plain,
! [X0] :
( compose(a,compose(domain(compose(a,b)),codomain(X0))) = compose(compose(a,domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0)
| domain(b) != domain(compose(a,b)) ),
inference(paramodulation,[status(thm)],[f117,f5774]) ).
fof(f6563,definition,
( sQ485_spl
<=> compose(a,compose(domain(b),codomain(a))) = compose(compose(a,domain(b)),codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f6566,plain,
( sQ485_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6547,f294,f6563]) ).
fof(f6567,definition,
! [X0] :
( sQ486_spl
<=> ( compose(a,compose(domain(compose(a,h)),codomain(X0))) = compose(compose(a,domain(compose(a,h))),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f6570,plain,
( sQ486_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f6548,f1276,f6567]) ).
fof(f6571,definition,
! [X0] :
( sQ487_spl
<=> ( compose(a,compose(domain(compose(a,b)),codomain(X0))) = compose(compose(a,domain(compose(a,b))),codomain(X0))
| domain(a) != codomain(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition]) ).
fof(f6574,plain,
( sQ487_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f6549,f1283,f6571]) ).
fof(f6598,plain,
( compose(a,compose(domain(g),compose(a,b))) = compose(compose(a,domain(g)),compose(a,b))
| domain(g) != domain(a) ),
inference(resolution,[status(thm)],[f5657,f52]) ).
fof(f6599,plain,
( compose(a,compose(domain(h),compose(a,b))) = compose(compose(a,domain(h)),compose(a,b))
| domain(h) != domain(a) ),
inference(resolution,[status(thm)],[f5657,f44]) ).
fof(f6600,plain,
( compose(a,compose(domain(domain(b)),compose(a,b))) = compose(compose(a,domain(domain(b))),compose(a,b))
| domain(domain(b)) != domain(a) ),
inference(resolution,[status(thm)],[f5657,f38]) ).
fof(f6601,plain,
( compose(a,compose(domain(compose(a,h)),compose(a,b))) = compose(compose(a,domain(compose(a,h))),compose(a,b))
| domain(compose(a,h)) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f414,f5657]) ).
fof(f6602,plain,
( compose(a,compose(domain(compose(a,b)),compose(a,b))) = compose(compose(a,domain(compose(a,b))),compose(a,b))
| domain(compose(a,b)) != domain(a)
| domain(b) != domain(a) ),
inference(paramodulation,[status(thm)],[f117,f5657]) ).
fof(f6604,plain,
( compose(a,compose(domain(g),compose(a,b))) = compose(compose(a,domain(g)),compose(a,b))
| domain(g) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f52,f5657]) ).
fof(f6605,plain,
( compose(a,compose(domain(h),compose(a,b))) = compose(compose(a,domain(h)),compose(a,b))
| domain(h) != domain(a)
| domain(b) != domain(b) ),
inference(paramodulation,[status(thm)],[f44,f5657]) ).
fof(f6607,plain,
( compose(a,compose(domain(b),compose(a,b))) = compose(compose(a,domain(b)),compose(a,b))
| domain(b) != domain(a) ),
inference(equality_resolution,[status(thm)],[f5657]) ).
fof(f6608,definition,
( sQ488_spl
<=> compose(a,compose(domain(g),compose(a,b))) = compose(compose(a,domain(g)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f6611,plain,
( sQ488_spl
| ~ sQ395_spl ),
inference(split_clause,[status(thm)],[f6598,f5578,f6608]) ).
fof(f6612,definition,
( sQ489_spl
<=> compose(a,compose(domain(h),compose(a,b))) = compose(compose(a,domain(h)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition]) ).
fof(f6615,plain,
( sQ489_spl
| ~ sQ397_spl ),
inference(split_clause,[status(thm)],[f6599,f5585,f6612]) ).
fof(f6616,definition,
( sQ490_spl
<=> compose(a,compose(domain(domain(b)),compose(a,b))) = compose(compose(a,domain(domain(b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f6619,plain,
( sQ490_spl
| ~ sQ399_spl ),
inference(split_clause,[status(thm)],[f6600,f5592,f6616]) ).
fof(f6620,definition,
( sQ491_spl
<=> compose(a,compose(domain(compose(a,h)),compose(a,b))) = compose(compose(a,domain(compose(a,h))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f6623,plain,
( sQ491_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6601,f285,f423,f6620]) ).
fof(f6624,definition,
( sQ492_spl
<=> compose(a,compose(domain(compose(a,b)),compose(a,b))) = compose(compose(a,domain(compose(a,b))),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition]) ).
fof(f6627,plain,
( sQ492_spl
| ~ sQ136_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6602,f285,f2252,f6624]) ).
fof(f6631,plain,
( sQ488_spl
| ~ sQ395_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6604,f294,f5578,f6608]) ).
fof(f6632,plain,
( sQ489_spl
| ~ sQ397_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6605,f294,f5585,f6612]) ).
fof(f6636,definition,
( sQ493_spl
<=> compose(a,compose(domain(b),compose(a,b))) = compose(compose(a,domain(b)),compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f6639,plain,
( sQ493_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6607,f285,f6636]) ).
fof(model,axiom,
( sQ0_spl
| sQ1_spl
| sQ2_spl
| ~ sQ3_spl
| sQ5_spl
| sQ6_spl
| sQ7_spl
| sQ9_spl
| sQ10_spl
| ~ sQ11_spl
| sQ13_spl
| sQ15_spl
| sQ17_spl
| sQ18_spl
| sQ24_spl
| sQ25_spl
| ~ sQ26_spl
| ~ sQ29_spl
| ~ sQ30_spl
| sQ37_spl
| sQ38_spl
| ~ sQ39_spl
| sQ52_spl
| sQ53_spl
| sQ54_spl
| sQ55_spl
| sQ56_spl
| sQ57_spl
| sQ60_spl
| sQ61_spl
| sQ62_spl
| sQ63_spl
| sQ73_spl
| sQ74_spl
| ~ sQ75_spl
| ~ sQ77_spl
| sQ84_spl
| sQ85_spl
| sQ86_spl
| ~ sQ87_spl
| sQ91_spl
| sQ92_spl
| sQ98_spl
| sQ99_spl
| sQ105_spl
| sQ109_spl
| sQ112_spl
| sQ113_spl
| sQ130_spl
| sQ131_spl
| sQ135_spl
| sQ136_spl
| sQ139_spl
| sQ140_spl
| sQ152_spl
| sQ153_spl
| sQ158_spl
| sQ159_spl
| sQ164_spl
| sQ165_spl
| sQ169_spl
| sQ173_spl
| sQ174_spl
| sQ191_spl
| sQ192_spl
| sQ195_spl
| sQ196_spl
| sQ203_spl
| sQ204_spl
| sQ214_spl
| sQ215_spl
| sQ219_spl
| sQ220_spl
| sQ224_spl
| sQ225_spl
| sQ229_spl
| sQ230_spl
| sQ234_spl
| sQ245_spl
| sQ246_spl
| sQ251_spl
| sQ252_spl
| sQ255_spl
| sQ256_spl
| sQ257_spl
| sQ264_spl
| sQ265_spl
| sQ268_spl
| sQ269_spl
| sQ273_spl
| sQ277_spl
| sQ284_spl
| sQ285_spl
| sQ295_spl
| sQ296_spl
| sQ297_spl
| ~ sQ299_spl
| sQ305_spl
| sQ306_spl
| sQ313_spl
| sQ314_spl
| sQ315_spl
| sQ332_spl
| sQ341_spl
| sQ342_spl
| sQ347_spl
| sQ348_spl
| sQ354_spl
| sQ355_spl
| sQ359_spl
| sQ360_spl
| sQ361_spl
| sQ366_spl
| sQ367_spl
| sQ371_spl
| sQ372_spl
| sQ376_spl
| sQ380_spl
| sQ383_spl
| sQ384_spl
| ~ sQ385_spl
| ~ sQ387_spl
| ~ sQ395_spl
| ~ sQ397_spl
| ~ sQ399_spl
| sQ410_spl
| sQ414_spl
| sQ415_spl
| sQ418_spl
| sQ419_spl
| sQ420_spl
| sQ426_spl
| sQ437_spl
| sQ438_spl
| sQ445_spl
| sQ450_spl
| sQ454_spl
| sQ457_spl
| sQ458_spl
| ~ sQ460_spl
| ~ sQ462_spl
| sQ470_spl
| sQ471_spl
| sQ480_spl
| sQ483_spl
| sQ484_spl
| sQ485_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n020.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Mon Sep 21 13:55:53 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.46 % Drodi V4.1.1
% 0.22/5.94 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.22/5.94 % SZS output start Saturation for theBenchmark
% See solution above
% 0.22/6.00 % Elapsed time: 0.529067 seconds
% 0.22/6.00 % CPU time: 3.640576 seconds
% 0.22/6.00 % Total memory used: 104.474 MB
% 0.22/6.00 % Net memory used: 100.714 MB
%------------------------------------------------------------------------------